(DARGP-LESS-THAN-OF-CADR-OF-CAR-WHEN-BOUNDED-DARG-LISTP-OF-STRIP-CADRS
 (2275 23 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-<))
 (2231 89 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (2024 8 (:DEFINITION BOUNDED-DARG-LISTP))
 (1915 42 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (1878 12 (:REWRITE DARGP-LESS-THAN-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (1048 12 (:REWRITE BOUNDED-DARG-LISTP-OF-CDR))
 (1020 32 (:REWRITE LEN-OF-CDR))
 (764 382 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (488 3 (:REWRITE ALL-<-OF-CONS))
 (384 16 (:REWRITE ALL-<-OF-CDR))
 (382 382 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (348 28 (:REWRITE EQUAL-OF-LEN-AND-0))
 (234 65 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (195 102 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (195 15 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-CAR-AND-QUOTE))
 (188 94 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (166 48 (:REWRITE DEFAULT-<-2))
 (144 6 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (142 20 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (107 15 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (96 25 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (96 25 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (94 94 (:TYPE-PRESCRIPTION DARGP))
 (94 94 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (94 94 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (94 94 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (92 15 (:REWRITE DARGP-LESS-THAN-WHEN-NATP-CHEAP))
 (89 89 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (89 89 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (82 42 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (78 78 (:TYPE-PRESCRIPTION ALL-<))
 (77 13 (:REWRITE DARGP-LESS-THAN-WHEN-CONSP-CHEAP))
 (74 38 (:REWRITE DEFAULT-+-2))
 (57 48 (:REWRITE DEFAULT-<-1))
 (52 28 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (48 48 (:REWRITE USE-ALL-<-2))
 (48 48 (:REWRITE USE-ALL-<))
 (46 23 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (46 23 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (42 42 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (42 42 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (42 42 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (42 42 (:REWRITE ALL-<-TRANSITIVE))
 (38 38 (:REWRITE DEFAULT-+-1))
 (30 15 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (28 28 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (28 28 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (28 28 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (24 24 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (23 23 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (23 23 (:REWRITE BOUNDED-DARG-LISTP-MONOTONE))
 (17 17 (:TYPE-PRESCRIPTION MYQUOTEP))
 (17 15 (:REWRITE DARGP-LESS-THAN-WHEN-QUOTEP-CHEAP))
 (15 15 (:REWRITE DARGP-LESS-THAN-MONO))
 (13 13 (:TYPE-PRESCRIPTION NATP))
 (12 4 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (12 3 (:REWRITE +-COMBINE-CONSTANTS))
 (12 2 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (4 4 (:REWRITE USE-ALL-RATIONALP-2))
 (4 4 (:REWRITE USE-ALL-RATIONALP))
 (4 4 (:REWRITE LEN-OF-CDDR-WHEN-EQUAL-OF-LEN))
 (4 4 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (4 2 (:DEFINITION FIX))
 )
(<-OF-CAR-OF-CAR-WHEN-ALL-<-OF-STRIP-CARS
 (406 159 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (318 159 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (161 161 (:TYPE-PRESCRIPTION NAT-LISTP))
 (159 159 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (130 5 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (125 8 (:REWRITE DEFAULT-CAR))
 (110 2 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (106 2 (:REWRITE DEFAULT-<-1))
 (88 2 (:DEFINITION STRIP-CARS))
 (73 1 (:REWRITE USE-ALL-<-FOR-CAR))
 (71 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (60 5 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (36 8 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (29 1 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (21 1 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (16 8 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (12 2 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (8 8 (:TYPE-PRESCRIPTION DARGP))
 (8 8 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (8 8 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (8 8 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (7 2 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (7 1 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (7 1 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (6 2 (:REWRITE DEFAULT-<-2))
 (5 5 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (5 1 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:REWRITE STRIP-CARS-WHEN-NOT-CONSP-CHEAP))
 (4 2 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (3 3 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (2 2 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (2 2 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (2 2 (:REWRITE USE-ALL-RATIONALP-2))
 (2 2 (:REWRITE USE-ALL-RATIONALP))
 (2 2 (:REWRITE USE-ALL-<-2))
 (2 2 (:REWRITE USE-ALL-<))
 (2 2 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (2 2 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (2 2 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (2 2 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (2 2 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (2 2 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (2 2 (:REWRITE ALL-<-TRANSITIVE))
 (2 1 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (1 1 (:REWRITE USE-ALL-<=-2))
 (1 1 (:REWRITE USE-ALL-<=))
 (1 1 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (1 1 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 )
(ALL-MYQUOTEP-BECOMES-ALL-CONSP-WHEN-DARG-LISTP
 (894 27 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (356 8 (:REWRITE DARGP-OF-CAR-WHEN-DARG-LISTP))
 (354 175 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (350 175 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (258 258 (:TYPE-PRESCRIPTION NAT-LISTP))
 (175 175 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (168 8 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (160 6 (:REWRITE ALL-MYQUOTEP-WHEN-NOT-CONSP))
 (140 46 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (138 8 (:REWRITE LEN-OF-CDR))
 (124 4 (:REWRITE <=-OF-0-WHEN-NATP))
 (108 54 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (96 12 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (93 23 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (93 23 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (88 4 (:REWRITE USE-ALL-<-FOR-CAR))
 (78 54 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (76 4 (:REWRITE INTEGERP-WHEN-NATP))
 (56 56 (:TYPE-PRESCRIPTION DARGP))
 (56 8 (:REWRITE DARGP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (54 54 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (54 54 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (54 54 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (48 27 (:REWRITE DEFAULT-<-2))
 (46 11 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (37 37 (:TYPE-PRESCRIPTION ALL-NATP))
 (32 4 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (28 14 (:REWRITE DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (27 27 (:REWRITE USE-ALL-<-2))
 (27 27 (:REWRITE USE-ALL-<))
 (27 27 (:REWRITE DEFAULT-<-1))
 (27 27 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (26 26 (:TYPE-PRESCRIPTION NATP))
 (24 4 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (23 23 (:REWRITE DEFAULT-CAR))
 (23 23 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (22 11 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (22 11 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (18 6 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (14 8 (:REWRITE DEFAULT-+-2))
 (14 2 (:REWRITE DARG-LISTP-OF-CDR))
 (12 12 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (12 12 (:TYPE-PRESCRIPTION ALL-<))
 (12 12 (:REWRITE USE-ALL-NATP-2))
 (12 12 (:REWRITE USE-ALL-NATP))
 (12 2 (:REWRITE DARGP-WHEN-NATP-CHEAP))
 (11 11 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (11 11 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (11 11 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (8 8 (:REWRITE DEFAULT-+-1))
 (8 8 (:REWRITE DARGP-WHEN-DARGP-LESS-THAN))
 (8 8 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (8 4 (:REWRITE INTEGERP-OF-CAR-WHEN-NAT-LISTP-CHEAP))
 (8 4 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (8 4 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (8 4 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (8 2 (:REWRITE ALL-CONSP-OF-CDR))
 (6 6 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (6 6 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (6 6 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 (6 6 (:REWRITE EQUAL-OF-LEN-AND-0))
 (6 6 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (6 6 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (5 5 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (4 4 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (4 4 (:REWRITE USE-ALL-<=-2))
 (4 4 (:REWRITE USE-ALL-<=))
 (4 4 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (4 4 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (4 4 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (4 4 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (4 4 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (4 4 (:REWRITE ALL-<-TRANSITIVE))
 (4 2 (:REWRITE DARGP-WHEN-MYQUOTEP-CHEAP))
 (4 2 (:REWRITE ALL-MYQUOTEP-OF-CDR-CHEAP))
 (3 3 (:REWRITE EQUAL-OF-NON-NATP-AND-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (2 2 (:TYPE-PRESCRIPTION MYQUOTEP))
 )
(CONSP-OF-STRIP-CADDRS
 (631 19 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (435 6 (:REWRITE DEFAULT-CAR))
 (318 10 (:REWRITE LEN-OF-CDR))
 (114 6 (:REWRITE EQUAL-OF-LEN-AND-0))
 (102 51 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (102 51 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (71 71 (:TYPE-PRESCRIPTION NAT-LISTP))
 (52 25 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (51 51 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (50 25 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (46 20 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (37 13 (:REWRITE DEFAULT-<-2))
 (33 10 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (33 10 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (25 25 (:TYPE-PRESCRIPTION DARGP))
 (25 25 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (25 25 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (25 25 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (25 10 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (19 19 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (19 19 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (16 10 (:REWRITE DEFAULT-+-2))
 (13 13 (:REWRITE USE-ALL-<-2))
 (13 13 (:REWRITE USE-ALL-<))
 (13 13 (:REWRITE DEFAULT-<-1))
 (12 6 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (12 1 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (10 10 (:REWRITE DEFAULT-+-1))
 (6 6 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (6 6 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (6 6 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (6 6 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (4 4 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (3 3 (:REWRITE LEN-OF-CDDR-WHEN-EQUAL-OF-LEN))
 )
(STRIP-CADDRS-OF-CDR
 (669 18 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (580 8 (:REWRITE DEFAULT-CAR))
 (445 14 (:REWRITE LEN-OF-CDR))
 (159 10 (:REWRITE EQUAL-OF-LEN-AND-0))
 (136 68 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (136 68 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (88 88 (:TYPE-PRESCRIPTION LEN))
 (76 76 (:TYPE-PRESCRIPTION NAT-LISTP))
 (68 68 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (57 25 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (50 25 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (41 9 (:DEFINITION NOT))
 (34 9 (:REWRITE DEFAULT-<-2))
 (25 25 (:TYPE-PRESCRIPTION DARGP))
 (25 25 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (25 25 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (25 25 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (24 14 (:REWRITE DEFAULT-+-2))
 (24 1 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (21 5 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (18 18 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (18 18 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (16 8 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (16 8 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (14 14 (:REWRITE DEFAULT-+-1))
 (12 4 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (12 4 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (9 9 (:REWRITE USE-ALL-<-2))
 (9 9 (:REWRITE USE-ALL-<))
 (9 9 (:REWRITE DEFAULT-<-1))
 (8 8 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (8 8 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (8 8 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (8 8 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (6 6 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (4 4 (:REWRITE LEN-OF-CDDR-WHEN-EQUAL-OF-LEN))
 )
(STRIP-CADDRS-OF-CONS
 (489 8 (:REWRITE DEFAULT-CAR))
 (488 17 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (355 15 (:REWRITE LEN-OF-CDR))
 (112 10 (:REWRITE EQUAL-OF-LEN-AND-0))
 (75 75 (:TYPE-PRESCRIPTION LEN))
 (68 34 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (68 34 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (44 22 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (38 38 (:TYPE-PRESCRIPTION NAT-LISTP))
 (38 22 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (34 34 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (26 10 (:DEFINITION NOT))
 (25 15 (:REWRITE DEFAULT-+-2))
 (22 22 (:TYPE-PRESCRIPTION DARGP))
 (22 22 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (22 22 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (22 22 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (22 7 (:REWRITE DEFAULT-<-2))
 (17 17 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (17 17 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (15 15 (:REWRITE DEFAULT-+-1))
 (8 4 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (8 4 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (7 7 (:REWRITE USE-ALL-<-2))
 (7 7 (:REWRITE USE-ALL-<))
 (7 7 (:REWRITE DEFAULT-<-1))
 (6 2 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (6 2 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (5 5 (:REWRITE LEN-OF-CDDR-WHEN-EQUAL-OF-LEN))
 (5 5 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (4 4 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (4 4 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (4 4 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (4 4 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (2 2 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 )
(<-OF--1-AND-LARGEST-NON-QUOTEP
 (65 1 (:REWRITE <=-OF-LARGEST-NON-QUOTEP-WHEN-BOUNDED-DARG-LISTP))
 (63 2 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-<))
 (56 28 (:TYPE-PRESCRIPTION NATP-OF-LARGEST-NON-QUOTEP))
 (43 4 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (38 1 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (29 29 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (26 1 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (20 1 (:REWRITE DARG-LISTP-WHEN-NOT-CONSP))
 (20 1 (:REWRITE <=-OF-LARGEST-NON-QUOTEP))
 (13 13 (:TYPE-PRESCRIPTION NAT-LISTP))
 (12 6 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (12 6 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (9 9 (:TYPE-PRESCRIPTION LEN))
 (9 2 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (7 2 (:REWRITE DEFAULT-<-2))
 (6 6 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (6 3 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (6 1 (:REWRITE BOUNDED-DARG-LISTP-OF-0))
 (6 1 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (6 1 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (5 5 (:TYPE-PRESCRIPTION BOUNDED-DARG-LISTP))
 (5 2 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (4 4 (:TYPE-PRESCRIPTION ALL-NATP))
 (4 4 (:TYPE-PRESCRIPTION ALL-<))
 (4 4 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (4 2 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (4 2 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (4 2 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (4 1 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (3 3 (:TYPE-PRESCRIPTION DARGP))
 (3 3 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (3 3 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (3 3 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (3 3 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (3 3 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (3 1 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (3 1 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (2 2 (:REWRITE USE-ALL-<-2))
 (2 2 (:REWRITE USE-ALL-<))
 (2 2 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (2 2 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (2 2 (:REWRITE ALL-<-TRANSITIVE))
 (2 1 (:REWRITE LARGEST-NON-QUOTEP-WHEN-ALL-MYQUOTEP-CHEAP))
 (2 1 (:REWRITE LARGEST-NON-QUOTEP-WHEN-ALL-CONSP-CHEAP))
 (2 1 (:REWRITE DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (2 1 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (2 1 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (2 1 (:REWRITE ALL-MYQUOTEP-BECOMES-ALL-CONSP-WHEN-DARG-LISTP))
 (1 1 (:REWRITE USE-ALL-<=-2))
 (1 1 (:REWRITE USE-ALL-<=))
 (1 1 (:REWRITE BOUNDED-DARG-LISTP-MONOTONE))
 (1 1 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 )
(<-OF-IF-ARG2)
(LARGEST-NON-QUOTEP-WHEN-ALL-CONSP
 (16 16 (:TYPE-PRESCRIPTION DARG-LISTP))
 (16 8 (:TYPE-PRESCRIPTION NATP-OF-LARGEST-NON-QUOTEP))
 (16 8 (:TYPE-PRESCRIPTION ACL2-NUMBERP-OF-LARGEST-NON-QUOTEP))
 )
(SUBST-CANDIDATEP
 (24 12 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (12 12 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 )
(NATP-OF-CAR-WHEN-SUBST-CANDIDATEP
 (10 5 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (10 5 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (5 5 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (5 5 (:TYPE-PRESCRIPTION NAT-LISTP))
 )
(CONSP-WHEN-SUBST-CANDIDATEP
 (6 3 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (3 3 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 )
(CONSP-OF-CDR-WHEN-SUBST-CANDIDATEP
 (6 3 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (3 3 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 )
(DARGP-OF-CADR-WHEN-SUBST-CANDIDATEP)
(LEN-OF-CADR-WHEN-SUBST-CANDIDATEP
 (204 102 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (102 102 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (92 7 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (87 2 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (44 2 (:REWRITE ALL-NATP-OF-CDR))
 (37 4 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (29 1 (:REWRITE DARGP-OF-CAR-WHEN-DARG-LISTP))
 (26 4 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (26 2 (:REWRITE LEN-OF-CDR))
 (22 1 (:REWRITE <-OF-IF-ARG2))
 (19 2 (:REWRITE DARG-LISTP-WHEN-NOT-CONSP))
 (15 15 (:TYPE-PRESCRIPTION ALL-NATP))
 (15 7 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (14 7 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (13 3 (:REWRITE NAT-LISTP-OF-CDR))
 (13 1 (:REWRITE DARGP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (11 4 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (10 10 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (8 4 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (7 7 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (7 7 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (7 7 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (7 7 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (7 1 (:REWRITE DARG-LISTP-OF-CDR))
 (6 6 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (6 2 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (6 1 (:REWRITE TRUE-LISTP-WHEN-NAT-LISTP-REWRITE))
 (6 1 (:REWRITE DARGP-WHEN-NATP-CHEAP))
 (5 1 (:REWRITE DARGP-WHEN-NOT-CONSP-CHEAP))
 (5 1 (:REWRITE DARGP-WHEN-CONSP-CHEAP))
 (4 4 (:TYPE-PRESCRIPTION DARG-LISTP))
 (4 4 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (4 4 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (4 4 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (4 4 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (4 4 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (4 2 (:REWRITE DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (3 1 (:REWRITE PSEUDO-DAGP-OF-CDR-WHEN-PSEUDO-DAGP))
 (2 2 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (2 2 (:REWRITE USE-ALL-NATP-2))
 (2 2 (:REWRITE USE-ALL-NATP))
 (2 1 (:REWRITE DARGP-WHEN-MYQUOTEP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION MYQUOTEP))
 (1 1 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (1 1 (:REWRITE LEN-OF-CDDR-WHEN-EQUAL-OF-LEN))
 (1 1 (:REWRITE DARGP-WHEN-DARGP-LESS-THAN))
 )
(NATP-OF-CADR-WHEN-SUBST-CANDIDATEP
 (28 14 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (14 14 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 )
(SUBST-CANDIDATE-LISTP
 (2 1 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (2 1 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (1 1 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (1 1 (:TYPE-PRESCRIPTION NAT-LISTP))
 )
(SUBST-CANDIDATEP-OF-CAR
 (7 1 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (2 1 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION DARGP))
 (1 1 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (1 1 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 )
(SUBST-CANDIDATE-LISTP-OF-CDR
 (23 1 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (5 5 (:TYPE-PRESCRIPTION LEN))
 (4 2 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (4 1 (:REWRITE SUBST-CANDIDATEP-OF-CAR))
 (3 1 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (3 1 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (2 2 (:TYPE-PRESCRIPTION NAT-LISTP))
 (2 1 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (2 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:TYPE-PRESCRIPTION DARGP))
 (1 1 (:REWRITE USE-ALL-<-2))
 (1 1 (:REWRITE USE-ALL-<))
 (1 1 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (1 1 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (1 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (1 1 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (1 1 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 )
(SUBST-CANDIDATE-LISTP-OF-CONS
 (46 2 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (10 10 (:TYPE-PRESCRIPTION LEN))
 (8 4 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (8 2 (:REWRITE SUBST-CANDIDATEP-OF-CAR))
 (8 2 (:REWRITE SUBST-CANDIDATE-LISTP-OF-CDR))
 (6 2 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (6 2 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (4 4 (:TYPE-PRESCRIPTION NAT-LISTP))
 (4 2 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (4 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:TYPE-PRESCRIPTION DARGP))
 (2 2 (:REWRITE USE-ALL-<-2))
 (2 2 (:REWRITE USE-ALL-<))
 (2 2 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (2 2 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (2 2 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (2 2 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 )
(SUBST-CANDIDATE-LISTP-FORWARD-TO-ALISTP
 (249 9 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (104 52 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (104 52 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (70 70 (:TYPE-PRESCRIPTION NAT-LISTP))
 (60 18 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (52 52 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (39 9 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (39 9 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (23 11 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (22 11 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (21 7 (:REWRITE DAG-VARIABLE-ALISTP-FORWARD-TO-ALIST))
 (18 9 (:REWRITE DEFAULT-<-2))
 (18 2 (:REWRITE ALISTP-OF-CDR))
 (17 4 (:REWRITE SUBST-CANDIDATEP-OF-CAR))
 (14 14 (:TYPE-PRESCRIPTION DAG-VARIABLE-ALISTP))
 (11 11 (:TYPE-PRESCRIPTION DARGP))
 (11 11 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (11 11 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (11 11 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (9 9 (:REWRITE USE-ALL-<-2))
 (9 9 (:REWRITE USE-ALL-<))
 (9 9 (:REWRITE DEFAULT-<-1))
 (9 9 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (9 9 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (9 3 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (8 2 (:REWRITE SUBST-CANDIDATE-LISTP-OF-CDR))
 (7 7 (:REWRITE ALISTP-WHEN-PSEUDO-DAGP-AUX))
 (7 7 (:REWRITE ALISTP-WHEN-BOUNDED-NATP-ALISTP))
 (6 6 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (3 3 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (3 3 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (3 3 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 )
(ALL->=-LEN-OF-2-WHEN-SUBST-CANDIDATE-LISTP
 (1654 28 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (1344 672 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (1207 61 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (948 14 (:REWRITE SUBST-CANDIDATEP-OF-CAR))
 (928 16 (:REWRITE SUBST-CANDIDATE-LISTP-OF-CDR))
 (854 56 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (828 28 (:REWRITE ALL-NATP-OF-CDR))
 (720 16 (:REWRITE DARGP-OF-CAR-WHEN-DARG-LISTP))
 (690 34 (:REWRITE LEN-OF-CDR))
 (672 672 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (560 32 (:REWRITE DARG-LISTP-WHEN-NOT-CONSP))
 (490 98 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (464 56 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (432 112 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (294 42 (:REWRITE NAT-LISTP-OF-CDR))
 (210 210 (:TYPE-PRESCRIPTION ALL-NATP))
 (210 105 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (208 16 (:REWRITE DARGP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (196 98 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (176 16 (:REWRITE DARG-LISTP-OF-CDR))
 (144 16 (:REWRITE DARGP-WHEN-NOT-CONSP-CHEAP))
 (144 16 (:REWRITE DARGP-WHEN-CONSP-CHEAP))
 (140 14 (:REWRITE TRUE-LISTP-WHEN-NAT-LISTP-REWRITE))
 (112 56 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (105 105 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (105 105 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (105 105 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (100 34 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (96 16 (:REWRITE DARGP-WHEN-NATP-CHEAP))
 (67 17 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (67 17 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (64 64 (:TYPE-PRESCRIPTION DARG-LISTP))
 (64 32 (:REWRITE DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (56 56 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (48 4 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (32 32 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (32 16 (:REWRITE DARGP-WHEN-MYQUOTEP-CHEAP))
 (30 17 (:REWRITE DEFAULT-<-2))
 (28 28 (:REWRITE USE-ALL-NATP-2))
 (28 28 (:REWRITE USE-ALL-NATP))
 (18 11 (:REWRITE DEFAULT-+-2))
 (17 17 (:REWRITE USE-ALL-<-2))
 (17 17 (:REWRITE USE-ALL-<))
 (17 17 (:REWRITE DEFAULT-<-1))
 (17 17 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (16 16 (:TYPE-PRESCRIPTION MYQUOTEP))
 (16 16 (:REWRITE DARGP-WHEN-DARGP-LESS-THAN))
 (16 16 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (14 14 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (14 14 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (14 14 (:REWRITE LEN-OF-CDDR-WHEN-EQUAL-OF-LEN))
 (12 4 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (11 11 (:REWRITE DEFAULT-+-1))
 (8 8 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (4 4 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (4 4 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (4 4 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (4 4 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 )
(ALL->=-LEN-OF-3-WHEN-SUBST-CANDIDATE-LISTP
 (1654 28 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (1344 672 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (1207 61 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (948 14 (:REWRITE SUBST-CANDIDATEP-OF-CAR))
 (928 16 (:REWRITE SUBST-CANDIDATE-LISTP-OF-CDR))
 (854 56 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (828 28 (:REWRITE ALL-NATP-OF-CDR))
 (720 16 (:REWRITE DARGP-OF-CAR-WHEN-DARG-LISTP))
 (690 34 (:REWRITE LEN-OF-CDR))
 (672 672 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (560 32 (:REWRITE DARG-LISTP-WHEN-NOT-CONSP))
 (490 98 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (464 56 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (432 112 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (294 42 (:REWRITE NAT-LISTP-OF-CDR))
 (210 210 (:TYPE-PRESCRIPTION ALL-NATP))
 (210 105 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (208 16 (:REWRITE DARGP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (196 98 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (176 16 (:REWRITE DARG-LISTP-OF-CDR))
 (144 16 (:REWRITE DARGP-WHEN-NOT-CONSP-CHEAP))
 (144 16 (:REWRITE DARGP-WHEN-CONSP-CHEAP))
 (140 14 (:REWRITE TRUE-LISTP-WHEN-NAT-LISTP-REWRITE))
 (112 56 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (105 105 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (105 105 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (105 105 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (100 34 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (96 16 (:REWRITE DARGP-WHEN-NATP-CHEAP))
 (67 17 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (67 17 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (64 64 (:TYPE-PRESCRIPTION DARG-LISTP))
 (64 32 (:REWRITE DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (56 56 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (48 4 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (32 32 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (32 16 (:REWRITE DARGP-WHEN-MYQUOTEP-CHEAP))
 (30 17 (:REWRITE DEFAULT-<-2))
 (28 28 (:REWRITE USE-ALL-NATP-2))
 (28 28 (:REWRITE USE-ALL-NATP))
 (18 11 (:REWRITE DEFAULT-+-2))
 (17 17 (:REWRITE USE-ALL-<-2))
 (17 17 (:REWRITE USE-ALL-<))
 (17 17 (:REWRITE DEFAULT-<-1))
 (17 17 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (16 16 (:TYPE-PRESCRIPTION MYQUOTEP))
 (16 16 (:REWRITE DARGP-WHEN-DARGP-LESS-THAN))
 (16 16 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (14 14 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (14 14 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (14 14 (:REWRITE LEN-OF-CDDR-WHEN-EQUAL-OF-LEN))
 (12 4 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (11 11 (:REWRITE DEFAULT-+-1))
 (8 8 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (4 4 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (4 4 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (4 4 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (4 4 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 )
(NATP-OF-CAR-OF-CAR-WHEN-SUBST-CANDIDATE-LISTP
 (72 27 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (54 27 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (27 27 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (27 27 (:TYPE-PRESCRIPTION NAT-LISTP))
 )
(RATIONAL-LISTP-OF-STRIP-CARS-WHEN-SUBST-CANDIDATE-LISTP
 (153 6 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (69 2 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (60 1 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (36 18 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (36 18 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (32 12 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (30 30 (:TYPE-PRESCRIPTION NAT-LISTP))
 (22 6 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (22 6 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (17 4 (:REWRITE SUBST-CANDIDATEP-OF-CAR))
 (16 6 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (14 7 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (12 6 (:REWRITE DEFAULT-<-2))
 (11 7 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (10 5 (:TYPE-PRESCRIPTION NATP-OF-CAR-OF-CAR-WHEN-SUBST-CANDIDATE-LISTP))
 (8 4 (:REWRITE RATIONAL-LISTP-WHEN-ALL-NATP-CHEAP))
 (8 4 (:REWRITE RATIONAL-LISTP-OF-STRIP-CARS-WHEN-WEAK-DAGP-AUX-CHEAP))
 (8 2 (:REWRITE SUBST-CANDIDATE-LISTP-OF-CDR))
 (7 7 (:TYPE-PRESCRIPTION DARGP))
 (7 7 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (7 7 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (7 7 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (6 6 (:REWRITE USE-ALL-<-2))
 (6 6 (:REWRITE USE-ALL-<))
 (6 6 (:REWRITE DEFAULT-<-1))
 (6 6 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (6 6 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (5 5 (:REWRITE STRIP-CARS-WHEN-NOT-CONSP-CHEAP))
 (5 1 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:TYPE-PRESCRIPTION WEAK-DAGP-AUX))
 (4 4 (:TYPE-PRESCRIPTION ALL-NATP))
 (3 3 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (3 1 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (2 2 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (2 2 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (2 2 (:REWRITE USE-ALL-RATIONALP-2))
 (2 2 (:REWRITE USE-ALL-RATIONALP))
 (1 1 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (1 1 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (1 1 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 )
(ALL-NATP-OF-STRIP-CARS-WHEN-SUBST-CANDIDATE-LISTP
 (450 4 (:REWRITE NOT-ALL-NATP-WHEN-NOT-NATP-AND-MEMBER-EQUAL))
 (235 10 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (170 5 (:REWRITE MEMBER-EQUAL-OF-CONS-NON-CONSTANT))
 (152 3 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (107 5 (:REWRITE MEMBER-EQUAL-OF-CONS-WHEN-NOT-EQUAL))
 (85 3 (:REWRITE CONSP-OF-STRIP-CARS))
 (84 42 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (84 42 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (68 68 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (42 42 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (42 21 (:TYPE-PRESCRIPTION NATP-OF-CAR-OF-CAR-WHEN-SUBST-CANDIDATE-LISTP))
 (40 20 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (34 17 (:REWRITE NOT-MEMBER-EQUAL-WHEN-NOT-MEMBER-EQUAL-OF-CDR-CHEAP))
 (34 17 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-CDR-CHEAP))
 (30 10 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (30 10 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (24 12 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (22 22 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-MEMBER-EQUAL))
 (22 22 (:REWRITE MEMBER-EQUAL-OF-SINGLETON-CONSTANT-IFF))
 (22 22 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-WHEN-NOT-EQUAL-CAR))
 (22 22 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-TRIM))
 (19 10 (:REWRITE DEFAULT-<-2))
 (19 5 (:REWRITE SUBST-CANDIDATEP-OF-CAR))
 (17 17 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-2))
 (17 17 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-1))
 (15 9 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (15 1 (:REWRITE LEN-OF-CDR))
 (12 12 (:TYPE-PRESCRIPTION DARGP))
 (12 12 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (12 12 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (12 12 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (12 12 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (12 1 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (10 10 (:REWRITE USE-ALL-<-2))
 (10 10 (:REWRITE USE-ALL-<))
 (10 10 (:REWRITE DEFAULT-<-1))
 (10 10 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (10 10 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (10 5 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (9 9 (:REWRITE STRIP-CARS-WHEN-NOT-CONSP-CHEAP))
 (8 2 (:REWRITE SUBST-CANDIDATE-LISTP-OF-CDR))
 (7 7 (:REWRITE EQUAL-OF-NON-NATP-AND-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (6 3 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (6 3 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (5 5 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 (1 1 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 )
(NAT-LISTP-OF-STRIP-CARS-WHEN-SUBST-CANDIDATE-LISTP
 (114 5 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (20 10 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (19 5 (:REWRITE SUBST-CANDIDATEP-OF-CAR))
 (15 5 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (15 5 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (12 6 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (11 5 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (10 5 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (10 5 (:REWRITE DEFAULT-<-2))
 (8 4 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (8 2 (:REWRITE SUBST-CANDIDATE-LISTP-OF-CDR))
 (6 6 (:TYPE-PRESCRIPTION DARGP))
 (6 6 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (6 6 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (6 6 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (6 6 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (5 5 (:REWRITE USE-ALL-<-2))
 (5 5 (:REWRITE USE-ALL-<))
 (5 5 (:REWRITE STRIP-CARS-WHEN-NOT-CONSP-CHEAP))
 (5 5 (:REWRITE DEFAULT-<-1))
 (5 5 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (5 5 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (4 4 (:TYPE-PRESCRIPTION ALL-NATP))
 (4 2 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (4 2 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (3 3 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (2 1 (:TYPE-PRESCRIPTION NATP-OF-CAR-OF-CAR-WHEN-SUBST-CANDIDATE-LISTP))
 )
(DARG-LISTP-OF-STRIP-CADRS-WHEN-SUBST-CANDIDATE-LISTP
 (472 8 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (440 23 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (323 5 (:REWRITE SUBST-CANDIDATEP-OF-CAR))
 (294 147 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (277 15 (:REWRITE DARG-LISTP-WHEN-NOT-CONSP))
 (244 16 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (236 8 (:REWRITE ALL-NATP-OF-CDR))
 (225 5 (:REWRITE DARGP-OF-CAR-WHEN-DARG-LISTP))
 (189 9 (:REWRITE LEN-OF-CDR))
 (147 147 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (140 28 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (133 37 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (132 16 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (84 12 (:REWRITE NAT-LISTP-OF-CDR))
 (74 37 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (62 12 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (60 60 (:TYPE-PRESCRIPTION ALL-NATP))
 (56 28 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (55 5 (:REWRITE DARGP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (55 5 (:REWRITE DARG-LISTP-OF-CDR))
 (45 5 (:REWRITE DARGP-WHEN-NOT-CONSP-CHEAP))
 (45 5 (:REWRITE DARGP-WHEN-CONSP-CHEAP))
 (40 20 (:TYPE-PRESCRIPTION NATP-OF-CAR-OF-CAR-WHEN-SUBST-CANDIDATE-LISTP))
 (40 4 (:REWRITE TRUE-LISTP-WHEN-NAT-LISTP-REWRITE))
 (37 37 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (37 37 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (37 37 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (32 32 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (32 16 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (30 15 (:REWRITE DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (30 5 (:REWRITE DARGP-WHEN-NATP-CHEAP))
 (24 12 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (20 4 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-SUBST-CANDIDATE-LISTP))
 (18 6 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (18 6 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (16 16 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (15 15 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (12 6 (:REWRITE DEFAULT-<-2))
 (10 5 (:REWRITE DARGP-WHEN-MYQUOTEP-CHEAP))
 (8 8 (:REWRITE USE-ALL-NATP-2))
 (8 8 (:REWRITE USE-ALL-NATP))
 (8 2 (:REWRITE SUBST-CANDIDATE-LISTP-OF-CDR))
 (7 7 (:TYPE-PRESCRIPTION NATP))
 (6 6 (:REWRITE USE-ALL-<-2))
 (6 6 (:REWRITE USE-ALL-<))
 (6 6 (:REWRITE DEFAULT-<-1))
 (6 6 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (5 5 (:TYPE-PRESCRIPTION MYQUOTEP))
 (5 5 (:REWRITE DARGP-WHEN-DARGP-LESS-THAN))
 (4 4 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (4 4 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (4 4 (:REWRITE LEN-OF-CDDR-WHEN-EQUAL-OF-LEN))
 (4 4 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (3 3 (:TYPE-PRESCRIPTION SUBST-CANDIDATEP))
 (1 1 (:TYPE-PRESCRIPTION TRUE-LISTP))
 )
(CHECK-FOR-VAR
 (113 113 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (38 10 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (36 18 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DIMENSIONS-WHEN-ARRAY1P))
 (20 10 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (18 9 (:TYPE-PRESCRIPTION POSP-OF-CAR-OF-DIMENSIONS-WHEN-ARRAY1P))
 (12 6 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (11 11 (:TYPE-PRESCRIPTION NAT-LISTP))
 (10 10 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (6 6 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (6 6 (:TYPE-PRESCRIPTION DAG-PARENT-ARRAYP))
 (5 1 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-CAR-AND-QUOTE))
 (3 1 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (2 1 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (2 1 (:REWRITE DARGP-LESS-THAN-WHEN-NATP-CHEAP))
 (2 1 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION NATP))
 (1 1 (:TYPE-PRESCRIPTION MYQUOTEP))
 (1 1 (:REWRITE USE-ALL-NATP-2))
 (1 1 (:REWRITE USE-ALL-NATP))
 (1 1 (:REWRITE USE-ALL-<=-2))
 (1 1 (:REWRITE USE-ALL-<=))
 (1 1 (:REWRITE USE-ALL-<-2))
 (1 1 (:REWRITE USE-ALL-<))
 (1 1 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE DARGP-LESS-THAN-WHEN-QUOTEP-CHEAP))
 (1 1 (:REWRITE DARGP-LESS-THAN-MONO))
 )
(FIND-VAR-AND-EXPR-TO-SUBST2
 (13 13 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 )
(NATP-OF-MV-NTH-2-OF-FIND-VAR-AND-EXPR-TO-SUBST2
 (420 210 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (236 118 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (236 118 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (210 210 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (144 6 (:LINEAR LEN-OF-CDR-LINEAR-STRONG))
 (132 6 (:LINEAR LEN-OF-CDR-LINEAR))
 (128 128 (:TYPE-PRESCRIPTION NAT-LISTP))
 (118 118 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (96 12 (:REWRITE SYMBOLP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-AND-NOT-CONSP))
 (93 12 (:REWRITE SYMBOLP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-2))
 (76 76 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (76 76 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (76 76 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (76 76 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (62 40 (:REWRITE DEFAULT-+-2))
 (55 11 (:REWRITE DARGP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (48 12 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (42 21 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (40 40 (:REWRITE DEFAULT-+-1))
 (30 6 (:REWRITE <-OF-IF-ARG2))
 (24 24 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (24 2 (:REWRITE TRUE-LISTP-WHEN-NAT-LISTP-REWRITE))
 (24 1 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (21 21 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (21 7 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (19 19 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (14 7 (:REWRITE DARGP-WHEN-NATP-CHEAP))
 (14 7 (:REWRITE DARGP-WHEN-MYQUOTEP-CHEAP))
 (12 12 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (12 12 (:REWRITE SYMBOLP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (12 12 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (12 12 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (12 12 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (12 2 (:REWRITE NAT-LISTP-OF-CDR))
 (11 11 (:REWRITE USE-ALL-NATP-2))
 (11 11 (:REWRITE USE-ALL-NATP))
 (11 11 (:REWRITE DARGP-WHEN-DARGP-LESS-THAN))
 (8 4 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (7 7 (:TYPE-PRESCRIPTION MYQUOTEP))
 (7 7 (:REWRITE USE-ALL-RATIONALP-2))
 (7 7 (:REWRITE USE-ALL-RATIONALP))
 (4 4 (:TYPE-PRESCRIPTION ALL-NATP))
 (4 4 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (4 2 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (3 1 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (3 1 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (2 2 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (2 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE USE-ALL-<-2))
 (1 1 (:REWRITE USE-ALL-<))
 (1 1 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 (1 1 (:REWRITE EQUAL-OF-LEN-AND-0))
 (1 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 )
(<-OF-MV-NTH-2-OF-FIND-VAR-AND-EXPR-TO-SUBST2
 (540 270 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (486 486 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (270 270 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (254 127 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (254 127 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (162 10 (:REWRITE SYMBOLP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-2))
 (158 158 (:TYPE-PRESCRIPTION NAT-LISTP))
 (144 72 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (144 6 (:LINEAR LEN-OF-CDR-LINEAR-STRONG))
 (132 6 (:LINEAR LEN-OF-CDR-LINEAR))
 (127 127 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (108 18 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (96 81 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (81 81 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (81 81 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (76 23 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (72 72 (:TYPE-PRESCRIPTION DARGP))
 (56 37 (:REWRITE DEFAULT-<-1))
 (56 7 (:REWRITE SYMBOLP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-AND-NOT-CONSP))
 (55 11 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-CAR-AND-QUOTE))
 (51 38 (:REWRITE DEFAULT-+-2))
 (43 37 (:REWRITE DEFAULT-<-2))
 (38 38 (:REWRITE DEFAULT-+-1))
 (38 6 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (38 6 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (37 37 (:REWRITE USE-ALL-<-2))
 (37 37 (:REWRITE USE-ALL-<))
 (34 11 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (33 11 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (31 13 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (30 6 (:REWRITE <-OF-IF-ARG2))
 (28 7 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (24 24 (:REWRITE USE-ALL-<=-2))
 (24 24 (:REWRITE USE-ALL-<=))
 (24 24 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (24 24 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (24 2 (:REWRITE TRUE-LISTP-WHEN-NAT-LISTP-REWRITE))
 (22 11 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (21 11 (:REWRITE DARGP-LESS-THAN-WHEN-NATP-CHEAP))
 (14 14 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (12 2 (:REWRITE NAT-LISTP-OF-CDR))
 (11 11 (:TYPE-PRESCRIPTION MYQUOTEP))
 (11 11 (:REWRITE DARGP-LESS-THAN-WHEN-QUOTEP-CHEAP))
 (11 11 (:REWRITE DARGP-LESS-THAN-MONO))
 (10 10 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (10 10 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (10 10 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (10 5 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (9 9 (:REWRITE USE-ALL-RATIONALP-2))
 (9 9 (:REWRITE USE-ALL-RATIONALP))
 (8 4 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (7 7 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (7 7 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (7 7 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (6 6 (:REWRITE USE-ALL-NATP-2))
 (6 6 (:REWRITE USE-ALL-NATP))
 (4 4 (:TYPE-PRESCRIPTION ALL-NATP))
 (4 4 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (1 1 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 (1 1 (:REWRITE EQUAL-OF-LEN-AND-0))
 (1 1 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 )
(DARGP-OF-MV-NTH-3-OF-FIND-VAR-AND-EXPR-TO-SUBST2
 (338 41 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (312 156 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (156 156 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (144 72 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (144 72 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (96 4 (:LINEAR LEN-OF-CDR-LINEAR-STRONG))
 (88 4 (:LINEAR LEN-OF-CDR-LINEAR))
 (82 82 (:TYPE-PRESCRIPTION NAT-LISTP))
 (72 72 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (72 9 (:REWRITE SYMBOLP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-AND-NOT-CONSP))
 (72 9 (:REWRITE SYMBOLP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-2))
 (70 14 (:REWRITE DARGP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (63 63 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (63 63 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (63 63 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (63 63 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (60 12 (:REWRITE <-OF-IF-ARG2))
 (48 24 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (47 28 (:REWRITE DEFAULT-+-2))
 (41 41 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (36 9 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (28 28 (:REWRITE DEFAULT-+-1))
 (24 24 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (24 1 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (20 10 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (18 18 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (18 9 (:REWRITE DARGP-WHEN-NATP-CHEAP))
 (18 9 (:REWRITE DARGP-WHEN-MYQUOTEP-CHEAP))
 (18 6 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (15 5 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (15 5 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (14 14 (:REWRITE DARGP-WHEN-DARGP-LESS-THAN))
 (10 5 (:REWRITE DEFAULT-<-2))
 (9 9 (:TYPE-PRESCRIPTION MYQUOTEP))
 (9 9 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (9 9 (:REWRITE SYMBOLP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (9 9 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (9 9 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (9 9 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (6 6 (:REWRITE USE-ALL-RATIONALP-2))
 (6 6 (:REWRITE USE-ALL-RATIONALP))
 (5 5 (:REWRITE USE-ALL-NATP-2))
 (5 5 (:REWRITE USE-ALL-NATP))
 (5 5 (:REWRITE USE-ALL-<-2))
 (5 5 (:REWRITE USE-ALL-<))
 (5 5 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 (1 1 (:REWRITE EQUAL-OF-LEN-AND-0))
 (1 1 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 )
(DARGP-LESS-THAN-OF-MV-NTH-3-OF-FIND-VAR-AND-EXPR-TO-SUBST2
 (446 446 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (400 200 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (298 149 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (298 149 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (200 200 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (185 185 (:TYPE-PRESCRIPTION NAT-LISTP))
 (156 78 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (149 149 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (144 6 (:LINEAR LEN-OF-CDR-LINEAR-STRONG))
 (132 6 (:LINEAR LEN-OF-CDR-LINEAR))
 (111 7 (:REWRITE SYMBOLP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-2))
 (99 87 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (87 87 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (87 87 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (78 78 (:TYPE-PRESCRIPTION DARGP))
 (77 14 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (72 24 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (42 35 (:REWRITE DEFAULT-+-2))
 (42 14 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (40 5 (:REWRITE SYMBOLP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-AND-NOT-CONSP))
 (36 3 (:REWRITE TRUE-LISTP-WHEN-NAT-LISTP-REWRITE))
 (35 35 (:REWRITE DEFAULT-+-1))
 (31 8 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (31 5 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (31 5 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (30 6 (:REWRITE <-OF-IF-ARG2))
 (28 14 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (27 22 (:REWRITE DEFAULT-<-2))
 (24 22 (:REWRITE DEFAULT-<-1))
 (23 23 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (23 12 (:REWRITE DARGP-LESS-THAN-WHEN-NATP-CHEAP))
 (22 22 (:REWRITE USE-ALL-<-2))
 (22 22 (:REWRITE USE-ALL-<))
 (20 5 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (18 18 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (18 3 (:REWRITE NAT-LISTP-OF-CDR))
 (14 14 (:TYPE-PRESCRIPTION MYQUOTEP))
 (12 12 (:REWRITE USE-ALL-<=-2))
 (12 12 (:REWRITE USE-ALL-<=))
 (12 12 (:REWRITE DARGP-LESS-THAN-WHEN-QUOTEP-CHEAP))
 (12 6 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (10 10 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (8 8 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (8 4 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (8 4 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (7 7 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (7 7 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (6 6 (:TYPE-PRESCRIPTION ALL-NATP))
 (6 6 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (5 5 (:REWRITE USE-ALL-NATP-2))
 (5 5 (:REWRITE USE-ALL-NATP))
 (5 5 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (5 5 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (5 5 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (3 3 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (2 2 (:REWRITE USE-ALL-RATIONALP-2))
 (2 2 (:REWRITE USE-ALL-RATIONALP))
 (2 2 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 (1 1 (:REWRITE EQUAL-OF-LEN-AND-0))
 (1 1 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 )
(CHECK-FOR-VAR-SUBST-LITERAL2
 (1067 389 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (782 51 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (690 558 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (657 558 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (626 247 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (393 393 (:TYPE-PRESCRIPTION NAT-LISTP))
 (328 176 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (230 115 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (228 228 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (213 115 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (206 2 (:REWRITE DARGP-LESS-THAN-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (176 176 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (173 27 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (173 27 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (144 72 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-SIMPLE))
 (142 42 (:REWRITE DEFAULT-+-2))
 (115 115 (:TYPE-PRESCRIPTION DARGP))
 (115 115 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (115 115 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (115 115 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (114 19 (:REWRITE NATP-OF-NTH-WHEN-NAT-LISTP))
 (113 113 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (100 5 (:REWRITE ACL2-NUMBERP-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (99 99 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (66 48 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DIMENSIONS-WHEN-ARRAY1P))
 (60 33 (:REWRITE DEFAULT-<-2))
 (60 30 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (51 51 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (51 51 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (42 42 (:REWRITE DEFAULT-+-1))
 (38 19 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (35 33 (:REWRITE DEFAULT-<-1))
 (33 33 (:REWRITE USE-ALL-<-2))
 (33 33 (:REWRITE USE-ALL-<))
 (33 24 (:TYPE-PRESCRIPTION POSP-OF-CAR-OF-DIMENSIONS-WHEN-ARRAY1P))
 (20 2 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (19 19 (:TYPE-PRESCRIPTION ALL-NATP))
 (19 19 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (18 18 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (16 5 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (14 7 (:REWRITE LEN-OF-NTH-OF-DARGS))
 (13 13 (:REWRITE USE-ALL-<=-2))
 (13 13 (:REWRITE USE-ALL-<=))
 (7 7 (:TYPE-PRESCRIPTION DAG-EXPRP))
 (7 7 (:REWRITE LEN-OF-NTH-WHEN-BOUNDED-DARG-LISTP))
 (5 5 (:REWRITE NATP-OF-+-WHEN-NEGATIVE-CONSTANT))
 (4 4 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (4 2 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (4 1 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (2 2 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (2 2 (:TYPE-PRESCRIPTION MYQUOTEP))
 (2 2 (:REWRITE USE-ALL-NATP-2))
 (2 2 (:REWRITE USE-ALL-NATP))
 (1 1 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (1 1 (:REWRITE NOT-<-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-2))
 (1 1 (:REWRITE NOT-<-OF-NTH-OF-DARGS-OF-AREF1-AND-CONSTANT-WHEN-PSEUDO-DAG-ARRAYP))
 )
(NATP-OF-MV-NTH-2-OF-CHECK-FOR-VAR-SUBST-LITERAL2
 (78 34 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (64 64 (:TYPE-PRESCRIPTION NAT-LISTP))
 (64 32 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (62 31 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (62 31 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (58 29 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (53 53 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (44 22 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (44 22 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (44 4 (:REWRITE <-OF-0-AND-LEN))
 (42 21 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-SIMPLE))
 (41 41 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-AUX))
 (41 1 (:REWRITE <-OF-IF-ARG2))
 (36 18 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (33 10 (:REWRITE DEFAULT-+-2))
 (32 32 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (32 32 (:TYPE-PRESCRIPTION DAG-PARENT-ARRAYP))
 (31 31 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (31 31 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (31 31 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (29 29 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (26 6 (:REWRITE NATP-OF-NTH-WHEN-NAT-LISTP))
 (24 1 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (22 22 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (20 1 (:REWRITE ACL2-NUMBERP-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (18 1 (:REWRITE EQUAL-OF-LEN-AND-0))
 (13 13 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (11 11 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (11 2 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (11 2 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (10 10 (:REWRITE DEFAULT-+-1))
 (8 4 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (5 3 (:REWRITE DEFAULT-<-2))
 (4 4 (:TYPE-PRESCRIPTION ALL-NATP))
 (4 4 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (4 2 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (3 3 (:REWRITE USE-ALL-<-2))
 (3 3 (:REWRITE USE-ALL-<))
 (3 3 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE USE-ALL-<=-2))
 (2 2 (:REWRITE USE-ALL-<=))
 (2 2 (:REWRITE NATP-OF-+-WHEN-NEGATIVE-CONSTANT))
 (2 1 (:REWRITE LEN-OF-NTH-OF-DARGS))
 (1 1 (:TYPE-PRESCRIPTION DAG-EXPRP))
 (1 1 (:REWRITE USE-ALL-NATP-2))
 (1 1 (:REWRITE USE-ALL-NATP))
 (1 1 (:REWRITE LEN-OF-NTH-WHEN-BOUNDED-DARG-LISTP))
 (1 1 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 )
(<-MV-NTH-2-OF-CHECK-FOR-VAR-SUBST-LITERAL2
 (110 2 (:REWRITE DARGP-LESS-THAN-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (102 41 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (73 73 (:TYPE-PRESCRIPTION NAT-LISTP))
 (70 35 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (66 35 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (64 32 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (62 31 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (53 53 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (46 23 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-SIMPLE))
 (44 22 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (44 22 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (44 4 (:REWRITE <-OF-0-AND-LEN))
 (43 43 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-AUX))
 (41 1 (:REWRITE <-OF-IF-ARG2))
 (40 40 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (38 15 (:REWRITE DEFAULT-+-2))
 (36 18 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (35 35 (:TYPE-PRESCRIPTION DARGP))
 (35 35 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (35 35 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (35 35 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (32 32 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (32 32 (:TYPE-PRESCRIPTION DAG-PARENT-ARRAYP))
 (30 5 (:REWRITE NATP-OF-NTH-WHEN-NAT-LISTP))
 (30 1 (:REWRITE NATP-OF-+-OF-1))
 (24 1 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (22 22 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (20 2 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (20 1 (:REWRITE ACL2-NUMBERP-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (18 1 (:REWRITE EQUAL-OF-LEN-AND-0))
 (15 15 (:REWRITE DEFAULT-+-1))
 (13 13 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (11 11 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (11 2 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (11 2 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (10 5 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (5 5 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (5 5 (:TYPE-PRESCRIPTION ALL-NATP))
 (5 5 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (5 3 (:REWRITE DEFAULT-<-2))
 (4 2 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (4 2 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (3 3 (:REWRITE USE-ALL-<-2))
 (3 3 (:REWRITE USE-ALL-<))
 (3 3 (:REWRITE DEFAULT-<-1))
 (2 2 (:TYPE-PRESCRIPTION MYQUOTEP))
 (2 2 (:REWRITE USE-ALL-<=-2))
 (2 2 (:REWRITE USE-ALL-<=))
 (2 1 (:REWRITE LEN-OF-NTH-OF-DARGS))
 (1 1 (:TYPE-PRESCRIPTION DAG-EXPRP))
 (1 1 (:REWRITE USE-ALL-NATP-2))
 (1 1 (:REWRITE USE-ALL-NATP))
 (1 1 (:REWRITE NATP-OF-+-WHEN-NEGATIVE-CONSTANT))
 (1 1 (:REWRITE LEN-OF-NTH-WHEN-BOUNDED-DARG-LISTP))
 (1 1 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 )
(DARGP-LESS-THAN-OF-MV-NTH-3-OF-CHECK-FOR-VAR-SUBST-LITERAL2
 (110 2 (:REWRITE DARGP-LESS-THAN-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (102 41 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (73 73 (:TYPE-PRESCRIPTION NAT-LISTP))
 (70 35 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (66 35 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (64 32 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (62 31 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (53 53 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (46 23 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-SIMPLE))
 (44 22 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (44 22 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (44 4 (:REWRITE <-OF-0-AND-LEN))
 (43 43 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-AUX))
 (41 1 (:REWRITE <-OF-IF-ARG2))
 (40 40 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (38 15 (:REWRITE DEFAULT-+-2))
 (36 18 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (35 35 (:TYPE-PRESCRIPTION DARGP))
 (35 35 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (35 35 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (35 35 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (32 32 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (32 32 (:TYPE-PRESCRIPTION DAG-PARENT-ARRAYP))
 (30 5 (:REWRITE NATP-OF-NTH-WHEN-NAT-LISTP))
 (30 1 (:REWRITE NATP-OF-+-OF-1))
 (24 1 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (22 22 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (20 2 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (20 1 (:REWRITE ACL2-NUMBERP-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (18 1 (:REWRITE EQUAL-OF-LEN-AND-0))
 (15 15 (:REWRITE DEFAULT-+-1))
 (13 13 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (11 11 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (11 2 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (11 2 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (10 5 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (5 5 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (5 5 (:TYPE-PRESCRIPTION ALL-NATP))
 (5 5 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (5 3 (:REWRITE DEFAULT-<-2))
 (4 2 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (4 2 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (3 3 (:REWRITE USE-ALL-<-2))
 (3 3 (:REWRITE USE-ALL-<))
 (3 3 (:REWRITE DEFAULT-<-1))
 (2 2 (:TYPE-PRESCRIPTION MYQUOTEP))
 (2 2 (:REWRITE USE-ALL-<=-2))
 (2 2 (:REWRITE USE-ALL-<=))
 (2 1 (:REWRITE LEN-OF-NTH-OF-DARGS))
 (1 1 (:TYPE-PRESCRIPTION DAG-EXPRP))
 (1 1 (:REWRITE USE-ALL-NATP-2))
 (1 1 (:REWRITE USE-ALL-NATP))
 (1 1 (:REWRITE NATP-OF-+-WHEN-NEGATIVE-CONSTANT))
 (1 1 (:REWRITE LEN-OF-NTH-WHEN-BOUNDED-DARG-LISTP))
 (1 1 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 )
(DARGP-LESS-THAN-OF-MV-NTH-3-OF-CHECK-FOR-VAR-SUBST-LITERAL2-GEN
 (57 57 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (10 2 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-CAR-AND-QUOTE))
 (6 3 (:REWRITE DEFAULT-<-1))
 (6 2 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (4 4 (:TYPE-PRESCRIPTION NAT-LISTP))
 (4 2 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (4 2 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (4 2 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (4 2 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (3 3 (:REWRITE USE-ALL-<=-2))
 (3 3 (:REWRITE USE-ALL-<=))
 (3 3 (:REWRITE USE-ALL-<-2))
 (3 3 (:REWRITE USE-ALL-<))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2 2 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (2 2 (:TYPE-PRESCRIPTION MYQUOTEP))
 (2 1 (:REWRITE DARGP-LESS-THAN-WHEN-NATP-CHEAP))
 (1 1 (:REWRITE USE-ALL-RATIONALP-2))
 (1 1 (:REWRITE USE-ALL-RATIONALP))
 (1 1 (:REWRITE USE-ALL-NATP-2))
 (1 1 (:REWRITE USE-ALL-NATP))
 (1 1 (:REWRITE DARGP-LESS-THAN-WHEN-QUOTEP-CHEAP))
 (1 1 (:REWRITE DARGP-LESS-THAN-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE DARGP-LESS-THAN-WHEN-CONSP-CHEAP))
 )
(DARGP-OF-MV-NTH-3-OF-CHECK-FOR-VAR-SUBST-LITERAL2
 (54 54 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (5 1 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-CAR-AND-QUOTE))
 (3 1 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (2 2 (:TYPE-PRESCRIPTION NAT-LISTP))
 (2 2 (:REWRITE USE-ALL-<=-2))
 (2 2 (:REWRITE USE-ALL-<=))
 (2 2 (:REWRITE USE-ALL-<-2))
 (2 2 (:REWRITE USE-ALL-<))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 1 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (2 1 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (2 1 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (2 1 (:REWRITE DARGP-LESS-THAN-WHEN-NATP-CHEAP))
 (2 1 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (1 1 (:TYPE-PRESCRIPTION MYQUOTEP))
 (1 1 (:REWRITE USE-ALL-NATP-2))
 (1 1 (:REWRITE USE-ALL-NATP))
 (1 1 (:REWRITE DARGP-LESS-THAN-WHEN-QUOTEP-CHEAP))
 (1 1 (:REWRITE DARGP-LESS-THAN-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE DARGP-LESS-THAN-WHEN-CONSP-CHEAP))
 (1 1 (:REWRITE DARGP-LESS-THAN-MONO))
 )
(NATP-OF-MV-NTH-3-OF-CHECK-FOR-VAR-SUBST-LITERAL2
 (59 59 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (15 3 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (5 1 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (5 1 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-CAR-AND-QUOTE))
 (5 1 (:REWRITE <-OF-IF-ARG2))
 (3 3 (:TYPE-PRESCRIPTION LEN))
 (3 3 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (3 3 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (3 1 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (2 2 (:TYPE-PRESCRIPTION NAT-LISTP))
 (2 2 (:REWRITE USE-ALL-NATP-2))
 (2 2 (:REWRITE USE-ALL-NATP))
 (2 2 (:REWRITE USE-ALL-<=-2))
 (2 2 (:REWRITE USE-ALL-<=))
 (2 2 (:REWRITE USE-ALL-<-2))
 (2 2 (:REWRITE USE-ALL-<))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 1 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (2 1 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (2 1 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (2 1 (:REWRITE DARGP-LESS-THAN-WHEN-NATP-CHEAP))
 (2 1 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (1 1 (:TYPE-PRESCRIPTION MYQUOTEP))
 (1 1 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (1 1 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (1 1 (:REWRITE DARGP-LESS-THAN-WHEN-QUOTEP-CHEAP))
 (1 1 (:REWRITE DARGP-LESS-THAN-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE DARGP-LESS-THAN-WHEN-CONSP-CHEAP))
 (1 1 (:REWRITE DARGP-LESS-THAN-MONO))
 )
(SUBST-CANDIDATES
 (485 5 (:DEFINITION ACL2-COUNT))
 (169 5 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (129 6 (:DEFINITION INTEGER-ABS))
 (108 108 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (61 30 (:REWRITE DEFAULT-+-2))
 (51 6 (:REWRITE <=-OF-0-WHEN-NATP))
 (43 22 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (42 30 (:REWRITE DEFAULT-+-1))
 (36 3 (:REWRITE INTEGERP-WHEN-NATP))
 (36 2 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (33 2 (:REWRITE LEN-OF-CDR))
 (32 6 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (28 10 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (27 3 (:DEFINITION LENGTH))
 (26 13 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (26 2 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (24 6 (:REWRITE COMMUTATIVITY-OF-+))
 (22 1 (:REWRITE USE-ALL-<-FOR-CAR))
 (19 5 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (19 5 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (17 13 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (17 12 (:REWRITE DEFAULT-<-2))
 (13 13 (:TYPE-PRESCRIPTION DARGP))
 (13 13 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (13 13 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (13 13 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (13 12 (:REWRITE DEFAULT-<-1))
 (13 3 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (12 12 (:REWRITE USE-ALL-<-2))
 (12 12 (:REWRITE USE-ALL-<))
 (11 11 (:TYPE-PRESCRIPTION ALL-NATP))
 (9 9 (:REWRITE USE-ALL-NATP-2))
 (9 9 (:REWRITE USE-ALL-NATP))
 (9 9 (:REWRITE FOLD-CONSTS-IN-+))
 (9 9 (:REWRITE +-COMBINE-CONSTANTS))
 (8 8 (:REWRITE USE-ALL-<=-2))
 (8 8 (:REWRITE USE-ALL-<=))
 (8 4 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (8 1 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (6 6 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (6 6 (:REWRITE DEFAULT-UNARY-MINUS))
 (6 3 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (6 1 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (5 5 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (5 5 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (5 5 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (5 1 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (3 3 (:REWRITE USE-ALL-RATIONALP-2))
 (3 3 (:REWRITE USE-ALL-RATIONALP))
 (3 3 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (3 3 (:REWRITE DEFAULT-REALPART))
 (3 3 (:REWRITE DEFAULT-NUMERATOR))
 (3 3 (:REWRITE DEFAULT-IMAGPART))
 (3 3 (:REWRITE DEFAULT-DENOMINATOR))
 (3 3 (:REWRITE DEFAULT-COERCE-2))
 (3 3 (:REWRITE DEFAULT-COERCE-1))
 (3 3 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (3 3 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (3 3 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (3 3 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (3 3 (:REWRITE ALL-<-TRANSITIVE))
 (3 1 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (2 2 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (2 2 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (2 2 (:REWRITE ZP-OPEN))
 (2 2 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (2 2 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (2 2 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (2 2 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (2 1 (:REWRITE INTEGERP-OF-CAR-WHEN-NAT-LISTP-CHEAP))
 (2 1 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (2 1 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (1 1 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (1 1 (:REWRITE EQUAL-OF-LEN-AND-0))
 (1 1 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (1 1 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (1 1 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (1 1 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 )
(SUBST-CANDIDATES-WHEN-NOT-CONSP
 (23 1 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (19 19 (:TYPE-PRESCRIPTION SUBST-CANDIDATES))
 (5 5 (:TYPE-PRESCRIPTION LEN))
 (4 2 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (3 1 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (3 1 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (2 2 (:TYPE-PRESCRIPTION NAT-LISTP))
 (2 1 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (2 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:TYPE-PRESCRIPTION DARGP))
 (1 1 (:REWRITE USE-ALL-<-2))
 (1 1 (:REWRITE USE-ALL-<))
 (1 1 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (1 1 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (1 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (1 1 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (1 1 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 )
(SUBST-CANDIDATE-LISTP-OF-SUBST-CANDIDATES
 (3707 113 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (2806 24 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (1978 48 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (1396 84 (:REWRITE LEN-OF-CDR))
 (1148 24 (:REWRITE ALL-NATP-OF-CDR))
 (899 41 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (540 48 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (534 267 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (456 228 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (444 12 (:REWRITE <-OF-IF-ARG2))
 (412 12 (:REWRITE DARGP-OF-CAR-WHEN-DARG-LISTP))
 (402 402 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (354 270 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (292 24 (:REWRITE DARG-LISTP-WHEN-NOT-CONSP))
 (291 291 (:TYPE-PRESCRIPTION DARGP))
 (280 136 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (267 267 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (267 267 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (267 267 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (208 68 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (208 68 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (188 36 (:REWRITE NAT-LISTP-OF-CDR))
 (186 186 (:TYPE-PRESCRIPTION ALL-NATP))
 (180 90 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (141 81 (:REWRITE DEFAULT-+-2))
 (141 73 (:REWRITE DEFAULT-<-2))
 (137 137 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (132 12 (:REWRITE DARGP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (121 12 (:REWRITE TRUE-LISTP-WHEN-NAT-LISTP-REWRITE))
 (100 12 (:REWRITE DARG-LISTP-OF-CDR))
 (99 48 (:TYPE-PRESCRIPTION NATP-OF-CAR-OF-CAR-WHEN-SUBST-CANDIDATE-LISTP))
 (96 48 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (81 81 (:REWRITE DEFAULT-+-1))
 (81 6 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (76 12 (:REWRITE DARGP-WHEN-NOT-CONSP-CHEAP))
 (76 12 (:REWRITE DARGP-WHEN-CONSP-CHEAP))
 (74 74 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (73 73 (:REWRITE USE-ALL-<-2))
 (73 73 (:REWRITE USE-ALL-<))
 (73 73 (:REWRITE DEFAULT-<-1))
 (72 12 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (72 12 (:REWRITE DARGP-WHEN-NATP-CHEAP))
 (63 17 (:REWRITE +-COMBINE-CONSTANTS))
 (58 18 (:REWRITE ZP-OPEN))
 (48 48 (:TYPE-PRESCRIPTION DARG-LISTP))
 (48 48 (:REWRITE EQUAL-OF-LEN-AND-0))
 (48 48 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (48 24 (:REWRITE DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (48 12 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-SUBST-CANDIDATE-LISTP))
 (42 42 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (24 24 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (24 24 (:REWRITE USE-ALL-NATP-2))
 (24 24 (:REWRITE USE-ALL-NATP))
 (24 24 (:REWRITE LEN-OF-CDDR-WHEN-EQUAL-OF-LEN))
 (24 12 (:REWRITE DARGP-WHEN-MYQUOTEP-CHEAP))
 (24 12 (:DEFINITION FIX))
 (12 12 (:TYPE-PRESCRIPTION NATP))
 (12 12 (:TYPE-PRESCRIPTION MYQUOTEP))
 (12 12 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (12 12 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (12 12 (:REWRITE DARGP-WHEN-DARGP-LESS-THAN))
 (12 12 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (8 8 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (8 8 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (8 8 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (8 8 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (8 8 (:REWRITE ALL-<-TRANSITIVE))
 (7 7 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (6 6 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (5 5 (:REWRITE USE-ALL-<=-2))
 (5 5 (:REWRITE USE-ALL-<=))
 )
(ALL-<-OF-STRIP-CARS-OF-SUBST-CANDIDATES
 (2135 53 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (951 19 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (644 38 (:REWRITE LEN-OF-CDR))
 (549 25 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (421 421 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (306 12 (:REWRITE CONSP-OF-STRIP-CARS))
 (296 8 (:REWRITE <-OF-IF-ARG2))
 (270 135 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (190 92 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (141 46 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (141 46 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (138 135 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (135 135 (:TYPE-PRESCRIPTION DARGP))
 (135 135 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (135 135 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (135 135 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (95 49 (:REWRITE DEFAULT-<-2))
 (89 51 (:REWRITE DEFAULT-+-2))
 (53 53 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (51 51 (:REWRITE DEFAULT-+-1))
 (50 50 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (49 49 (:REWRITE USE-ALL-<-2))
 (49 49 (:REWRITE USE-ALL-<))
 (49 49 (:REWRITE DEFAULT-<-1))
 (48 8 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (41 11 (:REWRITE +-COMBINE-CONSTANTS))
 (39 29 (:REWRITE STRIP-CARS-WHEN-NOT-CONSP-CHEAP))
 (36 12 (:REWRITE ZP-OPEN))
 (32 19 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (30 30 (:REWRITE EQUAL-OF-LEN-AND-0))
 (29 29 (:TYPE-PRESCRIPTION SUBST-CANDIDATES))
 (26 26 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (26 26 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (21 21 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (21 21 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (21 21 (:REWRITE ALL-<-TRANSITIVE))
 (16 8 (:DEFINITION FIX))
 (12 6 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (8 8 (:REWRITE LEN-OF-CDDR-WHEN-EQUAL-OF-LEN))
 (7 7 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (6 6 (:TYPE-PRESCRIPTION ALL-NATP))
 (3 3 (:REWRITE USE-ALL-<=-2))
 (3 3 (:REWRITE USE-ALL-<=))
 )
(SUBSETP-EQUAL-OF-STRIP-CADDRS-OF-SUBST-CANDIDATES-HELPER
 (1795 53 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (514 34 (:REWRITE LEN-OF-CDR))
 (420 18 (:DEFINITION STRIP-CADDRS))
 (381 21 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (278 55 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (274 91 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-2-ALT))
 (222 111 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (203 7 (:REWRITE PERM-OF-APPEND-WHEN-NOT-CONSP))
 (200 8 (:REWRITE <-OF-IF-ARG2))
 (192 92 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (182 91 (:REWRITE SUBSETP-EQUAL-OF-CDR-ARG2-CHEAP))
 (182 7 (:REWRITE CONSP-OF-STRIP-CADDRS))
 (143 9 (:REWRITE SUBSETP-EQUAL-OF-CDR-ARG2-WHEN-NOT-MEMBER-EQUAL-OF-CAR))
 (142 46 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (142 46 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (116 58 (:REWRITE SUBSETP-EQUAL-WHEN-SUBSETP-EQUAL-OF-CDR-CHEAP))
 (115 111 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (111 111 (:TYPE-PRESCRIPTION DARGP))
 (111 111 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (111 111 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (111 111 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (105 58 (:REWRITE SUBSETP-EQUAL-WHEN-NOT-CONSP-ARG2-CHEAP))
 (100 58 (:REWRITE SUBSETP-EQUAL-WHEN-NOT-CONSP-ARG1-CHEAP))
 (96 96 (:TYPE-PRESCRIPTION STRIP-CADDRS))
 (92 92 (:TYPE-PRESCRIPTION NAT-LISTP))
 (89 49 (:REWRITE DEFAULT-<-2))
 (64 44 (:REWRITE DEFAULT-+-2))
 (56 56 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (56 12 (:REWRITE SUBSETP-EQUAL-OF-CDR-ARG1))
 (55 1 (:REWRITE SUBSETP-EQUAL-OF-CONS-ARG2))
 (53 53 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (50 50 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (49 49 (:REWRITE USE-ALL-<-2))
 (49 49 (:REWRITE USE-ALL-<))
 (49 49 (:REWRITE DEFAULT-<-1))
 (45 12 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-1))
 (44 44 (:REWRITE DEFAULT-+-1))
 (37 11 (:REWRITE +-COMBINE-CONSTANTS))
 (32 16 (:REWRITE NOT-MEMBER-EQUAL-WHEN-NOT-MEMBER-EQUAL-OF-CDR-CHEAP))
 (32 16 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-CDR-CHEAP))
 (32 8 (:REWRITE ZP-OPEN))
 (32 8 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (27 27 (:TYPE-PRESCRIPTION SUBST-CANDIDATES))
 (22 22 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (16 16 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-MEMBER-EQUAL))
 (16 16 (:REWRITE MEMBER-EQUAL-OF-SINGLETON-CONSTANT-IFF))
 (16 16 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-WHEN-NOT-EQUAL-CAR))
 (16 16 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-TRIM))
 (16 16 (:REWRITE EQUAL-OF-LEN-AND-0))
 (14 7 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (14 7 (:REWRITE MEMBER-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (12 12 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-2))
 (12 8 (:DEFINITION FIX))
 (8 8 (:REWRITE LEN-OF-CDDR-WHEN-EQUAL-OF-LEN))
 (7 7 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (3 3 (:REWRITE USE-ALL-<=-2))
 (3 3 (:REWRITE USE-ALL-<=))
 )
(SUBSETP-EQUAL-OF-STRIP-CADDRS-OF-SUBST-CANDIDATES)
(<-OF-LARGEST-NON-QUOTEP-OF-STRIP-CADRS-OF-SUBST-CANDIDATES
 (56911 446 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (54937 74 (:LINEAR LARGEST-NON-QUOTEP-BOUND))
 (52778 431 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (21640 41 (:REWRITE <-OF-LARGEST-NON-QUOTEP))
 (20869 174 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (20014 5673 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (14230 7151 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (10451 3447 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (8903 1640 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (8804 4402 (:TYPE-PRESCRIPTION NATP-OF-LARGEST-NON-QUOTEP))
 (8608 4304 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-SIMPLE))
 (8153 121 (:REWRITE INTEGERP-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (7703 121 (:REWRITE INTEGERP-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (7030 1445 (:REWRITE DEFAULT-+-2))
 (6868 3434 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (6205 4304 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (6114 1008 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (6081 128 (:REWRITE NATP-OF-NTH-WHEN-DARG-LISTP))
 (5949 242 (:REWRITE <-OF-IF-ARG2))
 (5783 163 (:REWRITE DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (4722 2050 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (4443 74 (:LINEAR LARGEST-NON-QUOTEP-BOUND-ALT))
 (3991 1991 (:REWRITE DEFAULT-<-2))
 (3770 13 (:LINEAR LEN-OF-CDR-LINEAR-STRONG))
 (3437 3437 (:TYPE-PRESCRIPTION DARGP))
 (3434 3434 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (3434 3434 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (3434 3434 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (3422 253 (:REWRITE USE-ALL-<-FOR-CAR))
 (3421 135 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (3354 54 (:REWRITE NATP-OF-NTH-OF-DARGS))
 (3266 54 (:REWRITE INTEGERP-OF-NTH-OF-DARGS-ALT))
 (3266 54 (:REWRITE INTEGERP-OF-NTH-OF-DARGS))
 (2968 1484 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (2804 2804 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (2775 1484 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (2481 2125 (:REWRITE USE-ALL-<))
 (2447 336 (:REWRITE NATP-OF-NTH-WHEN-NAT-LISTP))
 (2388 1991 (:REWRITE DEFAULT-<-1))
 (2125 2125 (:REWRITE USE-ALL-<-2))
 (1959 363 (:REWRITE LARGEST-NON-QUOTEP-WHEN-ALL-CONSP))
 (1875 75 (:REWRITE DARG-LISTP-WHEN-NOT-CONSP))
 (1810 54 (:REWRITE DARG-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (1727 1727 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (1628 1628 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (1565 1565 (:TYPE-PRESCRIPTION ALL-CONSP))
 (1484 742 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (1445 1445 (:REWRITE DEFAULT-+-1))
 (1346 1346 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (1340 134 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (1130 478 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (1021 2 (:REWRITE LARGEST-NON-QUOTEP-OF-CONS))
 (862 431 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (764 265 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (726 363 (:REWRITE LARGEST-NON-QUOTEP-WHEN-ALL-MYQUOTEP-CHEAP))
 (726 363 (:REWRITE LARGEST-NON-QUOTEP-WHEN-ALL-CONSP-CHEAP))
 (716 179 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (714 238 (:REWRITE ALL-CONSP-OF-CDR))
 (714 119 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (670 134 (:REWRITE ALL-RATIONALP-OF-CDR))
 (637 637 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (625 2 (:REWRITE DARGP-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (598 75 (:REWRITE DARG-LISTP-OF-STRIP-CADRS-WHEN-SUBST-CANDIDATE-LISTP))
 (574 574 (:REWRITE USE-ALL-NATP-2))
 (574 574 (:REWRITE USE-ALL-NATP))
 (563 185 (:REWRITE +-COMBINE-CONSTANTS))
 (536 536 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (505 431 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (492 84 (:REWRITE ZP-OPEN))
 (479 479 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (415 415 (:REWRITE USE-ALL-<=-2))
 (415 415 (:REWRITE USE-ALL-<=))
 (410 54 (:REWRITE INTEGERP-OF-NTH-WHEN-ALL-INTEGERP))
 (398 398 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (387 387 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (372 62 (:REWRITE ALL-<-OF-+-OF-1))
 (367 32 (:REWRITE SUBST-CANDIDATE-LISTP-OF-SUBST-CANDIDATES))
 (358 358 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (357 119 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (356 356 (:TYPE-PRESCRIPTION MEMBERP))
 (351 351 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (336 336 (:REWRITE ALL-<-TRANSITIVE))
 (323 41 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (303 1 (:REWRITE DARGP-OF-NTH-OF-DARGS))
 (300 134 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (297 297 (:TYPE-PRESCRIPTION SUBST-CANDIDATES))
 (268 268 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (268 268 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (238 238 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (238 119 (:REWRITE INTEGERP-OF-CAR-WHEN-NAT-LISTP-CHEAP))
 (238 119 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (238 119 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (234 234 (:TYPE-PRESCRIPTION DAG-EXPRP))
 (232 116 (:REWRITE ALL-NATP-IMPLIES-ALL-INTEGERP-CHEAP))
 (215 174 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (214 214 (:TYPE-PRESCRIPTION SUBST-CANDIDATE-LISTP))
 (202 116 (:REWRITE ALL-INTEGERP-WHEN-NOT-CONSP-CHEAP))
 (196 196 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (179 179 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (173 173 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (160 160 (:REWRITE NAT-LISTP-OF-CDR))
 (158 2 (:REWRITE ALL-CONSP-OF-CONS))
 (150 75 (:REWRITE DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (142 134 (:DEFINITION FIX))
 (142 71 (:REWRITE LEN-OF-NTH-OF-DARGS))
 (135 135 (:REWRITE USE-ALL-RATIONALP-2))
 (135 135 (:REWRITE USE-ALL-RATIONALP))
 (134 134 (:REWRITE LEN-OF-CDDR-WHEN-EQUAL-OF-LEN))
 (128 128 (:REWRITE NATP-OF-NTH-WHEN-BOUNDED-DARG-LISTP-GEN))
 (119 119 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (119 119 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (119 119 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (119 119 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (92 23 (:REWRITE SUBST-CANDIDATE-LISTP-OF-CONS))
 (82 41 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (82 41 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (74 74 (:LINEAR <-OF-LARGEST-NON-QUOTEP))
 (71 71 (:REWRITE LEN-OF-NTH-WHEN-BOUNDED-DARG-LISTP))
 (62 62 (:REWRITE NATP-OF-+-WHEN-NEGATIVE-CONSTANT))
 (54 54 (:REWRITE INTEGERP-OF-NTH-WHEN-BOUNDED-DARG-LISTP))
 (46 46 (:TYPE-PRESCRIPTION SUBST-CANDIDATEP))
 (41 41 (:REWRITE BOUNDED-DARG-LISTP-MONOTONE))
 (30 1 (:REWRITE RATIONALP-OF-IF-STRONG))
 (19 1 (:REWRITE DARGP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (18 2 (:REWRITE NOT-<-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-2))
 (16 16 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (16 16 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (14 14 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (9 1 (:REWRITE DARGP-WHEN-NATP-CHEAP))
 (8 1 (:REWRITE DARGP-WHEN-NOT-CONSP-CHEAP))
 (8 1 (:REWRITE DARGP-WHEN-CONSP-CHEAP))
 (8 1 (:REWRITE DARGP-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (2 2 (:REWRITE NOT-<-OF-NTH-OF-DARGS-OF-AREF1-AND-CONSTANT-WHEN-PSEUDO-DAG-ARRAYP))
 (2 1 (:REWRITE DARGP-WHEN-MYQUOTEP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION MYQUOTEP))
 (1 1 (:REWRITE DARGP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE DARGP-OF-NTH-WHEN-BOUNDED-DARG-LISTP))
 )
(BOUNDED-DARG-LISTP-OF-STRIP-CADRS-OF-SUBST-CANDIDATES
 (22346 49 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (8114 2469 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (7488 50 (:REWRITE INTEGERP-WHEN-NATP))
 (7046 2 (:REWRITE ALL-<-OF-CONS))
 (5476 2766 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (5357 1975 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (4088 2044 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-SIMPLE))
 (3950 1975 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (3635 745 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (3612 50 (:REWRITE INTEGERP-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (3162 716 (:REWRITE DEFAULT-+-2))
 (2936 444 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (2838 50 (:REWRITE INTEGERP-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (2748 2044 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (2403 1135 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (1975 1975 (:TYPE-PRESCRIPTION DARGP))
 (1975 1975 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (1975 1975 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (1975 1975 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (1812 906 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (1801 2 (:REWRITE <-OF-NTH-OF-DARGS))
 (1798 815 (:REWRITE DEFAULT-<-1))
 (1685 906 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (1632 48 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (1628 2 (:REWRITE BOUNDED-DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (1616 815 (:REWRITE DEFAULT-<-2))
 (1514 1514 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (1499 37 (:REWRITE <-OF-IF-ARG2))
 (1226 1226 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (1202 1202 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (1170 78 (:REWRITE DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (1152 48 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (1152 48 (:REWRITE USE-ALL-<-FOR-CAR))
 (1086 26 (:REWRITE NATP-OF-NTH-WHEN-DARG-LISTP))
 (1086 26 (:REWRITE NATP-OF-NTH-OF-DARGS))
 (1086 26 (:REWRITE INTEGERP-OF-NTH-OF-DARGS-ALT))
 (1086 26 (:REWRITE INTEGERP-OF-NTH-OF-DARGS))
 (1061 8 (:REWRITE <-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-GEN))
 (963 863 (:REWRITE USE-ALL-<))
 (957 2 (:REWRITE ACL2-NUMBERP-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (912 48 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (863 863 (:REWRITE USE-ALL-<-2))
 (716 716 (:REWRITE DEFAULT-+-1))
 (682 53 (:REWRITE EQUAL-OF-LEN-AND-0))
 (534 72 (:REWRITE NATP-OF-NTH-WHEN-NAT-LISTP))
 (528 96 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (452 204 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (422 422 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (422 121 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (390 26 (:REWRITE DARG-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (265 265 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (248 62 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (246 30 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (240 48 (:REWRITE ALL-RATIONALP-OF-CDR))
 (226 226 (:REWRITE USE-ALL-<=-2))
 (226 226 (:REWRITE USE-ALL-<=))
 (206 46 (:REWRITE ZP-OPEN))
 (204 68 (:REWRITE +-COMBINE-CONSTANTS))
 (192 192 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (192 26 (:REWRITE INTEGERP-OF-NTH-WHEN-ALL-INTEGERP))
 (154 77 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (135 135 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (128 128 (:TYPE-PRESCRIPTION SUBST-CANDIDATES))
 (124 124 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (116 116 (:TYPE-PRESCRIPTION DAG-EXPRP))
 (111 111 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (100 100 (:TYPE-PRESCRIPTION MEMBERP))
 (99 99 (:REWRITE ALL-<-TRANSITIVE))
 (96 96 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (96 48 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (87 49 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (76 76 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (76 38 (:REWRITE LEN-OF-NTH-OF-DARGS))
 (76 38 (:REWRITE ALL-NATP-IMPLIES-ALL-INTEGERP-CHEAP))
 (74 74 (:REWRITE USE-ALL-NATP-2))
 (74 74 (:REWRITE USE-ALL-NATP))
 (74 38 (:REWRITE ALL-INTEGERP-WHEN-NOT-CONSP-CHEAP))
 (72 36 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (72 36 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (72 12 (:REWRITE ALL-<-OF-+-OF-1))
 (62 62 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (56 56 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (48 48 (:REWRITE USE-ALL-RATIONALP-2))
 (48 48 (:REWRITE USE-ALL-RATIONALP))
 (48 48 (:REWRITE NAT-LISTP-OF-CDR))
 (48 48 (:REWRITE LEN-OF-CDDR-WHEN-EQUAL-OF-LEN))
 (48 48 (:DEFINITION FIX))
 (38 38 (:REWRITE LEN-OF-NTH-WHEN-BOUNDED-DARG-LISTP))
 (36 36 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (26 26 (:REWRITE NATP-OF-NTH-WHEN-BOUNDED-DARG-LISTP-GEN))
 (26 26 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (26 26 (:REWRITE INTEGERP-OF-NTH-WHEN-BOUNDED-DARG-LISTP))
 (16 16 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (16 2 (:REWRITE <-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-GEN))
 (13 13 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (13 13 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (8 8 (:REWRITE NATP-OF-+-WHEN-NEGATIVE-CONSTANT))
 (4 4 (:REWRITE <=-OF-NTH-WHEN-ALL-<=-FREE))
 (2 2 (:TYPE-PRESCRIPTION BOUNDED-DAG-EXPRP))
 (2 2 (:REWRITE <-OF-NTH-WHEN-BOUNDED-DARG-LISTP-FREE))
 (2 1 (:REWRITE <-OF-NTH-OF-0-WHEN-ALL-<-CHEAP))
 (2 1 (:REWRITE <-OF-NTH-0-WHEN-BOUNDED-DARG-LISTP))
 )
(CANDIDATE-DEPS-ARRAYP-AUX
 (462 231 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (428 4 (:REWRITE SORTEDP-<=-WHEN-NOT-CONSP-OF-CDR))
 (368 8 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (208 104 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (172 4 (:REWRITE <-OF-IF-ARG2))
 (156 4 (:REWRITE LEN-OF-CDR))
 (105 5 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (104 104 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (90 15 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NO-DUPLICATESP-EQUAL-OF-CDR))
 (88 8 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (72 72 (:TYPE-PRESCRIPTION LEN))
 (60 15 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (48 4 (:REWRITE EQUAL-OF-LEN-AND-0))
 (45 5 (:REWRITE NO-DUPLICATESP-EQUAL-OF-CDR))
 (32 16 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (32 16 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (28 16 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (24 6 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (16 16 (:TYPE-PRESCRIPTION DARGP))
 (16 16 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (16 16 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (16 16 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (16 8 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (15 6 (:REWRITE NAT-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (12 7 (:REWRITE DEFAULT-+-2))
 (12 6 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (12 6 (:REWRITE DEFAULT-<-2))
 (12 4 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (12 4 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (8 8 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (8 8 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (7 7 (:TYPE-PRESCRIPTION ALL-NATP))
 (7 7 (:REWRITE DEFAULT-+-1))
 (6 6 (:REWRITE USE-ALL-<-2))
 (6 6 (:REWRITE USE-ALL-<))
 (6 6 (:REWRITE NAT-LISTP-OF-AREF1-WHEN-ALL-DAG-PARENT-ENTRIESP))
 (6 6 (:REWRITE DEFAULT-<-1))
 (4 4 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (4 4 (:REWRITE CONSP-OF-CDR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-AND-QUOTEP))
 (4 4 (:REWRITE CONSP-OF-CDR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (3 3 (:REWRITE DAG-PARENT-ARRAYP-WHEN-WF-DAGP))
 (2 2 (:REWRITE USE-ALL-<=-2))
 (2 2 (:REWRITE USE-ALL-<=))
 (2 2 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (2 2 (:LINEAR ARRAY2P-LINEAR))
 (2 1 (:REWRITE RATIONAL-LISTP-WHEN-ALL-NATP-CHEAP))
 (1 1 (:REWRITE USE-ALL-NATP-2))
 (1 1 (:REWRITE USE-ALL-NATP))
 (1 1 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (1 1 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (1 1 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 )
(CANDIDATE-DEPS-ARRAYP-AUX-OF-MINUS1)
(CANDIDATE-DEPS-ARRAYP-AUX-OF-0
 (215 3 (:REWRITE SORTEDP-<=-WHEN-NOT-CONSP-OF-CDR))
 (184 4 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (87 45 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (86 2 (:REWRITE <-OF-IF-ARG2))
 (78 2 (:REWRITE LEN-OF-CDR))
 (52 2 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (45 45 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (44 4 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (36 36 (:TYPE-PRESCRIPTION LEN))
 (36 6 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NO-DUPLICATESP-EQUAL-OF-CDR))
 (24 6 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (24 2 (:REWRITE EQUAL-OF-LEN-AND-0))
 (18 2 (:REWRITE NO-DUPLICATESP-EQUAL-OF-CDR))
 (16 8 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (16 8 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (14 8 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (8 8 (:TYPE-PRESCRIPTION DARGP))
 (8 8 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (8 8 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (8 8 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (8 4 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (8 2 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (8 2 (:REWRITE NAT-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (8 2 (:DEFINITION NOT))
 (6 2 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (6 2 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (4 4 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (4 4 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (4 2 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (4 2 (:REWRITE DEFAULT-<-2))
 (4 2 (:REWRITE DEFAULT-+-2))
 (4 2 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (2 2 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (2 2 (:TYPE-PRESCRIPTION ALL-NATP))
 (2 2 (:REWRITE USE-ALL-<-2))
 (2 2 (:REWRITE USE-ALL-<))
 (2 2 (:REWRITE NAT-LISTP-OF-AREF1-WHEN-ALL-DAG-PARENT-ENTRIESP))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE DAG-PARENT-ARRAYP-WHEN-WF-DAGP))
 (2 2 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (2 2 (:REWRITE CONSP-OF-CDR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-AND-QUOTEP))
 (2 2 (:REWRITE CONSP-OF-CDR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 )
(CANDIDATE-DEPS-ARRAYP-AUX-MONOTONE
 (1134 11 (:REWRITE SORTEDP-<=-WHEN-NOT-CONSP-OF-CDR))
 (1009 24 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (467 11 (:REWRITE <-OF-IF-ARG2))
 (410 11 (:REWRITE LEN-OF-CDR))
 (368 184 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (286 11 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (276 34 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NO-DUPLICATESP-EQUAL-OF-CDR))
 (246 23 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (204 204 (:TYPE-PRESCRIPTION LEN))
 (184 184 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (132 33 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (119 11 (:REWRITE EQUAL-OF-LEN-AND-0))
 (92 12 (:REWRITE NO-DUPLICATESP-EQUAL-OF-CDR))
 (90 45 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (90 45 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (81 45 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (65 1 (:REWRITE NOT-MEMBER-EQUAL-OF-CDR-WHEN-NOT-MEMBER-EQUAL))
 (52 13 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (52 13 (:REWRITE NAT-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (51 1 (:REWRITE MEMBER-EQUAL-OF-CAR-SAME))
 (48 24 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (45 45 (:TYPE-PRESCRIPTION DARGP))
 (45 45 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (45 45 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (45 45 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (40 12 (:REWRITE INTEGERP-WHEN-NATP))
 (37 12 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (37 12 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (34 17 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (30 18 (:REWRITE DEFAULT-<-2))
 (29 18 (:REWRITE DEFAULT-+-2))
 (26 13 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (24 24 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (24 24 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (21 21 (:REWRITE USE-ALL-NATP-2))
 (21 21 (:REWRITE USE-ALL-NATP))
 (18 18 (:REWRITE USE-ALL-<-2))
 (18 18 (:REWRITE USE-ALL-<))
 (18 18 (:REWRITE DEFAULT-<-1))
 (18 18 (:REWRITE DEFAULT-+-1))
 (17 17 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (13 13 (:TYPE-PRESCRIPTION ALL-NATP))
 (13 13 (:REWRITE NAT-LISTP-OF-AREF1-WHEN-ALL-DAG-PARENT-ENTRIESP))
 (13 13 (:REWRITE DAG-PARENT-ARRAYP-WHEN-WF-DAGP))
 (12 12 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (11 11 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (11 11 (:REWRITE CONSP-OF-CDR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-AND-QUOTEP))
 (11 11 (:REWRITE CONSP-OF-CDR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (8 2 (:REWRITE MEMBER-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (7 7 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (6 6 (:REWRITE USE-ALL-<=-2))
 (6 6 (:REWRITE USE-ALL-<=))
 (4 2 (:REWRITE NOT-MEMBER-EQUAL-WHEN-NOT-MEMBER-EQUAL-OF-CDR-CHEAP))
 (4 2 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-CDR-CHEAP))
 (2 2 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (2 2 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-MEMBER-EQUAL))
 (2 2 (:REWRITE MEMBER-EQUAL-OF-SINGLETON-CONSTANT-IFF))
 (2 2 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-WHEN-NOT-EQUAL-CAR))
 (2 2 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-TRIM))
 (1 1 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-2))
 (1 1 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-1))
 )
(TYPE-OF-AREF1-WHEN-CANDIDATE-DEPS-ARRAYP-AUX
 (864 26 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (851 9 (:REWRITE SORTEDP-<=-WHEN-NOT-CONSP-OF-CDR))
 (496 248 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (405 25 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NO-DUPLICATESP-EQUAL-OF-CDR))
 (375 9 (:REWRITE <-OF-IF-ARG2))
 (299 9 (:REWRITE LEN-OF-CDR))
 (248 248 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (236 4 (:REWRITE NOT-MEMBER-EQUAL-OF-CDR-WHEN-NOT-MEMBER-EQUAL))
 (235 10 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (205 22 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (189 4 (:REWRITE MEMBER-EQUAL-OF-CAR-SAME))
 (186 186 (:TYPE-PRESCRIPTION LEN))
 (80 40 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (80 40 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (80 9 (:REWRITE EQUAL-OF-LEN-AND-0))
 (66 21 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (58 40 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (58 26 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (47 10 (:REWRITE NO-DUPLICATESP-EQUAL-OF-CDR))
 (46 13 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (46 13 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (44 11 (:REWRITE NAT-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (40 40 (:TYPE-PRESCRIPTION DARGP))
 (40 40 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (40 40 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (40 40 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (35 11 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (30 15 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (29 16 (:REWRITE DEFAULT-<-2))
 (28 28 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (26 26 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (26 26 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (22 11 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (21 12 (:REWRITE DEFAULT-+-2))
 (16 16 (:REWRITE USE-ALL-<-2))
 (16 16 (:REWRITE USE-ALL-<))
 (16 16 (:REWRITE DEFAULT-<-1))
 (16 8 (:REWRITE NOT-MEMBER-EQUAL-WHEN-NOT-MEMBER-EQUAL-OF-CDR-CHEAP))
 (16 8 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-CDR-CHEAP))
 (15 15 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (14 8 (:REWRITE MEMBER-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (12 12 (:REWRITE DEFAULT-+-1))
 (11 11 (:TYPE-PRESCRIPTION ALL-NATP))
 (11 11 (:REWRITE NAT-LISTP-OF-AREF1-WHEN-ALL-DAG-PARENT-ENTRIESP))
 (11 11 (:REWRITE DAG-PARENT-ARRAYP-WHEN-WF-DAGP))
 (9 9 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (9 9 (:REWRITE CONSP-OF-CDR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-AND-QUOTEP))
 (9 9 (:REWRITE CONSP-OF-CDR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (8 8 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (8 8 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-MEMBER-EQUAL))
 (8 8 (:REWRITE MEMBER-EQUAL-OF-SINGLETON-CONSTANT-IFF))
 (8 8 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-WHEN-NOT-EQUAL-CAR))
 (8 8 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-TRIM))
 (6 6 (:REWRITE CANDIDATE-DEPS-ARRAYP-AUX-MONOTONE))
 (4 4 (:REWRITE USE-ALL-NATP-2))
 (4 4 (:REWRITE USE-ALL-NATP))
 (4 4 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-2))
 (4 4 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-1))
 (3 3 (:REWRITE USE-ALL-<=-2))
 (3 3 (:REWRITE USE-ALL-<=))
 (1 1 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (1 1 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 )
(CANDIDATE-DEPS-ARRAYP-AUX-OF-ASET1-TOO-HIGH
 (2280 1140 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (1022 11 (:REWRITE SORTEDP-<=-WHEN-NOT-CONSP-OF-CDR))
 (920 24 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (436 11 (:REWRITE <-OF-IF-ARG2))
 (364 11 (:REWRITE LEN-OF-CDR))
 (322 161 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (274 13 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (252 34 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NO-DUPLICATESP-EQUAL-OF-CDR))
 (215 23 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (204 204 (:TYPE-PRESCRIPTION LEN))
 (161 161 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (113 11 (:REWRITE EQUAL-OF-LEN-AND-0))
 (111 33 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (90 45 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (89 12 (:REWRITE NO-DUPLICATESP-EQUAL-OF-CDR))
 (69 45 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (53 1 (:REWRITE NOT-MEMBER-EQUAL-OF-CDR-WHEN-NOT-MEMBER-EQUAL))
 (48 24 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (46 13 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (45 45 (:TYPE-PRESCRIPTION DARGP))
 (45 45 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (45 45 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (45 45 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (44 26 (:REWRITE DEFAULT-<-2))
 (42 1 (:REWRITE MEMBER-EQUAL-OF-CAR-SAME))
 (37 12 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (37 12 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (34 17 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (34 17 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (26 26 (:REWRITE USE-ALL-<-2))
 (26 26 (:REWRITE USE-ALL-<))
 (26 26 (:REWRITE DEFAULT-<-1))
 (26 13 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (26 6 (:REWRITE INTEGERP-WHEN-NATP))
 (25 14 (:REWRITE DEFAULT-+-2))
 (24 24 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (24 24 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (24 6 (:REWRITE NAT-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (18 18 (:REWRITE TYPE-OF-AREF1-WHEN-CANDIDATE-DEPS-ARRAYP-AUX))
 (14 14 (:REWRITE USE-ALL-<=-2))
 (14 14 (:REWRITE USE-ALL-<=))
 (14 14 (:REWRITE DEFAULT-+-1))
 (13 13 (:TYPE-PRESCRIPTION ALL-NATP))
 (11 11 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (10 10 (:REWRITE CANDIDATE-DEPS-ARRAYP-AUX-MONOTONE))
 (8 8 (:REWRITE USE-ALL-NATP-2))
 (8 8 (:REWRITE USE-ALL-NATP))
 (7 7 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (6 6 (:REWRITE NAT-LISTP-OF-AREF1-WHEN-ALL-DAG-PARENT-ENTRIESP))
 (6 6 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (6 6 (:REWRITE DAG-PARENT-ARRAYP-WHEN-WF-DAGP))
 (6 6 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (6 6 (:LINEAR ARRAY2P-LINEAR))
 (4 4 (:REWRITE CONSP-OF-CDR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-AND-QUOTEP))
 (4 4 (:REWRITE CONSP-OF-CDR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (4 2 (:REWRITE NOT-MEMBER-EQUAL-WHEN-NOT-MEMBER-EQUAL-OF-CDR-CHEAP))
 (4 2 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-CDR-CHEAP))
 (2 2 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (2 2 (:REWRITE MEMBER-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-MEMBER-EQUAL))
 (2 2 (:REWRITE MEMBER-EQUAL-OF-SINGLETON-CONSTANT-IFF))
 (2 2 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-WHEN-NOT-EQUAL-CAR))
 (2 2 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-TRIM))
 (2 2 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (2 2 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (1 1 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-2))
 (1 1 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-1))
 )
(CANDIDATE-DEPS-ARRAYP-AUX-OF-ASET1
 (2030 1015 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (609 8 (:REWRITE SORTEDP-<=-WHEN-NOT-CONSP-OF-CDR))
 (564 16 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (272 7 (:REWRITE <-OF-IF-ARG2))
 (216 7 (:REWRITE LEN-OF-CDR))
 (176 11 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (156 20 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NO-DUPLICATESP-EQUAL-OF-CDR))
 (140 70 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (135 15 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (132 132 (:TYPE-PRESCRIPTION LEN))
 (70 70 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (65 7 (:REWRITE EQUAL-OF-LEN-AND-0))
 (58 29 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (55 19 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (51 7 (:REWRITE NO-DUPLICATESP-EQUAL-OF-CDR))
 (41 29 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (40 1 (:REWRITE NOT-MEMBER-EQUAL-OF-CDR-WHEN-NOT-MEMBER-EQUAL))
 (32 16 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (29 29 (:TYPE-PRESCRIPTION DARGP))
 (29 29 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (29 29 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (29 29 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (29 18 (:REWRITE DEFAULT-<-2))
 (29 1 (:REWRITE MEMBER-EQUAL-OF-CAR-SAME))
 (24 8 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (24 8 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (23 16 (:REWRITE DEFAULT-+-2))
 (19 7 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (18 18 (:REWRITE USE-ALL-<-2))
 (18 18 (:REWRITE USE-ALL-<))
 (18 18 (:REWRITE DEFAULT-<-1))
 (16 16 (:REWRITE DEFAULT-+-1))
 (16 16 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (16 16 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (16 8 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (14 7 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (10 10 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (9 1 (:REWRITE NATP-OF-+-WHEN-NEGATIVE-CONSTANT))
 (8 8 (:REWRITE USE-ALL-<=-2))
 (8 8 (:REWRITE USE-ALL-<=))
 (8 3 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (8 2 (:REWRITE NAT-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (7 7 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (7 7 (:TYPE-PRESCRIPTION ALL-NATP))
 (7 7 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (6 6 (:LINEAR ARRAY2P-LINEAR))
 (5 5 (:REWRITE USE-ALL-NATP-2))
 (5 5 (:REWRITE USE-ALL-NATP))
 (4 4 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (4 4 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (4 2 (:REWRITE NOT-MEMBER-EQUAL-WHEN-NOT-MEMBER-EQUAL-OF-CDR-CHEAP))
 (4 2 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-CDR-CHEAP))
 (3 3 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (3 1 (:REWRITE +-COMBINE-CONSTANTS))
 (2 2 (:REWRITE NAT-LISTP-OF-AREF1-WHEN-ALL-DAG-PARENT-ENTRIESP))
 (2 2 (:REWRITE MEMBER-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-MEMBER-EQUAL))
 (2 2 (:REWRITE MEMBER-EQUAL-OF-SINGLETON-CONSTANT-IFF))
 (2 2 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-WHEN-NOT-EQUAL-CAR))
 (2 2 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-TRIM))
 (2 2 (:REWRITE EQUAL-OF-+-COMBINE-CONSTANTS))
 (2 2 (:REWRITE DAG-PARENT-ARRAYP-WHEN-WF-DAGP))
 (2 2 (:REWRITE CONSP-OF-CDR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-AND-QUOTEP))
 (2 2 (:REWRITE CONSP-OF-CDR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (1 1 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-2))
 (1 1 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-1))
 (1 1 (:REWRITE INTEGERP-WHEN-NATP))
 (1 1 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE <-OF-+-CANCEL-1-2))
 (1 1 (:DEFINITION FIX))
 )
(CANDIDATE-DEPS-ARRAYP-AUX-OF-ASET1-AT-END
 (544 272 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (349 6 (:REWRITE SORTEDP-<=-WHEN-NOT-CONSP-OF-CDR))
 (333 10 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (158 4 (:REWRITE <-OF-IF-ARG2))
 (123 4 (:REWRITE LEN-OF-CDR))
 (109 12 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NO-DUPLICATESP-EQUAL-OF-CDR))
 (102 6 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (81 9 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (78 78 (:TYPE-PRESCRIPTION LEN))
 (56 28 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (40 1 (:REWRITE NOT-MEMBER-EQUAL-OF-CDR-WHEN-NOT-MEMBER-EQUAL))
 (35 4 (:REWRITE EQUAL-OF-LEN-AND-0))
 (34 17 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (32 32 (:TYPE-PRESCRIPTION DAG-PARENT-ARRAYP))
 (29 11 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (29 1 (:REWRITE MEMBER-EQUAL-OF-CAR-SAME))
 (28 28 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (27 4 (:REWRITE NO-DUPLICATESP-EQUAL-OF-CDR))
 (23 17 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (20 10 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (17 17 (:TYPE-PRESCRIPTION DARGP))
 (17 17 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (17 17 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (17 17 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (16 8 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (15 9 (:REWRITE TYPE-OF-AREF1-WHEN-CANDIDATE-DEPS-ARRAYP-AUX))
 (15 5 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (15 5 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (14 10 (:REWRITE DEFAULT-+-2))
 (14 8 (:REWRITE DEFAULT-<-2))
 (12 2 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (11 5 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (11 5 (:REWRITE CANDIDATE-DEPS-ARRAYP-AUX-MONOTONE))
 (10 10 (:REWRITE DEFAULT-+-1))
 (10 10 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (10 10 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (10 5 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (9 1 (:REWRITE NATP-OF-+-WHEN-NEGATIVE-CONSTANT))
 (8 8 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-AUX))
 (8 8 (:REWRITE USE-ALL-<-2))
 (8 8 (:REWRITE USE-ALL-<))
 (8 8 (:REWRITE DEFAULT-<-1))
 (8 2 (:REWRITE NAT-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (7 7 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (5 5 (:TYPE-PRESCRIPTION ALL-NATP))
 (5 1 (:REWRITE CANDIDATE-DEPS-ARRAYP-AUX-OF-ASET1-TOO-HIGH))
 (4 4 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (4 2 (:REWRITE NOT-MEMBER-EQUAL-WHEN-NOT-MEMBER-EQUAL-OF-CDR-CHEAP))
 (4 2 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-CDR-CHEAP))
 (3 2 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (3 1 (:REWRITE +-COMBINE-CONSTANTS))
 (2 2 (:REWRITE USE-ALL-<=-2))
 (2 2 (:REWRITE USE-ALL-<=))
 (2 2 (:REWRITE NAT-LISTP-OF-AREF1-WHEN-ALL-DAG-PARENT-ENTRIESP))
 (2 2 (:REWRITE MEMBER-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-MEMBER-EQUAL))
 (2 2 (:REWRITE MEMBER-EQUAL-OF-SINGLETON-CONSTANT-IFF))
 (2 2 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-WHEN-NOT-EQUAL-CAR))
 (2 2 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-TRIM))
 (2 2 (:REWRITE DAG-PARENT-ARRAYP-WHEN-WF-DAGP))
 (2 2 (:REWRITE CONSP-OF-CDR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-AND-QUOTEP))
 (2 2 (:REWRITE CONSP-OF-CDR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (2 2 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (2 2 (:REWRITE <-OF-+-CANCEL-1-2))
 (2 2 (:LINEAR ARRAY2P-LINEAR))
 (1 1 (:REWRITE USE-ALL-NATP-2))
 (1 1 (:REWRITE USE-ALL-NATP))
 (1 1 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-2))
 (1 1 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-1))
 (1 1 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (1 1 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 )
(CANDIDATE-DEPS-ARRAYP-AUX-OF-COMPRESS1
 (1526 763 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (674 7 (:REWRITE SORTEDP-<=-WHEN-NOT-CONSP-OF-CDR))
 (640 18 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (289 7 (:REWRITE <-OF-IF-ARG2))
 (256 23 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NO-DUPLICATESP-EQUAL-OF-CDR))
 (237 7 (:REWRITE LEN-OF-CDR))
 (212 106 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (182 9 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (152 16 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (138 138 (:TYPE-PRESCRIPTION LEN))
 (106 106 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (106 2 (:REWRITE NOT-MEMBER-EQUAL-OF-CDR-WHEN-NOT-MEMBER-EQUAL))
 (84 2 (:REWRITE MEMBER-EQUAL-OF-CAR-SAME))
 (78 21 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (66 7 (:REWRITE EQUAL-OF-LEN-AND-0))
 (60 30 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (53 9 (:REWRITE NO-DUPLICATESP-EQUAL-OF-CDR))
 (52 26 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (45 30 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (43 22 (:REWRITE DEFAULT-<-2))
 (41 11 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (40 10 (:REWRITE NAT-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (36 18 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (30 30 (:TYPE-PRESCRIPTION DARGP))
 (30 30 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (30 30 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (30 30 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (29 9 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (29 9 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (28 28 (:REWRITE TYPE-OF-AREF1-WHEN-CANDIDATE-DEPS-ARRAYP-AUX))
 (25 22 (:REWRITE DEFAULT-<-1))
 (22 22 (:REWRITE USE-ALL-<-2))
 (22 22 (:REWRITE USE-ALL-<))
 (22 13 (:REWRITE DEFAULT-+-2))
 (22 11 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (18 18 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (18 18 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (16 15 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (14 14 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (13 13 (:REWRITE USE-ALL-<=-2))
 (13 13 (:REWRITE USE-ALL-<=))
 (13 13 (:REWRITE DEFAULT-+-1))
 (13 13 (:REWRITE CANDIDATE-DEPS-ARRAYP-AUX-MONOTONE))
 (11 11 (:TYPE-PRESCRIPTION ALL-NATP))
 (10 10 (:REWRITE NAT-LISTP-OF-AREF1-WHEN-ALL-DAG-PARENT-ENTRIESP))
 (10 10 (:REWRITE DAG-PARENT-ARRAYP-WHEN-WF-DAGP))
 (9 1 (:REWRITE NATP-OF-+-WHEN-NEGATIVE-CONSTANT))
 (8 4 (:REWRITE NOT-MEMBER-EQUAL-WHEN-NOT-MEMBER-EQUAL-OF-CDR-CHEAP))
 (8 4 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-CDR-CHEAP))
 (7 7 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (7 7 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (6 6 (:REWRITE CONSP-OF-CDR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-AND-QUOTEP))
 (6 6 (:REWRITE CONSP-OF-CDR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (6 6 (:LINEAR ARRAY2P-LINEAR))
 (4 4 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (4 4 (:REWRITE MEMBER-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-MEMBER-EQUAL))
 (4 4 (:REWRITE MEMBER-EQUAL-OF-SINGLETON-CONSTANT-IFF))
 (4 4 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-WHEN-NOT-EQUAL-CAR))
 (4 4 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-TRIM))
 (3 3 (:REWRITE USE-ALL-NATP-2))
 (3 3 (:REWRITE USE-ALL-NATP))
 (3 3 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (3 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (3 1 (:REWRITE +-COMBINE-CONSTANTS))
 (2 2 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-2))
 (2 2 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-1))
 (2 2 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (2 1 (:REWRITE DEFAULT-WHEN-DAG-PARENT-ARRAYP))
 (1 1 (:REWRITE USE-ALL-RATIONALP-2))
 (1 1 (:REWRITE USE-ALL-RATIONALP))
 )
(CANDIDATE-DEPS-ARRAYP-AUX-OF-CONS-OF-CONS-OF-HEADER
 (645 215 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (534 5 (:REWRITE SORTEDP-<=-WHEN-NOT-CONSP-OF-CDR))
 (499 12 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (430 215 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (215 5 (:REWRITE <-OF-IF-ARG2))
 (194 5 (:REWRITE LEN-OF-CDR))
 (174 14 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NO-DUPLICATESP-EQUAL-OF-CDR))
 (132 7 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (114 11 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (108 108 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (96 96 (:TYPE-PRESCRIPTION LEN))
 (77 1 (:REWRITE NOT-MEMBER-EQUAL-OF-CDR-WHEN-NOT-MEMBER-EQUAL))
 (63 1 (:REWRITE MEMBER-EQUAL-OF-CAR-SAME))
 (59 5 (:REWRITE EQUAL-OF-LEN-AND-0))
 (52 13 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (42 21 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (42 21 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (41 5 (:REWRITE NO-DUPLICATESP-EQUAL-OF-CDR))
 (39 21 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (32 16 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (30 12 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (22 6 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (22 6 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (21 21 (:TYPE-PRESCRIPTION DARGP))
 (21 21 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (21 21 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (21 21 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (20 5 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (20 5 (:REWRITE NAT-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (19 13 (:REWRITE CANDIDATE-DEPS-ARRAYP-AUX-MONOTONE))
 (16 16 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (16 11 (:REWRITE DEFAULT-+-2))
 (12 12 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (12 12 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (12 6 (:REWRITE DEFAULT-<-2))
 (12 2 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (11 11 (:REWRITE DEFAULT-+-1))
 (10 5 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (8 8 (:REWRITE USE-ALL-NATP-2))
 (8 8 (:REWRITE USE-ALL-NATP))
 (8 4 (:REWRITE DEFAULT-WHEN-DAG-PARENT-ARRAYP))
 (8 2 (:REWRITE MEMBER-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (7 7 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (6 6 (:REWRITE USE-ALL-<-2))
 (6 6 (:REWRITE USE-ALL-<))
 (6 6 (:REWRITE DEFAULT-<-1))
 (5 5 (:TYPE-PRESCRIPTION ALL-NATP))
 (5 5 (:REWRITE NAT-LISTP-OF-AREF1-WHEN-ALL-DAG-PARENT-ENTRIESP))
 (5 5 (:REWRITE DAG-PARENT-ARRAYP-WHEN-WF-DAGP))
 (5 5 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (5 5 (:REWRITE CONSP-OF-CDR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-AND-QUOTEP))
 (5 5 (:REWRITE CONSP-OF-CDR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (4 2 (:REWRITE NOT-MEMBER-EQUAL-WHEN-NOT-MEMBER-EQUAL-OF-CDR-CHEAP))
 (4 2 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-CDR-CHEAP))
 (2 2 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (2 2 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-MEMBER-EQUAL))
 (2 2 (:REWRITE MEMBER-EQUAL-OF-SINGLETON-CONSTANT-IFF))
 (2 2 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-WHEN-NOT-EQUAL-CAR))
 (2 2 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-TRIM))
 (2 2 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (2 2 (:REWRITE <-OF-+-CANCEL-1-2))
 (1 1 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-2))
 (1 1 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-1))
 )
(CANDIDATE-DEPS-ARRAYP-AUX-OF-CONS-OF-CONS-OF-HEADER-IRREL
 (1818 18 (:REWRITE SORTEDP-<=-WHEN-NOT-CONSP-OF-CDR))
 (1665 42 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (900 9 (:REWRITE CANDIDATE-DEPS-ARRAYP-AUX-OF-CONS-OF-CONS-OF-HEADER))
 (759 18 (:REWRITE <-OF-IF-ARG2))
 (654 18 (:REWRITE LEN-OF-CDR))
 (609 203 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (590 295 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (573 57 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NO-DUPLICATESP-EQUAL-OF-CDR))
 (468 18 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (408 39 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (406 203 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (342 342 (:TYPE-PRESCRIPTION LEN))
 (295 295 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (216 54 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (195 3 (:REWRITE NOT-MEMBER-EQUAL-OF-CDR-WHEN-NOT-MEMBER-EQUAL))
 (183 18 (:REWRITE EQUAL-OF-LEN-AND-0))
 (156 21 (:REWRITE NO-DUPLICATESP-EQUAL-OF-CDR))
 (153 3 (:REWRITE MEMBER-EQUAL-OF-CAR-SAME))
 (150 75 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (150 75 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (138 75 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (96 24 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (90 24 (:REWRITE NAT-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
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 (78 78 (:REWRITE TYPE-OF-AREF1-WHEN-CANDIDATE-DEPS-ARRAYP-AUX))
 (75 75 (:TYPE-PRESCRIPTION DARGP))
 (75 75 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (75 75 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (75 75 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (66 21 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (66 21 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (60 30 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (48 24 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (43 25 (:REWRITE DEFAULT-+-2))
 (43 22 (:REWRITE DEFAULT-<-2))
 (42 42 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (42 42 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (30 30 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (29 29 (:REWRITE CANDIDATE-DEPS-ARRAYP-AUX-MONOTONE))
 (25 25 (:REWRITE DEFAULT-+-1))
 (24 24 (:TYPE-PRESCRIPTION ALL-NATP))
 (24 24 (:REWRITE NAT-LISTP-OF-AREF1-WHEN-ALL-DAG-PARENT-ENTRIESP))
 (24 6 (:REWRITE MEMBER-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (22 22 (:REWRITE USE-ALL-<-2))
 (22 22 (:REWRITE USE-ALL-<))
 (22 22 (:REWRITE DEFAULT-<-1))
 (22 22 (:REWRITE DAG-PARENT-ARRAYP-WHEN-WF-DAGP))
 (21 21 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (18 18 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (18 18 (:REWRITE CONSP-OF-CDR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-AND-QUOTEP))
 (18 18 (:REWRITE CONSP-OF-CDR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (14 7 (:REWRITE DEFAULT-WHEN-DAG-PARENT-ARRAYP))
 (12 6 (:REWRITE NOT-MEMBER-EQUAL-WHEN-NOT-MEMBER-EQUAL-OF-CDR-CHEAP))
 (12 6 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-CDR-CHEAP))
 (6 6 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (6 6 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-MEMBER-EQUAL))
 (6 6 (:REWRITE MEMBER-EQUAL-OF-SINGLETON-CONSTANT-IFF))
 (6 6 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-WHEN-NOT-EQUAL-CAR))
 (6 6 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-TRIM))
 (5 5 (:REWRITE USE-ALL-NATP-2))
 (5 5 (:REWRITE USE-ALL-NATP))
 (3 3 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-2))
 (3 3 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-1))
 (1 1 (:REWRITE USE-ALL-<=-2))
 (1 1 (:REWRITE USE-ALL-<=))
 (1 1 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 )
(ENSURE-DEFAULT-SATISFIES-PRED)
(<-OF-IF-ARG1-ALT)
(CANDIDATE-DEPS-ARRAYP-AUX-OF-MAKE-EMPTY-ARRAY-WITH-DEFAULT
 (32 32 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (20 4 (:REWRITE INTEGERP-WHEN-NATP))
 (13 13 (:REWRITE USE-ALL-<=-2))
 (13 13 (:REWRITE USE-ALL-<=))
 (13 13 (:REWRITE USE-ALL-<-2))
 (13 13 (:REWRITE USE-ALL-<))
 (13 13 (:REWRITE DEFAULT-<-2))
 (13 13 (:REWRITE DEFAULT-<-1))
 (12 6 (:REWRITE CANDIDATE-DEPS-ARRAYP-AUX-MONOTONE))
 (9 9 (:REWRITE USE-ALL-NATP-2))
 (9 9 (:REWRITE USE-ALL-NATP))
 (6 1 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (4 4 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (4 4 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (4 4 (:REWRITE DEFAULT-+-2))
 (4 4 (:REWRITE DEFAULT-+-1))
 (1 1 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (1 1 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (1 1 (:REWRITE <-OF-+-CANCEL-1-2))
 (1 1 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 )
(CANDIDATE-DEPS-ARRAYP-AUX-BEYOND-LENGTH
 (5392 2696 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (2088 19 (:REWRITE SORTEDP-<=-WHEN-NOT-CONSP-OF-CDR))
 (1810 40 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (822 19 (:REWRITE <-OF-IF-ARG1-ALT))
 (760 303 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (760 19 (:REWRITE LEN-OF-CDR))
 (614 64 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (558 70 (:REWRITE TYPE-OF-AREF1-WHEN-CANDIDATE-DEPS-ARRAYP-AUX))
 (447 60 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NO-DUPLICATESP-EQUAL-OF-CDR))
 (419 39 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (342 342 (:TYPE-PRESCRIPTION LEN))
 (303 303 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (257 59 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (237 19 (:REWRITE EQUAL-OF-LEN-AND-0))
 (189 21 (:REWRITE NO-DUPLICATESP-EQUAL-OF-CDR))
 (184 115 (:REWRITE DEFAULT-+-2))
 (154 77 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (154 77 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (139 77 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (128 35 (:REWRITE NOT-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP))
 (115 115 (:REWRITE DEFAULT-+-1))
 (105 70 (:REWRITE DEFAULT-<-1))
 (104 70 (:REWRITE DEFAULT-<-2))
 (100 23 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (92 23 (:REWRITE NAT-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (80 40 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (77 77 (:TYPE-PRESCRIPTION DARGP))
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 (77 77 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (77 77 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (70 70 (:REWRITE USE-ALL-<-2))
 (70 70 (:REWRITE USE-ALL-<))
 (67 16 (:REWRITE +-COMBINE-CONSTANTS))
 (61 20 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (61 20 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (53 1 (:REWRITE NOT-MEMBER-EQUAL-OF-CDR-WHEN-NOT-MEMBER-EQUAL))
 (50 50 (:REWRITE USE-ALL-<=-2))
 (50 50 (:REWRITE USE-ALL-<=))
 (46 23 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (42 21 (:REWRITE DEFAULT-WHEN-DAG-PARENT-ARRAYP))
 (42 1 (:REWRITE MEMBER-EQUAL-OF-CAR-SAME))
 (40 40 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (40 40 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (40 40 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (34 34 (:LINEAR ARRAY2P-LINEAR))
 (31 31 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (23 23 (:TYPE-PRESCRIPTION ALL-NATP))
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 (19 19 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (19 19 (:REWRITE CONSP-OF-CDR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-AND-QUOTEP))
 (19 19 (:REWRITE CONSP-OF-CDR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (15 15 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (14 14 (:REWRITE USE-ALL-NATP-2))
 (14 14 (:REWRITE USE-ALL-NATP))
 (8 4 (:REWRITE UNICITY-OF-0))
 (7 7 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (4 4 (:DEFINITION FIX))
 (4 2 (:REWRITE NOT-MEMBER-EQUAL-WHEN-NOT-MEMBER-EQUAL-OF-CDR-CHEAP))
 (4 2 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-CDR-CHEAP))
 (2 2 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (2 2 (:REWRITE MEMBER-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-MEMBER-EQUAL))
 (2 2 (:REWRITE MEMBER-EQUAL-OF-SINGLETON-CONSTANT-IFF))
 (2 2 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-WHEN-NOT-EQUAL-CAR))
 (2 2 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-TRIM))
 (2 2 (:REWRITE <-OF-+-CANCEL-1-2))
 (1 1 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-2))
 (1 1 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-1))
 (1 1 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 )
(CANDIDATE-DEPS-ARRAYP-AUX-OF-EXPAND-ARRAY-HELPER
 (18940 168 (:REWRITE SORTEDP-<=-WHEN-NOT-CONSP-OF-CDR))
 (18481 448 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (15566 7783 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (7750 204 (:REWRITE LEN-OF-CDR))
 (5026 487 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NO-DUPLICATESP-EQUAL-OF-CDR))
 (3816 428 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (2704 2704 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (2414 204 (:REWRITE EQUAL-OF-LEN-AND-0))
 (2234 467 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (2176 1221 (:REWRITE DEFAULT-<-2))
 (2055 860 (:REWRITE DEFAULT-*-2))
 (1825 1322 (:REWRITE DEFAULT-+-2))
 (1623 169 (:REWRITE NO-DUPLICATESP-EQUAL-OF-CDR))
 (1540 20 (:REWRITE NOT-MEMBER-EQUAL-OF-CDR-WHEN-NOT-MEMBER-EQUAL))
 (1528 764 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (1511 828 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (1322 1322 (:REWRITE DEFAULT-+-1))
 (1320 660 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (1260 20 (:REWRITE MEMBER-EQUAL-OF-CAR-SAME))
 (1246 1221 (:REWRITE DEFAULT-<-1))
 (1221 1221 (:REWRITE USE-ALL-<-2))
 (1221 1221 (:REWRITE USE-ALL-<))
 (1016 448 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (860 860 (:REWRITE DEFAULT-*-1))
 (801 169 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (783 783 (:REWRITE USE-ALL-<=-2))
 (783 783 (:REWRITE USE-ALL-<=))
 (766 76 (:REWRITE <-OF-+-AND-+-COMBINE-CONSTANTS))
 (764 764 (:TYPE-PRESCRIPTION DARGP))
 (764 764 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (764 764 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (764 764 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (752 224 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (752 224 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (644 161 (:REWRITE NAT-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (514 196 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (448 448 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (448 448 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (402 201 (:REWRITE DEFAULT-WHEN-DAG-PARENT-ARRAYP))
 (338 169 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (252 252 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (204 204 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (169 169 (:TYPE-PRESCRIPTION ALL-NATP))
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 (160 160 (:REWRITE CONSP-OF-CDR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-AND-QUOTEP))
 (160 160 (:REWRITE CONSP-OF-CDR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (160 40 (:REWRITE MEMBER-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (148 148 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (140 140 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (126 126 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (80 40 (:REWRITE NOT-MEMBER-EQUAL-WHEN-NOT-MEMBER-EQUAL-OF-CDR-CHEAP))
 (80 40 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-CDR-CHEAP))
 (42 42 (:REWRITE <-OF-+-CANCEL-1-2))
 (40 40 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (40 40 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-MEMBER-EQUAL))
 (40 40 (:REWRITE MEMBER-EQUAL-OF-SINGLETON-CONSTANT-IFF))
 (40 40 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-WHEN-NOT-EQUAL-CAR))
 (40 40 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-TRIM))
 (36 36 (:REWRITE CONSP-OF-HEADER-WHEN-ARRAY1P))
 (33 33 (:REWRITE USE-ALL-NATP-2))
 (33 33 (:REWRITE USE-ALL-NATP))
 (20 20 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-2))
 (20 20 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-1))
 (19 19 (:TYPE-PRESCRIPTION COMPRESS1))
 (16 16 (:LINEAR ARRAY2P-LINEAR))
 )
(CANDIDATE-DEPS-ARRAYP-AUX-OF-EXPAND-ARRAY
 (1677 8 (:DEFINITION CANDIDATE-DEPS-ARRAYP-AUX))
 (1454 727 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (1036 8 (:REWRITE SORTEDP-<=-WHEN-NOT-CONSP-OF-CDR))
 (950 20 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (727 727 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (476 112 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (430 10 (:REWRITE LEN-OF-CDR))
 (244 14 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (188 24 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NO-DUPLICATESP-EQUAL-OF-CDR))
 (180 20 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (178 72 (:REWRITE DEFAULT-*-2))
 (150 24 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (149 69 (:REWRITE DEFAULT-+-2))
 (144 10 (:REWRITE EQUAL-OF-LEN-AND-0))
 (112 112 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (112 51 (:REWRITE DEFAULT-<-2))
 (98 8 (:REWRITE NO-DUPLICATESP-EQUAL-OF-CDR))
 (81 39 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (78 2 (:REWRITE NATP-OF-+-WHEN-NEGATIVE-CONSTANT))
 (72 72 (:REWRITE DEFAULT-*-1))
 (72 36 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (69 69 (:REWRITE DEFAULT-+-1))
 (64 32 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (60 60 (:TYPE-PRESCRIPTION NO-DUPLICATESP-EQUAL))
 (51 51 (:REWRITE USE-ALL-<-2))
 (51 51 (:REWRITE USE-ALL-<))
 (51 51 (:REWRITE DEFAULT-<-1))
 (50 8 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (44 44 (:TYPE-PRESCRIPTION COMPRESS1))
 (40 20 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (36 36 (:TYPE-PRESCRIPTION DARGP))
 (36 36 (:REWRITE USE-ALL-<=-2))
 (36 36 (:REWRITE USE-ALL-<=))
 (36 36 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (36 36 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (36 36 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (32 32 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-AUX))
 (32 32 (:REWRITE TYPE-OF-AREF1-WHEN-CANDIDATE-DEPS-ARRAYP-AUX))
 (32 8 (:REWRITE NAT-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (30 15 (:REWRITE DEFAULT-WHEN-DAG-PARENT-ARRAYP))
 (30 10 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (30 10 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (30 8 (:REWRITE +-COMBINE-CONSTANTS))
 (28 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (20 20 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (20 20 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (20 20 (:REWRITE CANDIDATE-DEPS-ARRAYP-AUX-MONOTONE))
 (20 8 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (20 2 (:REWRITE LESS-THAN-MAX-HACK-ALT))
 (16 8 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (14 2 (:REWRITE LESS-THAN-MAX-HACK))
 (12 12 (:TYPE-PRESCRIPTION SORTEDP-<=))
 (12 12 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (10 10 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (8 8 (:TYPE-PRESCRIPTION ALL-NATP))
 (8 8 (:REWRITE NAT-LISTP-OF-AREF1-WHEN-ALL-DAG-PARENT-ENTRIESP))
 (8 8 (:REWRITE DAG-PARENT-ARRAYP-WHEN-WF-DAGP))
 (8 8 (:REWRITE CONSP-OF-CDR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-AND-QUOTEP))
 (8 8 (:REWRITE CONSP-OF-CDR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (8 2 (:REWRITE NOT-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP))
 (6 6 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (6 6 (:LINEAR ARRAY2P-LINEAR))
 (5 5 (:REWRITE USE-ALL-NATP-2))
 (5 5 (:REWRITE USE-ALL-NATP))
 (4 4 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP))
 (4 1 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (2 2 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (2 2 (:REWRITE CONSP-OF-HEADER-WHEN-ARRAY1P))
 (1 1 (:REWRITE USE-ALL-RATIONALP-2))
 (1 1 (:REWRITE USE-ALL-RATIONALP))
 )
(CANDIDATE-DEPS-ARRAYP
 (128 64 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (64 64 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 )
(ARRAY1P-WHEN-CANDIDATE-DEPS-ARRAYP)
(CANDIDATE-DEPS-ARRAYP-FORWARD-TO-<=-OF-ALEN1)
(CANDIDATE-DEPS-ARRAYP-FORWARD-TO-ARRAY1P
 (6 6 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 )
(TYPE-OF-AREF1-WHEN-CANDIDATE-DEPS-ARRAYP
 (514 257 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (257 257 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (223 6 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (213 2 (:REWRITE SORTEDP-<=-WHEN-NOT-CONSP-OF-CDR))
 (166 83 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (116 5 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NO-DUPLICATESP-EQUAL-OF-CDR))
 (86 2 (:REWRITE <-OF-IF-ARG1-ALT))
 (83 83 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (77 2 (:REWRITE LEN-OF-CDR))
 (77 1 (:REWRITE NOT-MEMBER-EQUAL-OF-CDR-WHEN-NOT-MEMBER-EQUAL))
 (63 1 (:REWRITE MEMBER-EQUAL-OF-CAR-SAME))
 (53 3 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (48 5 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (42 42 (:TYPE-PRESCRIPTION LEN))
 (40 6 (:REWRITE ARRAY1P-WHEN-CANDIDATE-DEPS-ARRAYP))
 (23 2 (:REWRITE EQUAL-OF-LEN-AND-0))
 (19 10 (:REWRITE DEFAULT-+-2))
 (18 9 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (18 9 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (18 9 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (18 6 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (16 4 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (13 3 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (13 3 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (10 10 (:REWRITE DEFAULT-+-1))
 (10 2 (:REWRITE NO-DUPLICATESP-EQUAL-OF-CDR))
 (9 9 (:TYPE-PRESCRIPTION DARGP))
 (9 9 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (9 9 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (9 9 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (9 5 (:REWRITE DEFAULT-<-2))
 (8 2 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (8 2 (:REWRITE NAT-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (8 2 (:REWRITE MEMBER-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (7 7 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (6 6 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (6 6 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (6 6 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (6 5 (:REWRITE DEFAULT-<-1))
 (6 3 (:REWRITE DEFAULT-WHEN-DAG-PARENT-ARRAYP))
 (5 5 (:REWRITE USE-ALL-<-2))
 (5 5 (:REWRITE USE-ALL-<))
 (4 2 (:REWRITE NOT-MEMBER-EQUAL-WHEN-NOT-MEMBER-EQUAL-OF-CDR-CHEAP))
 (4 2 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (4 2 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-CDR-CHEAP))
 (4 1 (:REWRITE NOT-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP))
 (2 2 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (2 2 (:TYPE-PRESCRIPTION ALL-NATP))
 (2 2 (:REWRITE USE-ALL-<=-2))
 (2 2 (:REWRITE USE-ALL-<=))
 (2 2 (:REWRITE NAT-LISTP-OF-AREF1-WHEN-ALL-DAG-PARENT-ENTRIESP))
 (2 2 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-MEMBER-EQUAL))
 (2 2 (:REWRITE MEMBER-EQUAL-OF-SINGLETON-CONSTANT-IFF))
 (2 2 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-WHEN-NOT-EQUAL-CAR))
 (2 2 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-TRIM))
 (2 2 (:REWRITE DAG-PARENT-ARRAYP-WHEN-WF-DAGP))
 (2 2 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (2 2 (:REWRITE CONSP-OF-CDR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-AND-QUOTEP))
 (2 2 (:REWRITE CONSP-OF-CDR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (2 2 (:REWRITE CANDIDATE-DEPS-ARRAYP-AUX-MONOTONE))
 (2 2 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (2 2 (:LINEAR ARRAY2P-LINEAR))
 (1 1 (:REWRITE USE-ALL-NATP-2))
 (1 1 (:REWRITE USE-ALL-NATP))
 (1 1 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (1 1 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-2))
 (1 1 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-1))
 (1 1 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (1 1 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 )
(CANDIDATE-DEPS-ARRAYP-OF-ASET1
 (564 282 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (518 2 (:DEFINITION CANDIDATE-DEPS-ARRAYP-AUX))
 (367 4 (:REWRITE SORTEDP-<=-WHEN-NOT-CONSP-OF-CDR))
 (347 10 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (160 4 (:REWRITE <-OF-IF-ARG1-ALT))
 (158 8 (:REWRITE TYPE-OF-AREF1-WHEN-CANDIDATE-DEPS-ARRAYP))
 (131 4 (:REWRITE LEN-OF-CDR))
 (114 11 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NO-DUPLICATESP-EQUAL-OF-CDR))
 (100 4 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (84 28 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (81 9 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (78 78 (:TYPE-PRESCRIPTION LEN))
 (40 20 (:REWRITE DEFAULT-+-2))
 (40 1 (:REWRITE NOT-MEMBER-EQUAL-OF-CDR-WHEN-NOT-MEMBER-EQUAL))
 (39 4 (:REWRITE EQUAL-OF-LEN-AND-0))
 (37 11 (:REWRITE ARRAY1P-WHEN-CANDIDATE-DEPS-ARRAYP))
 (34 17 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (34 10 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (31 4 (:REWRITE NO-DUPLICATESP-EQUAL-OF-CDR))
 (29 1 (:REWRITE MEMBER-EQUAL-OF-CAR-SAME))
 (28 28 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (25 17 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (24 12 (:REWRITE DEFAULT-WHEN-DAG-PARENT-ARRAYP))
 (20 20 (:REWRITE DEFAULT-+-1))
 (20 10 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (19 19 (:REWRITE CANDIDATE-DEPS-ARRAYP-AUX-MONOTONE))
 (17 17 (:TYPE-PRESCRIPTION DARGP))
 (17 17 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (17 17 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (17 17 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (16 8 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (15 5 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (15 5 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (12 6 (:REWRITE DEFAULT-<-2))
 (12 4 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (11 11 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (10 10 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (10 10 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (8 8 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-AUX))
 (8 8 (:REWRITE TYPE-OF-AREF1-WHEN-CANDIDATE-DEPS-ARRAYP-AUX))
 (8 4 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (8 2 (:REWRITE NAT-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (8 2 (:REWRITE +-COMBINE-CONSTANTS))
 (7 7 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (6 6 (:REWRITE USE-ALL-<-2))
 (6 6 (:REWRITE USE-ALL-<))
 (6 6 (:REWRITE DEFAULT-<-1))
 (6 2 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (4 4 (:TYPE-PRESCRIPTION ALL-NATP))
 (4 4 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (4 2 (:REWRITE NOT-MEMBER-EQUAL-WHEN-NOT-MEMBER-EQUAL-OF-CDR-CHEAP))
 (4 2 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-CDR-CHEAP))
 (2 2 (:REWRITE NAT-LISTP-OF-AREF1-WHEN-ALL-DAG-PARENT-ENTRIESP))
 (2 2 (:REWRITE MEMBER-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-MEMBER-EQUAL))
 (2 2 (:REWRITE MEMBER-EQUAL-OF-SINGLETON-CONSTANT-IFF))
 (2 2 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-WHEN-NOT-EQUAL-CAR))
 (2 2 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-TRIM))
 (2 2 (:REWRITE DAG-PARENT-ARRAYP-WHEN-WF-DAGP))
 (2 2 (:REWRITE CONSP-OF-CDR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-AND-QUOTEP))
 (2 2 (:REWRITE CONSP-OF-CDR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (2 2 (:LINEAR ARRAY2P-LINEAR))
 (1 1 (:REWRITE USE-ALL-NATP-2))
 (1 1 (:REWRITE USE-ALL-NATP))
 (1 1 (:REWRITE USE-ALL-<=-2))
 (1 1 (:REWRITE USE-ALL-<=))
 (1 1 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-2))
 (1 1 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-1))
 )
(CANDIDATE-DEPS-ARRAYP-OF-MAKE-EMPTY-ARRAY-WITH-DEFAULT
 (10 2 (:REWRITE INTEGERP-WHEN-NATP))
 (8 2 (:REWRITE ARRAY1P-WHEN-CANDIDATE-DEPS-ARRAYP))
 (5 5 (:REWRITE USE-ALL-<=-2))
 (5 5 (:REWRITE USE-ALL-<=))
 (5 5 (:REWRITE USE-ALL-<-2))
 (5 5 (:REWRITE USE-ALL-<))
 (5 5 (:REWRITE DEFAULT-<-2))
 (5 5 (:REWRITE DEFAULT-<-1))
 (4 4 (:TYPE-PRESCRIPTION NATP))
 (4 2 (:REWRITE DEFAULT-WHEN-DAG-PARENT-ARRAYP))
 (2 2 (:TYPE-PRESCRIPTION DAG-PARENT-ARRAYP))
 (2 2 (:REWRITE USE-ALL-NATP-2))
 (2 2 (:REWRITE USE-ALL-NATP))
 (2 2 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (1 1 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 )
(CANDIDATE-DEPS-ARRAYP-OF-EXPAND-ARRAY
 (1286 643 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (643 643 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (64 10 (:REWRITE ARRAY1P-WHEN-CANDIDATE-DEPS-ARRAYP))
 (36 15 (:REWRITE DEFAULT-+-2))
 (29 19 (:REWRITE DEFAULT-<-1))
 (28 19 (:REWRITE DEFAULT-<-2))
 (20 2 (:REWRITE LESS-THAN-MAX-HACK-ALT))
 (19 19 (:REWRITE USE-ALL-<-2))
 (19 19 (:REWRITE USE-ALL-<))
 (16 8 (:REWRITE DEFAULT-WHEN-DAG-PARENT-ARRAYP))
 (15 15 (:REWRITE DEFAULT-+-1))
 (14 2 (:REWRITE LESS-THAN-MAX-HACK))
 (13 13 (:REWRITE USE-ALL-<=-2))
 (13 13 (:REWRITE USE-ALL-<=))
 (10 10 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (10 5 (:REWRITE DEFAULT-*-2))
 (9 9 (:REWRITE CANDIDATE-DEPS-ARRAYP-AUX-MONOTONE))
 (6 6 (:LINEAR ARRAY2P-LINEAR))
 (5 5 (:REWRITE DEFAULT-*-1))
 (5 5 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (4 4 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (3 3 (:REWRITE USE-ALL-NATP-2))
 (3 3 (:REWRITE USE-ALL-NATP))
 )
(CANDIDATE-DEPS-ARRAYP-OF-MAYBE-EXPAND-ARRAY
 (582 291 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (291 291 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (56 1 (:DEFINITION ASSOC-KEYWORD))
 (44 2 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (23 1 (:REWRITE LEN-OF-CDR))
 (16 1 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (10 10 (:TYPE-PRESCRIPTION LEN))
 (10 6 (:REWRITE DEFAULT-<-2))
 (10 1 (:REWRITE MAYBE-EXPAND-ARRAY-DOES-NOTHING))
 (6 6 (:REWRITE USE-ALL-<-2))
 (6 6 (:REWRITE USE-ALL-<))
 (6 6 (:REWRITE DEFAULT-<-1))
 (6 1 (:REWRITE EQUAL-OF-LEN-AND-0))
 (4 4 (:REWRITE USE-ALL-<=-2))
 (4 4 (:REWRITE USE-ALL-<=))
 (4 4 (:LINEAR ARRAY2P-LINEAR))
 (4 2 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (4 2 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (3 1 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (3 1 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (2 2 (:TYPE-PRESCRIPTION DARGP))
 (2 2 (:REWRITE USE-ALL-NATP-2))
 (2 2 (:REWRITE USE-ALL-NATP))
 (2 2 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (2 2 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (2 2 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (2 2 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (2 2 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (2 2 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (2 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DIMENSIONS-WHEN-NOT-CONSP-OF-HEADER-CHEAP))
 (1 1 (:REWRITE DEFAULT-+-1))
 (1 1 (:REWRITE CONSP-OF-HEADER-WHEN-ARRAY1P))
 (1 1 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 )
(CANDIDATE-DEPS-ARRAYP-OF-MAKE-EMPTY-ARRAY
 (10 2 (:REWRITE INTEGERP-WHEN-NATP))
 (4 4 (:TYPE-PRESCRIPTION NATP))
 (4 4 (:REWRITE USE-ALL-<=-2))
 (4 4 (:REWRITE USE-ALL-<=))
 (4 4 (:REWRITE USE-ALL-<-2))
 (4 4 (:REWRITE USE-ALL-<))
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE USE-ALL-NATP-2))
 (2 2 (:REWRITE USE-ALL-NATP))
 (2 2 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 )
(ALL-RATIONALP-OF-AREF1-WHEN-CANDIDATE-DEPS-ARRAYP
 (64 32 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (32 32 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 )
(<=-OF-MAXELEM-OF-STRIP-CARS-OF-CDR
 (2879 2 (:REWRITE NOT-<-OF-MAXELEM-WHEN-ALL-<-2))
 (2716 4 (:REWRITE ALL-<-OF-+-OF-1))
 (2700 2 (:REWRITE ALL-INTEGERP-OF-STRIP-CARS-WHEN-WEAK-DAGP-AUX))
 (2346 6 (:DEFINITION WEAK-DAGP-AUX))
 (1872 12 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX-2))
 (1730 10 (:REWRITE WEAK-DAGP-AUX-OF-CDR))
 (1659 96 (:REWRITE DEFAULT-+-2))
 (1510 14 (:REWRITE MAXELEM-SINGLETON-ALT))
 (1452 14 (:REWRITE PSEUDO-DAGP-AUX-OF-CDR))
 (1232 14 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (1076 7 (:DEFINITION MAXELEM))
 (738 11 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (656 326 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (652 326 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (650 11 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (536 536 (:TYPE-PRESCRIPTION NAT-LISTP))
 (528 22 (:REWRITE LEN-OF-STRIP-CARS))
 (434 2 (:REWRITE <-OF-CAR-OF-CAR-WHEN-ALL-<-OF-STRIP-CARS))
 (406 1 (:REWRITE ALL-<-OF-CONS))
 (396 42 (:REWRITE <-OF-IF-ARG2))
 (388 4 (:REWRITE RATIONALP-OF-IF-STRONG))
 (364 12 (:DEFINITION TOP-NODENUM))
 (359 42 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (334 334 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (252 74 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (250 125 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (214 107 (:TYPE-PRESCRIPTION NATP-OF-CAR-OF-CAR-WHEN-SUBST-CANDIDATE-LISTP))
 (208 104 (:TYPE-PRESCRIPTION NATP-OF-MAXELEM-2))
 (200 100 (:TYPE-PRESCRIPTION NATP-OF-MAXELEM-OF-STRIP-CARS-WHEN-WEAK-DAGP-AUX))
 (178 126 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (174 36 (:REWRITE DEFAULT-<-2))
 (154 34 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (154 34 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (147 147 (:TYPE-PRESCRIPTION SUBST-CANDIDATE-LISTP))
 (142 142 (:TYPE-PRESCRIPTION WEAK-DAGP-AUX))
 (136 104 (:TYPE-PRESCRIPTION RATIONALP-OF-MAXELEM))
 (127 36 (:REWRITE DEFAULT-<-1))
 (125 125 (:TYPE-PRESCRIPTION DARGP))
 (125 125 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (125 125 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (125 125 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (106 106 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (104 8 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (103 103 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (97 97 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (96 96 (:REWRITE DEFAULT-+-1))
 (84 10 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (80 32 (:REWRITE PSEUDO-DAGP-OF-CDR-WHEN-PSEUDO-DAGP))
 (76 20 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (76 12 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP))
 (72 2 (:REWRITE USE-ALL-<-FOR-CAR))
 (70 10 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (63 2 (:REWRITE ACL2-NUMBERP-OF-MAXELEM))
 (57 2 (:REWRITE INTEGER-LISTP-WHEN-ALL-NATP))
 (55 11 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (48 48 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (42 42 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (40 8 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (37 37 (:REWRITE USE-ALL-<-2))
 (37 37 (:REWRITE USE-ALL-<))
 (36 8 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-SUBST-CANDIDATE-LISTP))
 (28 2 (:REWRITE RATIONALP-OF-MAXELEM))
 (25 25 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (25 2 (:REWRITE MAXELEM-BOUND-MAXINT))
 (23 14 (:REWRITE MAXELEM-WHEN-NON-CONSP))
 (23 10 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (22 22 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (22 22 (:TYPE-PRESCRIPTION ALL-<))
 (22 22 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (22 11 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (22 10 (:REWRITE SUBST-CANDIDATE-LISTP-OF-CDR))
 (22 1 (:LINEAR MAXELEM-OF-CDR-LINEAR))
 (20 20 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (20 20 (:REWRITE LEN-OF-CDDR-WHEN-EQUAL-OF-LEN))
 (20 20 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (20 20 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (20 10 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (19 4 (:REWRITE MAXELEM-OF-STRIP-CARS-WHEN-PSEUDO-DAGP))
 (18 18 (:REWRITE STRIP-CARS-WHEN-NOT-CONSP-CHEAP))
 (18 2 (:REWRITE NOT-<-OF-MAXELEM-WHEN-ALL-<))
 (17 10 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (16 16 (:TYPE-PRESCRIPTION BOUNDED-DAG-EXPRP))
 (16 8 (:REWRITE CAR-OF-STRIP-CARS))
 (16 8 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (16 8 (:REWRITE BOUNDED-DAG-EXPRP-OF-CDR-OF-CAR-WHEN-WEAK-DAGP-AUX))
 (14 11 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (13 13 (:REWRITE USE-ALL-RATIONALP-2))
 (13 13 (:REWRITE USE-ALL-RATIONALP))
 (12 12 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (12 10 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (12 2 (:REWRITE ALL-NATP-OF-STRIP-CARS-WHEN-SUBST-CANDIDATE-LISTP))
 (10 10 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (10 10 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (10 10 (:REWRITE ALL-<-TRANSITIVE))
 (9 3 (:REWRITE NAT-LISTP-OF-STRIP-CARS-WHEN-SUBST-CANDIDATE-LISTP))
 (9 2 (:REWRITE ALL-<-OF-+-OF-1-AND-MAXELEM))
 (9 1 (:REWRITE <-OF-MAXELEM-WHEN-ALL-<))
 (8 8 (:TYPE-PRESCRIPTION NATP))
 (8 8 (:TYPE-PRESCRIPTION MYQUOTEP))
 (8 8 (:REWRITE USE-ALL-NATP-2))
 (8 8 (:REWRITE USE-ALL-NATP))
 (8 8 (:REWRITE PSEUDO-DAGP-AUX-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (8 8 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (8 8 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP-CHEAP))
 (8 8 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP-CHEAP))
 (8 8 (:REWRITE BOUNDED-DAG-EXPRP-MONOTONE))
 (8 2 (:REWRITE RATIONAL-LISTP-OF-STRIP-CARS-WHEN-SUBST-CANDIDATE-LISTP))
 (7 3 (:REWRITE <-OF-MAXELEM-WHEN-ALL->))
 (6 1 (:LINEAR LEN-OF-CDR-LINEAR-STRONG))
 (4 4 (:TYPE-PRESCRIPTION INTEGER-LISTP))
 (4 4 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (4 4 (:TYPE-PRESCRIPTION ALL->))
 (4 2 (:REWRITE RATIONAL-LISTP-WHEN-ALL-NATP-CHEAP))
 (4 2 (:REWRITE RATIONAL-LISTP-OF-STRIP-CARS-WHEN-WEAK-DAGP-AUX-CHEAP))
 (4 2 (:REWRITE ALL-NATP-IMPLIES-ALL-INTEGERP-CHEAP))
 (4 2 (:REWRITE ALL-INTEGERP-WHEN-NOT-CONSP-CHEAP))
 (4 2 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (4 1 (:REWRITE CAR-OF-NTH-0-WHEN-PSEUDO-DAGP))
 (3 3 (:REWRITE LESS-THAN-MAXELEM-WHEN-LESS-THAN-SOME-ELEM))
 (2 2 (:REWRITE USE-ALL-<=-2))
 (2 2 (:REWRITE USE-ALL-<=))
 (2 1 (:REWRITE NOT-MEMBER-EQUAL-WHEN-NOT-MEMBER-EQUAL-OF-CDR-CHEAP))
 (2 1 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-CDR-CHEAP))
 (2 1 (:REWRITE <-OF-MAXELEM-WHEN-ALL-<-CHEAP))
 (1 1 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-2))
 (1 1 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-1))
 (1 1 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-MEMBER-EQUAL))
 (1 1 (:REWRITE MEMBER-EQUAL-OF-SINGLETON-CONSTANT-IFF))
 (1 1 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-WHEN-NOT-EQUAL-CAR))
 (1 1 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-TRIM))
 )
(MARK-ALL-RELEVANT-VARS
 (2056 1072 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (984 984 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (451 18 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (418 8 (:REWRITE NOT-<-OF-CAR-WHEN-ALL-<-2))
 (365 7 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (358 7 (:REWRITE ALL-<-OF-+-OF-1))
 (322 2 (:REWRITE <-OF-CAR-OF-CAR-WHEN-ALL-<-OF-STRIP-CARS))
 (291 1 (:REWRITE ALL-INTEGERP-OF-STRIP-CARS-WHEN-WEAK-DAGP-AUX))
 (277 1 (:DEFINITION WEAK-DAGP-AUX))
 (196 2 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX-2))
 (157 12 (:REWRITE DEFAULT-+-2))
 (151 1 (:REWRITE PSEUDO-DAGP-AUX-OF-CDR))
 (148 8 (:REWRITE USE-ALL-<=-FOR-CAR))
 (124 26 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (115 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (100 5 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (94 1 (:REWRITE RATIONALP-OF-IF-STRONG))
 (84 84 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DIMENSIONS-WHEN-ARRAY1P))
 (81 1 (:REWRITE USE-ALL-<-FOR-CAR))
 (75 13 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (75 13 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (74 22 (:REWRITE DEFAULT-<-2))
 (71 1 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (63 1 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (53 17 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (42 42 (:TYPE-PRESCRIPTION POSP-OF-CAR-OF-DIMENSIONS-WHEN-ARRAY1P))
 (36 2 (:DEFINITION TOP-NODENUM))
 (35 14 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (34 17 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (32 7 (:REWRITE ALL-INTEGERP-WHEN-NOT-CONSP-CHEAP))
 (32 7 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (27 22 (:REWRITE DEFAULT-<-1))
 (26 26 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (25 5 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (22 22 (:REWRITE USE-ALL-<-2))
 (22 22 (:REWRITE USE-ALL-<))
 (18 18 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (18 18 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (17 17 (:TYPE-PRESCRIPTION DARGP))
 (17 17 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (17 17 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (17 17 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (16 16 (:TYPE-PRESCRIPTION ALL-<))
 (15 1 (:REWRITE LEN-OF-CDR))
 (14 14 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (14 14 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (14 14 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (14 14 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (14 7 (:REWRITE ALL-NATP-IMPLIES-ALL-INTEGERP-CHEAP))
 (13 2 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (12 12 (:REWRITE DEFAULT-+-1))
 (10 10 (:TYPE-PRESCRIPTION ALL-<=))
 (10 10 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (9 9 (:REWRITE USE-ALL-<=-2))
 (9 9 (:REWRITE USE-ALL-<=))
 (9 2 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP))
 (9 1 (:REWRITE NO-DUPLICATESP-EQUAL-OF-CONS-NO-SPLIT))
 (8 8 (:TYPE-PRESCRIPTION ALL-NATP))
 (7 7 (:TYPE-PRESCRIPTION WEAK-DAGP-AUX))
 (7 7 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (7 7 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (7 7 (:REWRITE ALL-<-TRANSITIVE))
 (7 1 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (6 6 (:TYPE-PRESCRIPTION STRIP-CARS))
 (6 6 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (6 6 (:LINEAR ARRAY2P-LINEAR))
 (6 2 (:REWRITE PSEUDO-DAGP-OF-CDR-WHEN-PSEUDO-DAGP))
 (5 5 (:REWRITE ALL-<=-MONOTONE))
 (5 1 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (5 1 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (4 4 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (4 4 (:REWRITE EQUAL-OF-+-COMBINE-CONSTANTS))
 (4 2 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-CDR-CHEAP))
 (3 3 (:REWRITE USE-ALL-NATP-2))
 (3 3 (:REWRITE USE-ALL-NATP))
 (3 3 (:REWRITE STRIP-CARS-WHEN-NOT-CONSP-CHEAP))
 (3 3 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (3 2 (:REWRITE MEMBER-EQUAL-OF-SINGLETON-CONSTANT-IFF))
 (3 1 (:DEFINITION ATOM))
 (2 2 (:TYPE-PRESCRIPTION BOUNDED-DAG-EXPRP))
 (2 2 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (2 2 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (2 2 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-MEMBER-EQUAL))
 (2 2 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-WHEN-NOT-EQUAL-CAR))
 (2 2 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-TRIM))
 (2 2 (:REWRITE CONSP-OF-STRIP-CARS))
 (2 1 (:REWRITE WEAK-DAGP-AUX-OF-CDR))
 (2 1 (:REWRITE NOT-MEMBER-EQUAL-WHEN-NOT-MEMBER-EQUAL-OF-CDR-CHEAP))
 (2 1 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (2 1 (:REWRITE BOUNDED-DAG-EXPRP-OF-CDR-OF-CAR-WHEN-WEAK-DAGP-AUX))
 (2 1 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION MYQUOTEP))
 (1 1 (:REWRITE USE-ALL-RATIONALP-2))
 (1 1 (:REWRITE USE-ALL-RATIONALP))
 (1 1 (:REWRITE PSEUDO-DAGP-AUX-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (1 1 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (1 1 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP-CHEAP))
 (1 1 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE BOUNDED-DAG-EXPRP-MONOTONE))
 (1 1 (:REWRITE ALL-NATP-OF-STRIP-CARS-WHEN-SUBST-CANDIDATE-LISTP))
 (1 1 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (1 1 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 )
(ALEN1-OF-MARK-ALL-RELEVANT-VARS
 (1104 552 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (1104 552 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (783 9 (:REWRITE NOT-<-OF-CAR-WHEN-ALL-<-2))
 (586 586 (:TYPE-PRESCRIPTION NAT-LISTP))
 (563 29 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (552 552 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (549 9 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (343 26 (:REWRITE DEFAULT-<-2))
 (261 9 (:REWRITE USE-ALL-<=-FOR-CAR))
 (219 21 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (180 9 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (140 34 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (90 9 (:REWRITE ALL-<-OF-+-OF-1))
 (87 17 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (87 17 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (84 3 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (60 3 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (58 22 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (48 21 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (45 9 (:REWRITE ALL-INTEGERP-WHEN-NOT-CONSP-CHEAP))
 (45 9 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (45 9 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (45 3 (:REWRITE LEN-OF-CDR))
 (44 22 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (39 12 (:REWRITE DEFAULT-+-2))
 (36 3 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (35 26 (:REWRITE DEFAULT-<-1))
 (29 29 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (29 29 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (26 26 (:REWRITE USE-ALL-<-2))
 (26 26 (:REWRITE USE-ALL-<))
 (24 24 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (22 22 (:TYPE-PRESCRIPTION DARGP))
 (22 22 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (22 22 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (22 22 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (21 21 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (21 21 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (21 21 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (19 19 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (18 18 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (18 18 (:TYPE-PRESCRIPTION ALL-<=))
 (18 18 (:TYPE-PRESCRIPTION ALL-<))
 (18 9 (:REWRITE ALL-NATP-IMPLIES-ALL-INTEGERP-CHEAP))
 (15 3 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (12 12 (:REWRITE USE-ALL-RATIONALP-2))
 (12 12 (:REWRITE USE-ALL-RATIONALP))
 (12 12 (:REWRITE DEFAULT-+-1))
 (9 9 (:TYPE-PRESCRIPTION ALL-NATP))
 (9 9 (:REWRITE USE-ALL-<=-2))
 (9 9 (:REWRITE USE-ALL-<=))
 (9 9 (:REWRITE ALL-<=-MONOTONE))
 (9 9 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (9 9 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (9 9 (:REWRITE ALL-<-TRANSITIVE))
 (9 3 (:REWRITE PSEUDO-DAGP-OF-CDR-WHEN-PSEUDO-DAGP))
 (6 6 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (3 3 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 )
(CANDIDATE-DEPS-ARRAYP-OF-MARK-ALL-RELEVANT-VARS
 (4768 2384 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (2384 2384 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
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 (939 48 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (492 44 (:REWRITE DEFAULT-<-2))
 (464 16 (:REWRITE USE-ALL-<=-FOR-CAR))
 (332 44 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (320 16 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (240 56 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (160 16 (:REWRITE ALL-<-OF-+-OF-1))
 (148 28 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (148 28 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (112 4 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (101 37 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (101 29 (:REWRITE DEFAULT-+-2))
 (80 36 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (80 16 (:REWRITE ALL-INTEGERP-WHEN-NOT-CONSP-CHEAP))
 (80 16 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (80 16 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (80 4 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (74 37 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (60 44 (:REWRITE DEFAULT-<-1))
 (60 4 (:REWRITE LEN-OF-CDR))
 (48 48 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (48 48 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (48 4 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (44 44 (:REWRITE USE-ALL-<-2))
 (44 44 (:REWRITE USE-ALL-<))
 (40 40 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (37 37 (:TYPE-PRESCRIPTION DARGP))
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 (37 37 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (37 37 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (36 36 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (36 36 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (36 36 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
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 (16 16 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (16 16 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (16 16 (:REWRITE ALL-<-TRANSITIVE))
 (12 4 (:REWRITE PSEUDO-DAGP-OF-CDR-WHEN-PSEUDO-DAGP))
 (9 1 (:REWRITE NO-DUPLICATESP-EQUAL-OF-CONS-NO-SPLIT))
 (8 8 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (8 8 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (8 8 (:REWRITE EQUAL-OF-+-COMBINE-CONSTANTS))
 (4 4 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (4 4 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (4 2 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-CDR-CHEAP))
 (3 2 (:REWRITE MEMBER-EQUAL-OF-SINGLETON-CONSTANT-IFF))
 (2 2 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-MEMBER-EQUAL))
 (2 2 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-WHEN-NOT-EQUAL-CAR))
 (2 2 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-TRIM))
 (2 1 (:REWRITE NOT-MEMBER-EQUAL-WHEN-NOT-MEMBER-EQUAL-OF-CDR-CHEAP))
 (1 1 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 )
(MARK-NODES-OF-ORDERING-VARS
 (3394 1721 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (153 6 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (96 96 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DIMENSIONS-WHEN-ARRAY1P))
 (48 48 (:TYPE-PRESCRIPTION POSP-OF-CAR-OF-DIMENSIONS-WHEN-ARRAY1P))
 (45 3 (:REWRITE LEN-OF-CDR))
 (37 4 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (32 16 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (24 12 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (18 15 (:REWRITE DEFAULT-<-2))
 (18 6 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (18 6 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (16 16 (:TYPE-PRESCRIPTION DARGP))
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 (16 16 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (16 16 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (16 16 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (15 15 (:REWRITE USE-ALL-<-2))
 (15 15 (:REWRITE USE-ALL-<))
 (15 15 (:REWRITE DEFAULT-<-1))
 (14 14 (:LINEAR ARRAY2P-LINEAR))
 (13 13 (:REWRITE DEFAULT-+-2))
 (13 13 (:REWRITE DEFAULT-+-1))
 (11 11 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (9 9 (:REWRITE USE-ALL-<=-2))
 (9 9 (:REWRITE USE-ALL-<=))
 (9 1 (:REWRITE NO-DUPLICATESP-EQUAL-OF-CONS-NO-SPLIT))
 (8 8 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (8 8 (:REWRITE EQUAL-OF-+-COMBINE-CONSTANTS))
 (7 7 (:REWRITE USE-ALL-NATP-2))
 (7 7 (:REWRITE USE-ALL-NATP))
 (6 6 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (6 6 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (4 2 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-CDR-CHEAP))
 (4 1 (:REWRITE <-OF-LOOKUP-IN-DAG-VARIABLE-ALIST-WHEN-BOUNDED-DAG-VARIABLE-ALISTP))
 (3 3 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (3 2 (:REWRITE MEMBER-EQUAL-OF-SINGLETON-CONSTANT-IFF))
 (2 2 (:TYPE-PRESCRIPTION BOUNDED-DAG-VARIABLE-ALISTP))
 (2 2 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-MEMBER-EQUAL))
 (2 2 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-WHEN-NOT-EQUAL-CAR))
 (2 2 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-TRIM))
 (2 1 (:REWRITE NOT-MEMBER-EQUAL-WHEN-NOT-MEMBER-EQUAL-OF-CDR-CHEAP))
 (1 1 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE BOUNDED-DAG-VARIABLE-ALISTP-MONOTONE))
 (1 1 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (1 1 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 )
(ALEN1-OF-MARK-NODES-OF-ORDERING-VARS
 (268 134 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (268 134 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (193 8 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (40 16 (:REWRITE DEFAULT-<-1))
 (32 16 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (30 2 (:REWRITE LEN-OF-CDR))
 (26 13 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (24 8 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (24 8 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (24 8 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (24 2 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (22 16 (:REWRITE DEFAULT-<-2))
 (16 16 (:REWRITE USE-ALL-<-2))
 (16 16 (:REWRITE USE-ALL-<))
 (13 13 (:TYPE-PRESCRIPTION DARGP))
 (13 13 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (13 13 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (13 13 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (13 13 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (8 8 (:REWRITE USE-ALL-RATIONALP-2))
 (8 8 (:REWRITE USE-ALL-RATIONALP))
 (8 8 (:REWRITE USE-ALL-<=-2))
 (8 8 (:REWRITE USE-ALL-<=))
 (8 8 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (8 8 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 )
(CANDIDATE-DEPS-ARRAYP-OF-MARK-NODES-OF-ORDERING-VARS
 (5350 2675 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (288 12 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (73 25 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (72 27 (:REWRITE DEFAULT-<-1))
 (48 24 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (45 3 (:REWRITE LEN-OF-CDR))
 (42 21 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (41 13 (:REWRITE DEFAULT-+-2))
 (36 27 (:REWRITE DEFAULT-<-2))
 (36 12 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (36 12 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (36 3 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (27 27 (:REWRITE USE-ALL-<-2))
 (27 27 (:REWRITE USE-ALL-<))
 (24 24 (:REWRITE USE-ALL-RATIONALP-2))
 (24 24 (:REWRITE USE-ALL-RATIONALP))
 (22 22 (:LINEAR ARRAY2P-LINEAR))
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 (21 21 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (21 21 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (21 21 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (21 21 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
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 (15 15 (:REWRITE USE-ALL-<=))
 (13 13 (:REWRITE DEFAULT-+-1))
 (12 12 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (12 12 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (9 9 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (9 9 (:REWRITE EQUAL-OF-+-COMBINE-CONSTANTS))
 (9 1 (:REWRITE NO-DUPLICATESP-EQUAL-OF-CONS-NO-SPLIT))
 (4 2 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-CDR-CHEAP))
 (3 3 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (3 2 (:REWRITE MEMBER-EQUAL-OF-SINGLETON-CONSTANT-IFF))
 (2 2 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-MEMBER-EQUAL))
 (2 2 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-WHEN-NOT-EQUAL-CAR))
 (2 2 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-TRIM))
 (2 1 (:REWRITE NOT-MEMBER-EQUAL-WHEN-NOT-MEMBER-EQUAL-OF-CDR-CHEAP))
 (1 1 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 )
(MERGE-DEPS-FOR-ARGS
 (3952 1997 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (763 34 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (392 11 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-<))
 (186 52 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (186 5 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (156 22 (:REWRITE ALL-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (148 10 (:REWRITE USE-ALL-<-FOR-CAR))
 (145 27 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (139 27 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (119 25 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (119 25 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (111 76 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (108 42 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL))
 (108 9 (:REWRITE <-OF-CAR-AND-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (84 84 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DIMENSIONS-WHEN-ARRAY1P))
 (84 84 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (79 38 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (76 76 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (72 36 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (71 37 (:REWRITE DEFAULT-<-2))
 (64 64 (:TYPE-PRESCRIPTION ALL-<))
 (54 9 (:REWRITE <-OF-CAR-AND-ALEN1))
 (53 37 (:REWRITE DEFAULT-<-1))
 (48 24 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (42 42 (:TYPE-PRESCRIPTION POSP-OF-CAR-OF-DIMENSIONS-WHEN-ARRAY1P))
 (42 42 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (42 42 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP))
 (41 41 (:TYPE-PRESCRIPTION DAG-PARENT-ARRAYP))
 (40 3 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (37 37 (:REWRITE USE-ALL-<-2))
 (37 37 (:REWRITE USE-ALL-<))
 (36 36 (:TYPE-PRESCRIPTION DARGP))
 (36 36 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (36 36 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (36 36 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (35 35 (:TYPE-PRESCRIPTION ALL-NATP))
 (35 15 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (34 34 (:REWRITE CONSP-WHEN-LEN-GREATER))
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 (22 22 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP))
 (22 11 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (22 11 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (22 1 (:REWRITE INTEGERP-WHEN-NATP))
 (22 1 (:REWRITE <=-OF-0-WHEN-NATP))
 (20 20 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (20 10 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (18 18 (:LINEAR ARRAY2P-LINEAR))
 (18 10 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (18 3 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (15 15 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (15 15 (:REWRITE DEFAULT-+-1))
 (15 15 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (15 15 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (15 9 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (14 5 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (12 3 (:REWRITE NAT-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (12 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (11 11 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (11 11 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (11 11 (:REWRITE BOUNDED-DARG-LISTP-MONOTONE))
 (11 5 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (10 5 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (10 2 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-CAR-AND-QUOTE))
 (6 6 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (6 6 (:TYPE-PRESCRIPTION NATP))
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 (6 6 (:REWRITE USE-ALL-<=))
 (6 3 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (6 2 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (5 5 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (5 1 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (4 4 (:REWRITE USE-ALL-NATP-2))
 (4 4 (:REWRITE USE-ALL-NATP))
 (4 2 (:REWRITE DARGP-LESS-THAN-WHEN-NATP-CHEAP))
 (4 2 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (3 3 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-AUX))
 (3 3 (:REWRITE TYPE-OF-AREF1-WHEN-CANDIDATE-DEPS-ARRAYP-AUX))
 (3 3 (:REWRITE NAT-LISTP-OF-AREF1-WHEN-ALL-DAG-PARENT-ENTRIESP))
 (3 3 (:REWRITE DAG-PARENT-ARRAYP-WHEN-WF-DAGP))
 (2 2 (:TYPE-PRESCRIPTION MYQUOTEP))
 (2 2 (:REWRITE DARGP-LESS-THAN-WHEN-QUOTEP-CHEAP))
 (2 2 (:REWRITE DARGP-LESS-THAN-MONO))
 (2 2 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (2 2 (:REWRITE ALL-<-OF-+-OF-1))
 (2 1 (:REWRITE INTEGERP-OF-CAR-WHEN-NAT-LISTP-CHEAP))
 (2 1 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (2 1 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (1 1 (:REWRITE USE-ALL-RATIONALP-2))
 (1 1 (:REWRITE USE-ALL-RATIONALP))
 (1 1 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 )
(NAT-LISTP-OF-MERGE-DEPS-FOR-ARGS
 (4684 2342 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (821 32 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (196 54 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (128 14 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (125 27 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (125 27 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (114 15 (:REWRITE ALL-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (87 43 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (82 41 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (60 4 (:REWRITE LEN-OF-CDR))
 (56 30 (:REWRITE DEFAULT-<-2))
 (53 23 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL))
 (48 24 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (48 4 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (46 46 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (46 42 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (42 42 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (42 42 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (42 3 (:REWRITE USE-ALL-<-FOR-CAR))
 (41 41 (:TYPE-PRESCRIPTION DARGP))
 (39 11 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (36 27 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (36 3 (:REWRITE <-OF-CAR-AND-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (32 32 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (32 32 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (30 30 (:REWRITE USE-ALL-<-2))
 (30 30 (:REWRITE USE-ALL-<))
 (30 30 (:REWRITE DEFAULT-<-1))
 (28 2 (:REWRITE ALL-<-OF-CDR))
 (26 26 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (25 13 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (24 2 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-OF-CDR))
 (23 23 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (23 23 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP))
 (22 22 (:LINEAR ARRAY2P-LINEAR))
 (18 9 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (18 9 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (18 3 (:REWRITE <-OF-CAR-AND-ALEN1))
 (16 10 (:REWRITE DEFAULT-+-2))
 (15 15 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (15 15 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (15 15 (:REWRITE ALL-<-TRANSITIVE))
 (13 7 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (12 3 (:REWRITE NAT-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (11 11 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (11 11 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (11 11 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (10 10 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP))
 (10 10 (:REWRITE DEFAULT-+-1))
 (9 9 (:TYPE-PRESCRIPTION DAG-PARENT-ARRAYP))
 (9 9 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (9 9 (:REWRITE BOUNDED-DARG-LISTP-MONOTONE))
 (6 3 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (6 3 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (6 2 (:REWRITE PSEUDO-DAGP-OF-CDR-WHEN-PSEUDO-DAGP))
 (5 5 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (5 1 (:REWRITE <-OF-IF-ARG2))
 (4 4 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (3 3 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (3 3 (:REWRITE TYPE-OF-AREF1-WHEN-CANDIDATE-DEPS-ARRAYP-AUX))
 (3 3 (:REWRITE NAT-LISTP-OF-AREF1-WHEN-ALL-DAG-PARENT-ENTRIESP))
 (3 3 (:REWRITE DAG-PARENT-ARRAYP-WHEN-WF-DAGP))
 (3 1 (:REWRITE TRUE-LISTP-WHEN-NAT-LISTP-REWRITE))
 (3 1 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (2 1 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (1 1 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 )
(TRUE-LISTP-OF-MERGE-DEPS-FOR-ARGS
 (72 36 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 )
(SORTEDP-<=-OF-MERGE-DEPS-FOR-ARGS
 (6972 3486 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (3286 105 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (2350 30 (:REWRITE SORTEDP-<=-WHEN-NOT-CONSP-OF-CDR))
 (1133 32 (:REWRITE <-OF-IF-ARG2))
 (916 36 (:REWRITE LEN-OF-CDR))
 (798 36 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (396 134 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (354 177 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (276 181 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (265 67 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (265 67 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (242 30 (:REWRITE EQUAL-OF-LEN-AND-0))
 (220 120 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-MERGE-DEPS-FOR-ARGS))
 (187 179 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (179 179 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (179 179 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (177 177 (:TYPE-PRESCRIPTION DARGP))
 (150 21 (:REWRITE ALL-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (140 73 (:REWRITE DEFAULT-<-2))
 (134 20 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (105 105 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (105 105 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (86 46 (:REWRITE DEFAULT-+-2))
 (84 6 (:REWRITE USE-ALL-<-FOR-CAR))
 (83 35 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL))
 (73 73 (:REWRITE USE-ALL-<-2))
 (73 73 (:REWRITE USE-ALL-<))
 (73 73 (:REWRITE DEFAULT-<-1))
 (72 6 (:REWRITE <-OF-CAR-AND-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (70 70 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (66 33 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (60 16 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (46 46 (:REWRITE DEFAULT-+-1))
 (44 23 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (40 40 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (39 39 (:TYPE-PRESCRIPTION DAG-PARENT-ARRAYP))
 (36 36 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (36 6 (:REWRITE <-OF-CAR-AND-ALEN1))
 (35 35 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (35 35 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP))
 (34 17 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (33 33 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (30 30 (:LINEAR ARRAY2P-LINEAR))
 (29 20 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (28 2 (:REWRITE ALL-<-OF-CDR))
 (24 12 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (24 12 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (24 12 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (24 2 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-OF-CDR))
 (21 21 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (21 21 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (21 21 (:REWRITE ALL-<-TRANSITIVE))
 (16 16 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP))
 (16 16 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (16 16 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (16 16 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (16 10 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (12 12 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-AUX))
 (12 12 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (12 12 (:REWRITE BOUNDED-DARG-LISTP-MONOTONE))
 (12 6 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (12 4 (:REWRITE PSEUDO-DAGP-OF-CDR-WHEN-PSEUDO-DAGP))
 (12 3 (:REWRITE NAT-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (8 8 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (6 6 (:REWRITE TYPE-OF-AREF1-WHEN-CANDIDATE-DEPS-ARRAYP-AUX))
 (3 3 (:REWRITE NAT-LISTP-OF-AREF1-WHEN-ALL-DAG-PARENT-ENTRIESP))
 (3 3 (:REWRITE DAG-PARENT-ARRAYP-WHEN-WF-DAGP))
 (3 3 (:REWRITE CONSP-OF-CDR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-AND-QUOTEP))
 (3 3 (:REWRITE CONSP-OF-CDR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (3 1 (:REWRITE TRUE-LISTP-WHEN-NAT-LISTP-REWRITE))
 (3 1 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (2 1 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (1 1 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 )
(NO-DUPLICATESP-EQUAL-OF-MERGE-DEPS-FOR-ARGS
 (9576 4788 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (3224 112 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (1781 23 (:REWRITE SORTEDP-<=-WHEN-NOT-CONSP-OF-CDR))
 (1178 99 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NO-DUPLICATESP-EQUAL-OF-CDR))
 (885 26 (:REWRITE <-OF-IF-ARG2))
 (745 31 (:REWRITE LEN-OF-CDR))
 (698 34 (:REWRITE NO-DUPLICATESP-EQUAL-OF-CDR))
 (660 31 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (472 148 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (338 169 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (310 74 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (310 74 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (281 175 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (204 4 (:REWRITE NOT-MEMBER-EQUAL-OF-CDR-WHEN-NOT-MEMBER-EQUAL))
 (186 27 (:REWRITE ALL-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (184 172 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (174 23 (:REWRITE EQUAL-OF-LEN-AND-0))
 (172 172 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (172 172 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (171 95 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (169 169 (:TYPE-PRESCRIPTION DARGP))
 (158 83 (:REWRITE DEFAULT-<-2))
 (156 4 (:REWRITE MEMBER-EQUAL-OF-CAR-SAME))
 (140 26 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (126 63 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (126 9 (:REWRITE USE-ALL-<-FOR-CAR))
 (124 65 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-MERGE-DEPS-FOR-ARGS))
 (113 47 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL))
 (112 112 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (112 112 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (108 9 (:REWRITE <-OF-CAR-AND-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (94 94 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (83 83 (:REWRITE USE-ALL-<-2))
 (83 83 (:REWRITE USE-ALL-<))
 (83 83 (:REWRITE DEFAULT-<-1))
 (82 45 (:REWRITE DEFAULT-+-2))
 (81 21 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (69 69 (:TYPE-PRESCRIPTION DAG-PARENT-ARRAYP))
 (63 63 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (63 33 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (54 54 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (54 9 (:REWRITE <-OF-CAR-AND-ALEN1))
 (48 24 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (47 47 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (47 47 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP))
 (45 45 (:REWRITE DEFAULT-+-1))
 (40 20 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (38 38 (:LINEAR ARRAY2P-LINEAR))
 (32 23 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (31 31 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (30 15 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (30 15 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (28 28 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (28 2 (:REWRITE ALL-<-OF-CDR))
 (27 27 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (27 27 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (27 27 (:REWRITE ALL-<-TRANSITIVE))
 (24 24 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-AUX))
 (24 2 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-OF-CDR))
 (22 22 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP))
 (21 21 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (21 21 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (21 21 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (19 13 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (18 9 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (18 6 (:REWRITE PSEUDO-DAGP-OF-CDR-WHEN-PSEUDO-DAGP))
 (16 8 (:REWRITE NOT-MEMBER-EQUAL-WHEN-NOT-MEMBER-EQUAL-OF-CDR-CHEAP))
 (16 8 (:REWRITE MEMBER-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (16 8 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-CDR-CHEAP))
 (15 15 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (15 15 (:REWRITE BOUNDED-DARG-LISTP-MONOTONE))
 (12 3 (:REWRITE NAT-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (11 11 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (9 9 (:REWRITE TYPE-OF-AREF1-WHEN-CANDIDATE-DEPS-ARRAYP-AUX))
 (8 8 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-MEMBER-EQUAL))
 (8 8 (:REWRITE MEMBER-EQUAL-OF-SINGLETON-CONSTANT-IFF))
 (8 8 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-WHEN-NOT-EQUAL-CAR))
 (8 8 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-TRIM))
 (6 6 (:REWRITE CONSP-OF-CDR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-AND-QUOTEP))
 (6 6 (:REWRITE CONSP-OF-CDR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (4 4 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-2))
 (4 4 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-1))
 (3 3 (:REWRITE NAT-LISTP-OF-AREF1-WHEN-ALL-DAG-PARENT-ENTRIESP))
 (3 3 (:REWRITE DAG-PARENT-ARRAYP-WHEN-WF-DAGP))
 (3 1 (:REWRITE TRUE-LISTP-WHEN-NAT-LISTP-REWRITE))
 (3 1 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (2 1 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (1 1 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 )
(POPULATE-CANDIDATE-DEPS-ARRAY-AUX
 (4130 2335 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (1795 1795 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (733 21 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (620 310 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (332 37 (:REWRITE INTEGERP-WHEN-NATP))
 (310 310 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (280 140 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (219 5 (:REWRITE NATP-OF-+-OF-1))
 (188 36 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (182 20 (:REWRITE NATP-OF-+-WHEN-NATP-AND-NATP))
 (182 20 (:REWRITE NATP-OF-+))
 (172 2 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-<))
 (136 2 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (128 18 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (128 18 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (120 15 (:REWRITE NOT-EQUAL-OF-CAR-AND-QUOTE-WHEN-LEN-WRONG-AND-PSEUDO-DAG-ARRAYP-AUX))
 (119 93 (:REWRITE DEFAULT-<-2))
 (93 93 (:REWRITE USE-ALL-<-2))
 (93 93 (:REWRITE USE-ALL-<))
 (93 93 (:REWRITE DEFAULT-<-1))
 (92 24 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (84 21 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (70 70 (:REWRITE USE-ALL-<=-2))
 (70 70 (:REWRITE USE-ALL-<=))
 (66 52 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-MERGE-DEPS-FOR-ARGS))
 (64 20 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (59 59 (:REWRITE USE-ALL-NATP-2))
 (59 59 (:REWRITE USE-ALL-NATP))
 (59 6 (:REWRITE INTEGERP-OF-+-WHEN-INTEGERP-2))
 (59 6 (:REWRITE INTEGERP-OF-+-WHEN-INTEGERP-1))
 (56 28 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (56 28 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-SIMPLE))
 (50 2 (:REWRITE BOUNDED-DARG-LISTP-OF-DARGS-WHEN-<-SIMPLE))
 (48 24 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (45 1 (:REWRITE DARG-LISTP-WHEN-NOT-CONSP))
 (42 42 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (42 1 (:REWRITE DARG-LISTP-OF-DARGS-WHEN-DAG-EXPRP))
 (40 2 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (38 5 (:REWRITE BOUNDED-DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (35 35 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (32 32 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (30 30 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (28 28 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (27 27 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (24 24 (:TYPE-PRESCRIPTION DARGP))
 (24 24 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (24 24 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (24 24 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (23 1 (:REWRITE DAG-EXPRP-OF-AREF1-WHEN-BOUNDED-DAG-EXPRP-OF-AREF1))
 (22 19 (:REWRITE DEFAULT-+-1))
 (22 2 (:REWRITE BOUNDED-DARG-LISTP-OF-DARGS-WHEN-BOUNDED-DAG-EXPRP))
 (21 21 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (21 21 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (21 21 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (20 20 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (19 19 (:REWRITE DEFAULT-+-2))
 (18 18 (:REWRITE NATP-OF-+-WHEN-NEGATIVE-CONSTANT))
 (14 14 (:LINEAR ARRAY2P-LINEAR))
 (14 4 (:REWRITE CONSP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE-IFF))
 (13 13 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (12 2 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (12 2 (:REWRITE ALL-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (10 10 (:TYPE-PRESCRIPTION BOUNDED-DAG-EXPRP))
 (10 5 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (8 1 (:REWRITE SYMBOLP-OF-CAR-OF-AREF1))
 (8 1 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (8 1 (:REWRITE DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (6 3 (:REWRITE DEFAULT-UNARY-MINUS))
 (6 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (6 1 (:REWRITE DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (5 5 (:TYPE-PRESCRIPTION MYQUOTEP))
 (5 5 (:REWRITE FOLD-CONSTS-IN-+))
 (5 5 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP-CHEAP))
 (5 5 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP-CHEAP))
 (5 5 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (5 5 (:REWRITE BOUNDED-DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-GEN))
 (5 5 (:REWRITE BOUNDED-DAG-EXPRP-MONOTONE))
 (5 1 (:REWRITE SYMBOLP-OF-CAR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (5 1 (:REWRITE DARG-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (5 1 (:REWRITE BOUNDED-DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-BETTER))
 (4 4 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (4 4 (:TYPE-PRESCRIPTION ALL-<))
 (4 4 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (4 4 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (4 4 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (4 2 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (4 2 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (3 3 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (2 2 (:TYPE-PRESCRIPTION DAG-EXPRP))
 (2 2 (:REWRITE USE-ALL-RATIONALP-2))
 (2 2 (:REWRITE USE-ALL-RATIONALP))
 (2 2 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (2 2 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL))
 (2 2 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP))
 (2 2 (:REWRITE BOUNDED-DARG-LISTP-OF-DARGS-WHEN-BOUNDED-DAG-EXPRP-FREE))
 (2 2 (:REWRITE BOUNDED-DARG-LISTP-OF-DARGS-OF-AREF1))
 (2 2 (:REWRITE BOUNDED-DARG-LISTP-MONOTONE))
 (2 2 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (2 2 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (2 2 (:REWRITE ALL-<-TRANSITIVE))
 (2 1 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (2 1 (:REWRITE DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION ALL-NATP))
 (1 1 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (1 1 (:REWRITE DARG-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (1 1 (:REWRITE DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (1 1 (:REWRITE DAG-EXPRP-WHEN-BOUNDED-DAG-EXPRP))
 (1 1 (:REWRITE BOUNDED-DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 )
(CANDIDATE-DEPS-ARRAYP-OF-POPULATE-CANDIDATE-DEPS-ARRAY-AUX
 (5666 2833 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (2833 2833 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (484 242 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (352 10 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (326 163 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (242 242 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (94 18 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (86 1 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-<))
 (68 1 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (66 42 (:REWRITE DEFAULT-<-1))
 (64 9 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (64 9 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (60 42 (:REWRITE DEFAULT-<-2))
 (56 7 (:REWRITE NOT-EQUAL-OF-CAR-AND-QUOTE-WHEN-LEN-WRONG-AND-PSEUDO-DAG-ARRAYP-AUX))
 (45 9 (:REWRITE INTEGERP-WHEN-NATP))
 (42 42 (:REWRITE USE-ALL-<-2))
 (42 42 (:REWRITE USE-ALL-<))
 (39 10 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (32 32 (:REWRITE USE-ALL-<=-2))
 (32 32 (:REWRITE USE-ALL-<=))
 (32 8 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (25 25 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (25 1 (:REWRITE BOUNDED-DARG-LISTP-OF-DARGS-WHEN-<-SIMPLE))
 (24 12 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (24 12 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-SIMPLE))
 (24 9 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (24 8 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (20 20 (:LINEAR ARRAY2P-LINEAR))
 (20 10 (:REWRITE LEN-WHEN-DARGP-CHEAP))
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 (19 10 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
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 (17 17 (:REWRITE USE-ALL-NATP))
 (16 16 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (16 16 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (16 2 (:REWRITE BOUNDED-DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (12 12 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (11 1 (:REWRITE BOUNDED-DARG-LISTP-OF-DARGS-WHEN-BOUNDED-DAG-EXPRP))
 (10 10 (:TYPE-PRESCRIPTION DARGP))
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 (10 10 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (10 10 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (10 10 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (10 10 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (9 9 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (8 8 (:REWRITE USE-ALL-RATIONALP-2))
 (8 8 (:REWRITE USE-ALL-RATIONALP))
 (8 8 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (8 8 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (8 8 (:REWRITE DEFAULT-+-2))
 (8 8 (:REWRITE DEFAULT-+-1))
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 (7 2 (:REWRITE CONSP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE-IFF))
 (7 1 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-MERGE-DEPS-FOR-ARGS))
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 (6 1 (:REWRITE ALL-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (4 4 (:TYPE-PRESCRIPTION BOUNDED-DAG-EXPRP))
 (4 2 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (2 2 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (2 2 (:TYPE-PRESCRIPTION MYQUOTEP))
 (2 2 (:TYPE-PRESCRIPTION ALL-<))
 (2 2 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP-CHEAP))
 (2 2 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (2 2 (:REWRITE BOUNDED-DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-GEN))
 (2 2 (:REWRITE BOUNDED-DAG-EXPRP-MONOTONE))
 (2 1 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (2 1 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (2 1 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION ALL-NATP))
 (1 1 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (1 1 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (1 1 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL))
 (1 1 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP))
 (1 1 (:REWRITE BOUNDED-DARG-LISTP-OF-DARGS-WHEN-BOUNDED-DAG-EXPRP-FREE))
 (1 1 (:REWRITE BOUNDED-DARG-LISTP-OF-DARGS-OF-AREF1))
 (1 1 (:REWRITE BOUNDED-DARG-LISTP-MONOTONE))
 (1 1 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (1 1 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (1 1 (:REWRITE ALL-<-TRANSITIVE))
 (1 1 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (1 1 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (1 1 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 )
(ALEN1-OF-POPULATE-CANDIDATE-DEPS-ARRAY-AUX
 (4784 2392 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (2392 2392 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (568 284 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (374 187 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (353 11 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (284 284 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (165 1 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-<))
 (147 3 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (94 18 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (70 3 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (64 9 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (64 9 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (56 40 (:REWRITE DEFAULT-<-2))
 (56 7 (:REWRITE NOT-EQUAL-OF-CAR-AND-QUOTE-WHEN-LEN-WRONG-AND-PSEUDO-DAG-ARRAYP-AUX))
 (43 1 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (40 40 (:REWRITE USE-ALL-<-2))
 (40 40 (:REWRITE USE-ALL-<))
 (40 40 (:REWRITE DEFAULT-<-1))
 (40 20 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (40 20 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-SIMPLE))
 (39 10 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (32 8 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (30 30 (:REWRITE USE-ALL-<=-2))
 (30 30 (:REWRITE USE-ALL-<=))
 (27 27 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (25 1 (:REWRITE BOUNDED-DARG-LISTP-OF-DARGS-WHEN-<-SIMPLE))
 (24 9 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (21 1 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (20 20 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (20 10 (:REWRITE LEN-WHEN-DARGP-CHEAP))
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 (20 1 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
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 (16 16 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
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 (16 16 (:LINEAR ARRAY2P-LINEAR))
 (16 2 (:REWRITE BOUNDED-DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (14 14 (:REWRITE USE-ALL-NATP-2))
 (14 14 (:REWRITE USE-ALL-NATP))
 (11 11 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (11 11 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (11 1 (:REWRITE BOUNDED-DARG-LISTP-OF-DARGS-WHEN-BOUNDED-DAG-EXPRP))
 (11 1 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (11 1 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (10 10 (:TYPE-PRESCRIPTION DARGP))
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 (10 10 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (10 10 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (8 8 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (8 8 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (8 8 (:REWRITE DEFAULT-+-2))
 (8 8 (:REWRITE DEFAULT-+-1))
 (8 3 (:REWRITE CONSP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE-IFF))
 (7 1 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-MERGE-DEPS-FOR-ARGS))
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 (6 1 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (6 1 (:REWRITE ALL-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (5 5 (:TYPE-PRESCRIPTION ALL-NATP))
 (4 4 (:TYPE-PRESCRIPTION BOUNDED-DAG-EXPRP))
 (4 2 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (3 3 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (3 3 (:REWRITE ALL-<-TRANSITIVE))
 (2 2 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (2 2 (:TYPE-PRESCRIPTION MYQUOTEP))
 (2 2 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP-CHEAP))
 (2 2 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (2 2 (:REWRITE BOUNDED-DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-GEN))
 (2 2 (:REWRITE BOUNDED-DAG-EXPRP-MONOTONE))
 (2 1 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (2 1 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (2 1 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (1 1 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (1 1 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL))
 (1 1 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP))
 (1 1 (:REWRITE BOUNDED-DARG-LISTP-OF-DARGS-WHEN-BOUNDED-DAG-EXPRP-FREE))
 (1 1 (:REWRITE BOUNDED-DARG-LISTP-OF-DARGS-OF-AREF1))
 (1 1 (:REWRITE BOUNDED-DARG-LISTP-MONOTONE))
 (1 1 (:REWRITE ALL-<-OF-+-OF-1))
 (1 1 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (1 1 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (1 1 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 )
(POPULATE-CANDIDATE-DEPS-ARRAY
 (506 258 (:TYPE-PRESCRIPTION NATP-OF-LARGEST-NON-QUOTEP))
 (463 21 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (444 222 (:TYPE-PRESCRIPTION NATP-OF-MAXELEM-2))
 (436 218 (:TYPE-PRESCRIPTION NATP-OF-MAXELEM-OF-STRIP-CARS-WHEN-WEAK-DAGP-AUX))
 (268 9 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-<))
 (263 7 (:REWRITE MAXELEM-SINGLETON-ALT))
 (229 222 (:TYPE-PRESCRIPTION RATIONALP-OF-MAXELEM))
 (218 218 (:TYPE-PRESCRIPTION WEAK-DAGP-AUX))
 (163 4 (:REWRITE <=-OF-LARGEST-NON-QUOTEP-WHEN-BOUNDED-DARG-LISTP))
 (158 13 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (152 3 (:REWRITE <-OF-LARGEST-NON-QUOTEP))
 (141 13 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (113 7 (:REWRITE LEN-OF-CDR))
 (105 45 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (93 16 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (90 17 (:REWRITE DEFAULT-+-2))
 (69 26 (:REWRITE DEFAULT-<-2))
 (67 1 (:LINEAR LARGEST-NON-QUOTEP-BOUND))
 (60 18 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (60 18 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (60 4 (:REWRITE <=-OF-LARGEST-NON-QUOTEP))
 (56 8 (:REWRITE LEN-OF-STRIP-CARS))
 (54 27 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (51 1 (:LINEAR LARGEST-NON-QUOTEP-BOUND-ALT))
 (47 1 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (44 26 (:REWRITE DEFAULT-<-1))
 (37 15 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (33 33 (:TYPE-PRESCRIPTION ALL-<))
 (33 27 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (33 9 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (33 1 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (30 15 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (29 1 (:REWRITE NATP-OF-NTH-WHEN-DARG-LISTP))
 (27 27 (:TYPE-PRESCRIPTION DARGP))
 (27 27 (:TYPE-PRESCRIPTION BOUNDED-DARG-LISTP))
 (27 27 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (27 27 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (27 27 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
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 (26 26 (:REWRITE USE-ALL-<))
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 (21 21 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (21 21 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (20 7 (:REWRITE ALL-<-OF-+-OF-1))
 (19 7 (:REWRITE MAXELEM-WHEN-NON-CONSP))
 (18 9 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (18 9 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (17 17 (:REWRITE DEFAULT-+-1))
 (15 15 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (13 13 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (13 13 (:REWRITE ALL-<-TRANSITIVE))
 (12 6 (:REWRITE LARGEST-NON-QUOTEP-WHEN-ALL-MYQUOTEP-CHEAP))
 (12 4 (:REWRITE MAXELEM-OF-STRIP-CARS-WHEN-PSEUDO-DAGP))
 (10 10 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (9 9 (:REWRITE BOUNDED-DARG-LISTP-MONOTONE))
 (9 1 (:REWRITE ACL2-NUMBERP-OF-MAXELEM))
 (8 8 (:REWRITE USE-ALL-<=-2))
 (8 8 (:REWRITE USE-ALL-<=))
 (7 7 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
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 (7 1 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (7 1 (:REWRITE ALL-INTEGERP-WHEN-NAT-LISTP))
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 (6 3 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (4 1 (:REWRITE INTEGER-LISTP-WHEN-ALL-NATP))
 (3 3 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (3 3 (:REWRITE STRIP-CARS-WHEN-NOT-CONSP-CHEAP))
 (3 1 (:REWRITE CAR-OF-NTH-0-WHEN-PSEUDO-DAGP))
 (2 2 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (2 2 (:REWRITE USE-ALL-NATP-2))
 (2 2 (:REWRITE USE-ALL-NATP))
 (2 1 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (2 1 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (2 1 (:REWRITE ALL-NATP-IMPLIES-ALL-INTEGERP-CHEAP))
 (2 1 (:REWRITE ALL-INTEGERP-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE USE-ALL-RATIONALP-2))
 (1 1 (:REWRITE USE-ALL-RATIONALP))
 (1 1 (:REWRITE NATP-OF-NTH-WHEN-BOUNDED-DARG-LISTP-GEN))
 (1 1 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (1 1 (:REWRITE ALL-NATP-OF-STRIP-CARS-WHEN-SUBST-CANDIDATE-LISTP))
 (1 1 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (1 1 (:LINEAR <-OF-LARGEST-NON-QUOTEP))
 )
(CANDIDATE-DEPS-ARRAYP-OF-POPULATE-CANDIDATE-DEPS-ARRAY
 (184 92 (:TYPE-PRESCRIPTION NATP-OF-LARGEST-NON-QUOTEP))
 (144 72 (:TYPE-PRESCRIPTION NATP-OF-MAXELEM-OF-STRIP-CARS-WHEN-WEAK-DAGP-AUX))
 (144 72 (:TYPE-PRESCRIPTION NATP-OF-MAXELEM-2))
 (136 7 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (118 3 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-<))
 (92 5 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (72 72 (:TYPE-PRESCRIPTION WEAK-DAGP-AUX))
 (72 72 (:TYPE-PRESCRIPTION RATIONALP-OF-MAXELEM))
 (71 1 (:REWRITE <-OF-LARGEST-NON-QUOTEP))
 (69 5 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (67 1 (:REWRITE <=-OF-LARGEST-NON-QUOTEP-WHEN-BOUNDED-DARG-LISTP))
 (67 1 (:LINEAR LARGEST-NON-QUOTEP-BOUND))
 (51 1 (:LINEAR LARGEST-NON-QUOTEP-BOUND-ALT))
 (49 6 (:REWRITE DEFAULT-+-2))
 (47 1 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (41 15 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
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 (29 1 (:REWRITE NATP-OF-NTH-WHEN-DARG-LISTP))
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 (22 6 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
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 (17 1 (:REWRITE LEN-OF-CDR))
 (16 8 (:REWRITE LEN-WHEN-DARGP-CHEAP))
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 (15 4 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (15 3 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (14 2 (:REWRITE LEN-OF-STRIP-CARS))
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 (10 5 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (9 9 (:TYPE-PRESCRIPTION BOUNDED-DARG-LISTP))
 (9 9 (:REWRITE USE-ALL-<-2))
 (9 9 (:REWRITE USE-ALL-<))
 (9 3 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (9 3 (:REWRITE ALL-<-OF-+-OF-1))
 (9 1 (:REWRITE ACL2-NUMBERP-OF-MAXELEM))
 (8 8 (:TYPE-PRESCRIPTION DARGP))
 (8 8 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (8 8 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (8 8 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (7 7 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (7 7 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (7 1 (:REWRITE NATP-OF-NTH-WHEN-NAT-LISTP))
 (7 1 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (6 6 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (6 6 (:REWRITE DEFAULT-+-1))
 (6 3 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (6 3 (:REWRITE LARGEST-NON-QUOTEP-WHEN-ALL-MYQUOTEP-CHEAP))
 (6 3 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (6 3 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (5 5 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (5 5 (:REWRITE ALL-<-TRANSITIVE))
 (4 4 (:TYPE-PRESCRIPTION NATP))
 (4 2 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (4 2 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (4 1 (:REWRITE MAXELEM-WHEN-NON-CONSP))
 (4 1 (:REWRITE INTEGER-LISTP-WHEN-ALL-NATP))
 (3 3 (:REWRITE USE-ALL-<=-2))
 (3 3 (:REWRITE USE-ALL-<=))
 (3 3 (:REWRITE LARGEST-NON-QUOTEP-WHEN-ALL-CONSP-CHEAP))
 (3 3 (:REWRITE LARGEST-NON-QUOTEP-WHEN-ALL-CONSP))
 (3 3 (:REWRITE CONSP-OF-STRIP-CARS))
 (3 3 (:REWRITE BOUNDED-DARG-LISTP-MONOTONE))
 (3 1 (:REWRITE MAXELEM-OF-STRIP-CARS-WHEN-PSEUDO-DAGP))
 (2 2 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (2 2 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (2 2 (:REWRITE USE-ALL-NATP-2))
 (2 2 (:REWRITE USE-ALL-NATP))
 (2 1 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (2 1 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (2 1 (:REWRITE ALL-NATP-IMPLIES-ALL-INTEGERP-CHEAP))
 (2 1 (:REWRITE ALL-INTEGERP-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE STRIP-CARS-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (1 1 (:REWRITE NATP-OF-NTH-WHEN-BOUNDED-DARG-LISTP-GEN))
 (1 1 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (1 1 (:REWRITE ALL-NATP-OF-STRIP-CARS-WHEN-SUBST-CANDIDATE-LISTP))
 (1 1 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (1 1 (:LINEAR <-OF-LARGEST-NON-QUOTEP))
 )
(ALEN1-OF-POPULATE-CANDIDATE-DEPS-ARRAY
 (288 144 (:TYPE-PRESCRIPTION NATP-OF-LARGEST-NON-QUOTEP))
 (144 72 (:TYPE-PRESCRIPTION NATP-OF-MAXELEM-OF-STRIP-CARS-WHEN-WEAK-DAGP-AUX))
 (144 72 (:TYPE-PRESCRIPTION NATP-OF-MAXELEM-2))
 (136 7 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (118 3 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-<))
 (92 5 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (72 72 (:TYPE-PRESCRIPTION WEAK-DAGP-AUX))
 (72 72 (:TYPE-PRESCRIPTION RATIONALP-OF-MAXELEM))
 (71 1 (:REWRITE <-OF-LARGEST-NON-QUOTEP))
 (69 5 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (67 1 (:REWRITE <=-OF-LARGEST-NON-QUOTEP-WHEN-BOUNDED-DARG-LISTP))
 (67 1 (:LINEAR LARGEST-NON-QUOTEP-BOUND))
 (56 7 (:REWRITE DEFAULT-+-2))
 (51 1 (:LINEAR LARGEST-NON-QUOTEP-BOUND-ALT))
 (47 1 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (41 15 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (41 1 (:REWRITE MAXELEM-SINGLETON-ALT))
 (33 1 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (29 1 (:REWRITE NATP-OF-NTH-WHEN-DARG-LISTP))
 (28 9 (:REWRITE DEFAULT-<-2))
 (22 6 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (22 6 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (19 1 (:REWRITE <=-OF-LARGEST-NON-QUOTEP))
 (17 1 (:REWRITE LEN-OF-CDR))
 (16 8 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (15 9 (:REWRITE DEFAULT-<-1))
 (15 4 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (15 3 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (14 2 (:REWRITE LEN-OF-STRIP-CARS))
 (12 12 (:TYPE-PRESCRIPTION ALL-<))
 (12 8 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (10 5 (:REWRITE LARGEST-NON-QUOTEP-WHEN-ALL-MYQUOTEP-CHEAP))
 (10 5 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (9 9 (:TYPE-PRESCRIPTION BOUNDED-DARG-LISTP))
 (9 9 (:REWRITE USE-ALL-<-2))
 (9 9 (:REWRITE USE-ALL-<))
 (9 3 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (9 3 (:REWRITE ALL-<-OF-+-OF-1))
 (9 1 (:REWRITE ACL2-NUMBERP-OF-MAXELEM))
 (8 8 (:TYPE-PRESCRIPTION DARGP))
 (8 8 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (8 8 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (8 8 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (8 8 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (7 7 (:REWRITE DEFAULT-+-1))
 (7 7 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (7 7 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (7 1 (:REWRITE NATP-OF-NTH-WHEN-NAT-LISTP))
 (7 1 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (6 3 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (6 3 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (6 3 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (5 5 (:REWRITE LARGEST-NON-QUOTEP-WHEN-ALL-CONSP-CHEAP))
 (5 5 (:REWRITE LARGEST-NON-QUOTEP-WHEN-ALL-CONSP))
 (5 5 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (5 5 (:REWRITE ALL-<-TRANSITIVE))
 (4 2 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (4 2 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (4 1 (:REWRITE MAXELEM-WHEN-NON-CONSP))
 (4 1 (:REWRITE INTEGER-LISTP-WHEN-ALL-NATP))
 (3 3 (:REWRITE USE-ALL-<=-2))
 (3 3 (:REWRITE USE-ALL-<=))
 (3 3 (:REWRITE CONSP-OF-STRIP-CARS))
 (3 3 (:REWRITE BOUNDED-DARG-LISTP-MONOTONE))
 (3 1 (:REWRITE MAXELEM-OF-STRIP-CARS-WHEN-PSEUDO-DAGP))
 (2 2 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (2 2 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (2 2 (:REWRITE USE-ALL-NATP-2))
 (2 2 (:REWRITE USE-ALL-NATP))
 (2 1 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (2 1 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (2 1 (:REWRITE ALL-NATP-IMPLIES-ALL-INTEGERP-CHEAP))
 (2 1 (:REWRITE ALL-INTEGERP-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE STRIP-CARS-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (1 1 (:REWRITE NATP-OF-NTH-WHEN-BOUNDED-DARG-LISTP-GEN))
 (1 1 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (1 1 (:REWRITE ALL-NATP-OF-STRIP-CARS-WHEN-SUBST-CANDIDATE-LISTP))
 (1 1 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (1 1 (:LINEAR <-OF-LARGEST-NON-QUOTEP))
 )
(<-OF-CADR-OF-CAR-WHEN-BOUNDED-DARG-LISTP-OF-STRIP-CADRS
 (768 384 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (722 27 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (530 11 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (401 4 (:REWRITE USE-ALL-<-FOR-CAR))
 (384 384 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (252 27 (:REWRITE DEFAULT-<-1))
 (208 3 (:REWRITE ALL-<-OF-CONS))
 (181 9 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (162 41 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (106 2 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (93 19 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (93 19 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (84 2 (:REWRITE LEN-OF-CDR))
 (80 2 (:REWRITE <-OF-IF-ARG2))
 (74 4 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (64 32 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (64 27 (:REWRITE DEFAULT-<-2))
 (56 2 (:REWRITE ALL-RATIONALP-OF-CDR))
 (48 2 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (34 2 (:REWRITE EQUAL-OF-LEN-AND-0))
 (32 32 (:TYPE-PRESCRIPTION DARGP))
 (32 32 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (32 32 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (32 32 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (27 27 (:REWRITE USE-ALL-<-2))
 (27 27 (:REWRITE USE-ALL-<))
 (27 27 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (27 27 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (22 8 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (20 4 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (17 17 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (17 17 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (17 17 (:REWRITE ALL-<-TRANSITIVE))
 (17 3 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (16 8 (:REWRITE DEFAULT-+-2))
 (16 2 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-CAR-AND-QUOTE))
 (14 2 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (12 12 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (10 5 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (10 5 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (9 9 (:REWRITE USE-ALL-RATIONALP-2))
 (9 9 (:REWRITE USE-ALL-RATIONALP))
 (8 8 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (8 8 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (8 8 (:REWRITE DEFAULT-+-1))
 (8 8 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (8 8 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (8 4 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (7 2 (:REWRITE DARGP-LESS-THAN-WHEN-NATP-CHEAP))
 (6 3 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (6 2 (:REWRITE PSEUDO-DAGP-OF-CDR-WHEN-PSEUDO-DAGP))
 (5 5 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (5 5 (:REWRITE BOUNDED-DARG-LISTP-MONOTONE))
 (4 4 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (3 3 (:TYPE-PRESCRIPTION MYQUOTEP))
 (3 3 (:REWRITE USE-ALL-<=-2))
 (3 3 (:REWRITE USE-ALL-<=))
 (3 1 (:REWRITE TRUE-LISTP-WHEN-NAT-LISTP-REWRITE))
 (2 2 (:REWRITE DARGP-LESS-THAN-WHEN-QUOTEP-CHEAP))
 (2 2 (:REWRITE DARGP-LESS-THAN-MONO))
 (2 1 (:TYPE-PRESCRIPTION NATP-OF-CAR-OF-CAR-WHEN-SUBST-CANDIDATE-LISTP))
 (2 1 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (1 1 (:TYPE-PRESCRIPTION SUBST-CANDIDATE-LISTP))
 (1 1 (:TYPE-PRESCRIPTION NATP))
 (1 1 (:REWRITE USE-ALL-NATP-2))
 (1 1 (:REWRITE USE-ALL-NATP))
 (1 1 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (1 1 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 )
(STRIP-CADRS-OF-CDR
 (187 6 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (48 2 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (44 44 (:TYPE-PRESCRIPTION LEN))
 (41 2 (:REWRITE LEN-OF-CDR))
 (39 7 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (36 1 (:REWRITE <-OF-IF-ARG2))
 (22 11 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (20 10 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (15 5 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (15 5 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (11 11 (:TYPE-PRESCRIPTION DARGP))
 (11 11 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (11 11 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (11 11 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (11 11 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (10 10 (:TYPE-PRESCRIPTION NAT-LISTP))
 (10 5 (:REWRITE DEFAULT-<-2))
 (7 2 (:REWRITE EQUAL-OF-LEN-AND-0))
 (6 6 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (6 6 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (5 5 (:REWRITE USE-ALL-<-2))
 (5 5 (:REWRITE USE-ALL-<))
 (5 5 (:REWRITE DEFAULT-<-1))
 (4 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (1 1 (:DEFINITION NOT))
 )
(MEMBERP-ASSUMING-SORTEDP-<=
 (36 18 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (18 18 (:TYPE-PRESCRIPTION NAT-LISTP))
 )
(DISJOINTP-ASSUMING-SORTEDP-<=
 (1116 558 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (582 582 (:TYPE-PRESCRIPTION NAT-LISTP))
 (544 12 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (430 6 (:REWRITE SORTEDP-<=-WHEN-NOT-CONSP-OF-CDR))
 (286 12 (:REWRITE NOT-<-OF-CAR-WHEN-ALL-<-2))
 (168 12 (:REWRITE USE-ALL-<=-FOR-CAR))
 (164 39 (:REWRITE DEFAULT-+-2))
 (150 12 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (130 24 (:REWRITE DEFAULT-<-2))
 (114 18 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (96 12 (:REWRITE USE-ALL-<-FOR-CAR))
 (96 12 (:REWRITE ALL-<=-OF-CAR-WHEN-ALL-<=-OF-ALL))
 (92 46 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (82 6 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (80 24 (:REWRITE DEFAULT-<-1))
 (74 2 (:REWRITE <-OF-IF-ARG2))
 (72 12 (:REWRITE ALL-<-OF-+-OF-1))
 (60 60 (:TYPE-PRESCRIPTION ALL-<))
 (48 39 (:REWRITE DEFAULT-+-1))
 (48 24 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (46 46 (:TYPE-PRESCRIPTION DARGP))
 (46 46 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (46 46 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (46 46 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (46 46 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (36 36 (:TYPE-PRESCRIPTION ALL-<=-ALL))
 (36 12 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (36 12 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (24 24 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (24 24 (:TYPE-PRESCRIPTION ALL-<=))
 (24 24 (:REWRITE USE-ALL-<-2))
 (24 24 (:REWRITE USE-ALL-<))
 (24 24 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (24 24 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (24 24 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (24 24 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (24 24 (:REWRITE ALL-<-TRANSITIVE))
 (24 12 (:REWRITE ALL-NATP-IMPLIES-ALL-INTEGERP-CHEAP))
 (24 12 (:REWRITE ALL-<=-ALL-WHEN-ALL-<=-ALL-OF-CDR-ARG2))
 (24 12 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (20 4 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (16 16 (:TYPE-PRESCRIPTION ALL-NATP))
 (14 8 (:REWRITE +-COMBINE-CONSTANTS))
 (12 12 (:REWRITE USE-ALL-<=-2))
 (12 12 (:REWRITE USE-ALL-<=))
 (12 12 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (12 12 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (12 12 (:REWRITE ALL-INTEGERP-WHEN-NOT-CONSP-CHEAP))
 (12 12 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (12 12 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (12 12 (:REWRITE ALL-<=-MONOTONE))
 (12 12 (:REWRITE ALL-<=-ALL-WHEN-NOT-CONSP-ARG2))
 (12 12 (:REWRITE ALL-<=-ALL-WHEN-NOT-CONSP-ARG1-CHEAP))
 (12 12 (:REWRITE ALL-<=-ALL-WHEN-NOT-CONSP-ARG1))
 (12 2 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (8 8 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (8 4 (:REWRITE RATIONAL-LISTP-WHEN-ALL-NATP-CHEAP))
 (6 6 (:REWRITE FOLD-CONSTS-IN-+))
 (6 6 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (4 4 (:REWRITE USE-ALL-RATIONALP-2))
 (4 4 (:REWRITE USE-ALL-RATIONALP))
 (4 4 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (4 4 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (4 2 (:DEFINITION FIX))
 (2 2 (:REWRITE LEN-OF-CDDR-WHEN-EQUAL-OF-LEN))
 (2 2 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (2 2 (:REWRITE <-OF-+-AND-+-COMBINE-CONSTANTS))
 )
(<=-OF-CAR-WHEN-MEMBER-EQUAL-AND-SORTEDP-<=
 (1966 983 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (1966 983 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (1249 44 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (1041 1041 (:TYPE-PRESCRIPTION NAT-LISTP))
 (983 983 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (662 60 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (571 12 (:REWRITE NOT-<-OF-CAR-WHEN-ALL-<-2))
 (512 53 (:REWRITE DEFAULT-<-2))
 (383 53 (:REWRITE DEFAULT-<-1))
 (372 43 (:REWRITE DEFAULT-+-2))
 (285 14 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (269 14 (:REWRITE USE-ALL-<-FOR-CAR))
 (238 7 (:REWRITE <-OF-IF-ARG2))
 (213 12 (:REWRITE USE-ALL-<=-FOR-CAR))
 (200 100 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (200 26 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (132 14 (:REWRITE ALL-<-OF-CDR))
 (128 8 (:REWRITE ALL-<=-OF-CAR-WHEN-ALL-<=-OF-ALL))
 (120 44 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (116 58 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (102 102 (:TYPE-PRESCRIPTION ALL-<))
 (101 101 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (100 100 (:TYPE-PRESCRIPTION DARGP))
 (100 100 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (100 100 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (100 100 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (87 29 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (87 29 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (84 13 (:REWRITE ALL-<-OF-+-OF-1))
 (82 44 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (76 76 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (64 8 (:REWRITE ALL-<=-ALL-OF-CDR-ARG2))
 (60 12 (:REWRITE ALL-RATIONALP-OF-CDR))
 (53 53 (:REWRITE USE-ALL-<-2))
 (53 53 (:REWRITE USE-ALL-<))
 (48 48 (:TYPE-PRESCRIPTION ALL-<=-ALL))
 (48 38 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (48 2 (:LINEAR LEN-OF-CDR-LINEAR-STRONG))
 (45 45 (:REWRITE USE-ALL-RATIONALP-2))
 (45 45 (:REWRITE USE-ALL-RATIONALP))
 (44 44 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (44 44 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (44 44 (:REWRITE ALL-<-TRANSITIVE))
 (44 2 (:LINEAR LEN-OF-CDR-LINEAR))
 (43 43 (:REWRITE DEFAULT-+-1))
 (43 22 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-CDR-CHEAP))
 (40 40 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (38 38 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (32 16 (:REWRITE ALL-<=-ALL-WHEN-ALL-<=-ALL-OF-CDR-ARG2))
 (31 16 (:REWRITE EQUAL-OF-LEN-AND-0))
 (28 28 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (28 14 (:REWRITE ALL-NATP-IMPLIES-ALL-INTEGERP-CHEAP))
 (28 14 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (26 26 (:TYPE-PRESCRIPTION ALL-<=))
 (24 24 (:REWRITE USE-ALL-<=-2))
 (24 24 (:REWRITE USE-ALL-<=))
 (24 24 (:REWRITE MEMBER-EQUAL-OF-SINGLETON-CONSTANT-IFF))
 (24 4 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (23 23 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-MEMBER-EQUAL))
 (20 13 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (20 4 (:REWRITE SORTEDP-<=-OF-CDR))
 (18 18 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-2))
 (18 18 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-1))
 (16 16 (:REWRITE ALL-<=-ALL-WHEN-NOT-CONSP-ARG2))
 (16 16 (:REWRITE ALL-<=-ALL-WHEN-NOT-CONSP-ARG1-CHEAP))
 (16 16 (:REWRITE ALL-<=-ALL-WHEN-NOT-CONSP-ARG1))
 (16 4 (:REWRITE +-COMBINE-CONSTANTS))
 (15 15 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-WHEN-NOT-EQUAL-CAR))
 (15 15 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-TRIM))
 (14 14 (:TYPE-PRESCRIPTION ALL-NATP))
 (14 14 (:REWRITE ALL-INTEGERP-WHEN-NOT-CONSP-CHEAP))
 (13 13 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (13 13 (:REWRITE ALL-<=-MONOTONE))
 (8 4 (:DEFINITION FIX))
 (6 1 (:REWRITE ALL-INTEGERP-OF-CDR))
 (6 1 (:REWRITE ALL-<=-OF-CDR))
 (4 4 (:REWRITE LEN-OF-CDDR-WHEN-EQUAL-OF-LEN))
 )
(MEMBER-EQUAL-WHEN-<=-OF-LEN-AND-1
 (154 7 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (149 3 (:DEFINITION MEMBER-EQUAL))
 (130 65 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (130 65 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (85 85 (:TYPE-PRESCRIPTION NAT-LISTP))
 (65 65 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (40 20 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (39 3 (:REWRITE NOT-MEMBER-EQUAL-OF-CDR-WHEN-NOT-MEMBER-EQUAL))
 (32 16 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (30 10 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (30 10 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (26 13 (:REWRITE NOT-MEMBER-EQUAL-WHEN-NOT-MEMBER-EQUAL-OF-CDR-CHEAP))
 (26 13 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-CDR-CHEAP))
 (20 10 (:REWRITE DEFAULT-<-2))
 (16 16 (:TYPE-PRESCRIPTION DARGP))
 (16 16 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (16 16 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (16 16 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (14 14 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-MEMBER-EQUAL))
 (14 14 (:REWRITE MEMBER-EQUAL-OF-SINGLETON-CONSTANT-IFF))
 (10 10 (:REWRITE USE-ALL-<-2))
 (10 10 (:REWRITE USE-ALL-<))
 (10 10 (:REWRITE DEFAULT-<-1))
 (9 9 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-2))
 (9 9 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-1))
 (8 8 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-WHEN-NOT-EQUAL-CAR))
 (8 8 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-TRIM))
 (7 7 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (7 7 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (3 3 (:REWRITE USE-ALL-<=-2))
 (3 3 (:REWRITE USE-ALL-<=))
 )
(NOT-MEMBER-EQUAL-WHEN-<-OF-CAR
 (72 36 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (51 36 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (36 36 (:TYPE-PRESCRIPTION NAT-LISTP))
 )
(DISJOINTP-ASSUMING-SORTEDP-<=-IFF
 (21966 373 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (21008 514 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (19178 1244 (:REWRITE LEN-OF-CDR))
 (17072 324 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (14152 718 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (12592 628 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (8702 73 (:REWRITE SUBSETP-EQUAL-OF-CDR-ARG1))
 (8235 294 (:REWRITE <-OF-IF-ARG2))
 (7311 376 (:REWRITE USE-ALL-<-FOR-CAR))
 (5840 2920 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (4627 1143 (:REWRITE DEFAULT-<-1))
 (3810 1295 (:REWRITE DEFAULT-+-2))
 (3100 1550 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (2920 2920 (:TYPE-PRESCRIPTION DARGP))
 (2920 2920 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (2920 2920 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (2920 2920 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (2920 2920 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (2791 672 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (2763 61 (:REWRITE NOT-<-OF-CAR-WHEN-ALL-<-2))
 (2325 775 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (2325 775 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (2168 438 (:REWRITE ALL-RATIONALP-OF-CDR))
 (1997 474 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-2))
 (1870 672 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (1720 1720 (:TYPE-PRESCRIPTION ALL-<))
 (1642 169 (:REWRITE ALL-<-OF-CDR))
 (1570 61 (:REWRITE USE-ALL-<=-FOR-CAR))
 (1434 1434 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (1420 292 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (1299 72 (:REWRITE INTERSECTION-EQUAL-WHEN-MEMBER-EQUAL-AND-MEMBER-EQUAL))
 (1295 1295 (:REWRITE DEFAULT-+-1))
 (1173 65 (:REWRITE ALL-<=-OF-CAR-WHEN-ALL-<=-OF-ALL))
 (1154 1154 (:REWRITE USE-ALL-<-2))
 (1154 1154 (:REWRITE USE-ALL-<))
 (1085 292 (:REWRITE +-COMBINE-CONSTANTS))
 (1075 540 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-CDR-CHEAP))
 (1064 532 (:REWRITE NOT-MEMBER-EQUAL-WHEN-NOT-MEMBER-EQUAL-OF-CDR-CHEAP))
 (752 376 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (718 718 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (672 672 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (672 672 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (672 672 (:REWRITE ALL-<-TRANSITIVE))
 (629 619 (:REWRITE EQUAL-OF-LEN-AND-0))
 (589 72 (:REWRITE ALL-<=-ALL-OF-CDR-ARG2))
 (544 544 (:REWRITE MEMBER-EQUAL-OF-SINGLETON-CONSTANT-IFF))
 (540 540 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-MEMBER-EQUAL))
 (505 505 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (501 292 (:DEFINITION FIX))
 (497 497 (:REWRITE USE-ALL-<=-2))
 (497 497 (:REWRITE USE-ALL-<=))
 (474 474 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-1))
 (432 432 (:TYPE-PRESCRIPTION ALL-<=-ALL))
 (432 65 (:REWRITE ALL-<-OF-+-OF-1))
 (406 406 (:REWRITE MEMBER-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (374 187 (:REWRITE SUBSETP-EQUAL-WHEN-SUBSETP-EQUAL-OF-CDR-CHEAP))
 (374 187 (:REWRITE SUBSETP-EQUAL-OF-CDR-ARG2-CHEAP))
 (324 324 (:REWRITE USE-ALL-RATIONALP-2))
 (324 324 (:REWRITE USE-ALL-RATIONALP))
 (317 317 (:REWRITE LEN-OF-CDDR-WHEN-EQUAL-OF-LEN))
 (289 22 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (288 144 (:REWRITE ALL-<=-ALL-WHEN-ALL-<=-ALL-OF-CDR-ARG2))
 (278 278 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-WHEN-NOT-EQUAL-CAR))
 (278 278 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-TRIM))
 (254 19 (:REWRITE ALL-<=-ALL-OF-CDR-ARG1))
 (198 198 (:TYPE-PRESCRIPTION ALL-NATP))
 (187 187 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-ALT))
 (187 187 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-2-ALT))
 (178 178 (:REWRITE SUBSETP-EQUAL-WHEN-NOT-CONSP-ARG2-CHEAP))
 (178 178 (:REWRITE SUBSETP-EQUAL-WHEN-NOT-CONSP-ARG1-CHEAP))
 (149 144 (:REWRITE ALL-<=-ALL-WHEN-NOT-CONSP-ARG2))
 (148 144 (:REWRITE ALL-<=-ALL-WHEN-NOT-CONSP-ARG1))
 (144 144 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (144 144 (:REWRITE ALL-<=-ALL-WHEN-NOT-CONSP-ARG1-CHEAP))
 (144 72 (:REWRITE ALL-NATP-IMPLIES-ALL-INTEGERP-CHEAP))
 (136 23 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (130 130 (:TYPE-PRESCRIPTION ALL-<=))
 (120 22 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (112 56 (:REWRITE INTERSECTION-EQUAL-WHEN-MEMBER-EQUAL-OF-CAR-CHEAP))
 (104 7 (:REWRITE ALL-<=-OF-CDR))
 (82 41 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (78 39 (:REWRITE RATIONAL-LISTP-WHEN-ALL-NATP-CHEAP))
 (73 73 (:REWRITE INTERSECTION-EQUAL-WHEN-NOT-CONSP-ARG1-CHEAP))
 (72 72 (:REWRITE ALL-INTEGERP-WHEN-NOT-CONSP-CHEAP))
 (69 65 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (65 65 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (65 65 (:REWRITE ALL-<=-MONOTONE))
 (46 23 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (42 7 (:REWRITE ALL-INTEGERP-OF-CDR))
 (41 41 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (39 3 (:REWRITE ALL-NATP-OF-CDR))
 (31 2 (:REWRITE SUBSETP-EQUAL-OF-NIL-ARG2))
 (27 1 (:REWRITE <=-OF-0-WHEN-NATP))
 (25 23 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (23 23 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (21 6 (:REWRITE NAT-LISTP-OF-CDR))
 (13 1 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 (1 1 (:REWRITE USE-ALL-NATP-2))
 (1 1 (:REWRITE USE-ALL-NATP))
 (1 1 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 )
(FIND-SIMULTANEOUS-SUBST-CANDIDATES
 (84492 156 (:REWRITE INTERSECTION-EQUAL-WHEN-NOT-INTERSECTION-EQUAL-OF-CDR-ARG2-IFF))
 (79671 810 (:REWRITE NOT-MEMBER-EQUAL-WHEN-<-OF-CAR))
 (36636 356 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (31779 1538 (:REWRITE DEFAULT-<-2))
 (29257 15251 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (28150 356 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (22937 814 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (21650 552 (:REWRITE USE-ALL-<-FOR-CAR))
 (21413 1513 (:REWRITE DEFAULT-<-1))
 (18100 50 (:REWRITE NOT-MEMBER-EQUAL-OF-CDR-WHEN-NOT-MEMBER-EQUAL))
 (15759 249 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (15173 1137 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (11815 243 (:REWRITE <=-OF-CAR-WHEN-MEMBER-EQUAL-AND-SORTEDP-<=))
 (8645 4333 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (8500 50 (:REWRITE ALL-NATP-OF-CDR))
 (7125 100 (:REWRITE NOT-MEMBER-EQUAL-OF-MEMBER-EQUAL-WHEN-NOT-MEMBER-EQUAL))
 (6702 1972 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (6075 243 (:REWRITE USE-ALL-<=-FOR-CAR))
 (5235 243 (:REWRITE NOT-<-OF-CAR-WHEN-ALL-<-2))
 (5011 135 (:REWRITE <-OF-IF-ARG2))
 (4867 135 (:REWRITE LEN-OF-CDR))
 (4681 223 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (4617 243 (:REWRITE ALL-<=-OF-CAR-WHEN-ALL-<=-OF-ALL))
 (4412 986 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (4412 986 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (4333 4333 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (4288 4288 (:TYPE-PRESCRIPTION DAG-PARENT-ARRAYP))
 (4259 1137 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (3303 324 (:REWRITE <-OF-CAR-OF-CAR-WHEN-ALL-<-OF-STRIP-CARS))
 (3290 135 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (3282 1641 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (3171 1641 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (3000 100 (:REWRITE SUBSETP-EQUAL-OF-CDR-ARG1))
 (2916 243 (:REWRITE ALL-<=-ALL-WHEN-NOT-CONSP-ARG2))
 (2826 2826 (:TYPE-PRESCRIPTION ALL-<))
 (2270 135 (:REWRITE EQUAL-OF-LEN-AND-0))
 (2224 256 (:REWRITE SUBSETP-EQUAL-WHEN-NOT-CONSP-ARG2-CHEAP))
 (1856 928 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (1850 50 (:REWRITE ALL-RATIONALP-OF-CDR))
 (1740 384 (:REWRITE DEFAULT-+-2))
 (1641 1641 (:TYPE-PRESCRIPTION DARGP))
 (1641 1641 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (1641 1641 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (1641 1641 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (1538 1538 (:REWRITE USE-ALL-<-2))
 (1538 1538 (:REWRITE USE-ALL-<))
 (1494 747 (:REWRITE NOT-MEMBER-EQUAL-WHEN-NOT-MEMBER-EQUAL-OF-CDR-CHEAP))
 (1494 747 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-CDR-CHEAP))
 (1480 243 (:REWRITE ALL-<-OF-+-OF-1))
 (1397 330 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (1277 12 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-<))
 (1224 156 (:REWRITE INTERSECTION-EQUAL-WHEN-NOT-CONSP-ARG2-CHEAP))
 (1137 1137 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (1137 1137 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (1137 1137 (:REWRITE ALL-<-TRANSITIVE))
 (1104 552 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (1091 1091 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-AUX))
 (1030 119 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (1028 1028 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-WHEN-NOT-EQUAL-CAR))
 (975 26 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (935 785 (:REWRITE MEMBER-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (928 928 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (840 249 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (814 814 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (814 814 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (788 223 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (747 747 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-2))
 (747 747 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-1))
 (747 747 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-MEMBER-EQUAL))
 (747 747 (:REWRITE MEMBER-EQUAL-OF-SINGLETON-CONSTANT-IFF))
 (747 747 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-TRIM))
 (729 729 (:TYPE-PRESCRIPTION ALL-<=-ALL))
 (690 690 (:REWRITE USE-ALL-<=-2))
 (690 690 (:REWRITE USE-ALL-<=))
 (638 319 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (616 308 (:REWRITE SUBSETP-EQUAL-WHEN-SUBSETP-EQUAL-OF-CDR-CHEAP))
 (616 308 (:REWRITE SUBSETP-EQUAL-OF-CDR-ARG2-CHEAP))
 (528 44 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-OF-CAR))
 (500 125 (:REWRITE ALL-<-OF-AREF1-WHEN-BOUNDED-DAG-PARENT-ARRAYP))
 (498 249 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (486 486 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (486 486 (:TYPE-PRESCRIPTION ALL-<=))
 (486 243 (:REWRITE ALL-NATP-IMPLIES-ALL-INTEGERP-CHEAP))
 (486 243 (:REWRITE ALL-<=-ALL-WHEN-ALL-<=-ALL-OF-CDR-ARG2))
 (456 256 (:REWRITE SUBSETP-EQUAL-WHEN-NOT-CONSP-ARG1-CHEAP))
 (385 55 (:REWRITE NAT-LISTP-OF-CDR))
 (384 384 (:REWRITE DEFAULT-+-1))
 (372 186 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (356 356 (:REWRITE USE-ALL-RATIONALP-2))
 (356 356 (:REWRITE USE-ALL-RATIONALP))
 (342 342 (:TYPE-PRESCRIPTION STRIP-CARS))
 (336 50 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-OF-CDR))
 (333 333 (:REWRITE STRIP-CARS-WHEN-NOT-CONSP-CHEAP))
 (312 156 (:REWRITE INTERSECTION-EQUAL-WHEN-MEMBER-EQUAL-OF-CAR-CHEAP))
 (312 156 (:REWRITE INTERSECTION-EQUAL-WHEN-INTERSECTION-EQUAL-OF-CDR-ARG2-CHEAP))
 (312 156 (:REWRITE INTERSECTION-EQUAL-WHEN-INTERSECTION-EQUAL-OF-CDR-ARG1-CHEAP))
 (308 308 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-ALT))
 (308 308 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-2-ALT))
 (300 6 (:REWRITE ALL-<-OF-CDR))
 (286 286 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (285 285 (:REWRITE INTERSECTION-EQUAL-WHEN-MEMBER-EQUAL-AND-MEMBER-EQUAL))
 (256 156 (:REWRITE INTERSECTION-EQUAL-WHEN-NOT-CONSP-ARG1-CHEAP))
 (250 250 (:TYPE-PRESCRIPTION BOUNDED-DAG-PARENT-ARRAYP))
 (243 243 (:REWRITE EQUAL-OF-NON-NATP-AND-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (243 243 (:REWRITE ALL-INTEGERP-WHEN-NOT-CONSP-CHEAP))
 (243 243 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (243 243 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (243 243 (:REWRITE ALL-<=-MONOTONE))
 (243 243 (:REWRITE ALL-<=-ALL-WHEN-NOT-CONSP-ARG1-CHEAP))
 (243 243 (:REWRITE ALL-<=-ALL-WHEN-NOT-CONSP-ARG1))
 (241 86 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (222 222 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (182 26 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (176 44 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (174 17 (:REWRITE ALL-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (150 150 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (147 111 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL))
 (135 135 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (125 125 (:REWRITE BOUNDED-DAG-PARENT-ARRAYP-MONOTONE))
 (125 125 (:REWRITE ALL-<-OF-AREF1-WHEN-BOUNDED-DAG-PARENT-ENTRIESP))
 (124 124 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (111 111 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (111 111 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP))
 (93 31 (:REWRITE PSEUDO-DAGP-OF-CDR-WHEN-PSEUDO-DAGP))
 (88 88 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (86 86 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (86 86 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (86 86 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (58 29 (:REWRITE RATIONAL-LISTP-WHEN-ALL-NATP-CHEAP))
 (48 48 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DIMENSIONS-WHEN-ARRAY1P))
 (44 44 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (44 44 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (40 5 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (24 24 (:TYPE-PRESCRIPTION POSP-OF-CAR-OF-DIMENSIONS-WHEN-ARRAY1P))
 (24 12 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (22 22 (:REWRITE ALL-INTEGERP-OF-AREF1-WHEN-ALL-DAG-PARENT-ENTRIESP))
 (22 11 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (12 12 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP))
 (12 12 (:LINEAR ARRAY2P-LINEAR))
 (11 11 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (11 11 (:REWRITE BOUNDED-DARG-LISTP-MONOTONE))
 (9 9 (:REWRITE CONSP-OF-STRIP-CARS))
 (7 1 (:REWRITE BOUNDED-DARG-LISTP-OF-0))
 (6 6 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (6 6 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (4 4 (:TYPE-PRESCRIPTION ALL-CONSP))
 (2 1 (:REWRITE ALL-MYQUOTEP-BECOMES-ALL-CONSP-WHEN-DARG-LISTP))
 )
(SUBST-CANDIDATE-LISTP-OF-FIND-SIMULTANEOUS-SUBST-CANDIDATES
 (22474 198 (:REWRITE NOT-MEMBER-EQUAL-WHEN-<-OF-CAR))
 (18070 26 (:REWRITE INTERSECTION-EQUAL-WHEN-NOT-INTERSECTION-EQUAL-OF-CDR-ARG2-IFF))
 (15114 6092 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (12372 383 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (12184 6092 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (10625 173 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (10260 157 (:REWRITE USE-ALL-<-FOR-CAR))
 (10242 525 (:REWRITE DEFAULT-<-2))
 (8794 313 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (7112 161 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (6868 6868 (:TYPE-PRESCRIPTION NAT-LISTP))
 (6529 65 (:REWRITE NOT-<-OF-CAR-WHEN-ALL-<-2))
 (6197 174 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (6141 6141 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (5259 517 (:REWRITE DEFAULT-<-1))
 (4862 13 (:REWRITE NOT-MEMBER-EQUAL-OF-CDR-WHEN-NOT-MEMBER-EQUAL))
 (3826 8 (:REWRITE ALL-<-OF-MERGE-<-AND-REMOVE-DUPS))
 (3622 69 (:REWRITE ALL-<-OF-+-OF-1))
 (3527 72 (:REWRITE ALL-<=-OF-CAR-WHEN-ALL-<=-OF-ALL))
 (3274 736 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (2985 65 (:REWRITE <=-OF-CAR-WHEN-MEMBER-EQUAL-AND-SORTEDP-<=))
 (2843 65 (:REWRITE USE-ALL-<=-FOR-CAR))
 (2555 13 (:REWRITE ALL-RATIONALP-OF-CDR))
 (2316 65 (:REWRITE ALL-<=-ALL-WHEN-NOT-CONSP-ARG2))
 (2052 4 (:REWRITE ALL-<=-OF-CONS))
 (2016 633 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (2015 368 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (2015 368 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (1982 95 (:REWRITE DEFAULT-+-2))
 (1976 26 (:REWRITE NOT-MEMBER-EQUAL-OF-MEMBER-EQUAL-WHEN-NOT-MEMBER-EQUAL))
 (1602 801 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (1423 63 (:REWRITE CONSP-OF-MEMBER-EQUAL-IFF))
 (1258 629 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (1207 313 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (1206 34 (:REWRITE LEN-OF-CDR))
 (1138 30 (:REWRITE <-OF-IF-ARG2))
 (1116 102 (:REWRITE <-OF-CAR-OF-CAR-WHEN-ALL-<-OF-STRIP-CARS))
 (801 801 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (801 801 (:TYPE-PRESCRIPTION DAG-PARENT-ARRAYP))
 (792 26 (:REWRITE SUBSETP-EQUAL-OF-CDR-ARG1))
 (789 34 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (783 783 (:TYPE-PRESCRIPTION ALL-<))
 (696 4 (:REWRITE ALL-<=-ALL-OF-CONS-ARG1))
 (629 629 (:TYPE-PRESCRIPTION DARGP))
 (629 629 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (629 629 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (629 629 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (549 173 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (544 52 (:REWRITE SUBSETP-EQUAL-WHEN-NOT-CONSP-ARG2-CHEAP))
 (536 30 (:REWRITE EQUAL-OF-LEN-AND-0))
 (525 525 (:REWRITE USE-ALL-<-2))
 (525 525 (:REWRITE USE-ALL-<))
 (488 8 (:REWRITE <=-ALL-WHEN-SORTEDP-<=-AND-<=-OF-CAR))
 (472 4 (:REWRITE SORTEDP-<=-WHEN-NOT-CONSP-OF-CDR))
 (424 174 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (383 383 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (352 176 (:REWRITE NOT-MEMBER-EQUAL-WHEN-NOT-MEMBER-EQUAL-OF-CDR-CHEAP))
 (352 176 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-CDR-CHEAP))
 (348 348 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (332 332 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (330 330 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (326 163 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (314 157 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (313 313 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (313 313 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (313 313 (:REWRITE ALL-<-TRANSITIVE))
 (288 8 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (272 26 (:REWRITE INTERSECTION-EQUAL-WHEN-NOT-CONSP-ARG2-CHEAP))
 (251 251 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-WHEN-NOT-EQUAL-CAR))
 (229 190 (:REWRITE MEMBER-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (220 20 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (193 193 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-AUX))
 (176 176 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-2))
 (176 176 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-1))
 (176 176 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-MEMBER-EQUAL))
 (176 176 (:REWRITE MEMBER-EQUAL-OF-SINGLETON-CONSTANT-IFF))
 (176 176 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-TRIM))
 (176 8 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (175 7 (:REWRITE INTEGERP-WHEN-NATP))
 (173 173 (:TYPE-PRESCRIPTION ALL-<=-ALL))
 (173 173 (:REWRITE USE-ALL-<=-2))
 (173 173 (:REWRITE USE-ALL-<=))
 (173 173 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (173 173 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (173 173 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (164 164 (:TYPE-PRESCRIPTION STRIP-CARS))
 (163 163 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (161 161 (:REWRITE USE-ALL-RATIONALP-2))
 (161 161 (:REWRITE USE-ALL-RATIONALP))
 (141 65 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (141 65 (:REWRITE ALL-<=-ALL-WHEN-NOT-CONSP-ARG1))
 (132 66 (:REWRITE ALL-NATP-IMPLIES-ALL-INTEGERP-CHEAP))
 (132 44 (:REWRITE PSEUDO-DAGP-OF-CDR-WHEN-PSEUDO-DAGP))
 (131 131 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (131 131 (:REWRITE STRIP-CARS-WHEN-NOT-CONSP-CHEAP))
 (122 122 (:TYPE-PRESCRIPTION ALL-<=))
 (120 60 (:REWRITE SUBSETP-EQUAL-WHEN-SUBSETP-EQUAL-OF-CDR-CHEAP))
 (120 60 (:REWRITE SUBSETP-EQUAL-OF-CDR-ARG2-CHEAP))
 (120 10 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-OF-CAR))
 (119 119 (:TYPE-PRESCRIPTION ALL-NATP))
 (119 21 (:REWRITE DISJOINTP-ASSUMING-SORTEDP-<=-IFF))
 (108 54 (:REWRITE ALL-<=-ALL-WHEN-ALL-<=-ALL-OF-CDR-ARG2))
 (104 52 (:REWRITE SUBSETP-EQUAL-WHEN-NOT-CONSP-ARG1-CHEAP))
 (98 49 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (96 24 (:REWRITE ALL-<-OF-AREF1-WHEN-BOUNDED-DAG-PARENT-ARRAYP))
 (95 95 (:REWRITE DEFAULT-+-1))
 (88 72 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (87 87 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (85 66 (:REWRITE ALL-INTEGERP-WHEN-NOT-CONSP-CHEAP))
 (72 72 (:REWRITE ALL-<=-MONOTONE))
 (70 54 (:REWRITE ALL-<=-ALL-WHEN-NOT-CONSP-ARG1-CHEAP))
 (60 60 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-ALT))
 (60 60 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-2-ALT))
 (60 10 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-OF-CDR))
 (57 57 (:REWRITE EQUAL-OF-NON-NATP-AND-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (56 8 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (56 8 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (52 26 (:REWRITE INTERSECTION-EQUAL-WHEN-NOT-CONSP-ARG1-CHEAP))
 (52 26 (:REWRITE INTERSECTION-EQUAL-WHEN-MEMBER-EQUAL-OF-CAR-CHEAP))
 (52 26 (:REWRITE INTERSECTION-EQUAL-WHEN-INTERSECTION-EQUAL-OF-CDR-ARG2-CHEAP))
 (52 26 (:REWRITE INTERSECTION-EQUAL-WHEN-INTERSECTION-EQUAL-OF-CDR-ARG1-CHEAP))
 (49 49 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (48 48 (:TYPE-PRESCRIPTION BOUNDED-DAG-PARENT-ARRAYP))
 (47 47 (:REWRITE INTERSECTION-EQUAL-WHEN-MEMBER-EQUAL-AND-MEMBER-EQUAL))
 (42 21 (:REWRITE RATIONAL-LISTP-WHEN-ALL-NATP-CHEAP))
 (40 40 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (40 10 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (33 33 (:REWRITE CONSP-OF-STRIP-CARS))
 (33 11 (:REWRITE ALL-RATIONALP-OF-AREF1-WHEN-CANDIDATE-DEPS-ARRAYP))
 (32 16 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (32 16 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (24 24 (:REWRITE BOUNDED-DAG-PARENT-ARRAYP-MONOTONE))
 (24 24 (:REWRITE ALL-<-OF-AREF1-WHEN-BOUNDED-DAG-PARENT-ENTRIESP))
 (24 4 (:REWRITE ALL-INTEGERP-OF-CONS))
 (22 22 (:TYPE-PRESCRIPTION CANDIDATE-DEPS-ARRAYP))
 (21 21 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (21 7 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-SUBST-CANDIDATE-LISTP))
 (20 20 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (20 20 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (20 20 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (20 20 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL))
 (20 20 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP))
 (16 16 (:TYPE-PRESCRIPTION <=-ALL))
 (16 8 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (16 8 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (15 15 (:TYPE-PRESCRIPTION SORTEDP-<=))
 (10 10 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (10 10 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (8 8 (:REWRITE <=-ALL-TRANS-1))
 (7 7 (:TYPE-PRESCRIPTION NATP))
 (7 7 (:REWRITE SUBST-CANDIDATE-LISTP-OF-CDR))
 (6 6 (:REWRITE ALL-INTEGERP-OF-AREF1-WHEN-ALL-DAG-PARENT-ENTRIESP))
 )
(BOUNDED-DARG-LISTP-OF-STRIP-CADRS-OF-FIND-SIMULTANEOUS-SUBST-CANDIDATES
 (52837 762 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (39959 286 (:REWRITE NOT-MEMBER-EQUAL-WHEN-<-OF-CAR))
 (32044 42 (:REWRITE INTERSECTION-EQUAL-WHEN-NOT-INTERSECTION-EQUAL-OF-CDR-ARG2-IFF))
 (31784 1305 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (31386 15693 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (30573 512 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (26659 85 (:REWRITE NOT-<-OF-CAR-WHEN-ALL-<-2))
 (25377 34 (:REWRITE ALL-<-OF-CONS))
 (20254 390 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (18405 287 (:REWRITE USE-ALL-<-FOR-CAR))
 (17616 423 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (17139 1209 (:REWRITE DEFAULT-<-2))
 (16068 1200 (:REWRITE DEFAULT-<-1))
 (15764 15764 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (14971 261 (:REWRITE DEFAULT-+-2))
 (14200 16 (:REWRITE ALL-<-OF-MERGE-<-AND-REMOVE-DUPS))
 (12568 54 (:REWRITE <-OF-CADR-OF-CAR-WHEN-BOUNDED-DARG-LISTP-OF-STRIP-CADRS))
 (10574 125 (:REWRITE ALL-<-OF-+-OF-1))
 (8344 21 (:REWRITE NOT-MEMBER-EQUAL-OF-CDR-WHEN-NOT-MEMBER-EQUAL))
 (7910 153 (:REWRITE <-OF-CAR-OF-CAR-WHEN-ALL-<-OF-STRIP-CARS))
 (7848 1890 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (6208 8 (:REWRITE ALL-INTEGERP-OF-STRIP-CARS-WHEN-WEAK-DAGP-AUX))
 (6104 16 (:DEFINITION WEAK-DAGP-AUX))
 (5960 2552 (:TYPE-PRESCRIPTION NATP-OF-CAR-OF-CAR-WHEN-SUBST-CANDIDATE-LISTP))
 (5492 64 (:REWRITE DARGP-LESS-THAN-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (5465 33 (:REWRITE ALL-RATIONALP-OF-CDR))
 (4714 913 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (4714 913 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (4160 32 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX-2))
 (4065 85 (:REWRITE <=-OF-CAR-WHEN-MEMBER-EQUAL-AND-SORTEDP-<=))
 (3600 1392 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (3550 97 (:REWRITE <-OF-IF-ARG2))
 (3504 32 (:REWRITE PSEUDO-DAGP-AUX-OF-CDR))
 (3437 42 (:REWRITE NOT-MEMBER-EQUAL-OF-MEMBER-EQUAL-WHEN-NOT-MEMBER-EQUAL))
 (3211 61 (:REWRITE ALL-<-OF-CDR))
 (2941 143 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (2890 762 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (2805 85 (:REWRITE USE-ALL-<=-FOR-CAR))
 (2780 1390 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (2706 2706 (:TYPE-PRESCRIPTION SUBST-CANDIDATE-LISTP))
 (2612 1306 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-AREF1-WHEN-DAG-PARENT-ARRAYP))
 (2584 70 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (2468 30 (:REWRITE INTEGERP-WHEN-NATP))
 (2295 85 (:REWRITE ALL-<=-OF-CAR-WHEN-ALL-<=-OF-ALL))
 (2028 90 (:REWRITE CONSP-OF-MEMBER-EQUAL-IFF))
 (1700 85 (:REWRITE ALL-<=-ALL-WHEN-NOT-CONSP-ARG2))
 (1638 71 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (1609 151 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (1560 8 (:REWRITE ALL-INTEGERP-OF-CONS))
 (1545 111 (:REWRITE EQUAL-OF-LEN-AND-0))
 (1498 423 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (1465 634 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (1458 1392 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (1392 1392 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (1392 1392 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (1390 1390 (:TYPE-PRESCRIPTION DARGP))
 (1344 42 (:REWRITE SUBSETP-EQUAL-OF-CDR-ARG1))
 (1306 1306 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (1306 1306 (:TYPE-PRESCRIPTION DAG-PARENT-ARRAYP))
 (1305 1305 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (1209 1209 (:REWRITE USE-ALL-<-2))
 (1209 1209 (:REWRITE USE-ALL-<))
 (1008 84 (:REWRITE SUBSETP-EQUAL-WHEN-NOT-CONSP-ARG2-CHEAP))
 (960 24 (:REWRITE BOUNDED-DARG-LISTP-OF-CDR))
 (848 64 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-CAR-AND-QUOTE))
 (846 846 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (844 844 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (792 8 (:REWRITE RATIONALP-OF-IF-STRONG))
 (777 777 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (777 777 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (777 777 (:REWRITE ALL-<-TRANSITIVE))
 (667 71 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (634 634 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (634 634 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (634 634 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (574 287 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (518 259 (:REWRITE NOT-MEMBER-EQUAL-WHEN-NOT-MEMBER-EQUAL-OF-CDR-CHEAP))
 (518 259 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-CDR-CHEAP))
 (504 42 (:REWRITE INTERSECTION-EQUAL-WHEN-NOT-CONSP-ARG2-CHEAP))
 (504 32 (:DEFINITION TOP-NODENUM))
 (471 223 (:REWRITE LEN-OF-CADR-WHEN-SUBST-CANDIDATEP))
 (456 228 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (456 228 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (427 427 (:REWRITE USE-ALL-RATIONALP-2))
 (427 427 (:REWRITE USE-ALL-RATIONALP))
 (409 147 (:REWRITE PSEUDO-DAGP-OF-CDR-WHEN-PSEUDO-DAGP))
 (384 192 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (362 362 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-WHEN-NOT-EQUAL-CAR))
 (340 277 (:REWRITE MEMBER-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (336 64 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (328 64 (:REWRITE DARGP-LESS-THAN-WHEN-NATP-CHEAP))
 (324 9 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (320 8 (:REWRITE ALL-NATP-OF-CDR))
 (296 296 (:TYPE-PRESCRIPTION FIND-SIMULTANEOUS-SUBST-CANDIDATES))
 (290 88 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (266 25 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (261 261 (:REWRITE DEFAULT-+-1))
 (259 259 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-2))
 (259 259 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-1))
 (259 259 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-MEMBER-EQUAL))
 (259 259 (:REWRITE MEMBER-EQUAL-OF-SINGLETON-CONSTANT-IFF))
 (259 259 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-TRIM))
 (255 255 (:TYPE-PRESCRIPTION ALL-<=-ALL))
 (250 250 (:REWRITE USE-ALL-<=-2))
 (250 250 (:REWRITE USE-ALL-<=))
 (247 247 (:TYPE-PRESCRIPTION STRIP-CARS))
 (246 246 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (232 71 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (229 229 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-AUX))
 (228 228 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (221 221 (:TYPE-PRESCRIPTION SUBST-CANDIDATEP))
 (218 218 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (210 105 (:REWRITE ALL-NATP-IMPLIES-ALL-INTEGERP-CHEAP))
 (204 46 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-SUBST-CANDIDATE-LISTP))
 (192 192 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (192 192 (:REWRITE STRIP-CARS-WHEN-NOT-CONSP-CHEAP))
 (192 32 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP))
 (186 93 (:REWRITE SUBSETP-EQUAL-WHEN-SUBSETP-EQUAL-OF-CDR-CHEAP))
 (186 93 (:REWRITE SUBSETP-EQUAL-OF-CDR-ARG2-CHEAP))
 (176 88 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (173 31 (:REWRITE DISJOINTP-ASSUMING-SORTEDP-<=-IFF))
 (170 170 (:TYPE-PRESCRIPTION ALL-<=))
 (170 85 (:REWRITE ALL-<=-ALL-WHEN-ALL-<=-ALL-OF-CDR-ARG2))
 (168 84 (:REWRITE SUBSETP-EQUAL-WHEN-NOT-CONSP-ARG1-CHEAP))
 (158 79 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (151 105 (:REWRITE ALL-INTEGERP-WHEN-NOT-CONSP-CHEAP))
 (150 150 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (144 144 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (144 12 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-OF-CAR))
 (142 71 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (134 134 (:TYPE-PRESCRIPTION WEAK-DAGP-AUX))
 (128 64 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (120 120 (:TYPE-PRESCRIPTION NATP))
 (116 29 (:REWRITE ALL-<-OF-AREF1-WHEN-BOUNDED-DAG-PARENT-ARRAYP))
 (93 93 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-ALT))
 (93 93 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-2-ALT))
 (93 93 (:REWRITE EQUAL-OF-NON-NATP-AND-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (88 88 (:TYPE-PRESCRIPTION MYQUOTEP))
 (85 85 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (85 85 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (85 85 (:REWRITE ALL-<=-MONOTONE))
 (85 85 (:REWRITE ALL-<=-ALL-WHEN-NOT-CONSP-ARG1-CHEAP))
 (85 85 (:REWRITE ALL-<=-ALL-WHEN-NOT-CONSP-ARG1))
 (84 42 (:REWRITE INTERSECTION-EQUAL-WHEN-NOT-CONSP-ARG1-CHEAP))
 (84 42 (:REWRITE INTERSECTION-EQUAL-WHEN-MEMBER-EQUAL-OF-CAR-CHEAP))
 (84 42 (:REWRITE INTERSECTION-EQUAL-WHEN-INTERSECTION-EQUAL-OF-CDR-ARG2-CHEAP))
 (84 42 (:REWRITE INTERSECTION-EQUAL-WHEN-INTERSECTION-EQUAL-OF-CDR-ARG1-CHEAP))
 (80 8 (:REWRITE NAT-LISTP-OF-CDR))
 (79 79 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (72 72 (:REWRITE INTERSECTION-EQUAL-WHEN-MEMBER-EQUAL-AND-MEMBER-EQUAL))
 (72 12 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-OF-CDR))
 (70 70 (:REWRITE USE-ALL-NATP-2))
 (70 70 (:REWRITE USE-ALL-NATP))
 (68 68 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (66 22 (:REWRITE SUBST-CANDIDATE-LISTP-OF-CDR))
 (64 64 (:REWRITE DARGP-LESS-THAN-WHEN-QUOTEP-CHEAP))
 (64 64 (:REWRITE DARGP-LESS-THAN-MONO))
 (64 2 (:LINEAR LEN-OF-CDR-LINEAR-STRONG))
 (63 9 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (62 31 (:REWRITE RATIONAL-LISTP-WHEN-ALL-NATP-CHEAP))
 (60 30 (:REWRITE INTEGERP-OF-CAR-WHEN-NAT-LISTP-CHEAP))
 (60 30 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (60 30 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (60 30 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-CHEAP))
 (60 30 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-AUX-CHEAP))
 (60 2 (:LINEAR LEN-OF-CDR-LINEAR))
 (58 58 (:TYPE-PRESCRIPTION BOUNDED-DAG-PARENT-ARRAYP))
 (56 24 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (48 48 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (48 48 (:TYPE-PRESCRIPTION BOUNDED-DAG-EXPRP))
 (48 24 (:REWRITE WEAK-DAGP-AUX-OF-CDR))
 (48 24 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (48 24 (:REWRITE BOUNDED-DAG-EXPRP-OF-CDR-OF-CAR-WHEN-WEAK-DAGP-AUX))
 (48 12 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (47 47 (:REWRITE CONSP-OF-STRIP-CARS))
 (46 46 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (39 13 (:REWRITE ALL-RATIONALP-OF-AREF1-WHEN-CANDIDATE-DEPS-ARRAYP))
 (32 32 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (30 30 (:TYPE-PRESCRIPTION WEAK-DAGP))
 (30 30 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (30 30 (:REWRITE INTEGERP-OF-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (29 29 (:REWRITE BOUNDED-DAG-PARENT-ARRAYP-MONOTONE))
 (29 29 (:REWRITE ALL-<-OF-AREF1-WHEN-BOUNDED-DAG-PARENT-ENTRIESP))
 (27 9 (:REWRITE SUBST-CANDIDATEP-OF-CAR))
 (26 26 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (26 26 (:TYPE-PRESCRIPTION CANDIDATE-DEPS-ARRAYP))
 (24 24 (:REWRITE PSEUDO-DAGP-AUX-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (24 24 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (24 24 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL))
 (24 24 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP))
 (24 24 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (24 24 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 (24 24 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP-CHEAP))
 (24 24 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP-CHEAP))
 (24 24 (:REWRITE BOUNDED-DAG-EXPRP-MONOTONE))
 (24 8 (:REWRITE +-COMBINE-CONSTANTS))
 (16 16 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (16 16 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (12 12 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (9 9 (:TYPE-PRESCRIPTION SORTEDP-<=))
 (8 8 (:REWRITE LEN-OF-CDDR-WHEN-EQUAL-OF-LEN))
 (8 8 (:REWRITE ALL-INTEGERP-OF-AREF1-WHEN-ALL-DAG-PARENT-ENTRIESP))
 )
(SUBSETP-EQUAL-OF-STRIP-CADDRS-OF-FIND-SIMULTANEOUS-SUBST-CANDIDATES
 (48639 348 (:REWRITE NOT-MEMBER-EQUAL-WHEN-<-OF-CAR))
 (35506 50 (:REWRITE INTERSECTION-EQUAL-WHEN-NOT-INTERSECTION-EQUAL-OF-CDR-ARG2-IFF))
 (34522 553 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (31330 15665 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (31311 101 (:REWRITE NOT-<-OF-CAR-WHEN-ALL-<-2))
 (22764 922 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (22666 452 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (19634 489 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (19090 1016 (:REWRITE DEFAULT-<-2))
 (17380 1005 (:REWRITE DEFAULT-<-1))
 (17275 282 (:REWRITE USE-ALL-<-FOR-CAR))
 (17184 235 (:REWRITE DEFAULT-+-2))
 (16554 20 (:REWRITE ALL-<-OF-MERGE-<-AND-REMOVE-DUPS))
 (15750 15750 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (14340 568 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (12086 10 (:REWRITE ALL-<-OF-CONS))
 (11882 151 (:REWRITE ALL-<-OF-+-OF-1))
 (9448 25 (:REWRITE NOT-MEMBER-EQUAL-OF-CDR-WHEN-NOT-MEMBER-EQUAL))
 (8678 179 (:REWRITE <-OF-CAR-OF-CAR-WHEN-ALL-<-OF-STRIP-CARS))
 (6640 10 (:REWRITE ALL-INTEGERP-OF-STRIP-CARS-WHEN-WEAK-DAGP-AUX))
 (6624 1468 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (6508 18 (:DEFINITION WEAK-DAGP-AUX))
 (5641 37 (:REWRITE ALL-RATIONALP-OF-CDR))
 (5464 2732 (:TYPE-PRESCRIPTION NATP-OF-CAR-OF-CAR-WHEN-SUBST-CANDIDATE-LISTP))
 (4945 101 (:REWRITE <=-OF-CAR-WHEN-MEMBER-EQUAL-AND-SORTEDP-<=))
 (4416 36 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX-2))
 (4067 734 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (4067 734 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (3849 50 (:REWRITE NOT-MEMBER-EQUAL-OF-MEMBER-EQUAL-WHEN-NOT-MEMBER-EQUAL))
 (3732 34 (:REWRITE PSEUDO-DAGP-AUX-OF-CDR))
 (3333 101 (:REWRITE USE-ALL-<=-FOR-CAR))
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 (2434 108 (:REWRITE CONSP-OF-MEMBER-EQUAL-IFF))
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 (1950 10 (:REWRITE ALL-INTEGERP-OF-CONS))
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 (1080 1080 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (1080 1080 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (1016 1016 (:REWRITE USE-ALL-<-2))
 (1016 1016 (:REWRITE USE-ALL-<))
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 (922 922 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (922 922 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
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 (716 358 (:REWRITE SUBSETP-EQUAL-OF-CDR-ARG2-CHEAP))
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 (662 331 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-CDR-CHEAP))
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 (636 318 (:REWRITE SUBSETP-EQUAL-WHEN-SUBSETP-EQUAL-OF-CDR-CHEAP))
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 (603 603 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (603 603 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (584 584 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (584 584 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (584 584 (:REWRITE ALL-<-TRANSITIVE))
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 (564 282 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
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 (452 452 (:REWRITE USE-ALL-RATIONALP-2))
 (452 452 (:REWRITE USE-ALL-RATIONALP))
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 (331 331 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-2))
 (331 331 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-MEMBER-EQUAL))
 (331 331 (:REWRITE MEMBER-EQUAL-OF-SINGLETON-CONSTANT-IFF))
 (331 331 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-TRIM))
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 (308 308 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
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 (306 306 (:REWRITE USE-ALL-<=))
 (303 303 (:TYPE-PRESCRIPTION ALL-<=-ALL))
 (300 300 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (258 129 (:REWRITE ALL-NATP-IMPLIES-ALL-INTEGERP-CHEAP))
 (240 20 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-OF-CAR))
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 (235 235 (:REWRITE DEFAULT-+-1))
 (228 52 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-SUBST-CANDIDATE-LISTP))
 (226 226 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (210 36 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP))
 (207 37 (:REWRITE DISJOINTP-ASSUMING-SORTEDP-<=-IFF))
 (202 202 (:TYPE-PRESCRIPTION ALL-<=))
 (202 101 (:REWRITE ALL-<=-ALL-WHEN-ALL-<=-ALL-OF-CDR-ARG2))
 (200 74 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (196 98 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (191 129 (:REWRITE ALL-INTEGERP-WHEN-NOT-CONSP-CHEAP))
 (188 47 (:REWRITE ALL-<-OF-AREF1-WHEN-BOUNDED-DAG-PARENT-ARRAYP))
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 (172 172 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
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 (148 74 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (126 63 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (120 20 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-OF-CDR))
 (101 101 (:REWRITE EQUAL-OF-NON-NATP-AND-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (101 101 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (101 101 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (101 101 (:REWRITE ALL-<=-MONOTONE))
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 (101 101 (:REWRITE ALL-<=-ALL-WHEN-NOT-CONSP-ARG1))
 (100 50 (:REWRITE INTERSECTION-EQUAL-WHEN-NOT-CONSP-ARG1-CHEAP))
 (100 50 (:REWRITE INTERSECTION-EQUAL-WHEN-MEMBER-EQUAL-OF-CAR-CHEAP))
 (100 50 (:REWRITE INTERSECTION-EQUAL-WHEN-INTERSECTION-EQUAL-OF-CDR-ARG2-CHEAP))
 (100 50 (:REWRITE INTERSECTION-EQUAL-WHEN-INTERSECTION-EQUAL-OF-CDR-ARG1-CHEAP))
 (98 98 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (94 94 (:TYPE-PRESCRIPTION BOUNDED-DAG-PARENT-ARRAYP))
 (84 84 (:REWRITE INTERSECTION-EQUAL-WHEN-MEMBER-EQUAL-AND-MEMBER-EQUAL))
 (82 82 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (80 80 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (80 20 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (78 78 (:TYPE-PRESCRIPTION NATP))
 (77 11 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (74 37 (:REWRITE RATIONAL-LISTP-WHEN-ALL-NATP-CHEAP))
 (72 36 (:REWRITE INTEGERP-OF-CAR-WHEN-NAT-LISTP-CHEAP))
 (72 36 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (72 36 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (72 36 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-CHEAP))
 (72 36 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-AUX-CHEAP))
 (72 24 (:REWRITE SUBST-CANDIDATE-LISTP-OF-CDR))
 (67 67 (:REWRITE CONSP-OF-STRIP-CARS))
 (67 67 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (63 21 (:REWRITE ALL-RATIONALP-OF-AREF1-WHEN-CANDIDATE-DEPS-ARRAYP))
 (58 26 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (52 52 (:TYPE-PRESCRIPTION BOUNDED-DAG-EXPRP))
 (52 52 (:REWRITE USE-ALL-NATP-2))
 (52 52 (:REWRITE USE-ALL-NATP))
 (52 52 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (52 26 (:REWRITE WEAK-DAGP-AUX-OF-CDR))
 (52 26 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (52 26 (:REWRITE BOUNDED-DAG-EXPRP-OF-CDR-OF-CAR-WHEN-WEAK-DAGP-AUX))
 (47 47 (:REWRITE BOUNDED-DAG-PARENT-ARRAYP-MONOTONE))
 (47 47 (:REWRITE ALL-<-OF-AREF1-WHEN-BOUNDED-DAG-PARENT-ENTRIESP))
 (42 42 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (42 42 (:TYPE-PRESCRIPTION CANDIDATE-DEPS-ARRAYP))
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 (40 40 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL))
 (40 40 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP))
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 (36 36 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (36 36 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (36 36 (:REWRITE INTEGERP-OF-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (28 28 (:REWRITE PSEUDO-DAGP-AUX-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (26 26 (:TYPE-PRESCRIPTION MYQUOTEP))
 (26 26 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP-CHEAP))
 (26 26 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP-CHEAP))
 (26 26 (:REWRITE BOUNDED-DAG-EXPRP-MONOTONE))
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 (20 20 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (20 20 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
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 (14 14 (:REWRITE ALL-INTEGERP-OF-AREF1-WHEN-ALL-DAG-PARENT-ENTRIESP))
 (11 11 (:TYPE-PRESCRIPTION SORTEDP-<=))
 (8 8 (:DEFINITION FIX))
 )
(DROP-IRRELEVANT-SUBST-CANDIDATES
 (277 155 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (277 155 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (130 130 (:TYPE-PRESCRIPTION NAT-LISTP))
 (122 122 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (101 4 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (90 8 (:REWRITE NOT-<-OF-CAR-WHEN-ALL-<-2))
 (61 8 (:REWRITE <=-OF-CAR-WHEN-MEMBER-EQUAL-AND-SORTEDP-<=))
 (60 1 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (56 12 (:REWRITE DEFAULT-<-2))
 (41 1 (:REWRITE MEMBER-EQUAL-WHEN-<=-OF-LEN-AND-1))
 (40 8 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (36 8 (:REWRITE USE-ALL-<=-FOR-CAR))
 (24 4 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (24 4 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (22 4 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (20 1 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (17 5 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (12 12 (:REWRITE USE-ALL-<-2))
 (12 12 (:REWRITE USE-ALL-<))
 (12 12 (:REWRITE DEFAULT-<-1))
 (10 5 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (10 1 (:REWRITE ALL-<-OF-+-OF-1))
 (9 9 (:REWRITE USE-ALL-<=-2))
 (9 9 (:REWRITE USE-ALL-<=))
 (7 3 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (5 5 (:TYPE-PRESCRIPTION DARGP))
 (5 5 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (5 5 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (5 5 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (5 1 (:REWRITE ALL-INTEGERP-WHEN-NOT-CONSP-CHEAP))
 (5 1 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (5 1 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (4 4 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (4 4 (:REWRITE CONSP-WHEN-LEN-GREATER))
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 (3 3 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
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 (2 1 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-CDR-CHEAP))
 (2 1 (:REWRITE ALL-NATP-IMPLIES-ALL-INTEGERP-CHEAP))
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 (1 1 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-TRIM))
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 (1 1 (:REWRITE DEFAULT-+-1))
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 (1 1 (:REWRITE ALL-<=-MONOTONE))
 (1 1 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (1 1 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (1 1 (:REWRITE ALL-<-TRANSITIVE))
 )
(SUBST-CANDIDATE-LISTP-OF-DROP-IRRELEVANT-SUBST-CANDIDATES
 (824 412 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (824 412 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
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 (452 452 (:TYPE-PRESCRIPTION NAT-LISTP))
 (420 7 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (415 20 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (412 412 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (378 7 (:REWRITE <=-OF-CAR-WHEN-MEMBER-EQUAL-AND-SORTEDP-<=))
 (287 7 (:REWRITE MEMBER-EQUAL-WHEN-<=-OF-LEN-AND-1))
 (203 7 (:REWRITE USE-ALL-<=-FOR-CAR))
 (192 40 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (140 7 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (116 20 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (116 20 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (82 27 (:REWRITE DEFAULT-<-2))
 (79 23 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (70 7 (:REWRITE ALL-<-OF-+-OF-1))
 (46 23 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (35 7 (:REWRITE ALL-INTEGERP-WHEN-NOT-CONSP-CHEAP))
 (35 7 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (35 7 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (34 27 (:REWRITE DEFAULT-<-1))
 (28 28 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (28 14 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (28 14 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (28 7 (:REWRITE DEFAULT-+-2))
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 (27 27 (:REWRITE USE-ALL-<))
 (23 23 (:TYPE-PRESCRIPTION DARGP))
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 (23 23 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (23 23 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (20 20 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (20 20 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (14 14 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (14 14 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (14 14 (:TYPE-PRESCRIPTION ALL-<=))
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 (14 14 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
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 (14 14 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
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 (7 7 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-1))
 (7 7 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-MEMBER-EQUAL))
 (7 7 (:REWRITE MEMBER-EQUAL-OF-SINGLETON-CONSTANT-IFF))
 (7 7 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-WHEN-NOT-EQUAL-CAR))
 (7 7 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-TRIM))
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 (7 7 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (7 7 (:REWRITE ALL-<=-MONOTONE))
 (7 7 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (7 7 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (7 7 (:REWRITE ALL-<-TRANSITIVE))
 )
(ALL-<=-OF-STRIP-CARS-OF-DROP-IRRELEVANT-SUBST-CANDIDATES
 (1140 570 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (1140 570 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (946 11 (:REWRITE NOT-<-OF-CAR-WHEN-ALL-<-2))
 (900 21 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (839 39 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (660 11 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (654 654 (:TYPE-PRESCRIPTION NAT-LISTP))
 (594 11 (:REWRITE <=-OF-CAR-WHEN-MEMBER-EQUAL-AND-SORTEDP-<=))
 (570 570 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (537 14 (:REWRITE MEMBER-EQUAL-WHEN-<=-OF-LEN-AND-1))
 (354 84 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (319 11 (:REWRITE USE-ALL-<=-FOR-CAR))
 (228 9 (:REWRITE CONSP-OF-STRIP-CARS))
 (219 42 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (219 42 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (150 53 (:REWRITE DEFAULT-<-2))
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 (136 14 (:REWRITE NOT-ALL-<=-WHEN-<-AND-MEMBER-EQUAL))
 (110 11 (:REWRITE ALL-<-OF-+-OF-1))
 (92 46 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (75 21 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (64 53 (:REWRITE DEFAULT-<-1))
 (56 56 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (55 25 (:REWRITE USE-ALL-<=))
 (55 11 (:REWRITE ALL-INTEGERP-WHEN-NOT-CONSP-CHEAP))
 (55 11 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (53 53 (:REWRITE USE-ALL-<-2))
 (53 53 (:REWRITE USE-ALL-<))
 (46 46 (:TYPE-PRESCRIPTION DARGP))
 (46 46 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (46 46 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (46 46 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (44 22 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (44 22 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
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 (39 39 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (37 37 (:TYPE-PRESCRIPTION DROP-IRRELEVANT-SUBST-CANDIDATES))
 (32 22 (:REWRITE STRIP-CARS-WHEN-NOT-CONSP-CHEAP))
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 (28 14 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-CDR-CHEAP))
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 (22 22 (:TYPE-PRESCRIPTION ALL-INTEGERP))
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 (22 22 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (22 22 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
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 (14 14 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-MEMBER-EQUAL))
 (14 14 (:REWRITE MEMBER-EQUAL-OF-SINGLETON-CONSTANT-IFF))
 (14 14 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-WHEN-NOT-EQUAL-CAR))
 (14 14 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-TRIM))
 (11 11 (:TYPE-PRESCRIPTION ALL-NATP))
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 (11 11 (:REWRITE USE-ALL-RATIONALP))
 (11 11 (:REWRITE DEFAULT-+-1))
 (11 11 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (11 11 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (11 11 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (11 11 (:REWRITE ALL-<-TRANSITIVE))
 )
(ALL-<-OF-STRIP-CARS-OF-DROP-IRRELEVANT-SUBST-CANDIDATES
 (4100 64 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (3504 1752 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (3504 1752 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (2576 125 (:REWRITE DEFAULT-<-2))
 (2260 26 (:REWRITE NOT-<-OF-CAR-WHEN-ALL-<-2))
 (2246 125 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (1950 1950 (:TYPE-PRESCRIPTION NAT-LISTP))
 (1752 1752 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (1690 78 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (1404 26 (:REWRITE <=-OF-CAR-WHEN-MEMBER-EQUAL-AND-SORTEDP-<=))
 (1180 590 (:TYPE-PRESCRIPTION NATP-OF-CAR-OF-CAR-WHEN-SUBST-CANDIDATE-LISTP))
 (1066 26 (:REWRITE MEMBER-EQUAL-WHEN-<=-OF-LEN-AND-1))
 (824 198 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (754 26 (:REWRITE USE-ALL-<=-FOR-CAR))
 (744 37 (:REWRITE CONSP-OF-STRIP-CARS))
 (728 26 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (590 590 (:TYPE-PRESCRIPTION SUBST-CANDIDATE-LISTP))
 (520 26 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (520 26 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (511 99 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (511 99 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (353 85 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (336 122 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (260 26 (:REWRITE ALL-<-OF-+-OF-1))
 (244 122 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (210 14 (:REWRITE LEN-OF-CDR))
 (206 64 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (168 14 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (154 78 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (151 125 (:REWRITE DEFAULT-<-1))
 (130 26 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (130 26 (:REWRITE ALL-INTEGERP-WHEN-NOT-CONSP-CHEAP))
 (130 26 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (125 125 (:REWRITE USE-ALL-<-2))
 (125 125 (:REWRITE USE-ALL-<))
 (125 125 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (125 125 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (122 122 (:TYPE-PRESCRIPTION DARGP))
 (122 122 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (122 122 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (122 122 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (118 40 (:REWRITE DEFAULT-+-2))
 (104 104 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (78 78 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (78 78 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (78 78 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (77 69 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (69 69 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (68 68 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (62 62 (:TYPE-PRESCRIPTION DROP-IRRELEVANT-SUBST-CANDIDATES))
 (56 56 (:REWRITE USE-ALL-RATIONALP-2))
 (56 56 (:REWRITE USE-ALL-RATIONALP))
 (52 52 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (52 52 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (52 52 (:TYPE-PRESCRIPTION ALL-<=))
 (52 52 (:REWRITE USE-ALL-<=-2))
 (52 52 (:REWRITE USE-ALL-<=))
 (52 26 (:REWRITE NOT-MEMBER-EQUAL-WHEN-NOT-MEMBER-EQUAL-OF-CDR-CHEAP))
 (52 26 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-CDR-CHEAP))
 (52 26 (:REWRITE ALL-NATP-IMPLIES-ALL-INTEGERP-CHEAP))
 (40 40 (:REWRITE DEFAULT-+-1))
 (39 39 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (39 39 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (27 27 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (26 26 (:TYPE-PRESCRIPTION ALL-NATP))
 (26 26 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-2))
 (26 26 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-1))
 (26 26 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-MEMBER-EQUAL))
 (26 26 (:REWRITE MEMBER-EQUAL-OF-SINGLETON-CONSTANT-IFF))
 (26 26 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-WHEN-NOT-EQUAL-CAR))
 (26 26 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-TRIM))
 (26 26 (:REWRITE ALL-<=-MONOTONE))
 (24 8 (:REWRITE PSEUDO-DAGP-OF-CDR-WHEN-PSEUDO-DAGP))
 (14 14 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 )
(ALL-<-OF-STRIP-CARS-OF-DROP-IRRELEVANT-SUBST-CANDIDATES-2
 (1559 27 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (1470 735 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (1470 735 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (910 56 (:REWRITE DEFAULT-<-2))
 (904 51 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (813 813 (:TYPE-PRESCRIPTION NAT-LISTP))
 (747 9 (:REWRITE NOT-<-OF-CAR-WHEN-ALL-<-2))
 (735 735 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (610 10 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (534 267 (:TYPE-PRESCRIPTION NATP-OF-CAR-OF-CAR-WHEN-SUBST-CANDIDATE-LISTP))
 (486 9 (:REWRITE <=-OF-CAR-WHEN-MEMBER-EQUAL-AND-SORTEDP-<=))
 (413 16 (:REWRITE CONSP-OF-STRIP-CARS))
 (369 9 (:REWRITE MEMBER-EQUAL-WHEN-<=-OF-LEN-AND-1))
 (314 78 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (280 10 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (267 267 (:TYPE-PRESCRIPTION SUBST-CANDIDATE-LISTP))
 (262 6 (:REWRITE ALL-<-OF-STRIP-CARS-OF-DROP-IRRELEVANT-SUBST-CANDIDATES))
 (261 9 (:REWRITE USE-ALL-<=-FOR-CAR))
 (200 10 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (196 39 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (196 39 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (180 9 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (147 56 (:REWRITE DEFAULT-<-1))
 (125 46 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (92 46 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (90 9 (:REWRITE ALL-<-OF-+-OF-1))
 (84 27 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (74 56 (:REWRITE USE-ALL-<))
 (72 2 (:REWRITE USE-ALL-<-FOR-CAR))
 (60 4 (:REWRITE LEN-OF-CDR))
 (56 56 (:REWRITE USE-ALL-<-2))
 (51 51 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (51 51 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (50 10 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (49 29 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (48 4 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (46 46 (:TYPE-PRESCRIPTION DARGP))
 (46 46 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (46 46 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (46 46 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (46 36 (:REWRITE STRIP-CARS-WHEN-NOT-CONSP-CHEAP))
 (45 9 (:REWRITE ALL-INTEGERP-WHEN-NOT-CONSP-CHEAP))
 (45 9 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (36 36 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (31 31 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (29 29 (:TYPE-PRESCRIPTION DROP-IRRELEVANT-SUBST-CANDIDATES))
 (29 29 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (29 29 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (29 29 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (27 27 (:REWRITE ALL-<-TRANSITIVE))
 (26 26 (:REWRITE USE-ALL-<=-2))
 (26 26 (:REWRITE USE-ALL-<=))
 (20 20 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (20 20 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (18 18 (:TYPE-PRESCRIPTION MEMBERP))
 (18 18 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (18 18 (:TYPE-PRESCRIPTION ALL-<=))
 (18 9 (:REWRITE NOT-MEMBER-EQUAL-WHEN-NOT-MEMBER-EQUAL-OF-CDR-CHEAP))
 (18 9 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-CDR-CHEAP))
 (18 9 (:REWRITE ALL-NATP-IMPLIES-ALL-INTEGERP-CHEAP))
 (15 2 (:REWRITE <-OF-CAR-OF-CAR-WHEN-ALL-<-OF-STRIP-CARS))
 (13 13 (:REWRITE DEFAULT-+-2))
 (13 13 (:REWRITE DEFAULT-+-1))
 (12 12 (:REWRITE USE-ALL-NATP-2))
 (12 12 (:REWRITE USE-ALL-NATP))
 (10 10 (:REWRITE USE-ALL-RATIONALP-2))
 (10 10 (:REWRITE USE-ALL-RATIONALP))
 (10 10 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (10 10 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (10 10 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (9 9 (:TYPE-PRESCRIPTION ALL-NATP))
 (9 9 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-2))
 (9 9 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-1))
 (9 9 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-MEMBER-EQUAL))
 (9 9 (:REWRITE MEMBER-EQUAL-OF-SINGLETON-CONSTANT-IFF))
 (9 9 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-WHEN-NOT-EQUAL-CAR))
 (9 9 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-TRIM))
 (9 9 (:REWRITE ALL-<=-MONOTONE))
 (4 4 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (4 2 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 )
(BOUNDED-DARG-LISTP-OF-STRIP-CADRS-OF-DROP-IRRELEVANT-SUBST-CANDIDATES
 (3310 68 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (3229 5 (:REWRITE ALL-<-OF-CONS))
 (2948 150 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (2688 1344 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (1714 5 (:REWRITE <-OF-CADR-OF-CAR-WHEN-BOUNDED-DARG-LISTP-OF-STRIP-CADRS))
 (1344 1344 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (1036 12 (:REWRITE DARGP-LESS-THAN-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (946 11 (:REWRITE NOT-<-OF-CAR-WHEN-ALL-<-2))
 (870 214 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (768 117 (:REWRITE DEFAULT-<-1))
 (594 11 (:REWRITE <=-OF-CAR-WHEN-MEMBER-EQUAL-AND-SORTEDP-<=))
 (519 32 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (452 101 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (452 101 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (451 11 (:REWRITE MEMBER-EQUAL-WHEN-<=-OF-LEN-AND-1))
 (359 9 (:REWRITE ALL-<-OF-CDR))
 (323 33 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (319 11 (:REWRITE USE-ALL-<=-FOR-CAR))
 (316 123 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (288 117 (:REWRITE DEFAULT-<-2))
 (276 12 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-CAR-AND-QUOTE))
 (265 5 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (246 123 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (244 5 (:REWRITE USE-ALL-<-FOR-CAR))
 (223 68 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (220 11 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (210 5 (:REWRITE LEN-OF-CDR))
 (200 5 (:REWRITE <-OF-IF-ARG2))
 (185 10 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (180 12 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (168 12 (:REWRITE DARGP-LESS-THAN-WHEN-NATP-CHEAP))
 (160 4 (:REWRITE BOUNDED-DARG-LISTP-OF-CDR))
 (156 12 (:REWRITE DARGP-LESS-THAN-WHEN-NOT-CONSP-CHEAP))
 (156 12 (:REWRITE DARGP-LESS-THAN-WHEN-CONSP-CHEAP))
 (150 150 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (149 149 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (140 5 (:REWRITE ALL-RATIONALP-OF-CDR))
 (123 123 (:TYPE-PRESCRIPTION DARGP))
 (123 123 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (123 123 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (123 123 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (120 5 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (117 117 (:REWRITE USE-ALL-<-2))
 (117 117 (:REWRITE USE-ALL-<))
 (110 11 (:REWRITE ALL-<-OF-+-OF-1))
 (100 50 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (100 50 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (85 5 (:REWRITE EQUAL-OF-LEN-AND-0))
 (73 41 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (69 69 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (69 69 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (69 69 (:REWRITE ALL-<-TRANSITIVE))
 (55 11 (:REWRITE ALL-INTEGERP-WHEN-NOT-CONSP-CHEAP))
 (55 11 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (54 16 (:REWRITE DEFAULT-+-2))
 (52 52 (:TYPE-PRESCRIPTION DROP-IRRELEVANT-SUBST-CANDIDATES))
 (50 50 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (50 10 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (44 44 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (41 41 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (41 41 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (41 41 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (32 32 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (24 12 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (22 22 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (22 22 (:TYPE-PRESCRIPTION ALL-<=))
 (22 22 (:REWRITE USE-ALL-<=-2))
 (22 22 (:REWRITE USE-ALL-<=))
 (22 11 (:REWRITE NOT-MEMBER-EQUAL-WHEN-NOT-MEMBER-EQUAL-OF-CDR-CHEAP))
 (22 11 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-CDR-CHEAP))
 (22 11 (:REWRITE ALL-NATP-IMPLIES-ALL-INTEGERP-CHEAP))
 (21 21 (:REWRITE USE-ALL-RATIONALP-2))
 (21 21 (:REWRITE USE-ALL-RATIONALP))
 (20 20 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (16 16 (:REWRITE DEFAULT-+-1))
 (14 14 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (12 12 (:TYPE-PRESCRIPTION NATP))
 (12 12 (:TYPE-PRESCRIPTION MYQUOTEP))
 (12 12 (:REWRITE DARGP-LESS-THAN-WHEN-QUOTEP-CHEAP))
 (12 12 (:REWRITE DARGP-LESS-THAN-MONO))
 (11 11 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-2))
 (11 11 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-1))
 (11 11 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-MEMBER-EQUAL))
 (11 11 (:REWRITE MEMBER-EQUAL-OF-SINGLETON-CONSTANT-IFF))
 (11 11 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-WHEN-NOT-EQUAL-CAR))
 (11 11 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-TRIM))
 (11 11 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (11 11 (:REWRITE ALL-<=-MONOTONE))
 (10 5 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 )
(MARK-REPLACEMENTS
 (1481 785 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (325 10 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (126 6 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (103 7 (:REWRITE CONSP-OF-STRIP-CARS))
 (87 4 (:REWRITE LEN-OF-CDR))
 (60 4 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (52 18 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (49 7 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (40 1 (:REWRITE <-OF-IF-ARG2))
 (36 18 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (36 6 (:REWRITE ALL-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (35 9 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (35 9 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (30 18 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (18 18 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (18 18 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (18 18 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (18 5 (:REWRITE ARRAY1P-WHEN-CANDIDATE-DEPS-ARRAYP))
 (17 1 (:REWRITE EQUAL-OF-LEN-AND-0))
 (15 9 (:REWRITE DEFAULT-<-2))
 (13 13 (:REWRITE STRIP-CARS-WHEN-NOT-CONSP-CHEAP))
 (13 8 (:REWRITE DEFAULT-+-2))
 (12 12 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (12 6 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (10 10 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (10 10 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (9 9 (:REWRITE USE-ALL-<-2))
 (9 9 (:REWRITE USE-ALL-<))
 (9 9 (:REWRITE DEFAULT-<-1))
 (8 8 (:REWRITE DEFAULT-+-1))
 (8 4 (:REWRITE TRANSLATION-ARRAYP-AUX-WHEN-NEGATIVE))
 (7 3 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (7 1 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (6 6 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (6 6 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL))
 (6 6 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP))
 (6 6 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (6 6 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (6 6 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (6 6 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (6 6 (:REWRITE ALL-<-TRANSITIVE))
 (6 6 (:LINEAR ARRAY2P-LINEAR))
 (5 5 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (4 4 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (4 4 (:REWRITE TRANSLATION-ARRAYP-AUX-WHEN-BOUNDED-TRANSLATION-ARRAYP-AUX))
 (4 4 (:REWRITE TRANSLATION-ARRAYP-AUX-MONOTONE))
 (4 4 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (3 3 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (3 3 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (3 3 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (3 1 (:REWRITE CANDIDATE-DEPS-ARRAYP-OF-ASET1))
 (3 1 (:DEFINITION ATOM))
 (1 1 (:TYPE-PRESCRIPTION ALL-NATP))
 (1 1 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (1 1 (:REWRITE ALL-NATP-OF-STRIP-CARS-WHEN-SUBST-CANDIDATE-LISTP))
 )
(ARRAY1P-OF-MARK-REPLACEMENTS
 (3370 1685 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (1685 1685 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (370 15 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (191 9 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (155 9 (:REWRITE CONSP-OF-STRIP-CARS))
 (75 5 (:REWRITE LEN-OF-CDR))
 (60 30 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (60 10 (:REWRITE ALL-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (60 5 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (51 16 (:REWRITE ARRAY1P-WHEN-CANDIDATE-DEPS-ARRAYP))
 (50 25 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (45 15 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (45 15 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (40 10 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (25 25 (:TYPE-PRESCRIPTION DARGP))
 (25 25 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (25 25 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (25 25 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (25 25 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (25 15 (:REWRITE DEFAULT-<-2))
 (20 20 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (18 18 (:REWRITE STRIP-CARS-WHEN-NOT-CONSP-CHEAP))
 (18 18 (:LINEAR ARRAY2P-LINEAR))
 (18 9 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (16 16 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (15 15 (:REWRITE USE-ALL-<-2))
 (15 15 (:REWRITE USE-ALL-<))
 (15 15 (:REWRITE DEFAULT-<-1))
 (15 15 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (15 15 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (10 10 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (10 10 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL))
 (10 10 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP))
 (10 10 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (10 10 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (10 10 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (10 10 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (10 10 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (10 10 (:REWRITE ALL-<-TRANSITIVE))
 (5 5 (:REWRITE DEFAULT-+-2))
 (5 5 (:REWRITE DEFAULT-+-1))
 (5 5 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (3 1 (:REWRITE CANDIDATE-DEPS-ARRAYP-OF-ASET1))
 )
(ALEN1-OF-MARK-REPLACEMENTS
 (3578 1789 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (1789 1789 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (392 16 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (191 9 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (155 9 (:REWRITE CONSP-OF-STRIP-CARS))
 (75 5 (:REWRITE LEN-OF-CDR))
 (64 32 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (60 10 (:REWRITE ALL-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (60 5 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (54 27 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (48 16 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (48 16 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (47 11 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (27 27 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (27 27 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (27 27 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (27 27 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (27 16 (:REWRITE DEFAULT-<-2))
 (27 8 (:REWRITE ARRAY1P-WHEN-CANDIDATE-DEPS-ARRAYP))
 (21 13 (:REWRITE DEFAULT-+-2))
 (20 20 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (18 18 (:REWRITE STRIP-CARS-WHEN-NOT-CONSP-CHEAP))
 (18 18 (:LINEAR ARRAY2P-LINEAR))
 (18 9 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
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 (16 16 (:REWRITE USE-ALL-<))
 (16 16 (:REWRITE DEFAULT-<-1))
 (16 16 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (16 16 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (16 8 (:REWRITE TRANSLATION-ARRAYP-AUX-WHEN-NEGATIVE))
 (13 13 (:REWRITE DEFAULT-+-1))
 (13 13 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (10 10 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (10 10 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL))
 (10 10 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP))
 (10 10 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (10 10 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (10 10 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (10 10 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (10 10 (:REWRITE ALL-<-TRANSITIVE))
 (8 8 (:REWRITE TRANSLATION-ARRAYP-AUX-WHEN-BOUNDED-TRANSLATION-ARRAYP-AUX))
 (8 8 (:REWRITE TRANSLATION-ARRAYP-AUX-MONOTONE))
 (8 8 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (5 5 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (3 1 (:REWRITE CANDIDATE-DEPS-ARRAYP-OF-ASET1))
 )
(TRANSLATION-ARRAYP-AUX-OF-MARK-REPLACEMENTS
 (3578 1789 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (1789 1789 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (392 16 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (191 9 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (155 9 (:REWRITE CONSP-OF-STRIP-CARS))
 (75 5 (:REWRITE LEN-OF-CDR))
 (64 32 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (60 10 (:REWRITE ALL-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (60 5 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (54 27 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (48 16 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (48 16 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (47 11 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (37 21 (:REWRITE DEFAULT-+-2))
 (28 14 (:REWRITE TRANSLATION-ARRAYP-AUX-WHEN-NEGATIVE))
 (27 27 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (27 27 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (27 27 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (27 27 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (27 16 (:REWRITE DEFAULT-<-2))
 (27 8 (:REWRITE ARRAY1P-WHEN-CANDIDATE-DEPS-ARRAYP))
 (21 21 (:REWRITE DEFAULT-+-1))
 (20 20 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (18 18 (:REWRITE STRIP-CARS-WHEN-NOT-CONSP-CHEAP))
 (18 18 (:LINEAR ARRAY2P-LINEAR))
 (18 9 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (16 16 (:REWRITE USE-ALL-<-2))
 (16 16 (:REWRITE USE-ALL-<))
 (16 16 (:REWRITE TRANSLATION-ARRAYP-AUX-WHEN-BOUNDED-TRANSLATION-ARRAYP-AUX))
 (16 16 (:REWRITE DEFAULT-<-1))
 (16 16 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (16 16 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (13 13 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (10 10 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (10 10 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL))
 (10 10 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP))
 (10 10 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (10 10 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (10 10 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (10 10 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (10 10 (:REWRITE ALL-<-TRANSITIVE))
 (8 8 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (5 5 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (3 1 (:REWRITE CANDIDATE-DEPS-ARRAYP-OF-ASET1))
 )
(TRANSLATION-ARRAYP-AUX-OF-MARK-REPLACEMENTS-GEN
 (9139 10 (:REWRITE ALL-INTEGERP-OF-STRIP-CARS-WHEN-WEAK-DAGP-AUX))
 (8337 20 (:DEFINITION WEAK-DAGP-AUX))
 (6618 3309 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (6170 40 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX-2))
 (4580 40 (:REWRITE PSEUDO-DAGP-AUX-OF-CDR))
 (4507 114 (:REWRITE DEFAULT-+-2))
 (4289 122 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (3480 30 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (3309 3309 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (2850 30 (:REWRITE RATIONALP-OF-IF-STRONG))
 (2775 30 (:REWRITE WEAK-DAGP-AUX-OF-CDR))
 (2160 30 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (1920 30 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (1423 40 (:DEFINITION TOP-NODENUM))
 (944 244 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (894 65 (:REWRITE LEN-OF-CDR))
 (594 122 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (594 122 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (585 54 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (428 200 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (400 200 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (374 374 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (321 57 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (270 90 (:REWRITE PSEUDO-DAGP-OF-CDR-WHEN-PSEUDO-DAGP))
 (240 40 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP))
 (231 20 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (211 131 (:REWRITE DEFAULT-<-2))
 (200 200 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (200 200 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (200 200 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (181 10 (:REWRITE CONSP-OF-STRIP-CARS))
 (150 150 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (150 30 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (140 131 (:REWRITE DEFAULT-<-1))
 (135 27 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (133 133 (:TYPE-PRESCRIPTION WEAK-DAGP-AUX))
 (131 131 (:REWRITE USE-ALL-<-2))
 (131 131 (:REWRITE USE-ALL-<))
 (130 10 (:REWRITE <-OF-IF-ARG2))
 (122 122 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (122 122 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (114 114 (:REWRITE DEFAULT-+-1))
 (81 81 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (70 70 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (66 11 (:REWRITE ALL-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (60 60 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (57 57 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (57 57 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (57 57 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (54 54 (:TYPE-PRESCRIPTION BOUNDED-DAG-EXPRP))
 (54 27 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (54 27 (:REWRITE BOUNDED-DAG-EXPRP-OF-CDR-OF-CAR-WHEN-WEAK-DAGP-AUX))
 (45 45 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (40 40 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (40 20 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (36 9 (:REWRITE NOT-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP))
 (30 30 (:REWRITE USE-ALL-RATIONALP-2))
 (30 30 (:REWRITE USE-ALL-RATIONALP))
 (30 10 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-SUBST-CANDIDATE-LISTP))
 (30 10 (:REWRITE +-COMBINE-CONSTANTS))
 (30 9 (:REWRITE ARRAY1P-WHEN-CANDIDATE-DEPS-ARRAYP))
 (27 27 (:TYPE-PRESCRIPTION MYQUOTEP))
 (27 27 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP-CHEAP))
 (27 27 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP-CHEAP))
 (27 27 (:REWRITE BOUNDED-DAG-EXPRP-MONOTONE))
 (25 16 (:REWRITE TRANSLATION-ARRAYP-AUX-WHEN-NEGATIVE))
 (22 22 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (22 22 (:LINEAR ARRAY2P-LINEAR))
 (20 20 (:REWRITE STRIP-CARS-WHEN-NOT-CONSP-CHEAP))
 (20 20 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (20 20 (:REWRITE ALL-<-TRANSITIVE))
 (20 10 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (20 10 (:REWRITE ALL-NATP-IMPLIES-ALL-INTEGERP-CHEAP))
 (20 10 (:REWRITE ALL-INTEGERP-WHEN-NOT-CONSP-CHEAP))
 (18 18 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP))
 (18 18 (:REWRITE TRANSLATION-ARRAYP-AUX-WHEN-BOUNDED-TRANSLATION-ARRAYP-AUX))
 (11 11 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (11 11 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL))
 (11 11 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP))
 (10 10 (:TYPE-PRESCRIPTION ALL-NATP))
 (10 10 (:REWRITE SUBST-CANDIDATE-LISTP-OF-CDR))
 (10 10 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (10 10 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (10 10 (:REWRITE LEN-OF-CDDR-WHEN-EQUAL-OF-LEN))
 (10 10 (:DEFINITION FIX))
 (9 9 (:REWRITE USE-ALL-<=-2))
 (9 9 (:REWRITE USE-ALL-<=))
 (9 9 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (9 9 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (9 9 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (9 9 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (8 8 (:REWRITE USE-ALL-NATP-2))
 (8 8 (:REWRITE USE-ALL-NATP))
 (7 7 (:REWRITE PSEUDO-DAGP-AUX-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (3 3 (:REWRITE EQUAL-OF-LEN-AND-0))
 (3 1 (:REWRITE CANDIDATE-DEPS-ARRAYP-OF-ASET1))
 (1 1 (:REWRITE ALL-<=-MONOTONE))
 )
(BOUNDED-TRANSLATION-ARRAYP-AUX-OF-MARK-REPLACEMENTS
 (6742 3371 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (3371 3371 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (1116 53 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (911 38 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (401 41 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (368 26 (:REWRITE CONSP-OF-STRIP-CARS))
 (271 41 (:REWRITE ALL-<-TRANSITIVE))
 (190 84 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (176 11 (:REWRITE LEN-OF-CDR))
 (164 82 (:REWRITE DEFAULT-<-2))
 (144 11 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (137 42 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (137 42 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (132 82 (:REWRITE DEFAULT-<-1))
 (130 65 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (122 82 (:REWRITE USE-ALL-<))
 (120 33 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (84 14 (:REWRITE ALL-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (82 82 (:REWRITE USE-ALL-<-2))
 (77 65 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (76 38 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (70 10 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (65 65 (:TYPE-PRESCRIPTION DARGP))
 (65 65 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (65 65 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (65 65 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (62 36 (:REWRITE DEFAULT-+-2))
 (60 20 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (53 53 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (53 53 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (52 52 (:REWRITE STRIP-CARS-WHEN-NOT-CONSP-CHEAP))
 (50 20 (:REWRITE NOT-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP))
 (42 21 (:REWRITE BOUNDED-TRANSLATION-ARRAYP-AUX-WHEN-NOT-NATP))
 (41 41 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (41 1 (:REWRITE ALL-<-OF-CDR))
 (40 40 (:TYPE-PRESCRIPTION MEMBERP))
 (40 40 (:REWRITE USE-ALL-<=-2))
 (40 40 (:REWRITE USE-ALL-<=))
 (39 12 (:REWRITE ARRAY1P-WHEN-CANDIDATE-DEPS-ARRAYP))
 (37 1 (:REWRITE <-OF-IF-ARG2))
 (36 36 (:REWRITE DEFAULT-+-1))
 (28 28 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (28 28 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (28 28 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (28 28 (:LINEAR ARRAY2P-LINEAR))
 (22 11 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (22 11 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (20 20 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP))
 (20 20 (:REWRITE USE-ALL-RATIONALP-2))
 (20 20 (:REWRITE USE-ALL-RATIONALP))
 (20 20 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (14 14 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (14 14 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL))
 (14 14 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP))
 (12 12 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (11 11 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (11 11 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (11 11 (:REWRITE BOUNDED-DARG-LISTP-MONOTONE))
 (10 10 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (7 1 (:REWRITE EQUAL-OF-LEN-AND-0))
 (3 1 (:REWRITE CANDIDATE-DEPS-ARRAYP-OF-ASET1))
 )
(BOUNDED-TRANSLATION-ARRAYP-AUX-OF-MARK-REPLACEMENTS-GEN
 (11878 13 (:REWRITE ALL-INTEGERP-OF-STRIP-CARS-WHEN-WEAK-DAGP-AUX))
 (11037 26 (:DEFINITION WEAK-DAGP-AUX))
 (10374 5187 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (7976 52 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX-2))
 (6086 187 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (5954 52 (:REWRITE PSEUDO-DAGP-AUX-OF-CDR))
 (5866 154 (:REWRITE DEFAULT-+-2))
 (5187 5187 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (4584 59 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (3705 39 (:REWRITE RATIONALP-OF-IF-STRONG))
 (2808 39 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (2793 39 (:REWRITE WEAK-DAGP-AUX-OF-CDR))
 (2496 39 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (1804 52 (:DEFINITION TOP-NODENUM))
 (1326 352 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (1238 89 (:REWRITE LEN-OF-CDR))
 (924 51 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (839 176 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (839 176 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (816 75 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (596 284 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (568 284 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (513 53 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (488 488 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (420 75 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (415 248 (:REWRITE DEFAULT-<-2))
 (368 26 (:REWRITE CONSP-OF-STRIP-CARS))
 (363 53 (:REWRITE ALL-<-TRANSITIVE))
 (351 117 (:REWRITE PSEUDO-DAGP-OF-CDR-WHEN-PSEUDO-DAGP))
 (312 52 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP))
 (310 248 (:REWRITE DEFAULT-<-1))
 (308 248 (:REWRITE USE-ALL-<))
 (284 284 (:TYPE-PRESCRIPTION DARGP))
 (284 284 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (284 284 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (284 284 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (248 248 (:REWRITE USE-ALL-<-2))
 (206 14 (:REWRITE <-OF-IF-ARG2))
 (195 195 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (195 39 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (187 187 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (187 187 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (180 36 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (172 172 (:TYPE-PRESCRIPTION WEAK-DAGP-AUX))
 (154 154 (:REWRITE DEFAULT-+-1))
 (108 108 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (102 51 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (98 32 (:REWRITE NOT-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP))
 (91 91 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (84 14 (:REWRITE ALL-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (78 78 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (75 75 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (75 75 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (75 75 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (72 72 (:TYPE-PRESCRIPTION BOUNDED-DAG-EXPRP))
 (72 72 (:REWRITE USE-ALL-<=-2))
 (72 72 (:REWRITE USE-ALL-<=))
 (72 36 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (72 36 (:REWRITE BOUNDED-DAG-EXPRP-OF-CDR-OF-CAR-WHEN-WEAK-DAGP-AUX))
 (70 10 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (63 63 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (60 60 (:TYPE-PRESCRIPTION MEMBERP))
 (59 59 (:REWRITE USE-ALL-RATIONALP-2))
 (59 59 (:REWRITE USE-ALL-RATIONALP))
 (52 52 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (52 52 (:REWRITE STRIP-CARS-WHEN-NOT-CONSP-CHEAP))
 (44 44 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP))
 (41 1 (:REWRITE ALL-<-OF-CDR))
 (39 13 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-SUBST-CANDIDATE-LISTP))
 (39 13 (:REWRITE +-COMBINE-CONSTANTS))
 (39 12 (:REWRITE ARRAY1P-WHEN-CANDIDATE-DEPS-ARRAYP))
 (36 36 (:TYPE-PRESCRIPTION MYQUOTEP))
 (36 36 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP-CHEAP))
 (36 36 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP-CHEAP))
 (36 36 (:REWRITE BOUNDED-DAG-EXPRP-MONOTONE))
 (32 21 (:REWRITE BOUNDED-TRANSLATION-ARRAYP-AUX-WHEN-NOT-NATP))
 (30 30 (:LINEAR ARRAY2P-LINEAR))
 (28 28 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (27 27 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (27 27 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (26 13 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (26 13 (:REWRITE ALL-NATP-IMPLIES-ALL-INTEGERP-CHEAP))
 (26 13 (:REWRITE ALL-INTEGERP-WHEN-NOT-CONSP-CHEAP))
 (22 22 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (22 11 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (22 11 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (20 20 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (14 14 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (14 14 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL))
 (14 14 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP))
 (13 13 (:REWRITE SUBST-CANDIDATE-LISTP-OF-CDR))
 (13 13 (:REWRITE LEN-OF-CDDR-WHEN-EQUAL-OF-LEN))
 (13 13 (:DEFINITION FIX))
 (12 12 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (12 12 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (12 12 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (11 11 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (11 11 (:REWRITE USE-ALL-NATP-2))
 (11 11 (:REWRITE USE-ALL-NATP))
 (11 11 (:REWRITE BOUNDED-DARG-LISTP-MONOTONE))
 (10 10 (:REWRITE PSEUDO-DAGP-AUX-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (10 4 (:REWRITE EQUAL-OF-LEN-AND-0))
 (3 1 (:REWRITE CANDIDATE-DEPS-ARRAYP-OF-ASET1))
 (1 1 (:REWRITE ALL-<=-MONOTONE))
 )
(PRINT-SUBST-CANDIDATES
 (3598 14 (:REWRITE DARGP-LESS-THAN-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (3510 44 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-<))
 (3078 119 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (3049 68 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (2450 1142 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (2188 1142 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (1158 1158 (:TYPE-PRESCRIPTION NAT-LISTP))
 (1046 1046 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (994 14 (:REWRITE ALL-<-OF-CDR))
 (784 19 (:REWRITE <-OF-IF-ARG2))
 (784 14 (:REWRITE DARGP-LESS-THAN-OF-CADR-OF-CAR-WHEN-BOUNDED-DARG-LISTP-OF-STRIP-CADRS))
 (640 44 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (630 15 (:REWRITE LEN-OF-CDR))
 (560 112 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (560 14 (:REWRITE BOUNDED-DARG-LISTP-OF-CDR))
 (360 15 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (310 14 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-CAR-AND-QUOTE))
 (297 99 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (280 68 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (255 15 (:REWRITE EQUAL-OF-LEN-AND-0))
 (237 49 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (237 49 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (231 99 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (198 14 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (195 15 (:REWRITE USE-ALL-<-FOR-CAR))
 (190 95 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (183 183 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (182 13 (:REWRITE DARGP-LESS-THAN-WHEN-NATP-CHEAP))
 (169 13 (:REWRITE DARGP-LESS-THAN-WHEN-NOT-CONSP-CHEAP))
 (169 13 (:REWRITE DARGP-LESS-THAN-WHEN-CONSP-CHEAP))
 (154 154 (:TYPE-PRESCRIPTION STRIP-CADRS))
 (152 152 (:TYPE-PRESCRIPTION ALL-<))
 (139 64 (:REWRITE DEFAULT-<-1))
 (132 132 (:TYPE-PRESCRIPTION BOUNDED-DARG-LISTP))
 (127 61 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (122 4 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (119 119 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (119 119 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (113 64 (:REWRITE DEFAULT-<-2))
 (104 68 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (104 1 (:REWRITE <-OF-CAR-AND-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (99 99 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (99 99 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (99 16 (:REWRITE <-OF-CAR-OF-CAR-WHEN-ALL-<-OF-STRIP-CARS))
 (95 95 (:TYPE-PRESCRIPTION DARGP))
 (88 44 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (88 44 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (68 68 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (68 68 (:REWRITE ALL-<-TRANSITIVE))
 (64 64 (:REWRITE USE-ALL-<-2))
 (64 64 (:REWRITE USE-ALL-<))
 (62 62 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (61 61 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (61 61 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (61 61 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (60 60 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DIMENSIONS-WHEN-ARRAY1P))
 (44 44 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (44 44 (:REWRITE BOUNDED-DARG-LISTP-MONOTONE))
 (32 2 (:REWRITE ALL-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (30 30 (:TYPE-PRESCRIPTION POSP-OF-CAR-OF-DIMENSIONS-WHEN-ARRAY1P))
 (30 15 (:REWRITE DEFAULT-+-2))
 (30 15 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (29 29 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (28 14 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (15 15 (:REWRITE USE-ALL-<=-2))
 (15 15 (:REWRITE USE-ALL-<=))
 (15 15 (:REWRITE DEFAULT-+-1))
 (14 14 (:TYPE-PRESCRIPTION MYQUOTEP))
 (13 13 (:REWRITE DARGP-LESS-THAN-WHEN-QUOTEP-CHEAP))
 (12 12 (:TYPE-PRESCRIPTION STRIP-CARS))
 (12 4 (:REWRITE PSEUDO-DAGP-OF-CDR-WHEN-PSEUDO-DAGP))
 (10 1 (:DEFINITION SUBST-CANDIDATE-LISTP))
 (8 8 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (7 1 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (6 1 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (6 1 (:REWRITE <-OF-CAR-AND-ALEN1))
 (5 5 (:REWRITE STRIP-CARS-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL))
 (4 4 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP))
 (4 1 (:REWRITE SUBST-CANDIDATEP-OF-CAR))
 (3 3 (:REWRITE CONSP-OF-STRIP-CARS))
 (3 1 (:REWRITE ARRAY1P-WHEN-CANDIDATE-DEPS-ARRAYP))
 (3 1 (:DEFINITION ATOM))
 (2 2 (:REWRITE ALL-<-OF-+-OF-1))
 (1 1 (:TYPE-PRESCRIPTION SUBST-CANDIDATEP))
 (1 1 (:TYPE-PRESCRIPTION ALL-NATP))
 (1 1 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (1 1 (:REWRITE ALL-NATP-OF-STRIP-CARS-WHEN-SUBST-CANDIDATE-LISTP))
 )
(LOOKUP-VAR-NODES
 (150 75 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (150 75 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (80 3 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (30 2 (:REWRITE LEN-OF-CDR))
 (24 2 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (21 3 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (16 8 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (12 6 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (9 3 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (9 3 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (8 8 (:TYPE-PRESCRIPTION DARGP))
 (8 8 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (8 8 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (8 8 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (8 8 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (5 5 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (4 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE USE-ALL-<-2))
 (3 3 (:REWRITE USE-ALL-<))
 (3 3 (:REWRITE DEFAULT-<-1))
 (3 3 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (3 3 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 )
(NAT-LISTP-OF-LOOKUP-VAR-NODES
 (346 173 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (346 173 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (203 9 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (36 18 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (33 9 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (27 9 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (27 9 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (26 13 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (18 9 (:REWRITE DEFAULT-<-2))
 (14 7 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (13 13 (:TYPE-PRESCRIPTION DARGP))
 (13 13 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (13 13 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (13 13 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (13 13 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (12 6 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (9 9 (:REWRITE USE-ALL-<-2))
 (9 9 (:REWRITE USE-ALL-<))
 (9 9 (:REWRITE DEFAULT-<-1))
 (9 9 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (9 9 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (6 6 (:TYPE-PRESCRIPTION ALL-NATP))
 (6 6 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 )
(SUBSTITUTE-VAR-SET
 (17705 8909 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (7006 2086 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (4686 142 (:DEFINITION LOOKUP-VAR-NODES))
 (3329 3313 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (2086 2086 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (2056 2056 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (1342 104 (:REWRITE TRANSLATION-ARRAYP-AUX-WHEN-NEGATIVE))
 (1292 204 (:REWRITE <-WHEN-DARGP-LESS-THAN))
 (972 440 (:REWRITE SUBST-CANDIDATES-WHEN-NOT-CONSP))
 (890 408 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (710 142 (:TYPE-PRESCRIPTION LOOKUP-IN-DAG-VARIABLE-ALIST-TYPE))
 (588 194 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (588 194 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (548 274 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (530 265 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (490 226 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (488 468 (:REWRITE USE-ALL-<))
 (468 468 (:REWRITE USE-ALL-<-2))
 (430 276 (:REWRITE SET-DIFFERENCE-EQUAL-WHEN-SUBSETP-EQUAL))
 (398 204 (:REWRITE DEFAULT-<-2))
 (389 219 (:REWRITE DEFAULT-+-2))
 (368 368 (:REWRITE NATP-OF-+-WHEN-NEGATIVE-CONSTANT))
 (355 355 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (355 355 (:REWRITE ALL-<-TRANSITIVE))
 (328 10 (:REWRITE DARGP-LESS-THAN-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (300 276 (:REWRITE SET-DIFFERENCE-EQUAL-WHEN-NOT-CONSP))
 (283 143 (:REWRITE STRIP-CARS-WHEN-NOT-CONSP-CHEAP))
 (278 204 (:REWRITE DEFAULT-<-1))
 (275 3 (:REWRITE MAXELEM-SINGLETON-ALT))
 (269 265 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (265 265 (:TYPE-PRESCRIPTION DARGP))
 (265 265 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (265 265 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (265 265 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (252 252 (:REWRITE USE-ALL-<=-2))
 (252 252 (:REWRITE USE-ALL-<=))
 (246 246 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (238 10 (:REWRITE BOUNDED-DARG-LISTP-OF-0))
 (221 219 (:REWRITE DEFAULT-+-1))
 (215 193 (:TYPE-PRESCRIPTION NATP-OF-MAXELEM-OF-STRIP-CARS-WHEN-WEAK-DAGP-AUX))
 (215 193 (:TYPE-PRESCRIPTION NATP-OF-MAXELEM-2))
 (214 214 (:TYPE-PRESCRIPTION DARGP-LESS-THAN))
 (199 185 (:TYPE-PRESCRIPTION NATP-OF-LARGEST-NON-QUOTEP))
 (196 7 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (193 193 (:TYPE-PRESCRIPTION RATIONALP-OF-MAXELEM))
 (178 2 (:LINEAR LARGEST-NON-QUOTEP-BOUND))
 (174 14 (:REWRITE DARGP-LESS-THAN-WHEN-NATP-CHEAP))
 (174 2 (:LINEAR LARGEST-NON-QUOTEP-BOUND-ALT))
 (152 14 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-CAR-AND-QUOTE))
 (140 2 (:REWRITE CONSP-OF-CDR))
 (138 2 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (136 122 (:REWRITE ALL-<=-ALL-WHEN-NOT-CONSP-ARG2))
 (134 6 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (131 121 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (130 2 (:REWRITE NATP-OF-NTH-WHEN-DARG-LISTP))
 (130 2 (:REWRITE LAST-WHEN-NOT-CDR-CHEAP))
 (128 2 (:REWRITE CDR-IFF))
 (110 2 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (104 104 (:REWRITE TRANSLATION-ARRAYP-AUX-WHEN-BOUNDED-TRANSLATION-ARRAYP-AUX))
 (104 104 (:REWRITE TRANSLATION-ARRAYP-AUX-MONOTONE))
 (98 14 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (98 6 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (74 10 (:REWRITE ALL-MYQUOTEP-BECOMES-ALL-CONSP-WHEN-DARG-LISTP))
 (70 10 (:REWRITE DARGP-LESS-THAN-WHEN-CONSP-CHEAP))
 (62 10 (:REWRITE USE-ALL-<-FOR-CAR))
 (52 2 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (46 23 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (44 22 (:REWRITE SUBSETP-EQUAL-WHEN-SUBSETP-EQUAL-OF-CDR-CHEAP))
 (44 22 (:REWRITE SUBSETP-EQUAL-WHEN-NOT-CONSP-ARG2-CHEAP))
 (44 22 (:REWRITE SUBSETP-EQUAL-OF-CDR-ARG2-CHEAP))
 (42 6 (:REWRITE LEN-OF-STRIP-CARS))
 (40 4 (:REWRITE CONSP-OF-SET-DIFFERENCE-EQUAL))
 (40 2 (:REWRITE LEN-OF-CDR))
 (36 36 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (28 14 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (28 4 (:DEFINITION ATOM))
 (24 10 (:REWRITE DARG-LISTP-WHEN-NOT-CONSP))
 (24 10 (:REWRITE ALL-MYQUOTEP-WHEN-NOT-CONSP))
 (24 4 (:REWRITE ALL-NATP-OF-LAST))
 (22 22 (:TYPE-PRESCRIPTION WEAK-DAGP-AUX))
 (22 22 (:REWRITE SUBSETP-EQUAL-WHEN-NOT-CONSP-ARG1-CHEAP))
 (22 22 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-ALT))
 (22 22 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-2-ALT))
 (20 20 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (20 20 (:TYPE-PRESCRIPTION MEMBERP))
 (20 10 (:REWRITE DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (20 10 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (18 18 (:TYPE-PRESCRIPTION MYQUOTEP))
 (18 14 (:REWRITE DARGP-LESS-THAN-WHEN-QUOTEP-CHEAP))
 (16 4 (:REWRITE ALL-NATP-OF-MERGE-SORT-<))
 (14 14 (:REWRITE DARGP-LESS-THAN-MONO))
 (14 14 (:LINEAR ARRAY2P-LINEAR))
 (14 2 (:REWRITE NATP-OF-NTH-WHEN-NAT-LISTP))
 (12 12 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (12 6 (:REWRITE LARGEST-NON-QUOTEP-WHEN-ALL-MYQUOTEP-CHEAP))
 (12 6 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (10 6 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (9 9 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (9 9 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (9 9 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (9 3 (:REWRITE MAXELEM-WHEN-NON-CONSP))
 (8 8 (:REWRITE CONSP-OF-STRIP-CADDRS))
 (7 7 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (7 3 (:REWRITE MAXELEM-OF-STRIP-CARS-WHEN-PSEUDO-DAGP))
 (6 6 (:REWRITE LARGEST-NON-QUOTEP-WHEN-ALL-CONSP-CHEAP))
 (6 6 (:REWRITE LARGEST-NON-QUOTEP-WHEN-ALL-CONSP))
 (4 4 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (4 4 (:REWRITE USE-ALL-NATP-2))
 (4 4 (:REWRITE USE-ALL-NATP))
 (4 2 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE TRUE-LISTP-OF-MERGE-SORT-<))
 (2 2 (:REWRITE NATP-OF-NTH-WHEN-BOUNDED-DARG-LISTP-GEN))
 (2 2 (:REWRITE LAST-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE EQUAL-OF-LEN-AND-0))
 (2 2 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (2 2 (:REWRITE APPEND-WHEN-NOT-CONSP-ARG1-CHEAP))
 (2 2 (:LINEAR <-OF-LARGEST-NON-QUOTEP))
 )
(LEN-OF-MV-NTH-3-OF-SUBSTITUTE-VAR-SET
 (1058 64 (:REWRITE DEFAULT-+-2))
 (797 9 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (616 37 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (580 35 (:REWRITE LAST-WHEN-NOT-CDR-CHEAP))
 (545 9 (:REWRITE CDR-IFF))
 (441 36 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (385 9 (:REWRITE USE-ALL-RATIONALP-FOR-CAR-OF-LAST))
 (266 133 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (223 9 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (218 20 (:REWRITE INTERSECTION-EQUAL-WHEN-SUBSETP-EQUAL))
 (194 90 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (163 163 (:TYPE-PRESCRIPTION NAT-LISTP))
 (162 54 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (154 133 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (142 45 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (142 45 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (135 135 (:TYPE-PRESCRIPTION LAST))
 (133 133 (:TYPE-PRESCRIPTION DARGP))
 (133 133 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (133 133 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (133 133 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (131 87 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (108 54 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (96 64 (:REWRITE DEFAULT-+-1))
 (92 26 (:REWRITE SET-DIFFERENCE-EQUAL-WHEN-SUBSETP-EQUAL))
 (90 45 (:REWRITE DEFAULT-<-2))
 (86 41 (:REWRITE TRUE-LIST-FIX-WHEN-TRUE-LISTP))
 (72 72 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (59 18 (:REWRITE ALL-RATIONALP-OF-MERGE-SORT-<))
 (55 9 (:REWRITE CONSP-OF-LAST))
 (54 54 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (54 9 (:REWRITE ALL-RATIONALP-OF-LAST))
 (50 25 (:REWRITE SUBSETP-EQUAL-WHEN-SUBSETP-EQUAL-OF-CDR-CHEAP))
 (50 25 (:REWRITE SUBSETP-EQUAL-OF-CDR-ARG2-CHEAP))
 (49 45 (:REWRITE DEFAULT-<-1))
 (48 24 (:REWRITE SUBSETP-EQUAL-WHEN-NOT-CONSP-ARG2-CHEAP))
 (48 14 (:REWRITE TRUE-LISTP-WHEN-NAT-LISTP-REWRITE))
 (45 45 (:REWRITE USE-ALL-<-2))
 (45 45 (:REWRITE USE-ALL-<))
 (45 36 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (41 41 (:REWRITE TRUE-LIST-FIX-WHEN-NOT-CONSP-CHEAP))
 (38 18 (:REWRITE CONSP-OF-MERGE-SORT-<))
 (37 37 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (36 18 (:REWRITE INTERSECTION-EQUAL-WHEN-NOT-CONSP-ARG2-CHEAP))
 (35 35 (:REWRITE LAST-WHEN-NOT-CONSP-CHEAP))
 (34 34 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (25 25 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-ALT))
 (25 25 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-2-ALT))
 (24 24 (:REWRITE SUBSETP-EQUAL-WHEN-NOT-CONSP-ARG1-CHEAP))
 (21 21 (:REWRITE USE-ALL-<=-2))
 (21 21 (:REWRITE USE-ALL-<=))
 (20 5 (:REWRITE ALL-RATIONALP-OF-TRUE-LIST-FIX))
 (18 18 (:REWRITE INTERSECTION-EQUAL-WHEN-NOT-CONSP-ARG1-CHEAP))
 (16 8 (:REWRITE DEFAULT-UNARY-MINUS))
 (15 15 (:TYPE-PRESCRIPTION TRUE-LIST-FIX))
 (14 14 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (14 9 (:REWRITE TRUE-LISTP-OF-MERGE-SORT-<))
 (10 10 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (10 10 (:REWRITE CONSP-OF-TRUE-LIST-FIX))
 (10 5 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (9 9 (:REWRITE USE-ALL-RATIONALP-2))
 (9 9 (:REWRITE USE-ALL-RATIONALP))
 (5 5 (:TYPE-PRESCRIPTION ALL-NATP))
 (5 5 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:REWRITE FOLD-CONSTS-IN-+))
 (4 4 (:REWRITE +-COMBINE-CONSTANTS))
 (3 3 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (3 3 (:REWRITE EQUAL-OF-+-COMBINE-CONSTANTS))
 (2 2 (:REWRITE INTERSECTION-EQUAL-WHEN-MEMBER-EQUAL-AND-MEMBER-EQUAL))
 (2 2 (:REWRITE APPEND-WHEN-NOT-CONSP-ARG1-CHEAP))
 (1 1 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (1 1 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 )
(LEN-OF-MV-NTH-3-OF-SUBSTITUTE-VAR-SET-GEN
 (3707 96 (:REWRITE DEFAULT-+-2))
 (3223 45 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2166 96 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (2035 133 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (1731 24 (:REWRITE USE-ALL-RATIONALP-FOR-CAR-OF-LAST))
 (1532 74 (:REWRITE LAST-WHEN-NOT-CDR-CHEAP))
 (1458 24 (:REWRITE CDR-IFF))
 (906 26 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (834 51 (:REWRITE CONSP-OF-SET-DIFFERENCE-EQUAL))
 (652 50 (:REWRITE CONSP-OF-MERGE-SORT-<))
 (628 314 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (620 302 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (525 46 (:REWRITE ALL-RATIONALP-OF-MERGE-SORT-<))
 (493 493 (:TYPE-PRESCRIPTION NAT-LISTP))
 (480 163 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (461 151 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (461 151 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (428 153 (:REWRITE SET-DIFFERENCE-EQUAL-WHEN-SUBSETP-EQUAL))
 (418 24 (:REWRITE CONSP-OF-LAST))
 (359 359 (:TYPE-PRESCRIPTION LAST))
 (359 314 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (326 163 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (314 314 (:TYPE-PRESCRIPTION DARGP))
 (314 314 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (314 314 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (314 314 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (234 117 (:REWRITE SUBSETP-EQUAL-WHEN-SUBSETP-EQUAL-OF-CDR-CHEAP))
 (234 117 (:REWRITE SUBSETP-EQUAL-OF-CDR-ARG2-CHEAP))
 (230 115 (:REWRITE SUBSETP-EQUAL-WHEN-NOT-CONSP-ARG2-CHEAP))
 (194 2 (:REWRITE INTERSECTION-EQUAL-WHEN-NOT-INTERSECTION-EQUAL-OF-CDR-ARG2-IFF))
 (190 190 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (177 1 (:REWRITE SUBSETP-EQUAL-OF-CDR-ARG2-WHEN-NOT-MEMBER-EQUAL-OF-CAR))
 (166 166 (:REWRITE USE-ALL-<-2))
 (166 166 (:REWRITE USE-ALL-<))
 (163 163 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (163 1 (:REWRITE NOT-MEMBER-EQUAL-WHEN-<-OF-CAR))
 (152 96 (:REWRITE DEFAULT-+-1))
 (151 24 (:REWRITE ALL-RATIONALP-OF-LAST))
 (137 96 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (133 133 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (117 117 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-ALT))
 (117 117 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-2-ALT))
 (115 115 (:REWRITE SUBSETP-EQUAL-WHEN-NOT-CONSP-ARG1-CHEAP))
 (78 39 (:REWRITE INTERSECTION-EQUAL-WHEN-NOT-CONSP-ARG2-CHEAP))
 (77 77 (:REWRITE USE-ALL-<=-2))
 (77 77 (:REWRITE USE-ALL-<=))
 (74 74 (:REWRITE LAST-WHEN-NOT-CONSP-CHEAP))
 (60 26 (:REWRITE TRUE-LISTP-WHEN-NAT-LISTP-REWRITE))
 (43 1 (:REWRITE USE-ALL-<-FOR-CAR))
 (42 24 (:REWRITE TRUE-LISTP-OF-MERGE-SORT-<))
 (41 41 (:REWRITE USE-ALL-RATIONALP-2))
 (41 41 (:REWRITE USE-ALL-RATIONALP))
 (39 39 (:REWRITE INTERSECTION-EQUAL-WHEN-NOT-CONSP-ARG1-CHEAP))
 (35 1 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (27 9 (:REWRITE TRUE-LIST-FIX-WHEN-TRUE-LISTP))
 (26 26 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (24 12 (:REWRITE DEFAULT-UNARY-MINUS))
 (9 9 (:REWRITE TRUE-LIST-FIX-WHEN-NOT-CONSP-CHEAP))
 (8 8 (:REWRITE FOLD-CONSTS-IN-+))
 (8 8 (:REWRITE +-COMBINE-CONSTANTS))
 (8 4 (:REWRITE CONSP-OF-TRUE-LIST-FIX))
 (5 5 (:TYPE-PRESCRIPTION TRUE-LIST-FIX))
 (4 4 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (4 4 (:REWRITE INTERSECTION-EQUAL-WHEN-MEMBER-EQUAL-AND-MEMBER-EQUAL))
 (4 4 (:REWRITE APPEND-WHEN-NOT-CONSP-ARG1-CHEAP))
 (4 2 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (4 2 (:REWRITE INTERSECTION-EQUAL-WHEN-MEMBER-EQUAL-OF-CAR-CHEAP))
 (4 2 (:REWRITE INTERSECTION-EQUAL-WHEN-INTERSECTION-EQUAL-OF-CDR-ARG2-CHEAP))
 (4 2 (:REWRITE INTERSECTION-EQUAL-WHEN-INTERSECTION-EQUAL-OF-CDR-ARG1-CHEAP))
 (3 3 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (3 3 (:TYPE-PRESCRIPTION ALL-<))
 (2 2 (:TYPE-PRESCRIPTION ALL-NATP))
 (2 2 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (2 2 (:REWRITE EQUAL-OF-+-COMBINE-CONSTANTS))
 (2 2 (:REWRITE <=-OF-0-WHEN-NATP))
 (2 2 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (2 2 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (2 1 (:REWRITE MEMBER-EQUAL-WHEN-<=-OF-LEN-AND-1))
 (2 1 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (2 1 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (1 1 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (1 1 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (1 1 (:REWRITE ALL-<-TRANSITIVE))
 )
(MV-NTH-3-OF-SUBSTITUTE-VAR-SET-WHEN-NOT-CONSP
 (46 2 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (10 10 (:TYPE-PRESCRIPTION LEN))
 (8 4 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (6 2 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (6 2 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (4 4 (:TYPE-PRESCRIPTION NAT-LISTP))
 (4 2 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (4 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:TYPE-PRESCRIPTION DARGP))
 (2 2 (:REWRITE USE-ALL-<-2))
 (2 2 (:REWRITE USE-ALL-<))
 (2 2 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (2 2 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (2 2 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (2 2 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 )
(NATP-OF-MV-NTH-5-OF-SUBSTITUTE-VAR-SET
 (501 2 (:REWRITE DEFAULT-+-2))
 (337 2 (:REWRITE ACL2-NUMBERP-WHEN-NATP))
 (230 15 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (157 8 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (152 19 (:REWRITE SUBST-CANDIDATES-WHEN-NOT-CONSP))
 (145 2 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (134 6 (:REWRITE LAST-WHEN-NOT-CDR-CHEAP))
 (128 2 (:REWRITE CDR-IFF))
 (126 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (122 4 (:REWRITE ALL-NATP-OF-MERGE-SORT-<))
 (110 2 (:REWRITE USE-ALL-NATP-FOR-CAR-OF-LAST))
 (82 4 (:REWRITE ALL-NATP-OF-SET-DIFFERENCE-EQUAL))
 (80 80 (:TYPE-PRESCRIPTION LEN))
 (68 68 (:TYPE-PRESCRIPTION NAT-LISTP))
 (68 4 (:REWRITE CONSP-OF-LAST))
 (66 17 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (54 18 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (52 8 (:REWRITE SET-DIFFERENCE-EQUAL-WHEN-SUBSETP-EQUAL))
 (50 50 (:TYPE-PRESCRIPTION LAST))
 (50 25 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (49 2 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (48 8 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (42 8 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (36 18 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (36 2 (:REWRITE NATP-OF-CAR-OF-LAST-WHEN-NAT-LISTP))
 (35 2 (:REWRITE USE-ALL-RATIONALP-FOR-CAR-OF-LAST))
 (32 16 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (28 28 (:TYPE-PRESCRIPTION ALL-NATP))
 (25 25 (:TYPE-PRESCRIPTION DARGP))
 (25 25 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (25 25 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (25 25 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (25 25 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (24 12 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (24 8 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (24 8 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (24 2 (:REWRITE NAT-LISTP-OF-MERGE-SORT-<))
 (20 2 (:REWRITE ALL-NATP-OF-LAST))
 (18 18 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (16 16 (:TYPE-PRESCRIPTION SUBSETP-EQUAL))
 (16 16 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (16 8 (:REWRITE DEFAULT-<-2))
 (16 8 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (16 8 (:REWRITE <-WHEN-DARGP-LESS-THAN))
 (15 15 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (14 12 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (14 8 (:REWRITE SET-DIFFERENCE-EQUAL-WHEN-NOT-CONSP))
 (14 4 (:REWRITE NAT-LISTP-OF-SET-DIFFERENCE-EQUAL))
 (12 4 (:REWRITE ALL-RATIONALP-OF-MERGE-SORT-<))
 (12 2 (:REWRITE ALL-RATIONALP-OF-LAST))
 (10 8 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (10 8 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (8 8 (:TYPE-PRESCRIPTION STRIP-CADDRS))
 (8 8 (:TYPE-PRESCRIPTION DARGP-LESS-THAN))
 (8 8 (:REWRITE USE-ALL-NATP-2))
 (8 8 (:REWRITE USE-ALL-NATP))
 (8 8 (:REWRITE USE-ALL-<-2))
 (8 8 (:REWRITE USE-ALL-<))
 (8 8 (:REWRITE DEFAULT-<-1))
 (8 8 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (8 4 (:REWRITE SUBSETP-EQUAL-WHEN-SUBSETP-EQUAL-OF-CDR-CHEAP))
 (8 4 (:REWRITE SUBSETP-EQUAL-WHEN-NOT-CONSP-ARG2-CHEAP))
 (8 4 (:REWRITE SUBSETP-EQUAL-OF-CDR-ARG2-CHEAP))
 (6 6 (:REWRITE LAST-WHEN-NOT-CONSP-CHEAP))
 (6 6 (:REWRITE CONSP-OF-MERGE-SORT-<))
 (4 4 (:REWRITE USE-ALL-<=-2))
 (4 4 (:REWRITE USE-ALL-<=))
 (4 4 (:REWRITE SUBSETP-EQUAL-WHEN-NOT-CONSP-ARG1-CHEAP))
 (4 4 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-ALT))
 (4 4 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-2-ALT))
 (4 2 (:REWRITE TRUE-LISTP-WHEN-NAT-LISTP-REWRITE))
 (2 2 (:REWRITE USE-ALL-RATIONALP-2))
 (2 2 (:REWRITE USE-ALL-RATIONALP))
 (2 2 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (2 2 (:REWRITE TRUE-LISTP-OF-MERGE-SORT-<))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE CONSP-OF-STRIP-CADDRS))
 (2 2 (:REWRITE APPEND-WHEN-NOT-CONSP-ARG1-CHEAP))
 )
(BOUND-ON-MV-NTH-5-OF-SUBSTITUTE-VAR-SET-3
 (501 2 (:REWRITE DEFAULT-+-2))
 (352 5 (:REWRITE ACL2-NUMBERP-WHEN-NATP))
 (230 15 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (157 8 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (152 19 (:REWRITE SUBST-CANDIDATES-WHEN-NOT-CONSP))
 (145 2 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (135 5 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (134 6 (:REWRITE LAST-WHEN-NOT-CDR-CHEAP))
 (128 2 (:REWRITE CDR-IFF))
 (122 4 (:REWRITE ALL-NATP-OF-MERGE-SORT-<))
 (110 2 (:REWRITE USE-ALL-NATP-FOR-CAR-OF-LAST))
 (82 4 (:REWRITE ALL-NATP-OF-SET-DIFFERENCE-EQUAL))
 (80 80 (:TYPE-PRESCRIPTION LEN))
 (74 74 (:TYPE-PRESCRIPTION NAT-LISTP))
 (73 11 (:REWRITE <-WHEN-DARGP-LESS-THAN))
 (68 4 (:REWRITE CONSP-OF-LAST))
 (66 17 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (60 21 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (52 8 (:REWRITE SET-DIFFERENCE-EQUAL-WHEN-SUBSETP-EQUAL))
 (50 50 (:TYPE-PRESCRIPTION LAST))
 (50 25 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (49 2 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (48 8 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (42 21 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (42 8 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (38 19 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (36 2 (:REWRITE NATP-OF-CAR-OF-LAST-WHEN-NAT-LISTP))
 (35 11 (:REWRITE DEFAULT-<-1))
 (35 2 (:REWRITE USE-ALL-RATIONALP-FOR-CAR-OF-LAST))
 (28 28 (:TYPE-PRESCRIPTION ALL-NATP))
 (25 25 (:TYPE-PRESCRIPTION DARGP))
 (25 25 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (25 25 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (25 25 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (25 25 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (24 12 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (24 8 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (24 8 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (24 2 (:REWRITE NAT-LISTP-OF-MERGE-SORT-<))
 (21 21 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (20 2 (:REWRITE ALL-NATP-OF-LAST))
 (19 11 (:REWRITE DEFAULT-<-2))
 (16 16 (:TYPE-PRESCRIPTION SUBSETP-EQUAL))
 (16 16 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (16 8 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (15 15 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (15 3 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-CAR-AND-QUOTE))
 (14 14 (:TYPE-PRESCRIPTION DARGP-LESS-THAN))
 (14 12 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (14 8 (:REWRITE SET-DIFFERENCE-EQUAL-WHEN-NOT-CONSP))
 (14 4 (:REWRITE NAT-LISTP-OF-SET-DIFFERENCE-EQUAL))
 (12 4 (:REWRITE ALL-RATIONALP-OF-MERGE-SORT-<))
 (12 2 (:REWRITE ALL-RATIONALP-OF-LAST))
 (11 11 (:REWRITE USE-ALL-<-2))
 (11 11 (:REWRITE USE-ALL-<))
 (10 8 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (10 8 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (9 3 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (8 8 (:TYPE-PRESCRIPTION STRIP-CADDRS))
 (8 8 (:REWRITE USE-ALL-NATP-2))
 (8 8 (:REWRITE USE-ALL-NATP))
 (8 8 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (8 4 (:REWRITE SUBSETP-EQUAL-WHEN-SUBSETP-EQUAL-OF-CDR-CHEAP))
 (8 4 (:REWRITE SUBSETP-EQUAL-WHEN-NOT-CONSP-ARG2-CHEAP))
 (8 4 (:REWRITE SUBSETP-EQUAL-OF-CDR-ARG2-CHEAP))
 (7 7 (:REWRITE USE-ALL-<=-2))
 (7 7 (:REWRITE USE-ALL-<=))
 (6 6 (:REWRITE LAST-WHEN-NOT-CONSP-CHEAP))
 (6 6 (:REWRITE CONSP-OF-MERGE-SORT-<))
 (6 3 (:REWRITE DARGP-LESS-THAN-WHEN-NATP-CHEAP))
 (6 3 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (5 5 (:REWRITE USE-ALL-RATIONALP-2))
 (5 5 (:REWRITE USE-ALL-RATIONALP))
 (4 4 (:REWRITE SUBSETP-EQUAL-WHEN-NOT-CONSP-ARG1-CHEAP))
 (4 4 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-ALT))
 (4 4 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-2-ALT))
 (4 2 (:REWRITE TRUE-LISTP-WHEN-NAT-LISTP-REWRITE))
 (3 3 (:TYPE-PRESCRIPTION MYQUOTEP))
 (3 3 (:REWRITE DARGP-LESS-THAN-WHEN-QUOTEP-CHEAP))
 (3 3 (:REWRITE DARGP-LESS-THAN-WHEN-NOT-CONSP-CHEAP))
 (3 3 (:REWRITE DARGP-LESS-THAN-WHEN-CONSP-CHEAP))
 (3 3 (:REWRITE DARGP-LESS-THAN-MONO))
 (2 2 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (2 2 (:REWRITE TRUE-LISTP-OF-MERGE-SORT-<))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE CONSP-OF-STRIP-CADDRS))
 (2 2 (:REWRITE APPEND-WHEN-NOT-CONSP-ARG1-CHEAP))
 )
(BOUND-ON-MV-NTH-5-OF-SUBSTITUTE-VAR-SET-3-GEN)
(TYPE-OF-SUBSTITUTE-VAR-SET
 (3418 1709 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (1574 1574 (:TYPE-PRESCRIPTION LAST))
 (1200 244 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (930 32 (:REWRITE LAST-WHEN-NOT-CDR-CHEAP))
 (920 42 (:REWRITE DEFAULT-+-2))
 (898 14 (:REWRITE CDR-IFF))
 (662 130 (:REWRITE SUBST-CANDIDATES-WHEN-NOT-CONSP))
 (576 10 (:REWRITE TRANSLATION-ARRAYP-AUX-WHEN-NEGATIVE))
 (546 364 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (448 448 (:TYPE-PRESCRIPTION LEN))
 (436 218 (:REWRITE SUBSETP-EQUAL-WHEN-SUBSETP-EQUAL-OF-CDR-CHEAP))
 (436 218 (:REWRITE SUBSETP-EQUAL-WHEN-NOT-CONSP-ARG2-CHEAP))
 (436 218 (:REWRITE SUBSETP-EQUAL-OF-CDR-ARG2-CHEAP))
 (386 50 (:REWRITE <-WHEN-DARGP-LESS-THAN))
 (286 90 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (250 250 (:TYPE-PRESCRIPTION STRIP-CADDRS))
 (244 244 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (234 117 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (224 70 (:REWRITE SET-DIFFERENCE-EQUAL-WHEN-SUBSETP-EQUAL))
 (218 218 (:REWRITE SUBSETP-EQUAL-WHEN-NOT-CONSP-ARG1-CHEAP))
 (218 218 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-ALT))
 (218 218 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-2-ALT))
 (216 216 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (208 98 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (186 2 (:REWRITE DARGP-LESS-THAN-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (168 6 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (168 6 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (148 50 (:REWRITE DEFAULT-<-1))
 (144 48 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (144 48 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (118 70 (:REWRITE SET-DIFFERENCE-EQUAL-WHEN-NOT-CONSP))
 (117 117 (:TYPE-PRESCRIPTION DARGP))
 (117 117 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (117 117 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (117 117 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (117 117 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (114 2 (:REWRITE BOUNDED-DARG-LISTP-OF-0))
 (98 50 (:REWRITE DEFAULT-<-2))
 (96 6 (:DEFINITION ATOM))
 (80 76 (:REWRITE USE-ALL-<))
 (76 76 (:REWRITE USE-ALL-<-2))
 (76 2 (:REWRITE USE-ALL-<-FOR-CAR))
 (56 28 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (52 52 (:TYPE-PRESCRIPTION DARGP-LESS-THAN))
 (52 52 (:REWRITE USE-ALL-<=-2))
 (52 52 (:REWRITE USE-ALL-<=))
 (48 12 (:REWRITE ALL-<=-ALL-WHEN-NOT-CONSP-ARG2))
 (48 2 (:REWRITE ALL-MYQUOTEP-BECOMES-ALL-CONSP-WHEN-DARG-LISTP))
 (42 42 (:REWRITE DEFAULT-+-1))
 (42 16 (:REWRITE TRUE-LISTP-WHEN-NAT-LISTP-REWRITE))
 (41 41 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (41 41 (:REWRITE ALL-<-TRANSITIVE))
 (38 2 (:REWRITE DARG-LISTP-WHEN-NOT-CONSP))
 (38 2 (:REWRITE ALL-MYQUOTEP-WHEN-NOT-CONSP))
 (36 36 (:REWRITE NATP-OF-+-WHEN-NEGATIVE-CONSTANT))
 (32 32 (:REWRITE LAST-WHEN-NOT-CONSP-CHEAP))
 (28 14 (:REWRITE STRIP-CARS-WHEN-NOT-CONSP-CHEAP))
 (28 2 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-CAR-AND-QUOTE))
 (24 24 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (24 4 (:REWRITE ALL-NATP-OF-LAST))
 (20 10 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (18 2 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (16 16 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (16 16 (:REWRITE CONSP-OF-STRIP-CADDRS))
 (16 14 (:REWRITE TRUE-LISTP-OF-MERGE-SORT-<))
 (16 4 (:REWRITE ALL-NATP-OF-MERGE-SORT-<))
 (16 2 (:REWRITE DARGP-LESS-THAN-WHEN-NATP-CHEAP))
 (14 14 (:TYPE-PRESCRIPTION DROP-IRRELEVANT-SUBST-CANDIDATES))
 (14 2 (:REWRITE DARGP-LESS-THAN-WHEN-NOT-CONSP-CHEAP))
 (14 2 (:REWRITE DARGP-LESS-THAN-WHEN-CONSP-CHEAP))
 (12 12 (:REWRITE APPEND-WHEN-NOT-CONSP-ARG1-CHEAP))
 (10 10 (:REWRITE TRANSLATION-ARRAYP-AUX-WHEN-BOUNDED-TRANSLATION-ARRAYP-AUX))
 (10 10 (:REWRITE TRANSLATION-ARRAYP-AUX-MONOTONE))
 (8 8 (:LINEAR ARRAY2P-LINEAR))
 (8 4 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (6 6 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (6 6 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (6 6 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (6 6 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:TYPE-PRESCRIPTION MEMBERP))
 (4 4 (:TYPE-PRESCRIPTION DARG-LISTP))
 (4 2 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (4 2 (:REWRITE DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (4 2 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (2 2 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (2 2 (:TYPE-PRESCRIPTION MYQUOTEP))
 (2 2 (:REWRITE DARGP-LESS-THAN-WHEN-QUOTEP-CHEAP))
 (2 2 (:REWRITE DARGP-LESS-THAN-MONO))
 )
(TYPE-OF-SUBSTITUTE-VAR-SET-ONE)
(TYPE-OF-SUBSTITUTE-VAR-SET-TWO)
(TYPE-OF-SUBSTITUTE-VAR-SET-THREE)
(TYPE-OF-SUBSTITUTE-VAR-SET-FOUR)
(BOUNDED-DAG-PARENT-ARRAYP-OF-MV-NTH-6-OF-SUBSTITUTE-VAR-SET)
(BOUNDED-DAG-DAG-CONSTANT-ALISTP-OF-MV-NTH-7-OF-SUBSTITUTE-VAR-SET)
(DAG-DAG-CONSTANT-ALISTP-OF-MV-NTH-7-OF-SUBSTITUTE-VAR-SET)
(BOUNDED-DAG-DAG-VARIABLE-ALISTP-OF-MV-NTH-8-OF-SUBSTITUTE-VAR-SET)
(NAT-LISTP-OF-MV-NTH-3-OF-SUBSTITUTE-VAR-SET
 (20442 10221 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (18714 18714 (:TYPE-PRESCRIPTION LAST))
 (6742 4378 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (5072 2536 (:REWRITE SUBSETP-EQUAL-WHEN-SUBSETP-EQUAL-OF-CDR-CHEAP))
 (5072 2536 (:REWRITE SUBSETP-EQUAL-WHEN-NOT-CONSP-ARG2-CHEAP))
 (5072 2536 (:REWRITE SUBSETP-EQUAL-OF-CDR-ARG2-CHEAP))
 (3250 2526 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (2560 2560 (:TYPE-PRESCRIPTION STRIP-CADDRS))
 (2536 2536 (:REWRITE SUBSETP-EQUAL-WHEN-NOT-CONSP-ARG1-CHEAP))
 (2536 2536 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-ALT))
 (2536 2536 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-2-ALT))
 (2526 2526 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (2506 2506 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (978 598 (:REWRITE SUBST-CANDIDATES-WHEN-NOT-CONSP))
 (964 282 (:REWRITE DEFAULT-+-2))
 (704 138 (:REWRITE TRANSLATION-ARRAYP-AUX-WHEN-NEGATIVE))
 (700 350 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (666 20 (:REWRITE LAST-WHEN-NOT-CDR-CHEAP))
 (646 10 (:REWRITE CDR-IFF))
 (486 486 (:REWRITE NATP-OF-+-WHEN-NEGATIVE-CONSTANT))
 (462 462 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (462 462 (:REWRITE ALL-<-TRANSITIVE))
 (450 384 (:REWRITE SET-DIFFERENCE-EQUAL-WHEN-SUBSETP-EQUAL))
 (420 384 (:REWRITE SET-DIFFERENCE-EQUAL-WHEN-NOT-CONSP))
 (390 386 (:REWRITE USE-ALL-<))
 (386 386 (:REWRITE USE-ALL-<-2))
 (372 186 (:REWRITE STRIP-CARS-WHEN-NOT-CONSP-CHEAP))
 (362 38 (:REWRITE <-WHEN-DARGP-LESS-THAN))
 (344 344 (:REWRITE USE-ALL-<=-2))
 (344 344 (:REWRITE USE-ALL-<=))
 (332 332 (:TYPE-PRESCRIPTION LEN))
 (324 324 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (282 282 (:REWRITE DEFAULT-+-1))
 (206 66 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (198 162 (:REWRITE ALL-<=-ALL-WHEN-NOT-CONSP-ARG2))
 (186 186 (:TYPE-PRESCRIPTION DROP-IRRELEVANT-SUBST-CANDIDATES))
 (186 2 (:REWRITE DARGP-LESS-THAN-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (168 6 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (168 6 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (162 81 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (160 74 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (138 138 (:REWRITE TRANSLATION-ARRAYP-AUX-WHEN-BOUNDED-TRANSLATION-ARRAYP-AUX))
 (138 138 (:REWRITE TRANSLATION-ARRAYP-AUX-MONOTONE))
 (136 38 (:REWRITE DEFAULT-<-1))
 (114 2 (:REWRITE BOUNDED-DARG-LISTP-OF-0))
 (108 36 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (108 36 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (96 6 (:DEFINITION ATOM))
 (81 81 (:TYPE-PRESCRIPTION DARGP))
 (81 81 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (81 81 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (81 81 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (81 81 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (76 2 (:REWRITE USE-ALL-<-FOR-CAR))
 (74 38 (:REWRITE DEFAULT-<-2))
 (48 2 (:REWRITE ALL-MYQUOTEP-BECOMES-ALL-CONSP-WHEN-DARG-LISTP))
 (40 40 (:TYPE-PRESCRIPTION DARGP-LESS-THAN))
 (38 2 (:REWRITE DARG-LISTP-WHEN-NOT-CONSP))
 (38 2 (:REWRITE ALL-MYQUOTEP-WHEN-NOT-CONSP))
 (28 14 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (28 2 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-CAR-AND-QUOTE))
 (24 4 (:REWRITE ALL-NATP-OF-LAST))
 (20 20 (:REWRITE LAST-WHEN-NOT-CONSP-CHEAP))
 (18 2 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (16 10 (:REWRITE TRUE-LISTP-OF-MERGE-SORT-<))
 (16 4 (:REWRITE ALL-NATP-OF-MERGE-SORT-<))
 (16 2 (:REWRITE DARGP-LESS-THAN-WHEN-NATP-CHEAP))
 (14 2 (:REWRITE DARGP-LESS-THAN-WHEN-NOT-CONSP-CHEAP))
 (14 2 (:REWRITE DARGP-LESS-THAN-WHEN-CONSP-CHEAP))
 (12 12 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (12 12 (:REWRITE CONSP-OF-STRIP-CADDRS))
 (8 8 (:LINEAR ARRAY2P-LINEAR))
 (8 4 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (6 6 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (6 6 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (6 6 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (6 6 (:REWRITE APPEND-WHEN-NOT-CONSP-ARG1-CHEAP))
 (6 6 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:TYPE-PRESCRIPTION MEMBERP))
 (4 4 (:TYPE-PRESCRIPTION DARG-LISTP))
 (4 2 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (4 2 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (4 2 (:REWRITE DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (4 2 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (2 2 (:TYPE-PRESCRIPTION MYQUOTEP))
 (2 2 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (2 2 (:REWRITE TRUE-LIST-FIX-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE DARGP-LESS-THAN-WHEN-QUOTEP-CHEAP))
 (2 2 (:REWRITE DARGP-LESS-THAN-MONO))
 )
(TRUE-LISTP-OF-MV-NTH-3-OF-SUBSTITUTE-VAR-SET
 (2408 10 (:REWRITE DEFAULT-+-2))
 (1483 12 (:REWRITE ACL2-NUMBERP-WHEN-NATP))
 (776 52 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (769 12 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (721 32 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (599 16 (:REWRITE ALL-NATP-OF-MERGE-SORT-<))
 (586 8 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (548 30 (:REWRITE LAST-WHEN-NOT-CDR-CHEAP))
 (545 8 (:REWRITE USE-ALL-NATP-FOR-CAR-OF-LAST))
 (518 8 (:REWRITE CDR-IFF))
 (495 115 (:REWRITE SUBST-CANDIDATES-WHEN-NOT-CONSP))
 (417 32 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (404 16 (:REWRITE CONSP-OF-LAST))
 (328 16 (:REWRITE ALL-NATP-OF-SET-DIFFERENCE-EQUAL))
 (305 8 (:REWRITE USE-ALL-RATIONALP-FOR-CAR-OF-LAST))
 (300 30 (:REWRITE CONSP-OF-SET-DIFFERENCE-EQUAL))
 (296 296 (:TYPE-PRESCRIPTION NAT-LISTP))
 (288 288 (:TYPE-PRESCRIPTION LEN))
 (262 8 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (244 18 (:REWRITE TRUE-LISTP-WHEN-NAT-LISTP-REWRITE))
 (222 74 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (222 24 (:REWRITE CONSP-OF-MERGE-SORT-<))
 (200 200 (:TYPE-PRESCRIPTION LAST))
 (200 60 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (174 32 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (168 2 (:REWRITE NAT-LISTP-OF-MV-NTH-2-OF-TRANSLATE-LITERALS))
 (150 75 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (150 8 (:REWRITE NATP-OF-CAR-OF-LAST-WHEN-NAT-LISTP))
 (148 74 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (147 16 (:REWRITE ALL-RATIONALP-OF-MERGE-SORT-<))
 (134 66 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (128 62 (:REWRITE SET-DIFFERENCE-EQUAL-WHEN-SUBSETP-EQUAL))
 (122 122 (:TYPE-PRESCRIPTION ALL-NATP))
 (116 58 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (114 34 (:REWRITE <-WHEN-DARGP-LESS-THAN))
 (102 8 (:REWRITE NAT-LISTP-OF-MERGE-SORT-<))
 (96 32 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (96 32 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (92 62 (:REWRITE SET-DIFFERENCE-EQUAL-WHEN-NOT-CONSP))
 (88 2 (:REWRITE TRANSLATION-ARRAYP-AUX-WHEN-NEGATIVE))
 (86 8 (:REWRITE ALL-NATP-OF-LAST))
 (80 2 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (78 58 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (76 38 (:REWRITE SUBSETP-EQUAL-WHEN-SUBSETP-EQUAL-OF-CDR-CHEAP))
 (76 38 (:REWRITE SUBSETP-EQUAL-WHEN-NOT-CONSP-ARG2-CHEAP))
 (76 38 (:REWRITE SUBSETP-EQUAL-OF-CDR-ARG2-CHEAP))
 (75 75 (:TYPE-PRESCRIPTION DARGP))
 (75 75 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (75 75 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (75 75 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (75 75 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (74 74 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (66 34 (:REWRITE DEFAULT-<-2))
 (64 64 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (64 32 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (58 58 (:TYPE-PRESCRIPTION STRIP-CADDRS))
 (56 16 (:REWRITE NAT-LISTP-OF-SET-DIFFERENCE-EQUAL))
 (52 52 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (52 32 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (48 48 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (48 8 (:REWRITE ALL-RATIONALP-OF-LAST))
 (46 32 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (44 34 (:REWRITE DEFAULT-<-1))
 (38 38 (:REWRITE SUBSETP-EQUAL-WHEN-NOT-CONSP-ARG1-CHEAP))
 (38 38 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-ALT))
 (38 38 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-2-ALT))
 (36 36 (:TYPE-PRESCRIPTION DARGP-LESS-THAN))
 (34 34 (:REWRITE USE-ALL-<-2))
 (34 34 (:REWRITE USE-ALL-<))
 (32 32 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (30 30 (:REWRITE LAST-WHEN-NOT-CONSP-CHEAP))
 (22 22 (:TYPE-PRESCRIPTION NATP))
 (20 2 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (16 16 (:REWRITE USE-ALL-<=-2))
 (16 16 (:REWRITE USE-ALL-<=))
 (16 16 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (14 8 (:REWRITE TRUE-LISTP-OF-MERGE-SORT-<))
 (14 2 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-CAR-AND-QUOTE))
 (12 12 (:TYPE-PRESCRIPTION WF-DAGP))
 (10 10 (:REWRITE USE-ALL-RATIONALP-2))
 (10 10 (:REWRITE USE-ALL-RATIONALP))
 (10 10 (:REWRITE USE-ALL-NATP-2))
 (10 10 (:REWRITE USE-ALL-NATP))
 (10 10 (:REWRITE DEFAULT-+-1))
 (10 10 (:REWRITE CONSP-OF-STRIP-CADDRS))
 (8 2 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (6 2 (:REWRITE TRANSLATION-ARRAYP-AUX-OF-MV-NTH-1-OF-REBUILD-NODES-WITH-VAR-SUBST))
 (6 2 (:REWRITE DARGP-LESS-THAN-WHEN-NATP-CHEAP))
 (6 2 (:REWRITE ARRAY1P-WHEN-CANDIDATE-DEPS-ARRAYP))
 (6 2 (:REWRITE ARRAY1P-OF-MV-NTH-1-OF-REBUILD-NODES-WITH-VAR-SUBST))
 (6 2 (:REWRITE ALEN1-OF-MV-NTH-1-OF-REBUILD-NODES-WITH-VAR-SUBST))
 (4 4 (:TYPE-PRESCRIPTION TRANSLATION-ARRAYP-AUX))
 (4 4 (:TYPE-PRESCRIPTION CANDIDATE-DEPS-ARRAYP))
 (4 4 (:TYPE-PRESCRIPTION ARRAY1P))
 (4 2 (:REWRITE DARGP-LESS-THAN-WHEN-NOT-CONSP-CHEAP))
 (4 2 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (4 2 (:REWRITE DARGP-LESS-THAN-WHEN-CONSP-CHEAP))
 (2 2 (:TYPE-PRESCRIPTION MYQUOTEP))
 (2 2 (:REWRITE TRANSLATION-ARRAYP-AUX-WHEN-BOUNDED-TRANSLATION-ARRAYP-AUX))
 (2 2 (:REWRITE TRANSLATION-ARRAYP-AUX-MONOTONE))
 (2 2 (:REWRITE DARGP-LESS-THAN-WHEN-QUOTEP-CHEAP))
 (2 2 (:REWRITE DARGP-LESS-THAN-MONO))
 (2 2 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (2 2 (:REWRITE APPEND-WHEN-NOT-CONSP-ARG1-CHEAP))
 (2 2 (:REWRITE <-OF-+-OF-1-WHEN-INTEGERS))
 (2 2 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 )
(ALL-<-OF-MV-NTH-3-OF-SUBSTITUTE-VAR-SET
 (20710 10355 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (18986 18986 (:TYPE-PRESCRIPTION LAST))
 (6812 4426 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (5152 2576 (:REWRITE SUBSETP-EQUAL-WHEN-SUBSETP-EQUAL-OF-CDR-CHEAP))
 (5152 2576 (:REWRITE SUBSETP-EQUAL-WHEN-NOT-CONSP-ARG2-CHEAP))
 (5152 2576 (:REWRITE SUBSETP-EQUAL-OF-CDR-ARG2-CHEAP))
 (3849 2578 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (2612 2612 (:TYPE-PRESCRIPTION STRIP-CADDRS))
 (2578 2578 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (2576 2576 (:REWRITE SUBSETP-EQUAL-WHEN-NOT-CONSP-ARG1-CHEAP))
 (2576 2576 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-ALT))
 (2576 2576 (:REWRITE SUBSETP-EQUAL-TRANSITIVE-2-ALT))
 (2551 2551 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (2280 11 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (1538 114 (:REWRITE LAST-WHEN-NOT-CDR-CHEAP))
 (1424 22 (:REWRITE CDR-IFF))
 (1383 908 (:REWRITE SUBST-CANDIDATES-WHEN-NOT-CONSP))
 (1302 344 (:REWRITE DEFAULT-+-2))
 (708 354 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (706 140 (:REWRITE TRANSLATION-ARRAYP-AUX-WHEN-NEGATIVE))
 (652 542 (:REWRITE SET-DIFFERENCE-EQUAL-WHEN-SUBSETP-EQUAL))
 (647 647 (:TYPE-PRESCRIPTION LEN))
 (590 542 (:REWRITE SET-DIFFERENCE-EQUAL-WHEN-NOT-CONSP))
 (492 492 (:REWRITE NATP-OF-+-WHEN-NEGATIVE-CONSTANT))
 (477 477 (:REWRITE ALL-<-TRANSITIVE))
 (432 73 (:REWRITE <-WHEN-DARGP-LESS-THAN))
 (429 425 (:REWRITE USE-ALL-<))
 (425 425 (:REWRITE USE-ALL-<-2))
 (376 188 (:REWRITE STRIP-CARS-WHEN-NOT-CONSP-CHEAP))
 (372 372 (:REWRITE USE-ALL-<=-2))
 (372 372 (:REWRITE USE-ALL-<=))
 (350 344 (:REWRITE DEFAULT-+-1))
 (328 328 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (315 124 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (300 144 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (284 142 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (274 2 (:REWRITE CONSP-OF-APPEND))
 (213 71 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (213 71 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (200 164 (:REWRITE ALL-<=-ALL-WHEN-NOT-CONSP-ARG2))
 (188 188 (:TYPE-PRESCRIPTION DROP-IRRELEVANT-SUBST-CANDIDATES))
 (186 2 (:REWRITE DARGP-LESS-THAN-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (171 73 (:REWRITE DEFAULT-<-1))
 (168 6 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (148 144 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (144 73 (:REWRITE DEFAULT-<-2))
 (142 142 (:TYPE-PRESCRIPTION DARGP))
 (142 142 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (142 142 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (142 142 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (140 140 (:REWRITE TRANSLATION-ARRAYP-AUX-WHEN-BOUNDED-TRANSLATION-ARRAYP-AUX))
 (140 140 (:REWRITE TRANSLATION-ARRAYP-AUX-MONOTONE))
 (118 2 (:LINEAR LEN-OF-TRANSLATE-LITERALS))
 (114 114 (:REWRITE LAST-WHEN-NOT-CONSP-CHEAP))
 (114 2 (:REWRITE BOUNDED-DARG-LISTP-OF-0))
 (96 6 (:DEFINITION ATOM))
 (76 2 (:REWRITE USE-ALL-<-FOR-CAR))
 (75 75 (:TYPE-PRESCRIPTION DARGP-LESS-THAN))
 (58 24 (:REWRITE TRUE-LISTP-WHEN-NAT-LISTP-REWRITE))
 (48 2 (:REWRITE LEN-OF-SET-DIFFERENCE-EQUAL))
 (48 2 (:REWRITE ALL-MYQUOTEP-BECOMES-ALL-CONSP-WHEN-DARG-LISTP))
 (40 2 (:REWRITE PERM-OF-APPEND-WHEN-NOT-CONSP))
 (40 2 (:LINEAR <=-OF-LEN-OF-INTERSECTION-EQUAL-LINEAR))
 (38 22 (:REWRITE TRUE-LISTP-OF-MERGE-SORT-<))
 (38 2 (:REWRITE DARG-LISTP-WHEN-NOT-CONSP))
 (38 2 (:REWRITE ALL-MYQUOTEP-WHEN-NOT-CONSP))
 (28 2 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-CAR-AND-QUOTE))
 (24 24 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (24 4 (:REWRITE ALL-NATP-OF-LAST))
 (22 2 (:REWRITE COMMUTATIVITY-OF-+))
 (20 10 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (18 2 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (17 11 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (16 16 (:REWRITE CONSP-OF-STRIP-CADDRS))
 (16 8 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (16 4 (:REWRITE ALL-NATP-OF-MERGE-SORT-<))
 (16 2 (:REWRITE DARGP-LESS-THAN-WHEN-NATP-CHEAP))
 (14 2 (:REWRITE DARGP-LESS-THAN-WHEN-NOT-CONSP-CHEAP))
 (14 2 (:REWRITE DARGP-LESS-THAN-WHEN-CONSP-CHEAP))
 (12 12 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (12 12 (:REWRITE APPEND-WHEN-NOT-CONSP-ARG1-CHEAP))
 (11 11 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (11 11 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (8 8 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (8 8 (:LINEAR ARRAY2P-LINEAR))
 (8 4 (:REWRITE INTERSECTION-EQUAL-WHEN-NOT-CONSP-ARG2-CHEAP))
 (8 4 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (6 6 (:TYPE-PRESCRIPTION INTERSECTION-EQUAL))
 (6 6 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (4 4 (:TYPE-PRESCRIPTION MEMBERP))
 (4 4 (:TYPE-PRESCRIPTION DARG-LISTP))
 (4 4 (:REWRITE INTERSECTION-EQUAL-WHEN-SUBSETP-EQUAL))
 (4 4 (:REWRITE INTERSECTION-EQUAL-WHEN-NOT-CONSP-ARG1-CHEAP))
 (4 2 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-MV-NTH-3-OF-SUBSTITUTE-VAR-SET))
 (4 2 (:REWRITE DEFAULT-UNARY-MINUS))
 (4 2 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (4 2 (:REWRITE DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (4 2 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (2 2 (:TYPE-PRESCRIPTION MYQUOTEP))
 (2 2 (:REWRITE FOLD-CONSTS-IN-+))
 (2 2 (:REWRITE DARGP-LESS-THAN-WHEN-QUOTEP-CHEAP))
 (2 2 (:REWRITE DARGP-LESS-THAN-MONO))
 )
(SUBSTITUTE-VARS2
 (2277 1141 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (1404 55 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (382 61 (:REWRITE <-WHEN-DARGP-LESS-THAN))
 (313 115 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (201 53 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (201 53 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (174 87 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (172 9 (:REWRITE DARGP-LESS-THAN-WHEN-NATP-CHEAP))
 (114 61 (:REWRITE DEFAULT-<-2))
 (108 108 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (91 91 (:TYPE-PRESCRIPTION DARGP))
 (87 87 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (87 87 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (87 87 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (69 61 (:REWRITE DEFAULT-<-1))
 (61 61 (:TYPE-PRESCRIPTION DARGP-LESS-THAN))
 (61 61 (:REWRITE USE-ALL-<-2))
 (61 61 (:REWRITE USE-ALL-<))
 (57 3 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (55 55 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (48 4 (:REWRITE INTEGERP-WHEN-DARGP))
 (43 43 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (39 9 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-CAR-AND-QUOTE))
 (26 9 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (20 4 (:REWRITE INTEGERP-WHEN-NATP))
 (20 4 (:REWRITE DARGP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (18 9 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (16 4 (:REWRITE DARGP-WHEN-NOT-CONSP-CHEAP))
 (14 14 (:TYPE-PRESCRIPTION MYQUOTEP))
 (14 9 (:REWRITE DARGP-LESS-THAN-WHEN-QUOTEP-CHEAP))
 (11 11 (:REWRITE USE-ALL-NATP-2))
 (11 11 (:REWRITE USE-ALL-NATP))
 (10 5 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (9 9 (:REWRITE USE-ALL-<=-2))
 (9 9 (:REWRITE USE-ALL-<=))
 (9 9 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (9 9 (:REWRITE DARGP-LESS-THAN-MONO))
 (8 8 (:LINEAR ARRAY2P-LINEAR))
 (7 7 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (5 5 (:TYPE-PRESCRIPTION ALL-NATP))
 (5 5 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (5 5 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (5 5 (:REWRITE ALL-<-TRANSITIVE))
 (4 4 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (4 4 (:REWRITE DARGP-WHEN-DARGP-LESS-THAN))
 (3 3 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 )
(SUBSTITUTE-VARS2-RETURN-TYPE
 (42233 21127 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (8561 360 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (8470 10 (:REWRITE NOT-ALL-NATP-WHEN-NOT-NATP-AND-MEMBER-EQUAL))
 (2424 2424 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (1461 50 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (1418 500 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (1212 606 (:REWRITE NOT-MEMBER-EQUAL-WHEN-NOT-MEMBER-EQUAL-OF-CDR-CHEAP))
 (1212 606 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-CDR-CHEAP))
 (1188 606 (:REWRITE MEMBER-EQUAL-WHEN-<=-OF-LEN-AND-1))
 (1146 573 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (928 643 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (927 236 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (927 236 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (606 606 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-2))
 (606 606 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-1))
 (606 606 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-MEMBER-EQUAL))
 (606 606 (:REWRITE MEMBER-EQUAL-OF-SINGLETON-CONSTANT-IFF))
 (606 606 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-WHEN-NOT-EQUAL-CAR))
 (606 606 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-TRIM))
 (573 573 (:TYPE-PRESCRIPTION DARGP))
 (573 573 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (573 573 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (573 573 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (564 257 (:REWRITE DEFAULT-<-2))
 (490 70 (:REWRITE LEN-OF-MV-NTH-5-OF-CRUNCH-DAG-ARRAY2-WITH-INDICES))
 (360 360 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (294 257 (:REWRITE DEFAULT-<-1))
 (271 263 (:REWRITE USE-ALL-<))
 (263 263 (:REWRITE USE-ALL-<-2))
 (249 75 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (218 218 (:LINEAR ARRAY2P-LINEAR))
 (216 216 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (164 75 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (99 28 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-CAR-AND-QUOTE))
 (96 96 (:REWRITE USE-ALL-NATP-2))
 (96 96 (:REWRITE USE-ALL-NATP))
 (92 46 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (66 66 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (66 66 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (64 28 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (58 8 (:REWRITE ACL2-NUMBERP-WHEN-NATP))
 (56 28 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (50 50 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (49 49 (:TYPE-PRESCRIPTION MYQUOTEP))
 (49 28 (:REWRITE DARGP-LESS-THAN-WHEN-QUOTEP-CHEAP))
 (34 8 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (30 30 (:REWRITE USE-ALL-<=-2))
 (30 30 (:REWRITE USE-ALL-<=))
 (28 28 (:REWRITE DARGP-LESS-THAN-MONO))
 (10 2 (:REWRITE NATP-OF-MV-NTH-5-OF-SUBSTITUTE-VAR-SET))
 (9 9 (:REWRITE USE-ALL-RATIONALP-2))
 (9 9 (:REWRITE USE-ALL-RATIONALP))
 (9 2 (:REWRITE BOUND-ON-MV-NTH-5-OF-SUBSTITUTE-VAR-SET-3-GEN))
 (8 8 (:TYPE-PRESCRIPTION MEMBERP))
 (5 5 (:REWRITE DARGP-LESS-THAN-WHEN-NOT-CONSP-CHEAP))
 (5 5 (:REWRITE DARGP-LESS-THAN-WHEN-CONSP-CHEAP))
 )
(SUBSTITUTE-VARS2-RETURN-TYPE-COROLLARY
 (815 409 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (809 1 (:REWRITE NOT-ALL-NATP-WHEN-NOT-NATP-AND-MEMBER-EQUAL))
 (232 232 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (116 58 (:REWRITE NOT-MEMBER-EQUAL-WHEN-NOT-MEMBER-EQUAL-OF-CDR-CHEAP))
 (116 58 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-CDR-CHEAP))
 (112 58 (:REWRITE MEMBER-EQUAL-WHEN-<=-OF-LEN-AND-1))
 (112 11 (:REWRITE <-WHEN-DARGP-LESS-THAN))
 (84 3 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (75 3 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (58 58 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-2))
 (58 58 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-1))
 (58 58 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-MEMBER-EQUAL))
 (58 58 (:REWRITE MEMBER-EQUAL-OF-SINGLETON-CONSTANT-IFF))
 (58 58 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-WHEN-NOT-EQUAL-CAR))
 (58 58 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-TRIM))
 (36 5 (:REWRITE DARGP-LESS-THAN-WHEN-NATP-CHEAP))
 (34 34 (:TYPE-PRESCRIPTION LEN))
 (27 15 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (27 11 (:REWRITE DEFAULT-<-1))
 (19 5 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-CAR-AND-QUOTE))
 (16 11 (:REWRITE DEFAULT-<-2))
 (15 11 (:REWRITE USE-ALL-<))
 (15 5 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (15 5 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (13 13 (:TYPE-PRESCRIPTION DARGP-LESS-THAN))
 (12 5 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (11 11 (:REWRITE USE-ALL-<-2))
 (10 5 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (10 2 (:REWRITE ACL2-NUMBERP-WHEN-NATP))
 (8 8 (:TYPE-PRESCRIPTION MYQUOTEP))
 (8 5 (:REWRITE DARGP-LESS-THAN-WHEN-QUOTEP-CHEAP))
 (8 4 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (8 4 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (6 6 (:REWRITE USE-ALL-NATP-2))
 (6 6 (:REWRITE USE-ALL-NATP))
 (6 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (5 5 (:REWRITE USE-ALL-<=-2))
 (5 5 (:REWRITE USE-ALL-<=))
 (5 5 (:REWRITE DARGP-LESS-THAN-MONO))
 (5 5 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (4 4 (:TYPE-PRESCRIPTION MEMBERP))
 (4 4 (:TYPE-PRESCRIPTION DARGP))
 (4 4 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (4 4 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (4 4 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (4 4 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (3 3 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (3 3 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (3 3 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (3 3 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (3 3 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (3 3 (:REWRITE ALL-<-TRANSITIVE))
 (2 2 (:REWRITE USE-ALL-RATIONALP-2))
 (2 2 (:REWRITE USE-ALL-RATIONALP))
 (2 2 (:REWRITE DARGP-LESS-THAN-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE DARGP-LESS-THAN-WHEN-CONSP-CHEAP))
 (2 2 (:LINEAR ARRAY2P-LINEAR))
 )
(SUBSTITUTE-VARS2-RETURN-TYPE-COROLLARY2
 (1236 619 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (809 1 (:REWRITE NOT-ALL-NATP-WHEN-NOT-NATP-AND-MEMBER-EQUAL))
 (232 232 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (116 58 (:REWRITE NOT-MEMBER-EQUAL-WHEN-NOT-MEMBER-EQUAL-OF-CDR-CHEAP))
 (116 58 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-CDR-CHEAP))
 (112 58 (:REWRITE MEMBER-EQUAL-WHEN-<=-OF-LEN-AND-1))
 (112 4 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (100 4 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (76 9 (:REWRITE <-WHEN-DARGP-LESS-THAN))
 (58 58 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-2))
 (58 58 (:REWRITE MEMBER-EQUAL-WHEN-SUBSETP-EQUAL-1))
 (58 58 (:REWRITE MEMBER-EQUAL-WHEN-MEMBER-EQUAL-OF-MEMBER-EQUAL))
 (58 58 (:REWRITE MEMBER-EQUAL-OF-SINGLETON-CONSTANT-IFF))
 (58 58 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-WHEN-NOT-EQUAL-CAR))
 (58 58 (:REWRITE MEMBER-EQUAL-OF-CONSTANT-TRIM))
 (41 41 (:TYPE-PRESCRIPTION LEN))
 (28 15 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (27 3 (:REWRITE DARGP-LESS-THAN-WHEN-NATP-CHEAP))
 (18 6 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (18 6 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (17 9 (:REWRITE DEFAULT-<-1))
 (15 9 (:REWRITE DEFAULT-<-2))
 (11 9 (:REWRITE USE-ALL-<))
 (11 3 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-CAR-AND-QUOTE))
 (10 10 (:TYPE-PRESCRIPTION DARGP-LESS-THAN))
 (10 5 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (10 5 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (9 9 (:REWRITE USE-ALL-<-2))
 (7 7 (:REWRITE USE-ALL-NATP-2))
 (7 7 (:REWRITE USE-ALL-NATP))
 (7 3 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (6 6 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (6 6 (:LINEAR ARRAY2P-LINEAR))
 (6 3 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (5 5 (:TYPE-PRESCRIPTION MYQUOTEP))
 (5 5 (:TYPE-PRESCRIPTION DARGP))
 (5 5 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (5 5 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (5 5 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (5 5 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (5 5 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (5 5 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (5 3 (:REWRITE DARGP-LESS-THAN-WHEN-QUOTEP-CHEAP))
 (5 1 (:REWRITE ACL2-NUMBERP-WHEN-NATP))
 (4 4 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (4 4 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (4 4 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (4 4 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (4 4 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:REWRITE ALL-<-TRANSITIVE))
 (3 3 (:REWRITE USE-ALL-<=-2))
 (3 3 (:REWRITE USE-ALL-<=))
 (3 3 (:REWRITE DARGP-LESS-THAN-MONO))
 (3 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2 2 (:TYPE-PRESCRIPTION MEMBERP))
 (2 2 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (1 1 (:REWRITE USE-ALL-RATIONALP-2))
 (1 1 (:REWRITE USE-ALL-RATIONALP))
 (1 1 (:REWRITE DARGP-LESS-THAN-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE DARGP-LESS-THAN-WHEN-CONSP-CHEAP))
 (1 1 (:LINEAR SUBSTITUTE-VARS2-RETURN-TYPE-COROLLARY))
 )
(SUBSTITUTE-VARS2-RETURN-TYPE-2
 (3668 149 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (540 180 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (442 221 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (360 90 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (360 90 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (359 245 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (302 51 (:REWRITE TRUE-LISTP-WHEN-NAT-LISTP-REWRITE))
 (276 276 (:TYPE-PRESCRIPTION NAT-LISTP))
 (221 221 (:TYPE-PRESCRIPTION DARGP))
 (221 221 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (221 221 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (221 221 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (180 90 (:REWRITE DEFAULT-<-2))
 (180 90 (:REWRITE <-WHEN-DARGP-LESS-THAN))
 (168 24 (:REWRITE LEN-OF-MV-NTH-5-OF-CRUNCH-DAG-ARRAY2-WITH-INDICES))
 (149 149 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (90 90 (:TYPE-PRESCRIPTION DARGP-LESS-THAN))
 (90 90 (:REWRITE USE-ALL-<-2))
 (90 90 (:REWRITE USE-ALL-<))
 (90 90 (:REWRITE DEFAULT-<-1))
 (90 90 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (90 45 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (84 42 (:TYPE-PRESCRIPTION NATP-OF-MV-NTH-5-OF-SUBSTITUTE-VAR-SET))
 (51 51 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (51 51 (:REWRITE NAT-LISTP-WHEN-NOT-CONSP-CHEAP))
 (45 45 (:TYPE-PRESCRIPTION ALL-NATP))
 (42 42 (:TYPE-PRESCRIPTION NATP))
 (30 3 (:REWRITE TRUE-LISTP-OF-MV-NTH-3-OF-SUBSTITUTE-VAR-SET))
 (29 10 (:REWRITE SUBSTITUTE-VARS2-RETURN-TYPE))
 (22 22 (:TYPE-PRESCRIPTION WF-DAGP))
 (9 3 (:REWRITE TYPE-OF-SUBSTITUTE-VAR-SET))
 (9 3 (:REWRITE NAT-LISTP-OF-MV-NTH-3-OF-SUBSTITUTE-VAR-SET))
 )
(SUBSTITUTE-VARS2-RETURN-TYPE-3
 (41302 20651 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (11844 499 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (2207 2207 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (1620 552 (:TYPE-PRESCRIPTION NATP-OF-NTH-WHEN-NAT-LISTP-TYPE))
 (1602 801 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (1289 916 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (1086 276 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (1086 276 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (805 115 (:REWRITE LEN-OF-MV-NTH-5-OF-CRUNCH-DAG-ARRAY2-WITH-INDICES))
 (801 801 (:TYPE-PRESCRIPTION DARGP))
 (801 801 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (801 801 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (801 801 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (552 276 (:REWRITE DEFAULT-<-2))
 (552 276 (:REWRITE <-WHEN-DARGP-LESS-THAN))
 (499 499 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (419 41 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (276 276 (:TYPE-PRESCRIPTION DARGP-LESS-THAN))
 (276 276 (:REWRITE USE-ALL-<-2))
 (276 276 (:REWRITE USE-ALL-<))
 (276 276 (:REWRITE DEFAULT-<-1))
 (276 276 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (174 174 (:LINEAR ARRAY2P-LINEAR))
 (153 153 (:REWRITE USE-ALL-NATP-2))
 (153 153 (:REWRITE USE-ALL-NATP))
 (82 41 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (50 50 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (50 50 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (50 50 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (50 50 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (50 50 (:REWRITE ALL-<-TRANSITIVE))
 (41 41 (:TYPE-PRESCRIPTION ALL-NATP))
 (41 41 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 )
