(ADE::V-<-CORRECT-INSTANCE
 (180 3 (:DEFINITION TAKE))
 (174 6 (:REWRITE TAKE-OF-TOO-MANY))
 (88 7 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (42 6 (:DEFINITION LEN))
 (25 16 (:REWRITE DEFAULT-+-2))
 (24 3 (:DEFINITION NTHCDR))
 (16 16 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (16 16 (:REWRITE DEFAULT-+-1))
 (15 2 (:REWRITE REV-WHEN-NOT-CONSP))
 (14 14 (:LINEAR LEN-WHEN-PREFIXP))
 (13 7 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (12 12 (:REWRITE DEFAULT-CDR))
 (8 8 (:REWRITE ZP-OPEN))
 (8 8 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (7 7 (:REWRITE |(< (- x) (- y))|))
 (7 7 (:LINEAR ADE::A-HELPFUL-LEMMA-FOR-TREE-INDUCTIONS))
 (7 4 (:REWRITE SIMPLIFY-SUMS-<))
 (7 4 (:REWRITE DEFAULT-<-2))
 (7 4 (:REWRITE |(+ c (+ d x))|))
 (6 6 (:REWRITE TAKE-WHEN-ATOM))
 (6 3 (:TYPE-PRESCRIPTION TRUE-LISTP-NTHCDR-TYPE-PRESCRIPTION))
 (6 3 (:REWRITE |(< d (+ c x))|))
 (5 1 (:REWRITE CONSP-OF-TAKE))
 (4 4 (:TYPE-PRESCRIPTION NFIX))
 (4 4 (:REWRITE DEFAULT-<-1))
 (3 3 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (3 3 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE |(< (+ c x) d)|))
 (2 2 (:TYPE-PRESCRIPTION TAKE))
 (2 2 (:LINEAR ADE::V-<-CORRECT-2))
 (1 1 (:TYPE-PRESCRIPTION ZP))
 (1 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (1 1 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (1 1 (:REWRITE DEFAULT-UNARY-MINUS))
 (1 1 (:REWRITE DEFAULT-*-2))
 (1 1 (:REWRITE DEFAULT-*-1))
 (1 1 (:REWRITE |(equal (- x) (- y))|))
 (1 1 (:REWRITE |(equal (+ c x) d)|))
 )
(ADE::V-TO-NAT-OF-V-ZP
 (88 44 (:TYPE-PRESCRIPTION ADE::BOOLEANP-V-NZP))
 (44 44 (:TYPE-PRESCRIPTION ADE::BVP))
 (34 34 (:REWRITE ADE::V-NZP-AS-OR-CROCK))
 (22 12 (:REWRITE DEFAULT-*-2))
 (19 19 (:REWRITE DEFAULT-CDR))
 (17 17 (:REWRITE ADE::NOT-V-NZP-TAKE-NTHCDR))
 (15 15 (:REWRITE DEFAULT-CAR))
 (12 12 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (12 12 (:REWRITE DEFAULT-*-1))
 (12 6 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (12 6 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (12 6 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (11 6 (:REWRITE DEFAULT-+-2))
 (10 10 (:LINEAR ADE::V-<-CORRECT-2))
 (10 10 (:LINEAR ADE::V-<-CORRECT-1))
 (6 6 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-A+AB-=-0))
 (6 6 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (6 6 (:REWRITE NORMALIZE-ADDENDS))
 (6 6 (:REWRITE DEFAULT-+-1))
 (6 6 (:REWRITE |(equal (- x) 0)|))
 (6 6 (:REWRITE |(equal (- x) (- y))|))
 (5 5 (:REWRITE ADE::V-ZP-AS-AND-CROCK))
 )
(ADE::MY-COUNT
 (3 3 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (3 3 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (3 3 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 )
(ADE::GCD$OP
 (2955 63 (:REWRITE TAKE-OF-TOO-MANY))
 (1913 29 (:DEFINITION TAKE))
 (1414 202 (:DEFINITION LEN))
 (537 303 (:REWRITE DEFAULT-+-2))
 (304 303 (:REWRITE DEFAULT-+-1))
 (303 303 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (270 31 (:DEFINITION NTHCDR))
 (266 266 (:REWRITE DEFAULT-CDR))
 (173 173 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (173 173 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (173 173 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (143 137 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (142 142 (:LINEAR LEN-WHEN-PREFIXP))
 (137 137 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (132 132 (:REWRITE |(< (- x) (- y))|))
 (128 125 (:REWRITE DEFAULT-*-2))
 (125 125 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (125 125 (:REWRITE DEFAULT-*-1))
 (110 62 (:REWRITE TAKE-WHEN-ATOM))
 (105 72 (:REWRITE DEFAULT-<-2))
 (102 2 (:REWRITE ADE::V-<-CORRECT-1))
 (92 20 (:REWRITE REV-WHEN-NOT-CONSP))
 (77 1 (:REWRITE |(< (if a b c) x)|))
 (74 72 (:REWRITE DEFAULT-<-1))
 (71 71 (:LINEAR ADE::A-HELPFUL-LEMMA-FOR-TREE-INDUCTIONS))
 (67 38 (:REWRITE |(+ c (+ d x))|))
 (62 62 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (62 62 (:REWRITE DEFAULT-UNARY-/))
 (62 33 (:REWRITE |(< d (+ c x))|))
 (56 56 (:TYPE-PRESCRIPTION NFIX))
 (44 26 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (44 26 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (38 38 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-A+AB))
 (38 38 (:REWRITE |(< 0 (- x))|))
 (36 2 (:DEFINITION NATP))
 (34 34 (:REWRITE |(* (- x) y)|))
 (33 33 (:REWRITE DEFAULT-CAR))
 (32 32 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (32 32 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (32 32 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (31 31 (:REWRITE |(equal (- x) (- y))|))
 (31 31 (:REWRITE |(< (+ c x) d)|))
 (26 1 (:DEFINITION NFIX))
 (24 4 (:DEFINITION BINARY-APPEND))
 (20 8 (:REWRITE APPEND-WHEN-NOT-CONSP))
 (18 18 (:LINEAR ADE::V-<-CORRECT-2))
 (18 18 (:LINEAR ADE::V-<-CORRECT-1))
 (16 16 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-A+AB-=-0))
 (16 16 (:REWRITE |(equal (- x) 0)|))
 (16 8 (:TYPE-PRESCRIPTION NOT-INTEGERP-4E))
 (14 2 (:REWRITE CONSP-OF-APPEND))
 (9 9 (:REWRITE REDUCE-INTEGERP-+))
 (9 9 (:REWRITE INTEGERP-MINUS-X))
 (9 9 (:REWRITE |(integerp (* c x))|))
 (9 9 (:META META-INTEGERP-CORRECT))
 (8 8 (:TYPE-PRESCRIPTION NOT-INTEGERP-3E))
 (8 8 (:TYPE-PRESCRIPTION NOT-INTEGERP-2E))
 (8 8 (:TYPE-PRESCRIPTION NOT-INTEGERP-1E))
 (8 8 (:REWRITE DEFAULT-UNARY-MINUS))
 (8 8 (:REWRITE CONSP-OF-TAKE))
 (7 7 (:REWRITE INSERT-0-*))
 (6 6 (:TYPE-PRESCRIPTION NOT-INTEGERP-4D))
 (6 6 (:TYPE-PRESCRIPTION NOT-INTEGERP-3D))
 (6 6 (:TYPE-PRESCRIPTION NOT-INTEGERP-2D))
 (6 6 (:TYPE-PRESCRIPTION NOT-INTEGERP-1D))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-A+AB-<-0))
 (2 2 (:REWRITE ADE::BVP-V-ADDER-OUTPUT))
 (2 2 (:REWRITE |(< (- x) 0)|))
 (1 1 (:REWRITE |(< (+ d x) (+ c y))|))
 (1 1 (:REWRITE |(< (+ c x) (+ d y))|))
 )
(ADE::BVP-GCD$OP
 (2831 249 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (1939 9 (:LINEAR ADE::V-<-CORRECT-INSTANCE))
 (1878 201 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (1254 2 (:REWRITE |(< (if a b c) x)|))
 (846 476 (:REWRITE DEFAULT-+-2))
 (733 54 (:DEFINITION NTHCDR))
 (630 450 (:REWRITE DEFAULT-CDR))
 (476 476 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (476 476 (:REWRITE DEFAULT-+-1))
 (452 90 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (400 80 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (327 108 (:REWRITE TAKE-WHEN-ATOM))
 (326 326 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (326 326 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (326 326 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (285 86 (:REWRITE |(* y (* x z))|))
 (281 279 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (279 279 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (270 54 (:REWRITE |(+ y x)|))
 (269 2 (:REWRITE TAKE-OF-APPEND))
 (249 249 (:REWRITE |(< (- x) (- y))|))
 (242 242 (:LINEAR LEN-WHEN-PREFIXP))
 (241 241 (:TYPE-PRESCRIPTION ADE::V-NOT))
 (239 239 (:TYPE-PRESCRIPTION ADE::V-ADDER-OUTPUT))
 (203 149 (:REWRITE SIMPLIFY-SUMS-<))
 (203 149 (:REWRITE DEFAULT-<-2))
 (179 165 (:REWRITE DEFAULT-*-2))
 (172 26 (:DEFINITION BINARY-APPEND))
 (165 165 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (165 165 (:REWRITE DEFAULT-*-1))
 (165 78 (:REWRITE DEFAULT-CAR))
 (161 24 (:REWRITE CONSP-OF-TAKE))
 (160 80 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (151 149 (:REWRITE DEFAULT-<-1))
 (135 81 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (134 13 (:REWRITE ADE::LEN-V-NOT))
 (130 52 (:REWRITE APPEND-WHEN-NOT-CONSP))
 (128 81 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (122 122 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (122 122 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (122 122 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (121 121 (:LINEAR ADE::A-HELPFUL-LEMMA-FOR-TREE-INDUCTIONS))
 (114 114 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (114 114 (:REWRITE DEFAULT-UNARY-/))
 (114 114 (:REWRITE |(* a (/ a))|))
 (104 52 (:REWRITE |(< d (+ c x))|))
 (104 52 (:REWRITE |(+ c (+ d x))|))
 (95 95 (:REWRITE |(* c (* d x))|))
 (95 2 (:REWRITE ADE::NTHCDR-APPEND))
 (90 90 (:REWRITE |(equal (- x) (- y))|))
 (86 86 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-A+AB))
 (86 86 (:REWRITE |(< 0 (- x))|))
 (72 72 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-A+AB-=-0))
 (72 72 (:REWRITE |(equal (- x) 0)|))
 (72 36 (:TYPE-PRESCRIPTION NOT-INTEGERP-4E))
 (53 53 (:REWRITE |(+ 0 x)|))
 (52 52 (:REWRITE |(< (+ c x) d)|))
 (52 2 (:DEFINITION NFIX))
 (38 8 (:REWRITE APPEND-ATOM-UNDER-LIST-EQUIV))
 (38 1 (:REWRITE TAKE-OF-TAKE-SPLIT))
 (36 36 (:TYPE-PRESCRIPTION NOT-INTEGERP-3E))
 (36 36 (:TYPE-PRESCRIPTION NOT-INTEGERP-2E))
 (36 36 (:TYPE-PRESCRIPTION NOT-INTEGERP-1E))
 (36 36 (:REWRITE |(* (- x) y)|))
 (35 35 (:REWRITE INSERT-0-*))
 (24 4 (:REWRITE CONSP-OF-APPEND))
 (18 18 (:REWRITE REDUCE-INTEGERP-+))
 (18 18 (:REWRITE INTEGERP-MINUS-X))
 (18 18 (:REWRITE |(integerp (* c x))|))
 (18 18 (:META META-INTEGERP-CORRECT))
 (18 18 (:LINEAR ADE::V-<-CORRECT-2))
 (18 18 (:LINEAR ADE::V-<-CORRECT-1))
 (11 11 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-A+AB-<-0))
 (11 11 (:REWRITE |(< (- x) 0)|))
 (10 1 (:REWRITE ADE::NTHCDR-OF-NTHCDR))
 (9 9 (:TYPE-PRESCRIPTION NATP))
 (4 4 (:REWRITE |(* 0 x)|))
 (2 2 (:REWRITE TAKE-OF-ZERO))
 (2 2 (:REWRITE ADE::BVP-V-ADDER-OUTPUT))
 )
(ADE::LEN-GCD$OP
 (2831 249 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (1939 9 (:LINEAR ADE::V-<-CORRECT-INSTANCE))
 (1878 201 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (1254 2 (:REWRITE |(< (if a b c) x)|))
 (899 503 (:REWRITE DEFAULT-+-2))
 (740 55 (:DEFINITION NTHCDR))
 (657 477 (:REWRITE DEFAULT-CDR))
 (503 503 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (503 503 (:REWRITE DEFAULT-+-1))
 (460 94 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (400 80 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (379 379 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (379 379 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (379 379 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (327 108 (:REWRITE TAKE-WHEN-ATOM))
 (296 296 (:LINEAR LEN-WHEN-PREFIXP))
 (285 86 (:REWRITE |(* y (* x z))|))
 (281 279 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (279 279 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (275 55 (:REWRITE |(+ y x)|))
 (269 2 (:REWRITE TAKE-OF-APPEND))
 (249 249 (:REWRITE |(< (- x) (- y))|))
 (241 241 (:TYPE-PRESCRIPTION ADE::V-NOT))
 (239 239 (:TYPE-PRESCRIPTION ADE::V-ADDER-OUTPUT))
 (203 149 (:REWRITE SIMPLIFY-SUMS-<))
 (203 149 (:REWRITE DEFAULT-<-2))
 (199 182 (:REWRITE DEFAULT-*-2))
 (182 182 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (182 182 (:REWRITE DEFAULT-*-1))
 (172 26 (:DEFINITION BINARY-APPEND))
 (165 78 (:REWRITE DEFAULT-CAR))
 (161 24 (:REWRITE CONSP-OF-TAKE))
 (160 80 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (151 149 (:REWRITE DEFAULT-<-1))
 (148 148 (:LINEAR ADE::A-HELPFUL-LEMMA-FOR-TREE-INDUCTIONS))
 (143 85 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (136 85 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (134 134 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (134 134 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (134 134 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (134 13 (:REWRITE ADE::LEN-V-NOT))
 (130 52 (:REWRITE APPEND-WHEN-NOT-CONSP))
 (114 114 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (114 114 (:REWRITE DEFAULT-UNARY-/))
 (114 114 (:REWRITE |(* a (/ a))|))
 (104 52 (:REWRITE |(< d (+ c x))|))
 (104 52 (:REWRITE |(+ c (+ d x))|))
 (95 95 (:REWRITE |(* c (* d x))|))
 (95 2 (:REWRITE ADE::NTHCDR-APPEND))
 (94 94 (:REWRITE |(equal (- x) (- y))|))
 (86 86 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-A+AB))
 (86 86 (:REWRITE |(< 0 (- x))|))
 (72 72 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-A+AB-=-0))
 (72 72 (:REWRITE |(equal (- x) 0)|))
 (72 36 (:TYPE-PRESCRIPTION NOT-INTEGERP-4E))
 (53 53 (:REWRITE |(+ 0 x)|))
 (52 52 (:REWRITE |(< (+ c x) d)|))
 (52 2 (:DEFINITION NFIX))
 (39 39 (:REWRITE |(* (- x) y)|))
 (38 8 (:REWRITE APPEND-ATOM-UNDER-LIST-EQUIV))
 (38 1 (:REWRITE TAKE-OF-TAKE-SPLIT))
 (36 36 (:TYPE-PRESCRIPTION NOT-INTEGERP-3E))
 (36 36 (:TYPE-PRESCRIPTION NOT-INTEGERP-2E))
 (36 36 (:TYPE-PRESCRIPTION NOT-INTEGERP-1E))
 (35 35 (:REWRITE INSERT-0-*))
 (24 4 (:REWRITE CONSP-OF-APPEND))
 (18 18 (:LINEAR ADE::V-<-CORRECT-2))
 (18 18 (:LINEAR ADE::V-<-CORRECT-1))
 (16 16 (:REWRITE REDUCE-INTEGERP-+))
 (16 16 (:REWRITE INTEGERP-MINUS-X))
 (16 16 (:REWRITE |(integerp (* c x))|))
 (16 16 (:META META-INTEGERP-CORRECT))
 (11 11 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-A+AB-<-0))
 (11 11 (:REWRITE |(< (- x) 0)|))
 (10 1 (:REWRITE ADE::NTHCDR-OF-NTHCDR))
 (4 4 (:REWRITE |(* 0 x)|))
 (2 2 (:REWRITE TAKE-OF-ZERO))
 (2 2 (:REWRITE ADE::BVP-V-ADDER-OUTPUT))
 )
(ADE::GCD$OP-LEMMA-AUX
 (8 4 (:REWRITE DEFAULT-+-2))
 (4 4 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (4 4 (:REWRITE NORMALIZE-ADDENDS))
 (4 4 (:REWRITE DEFAULT-CDR))
 (4 4 (:REWRITE DEFAULT-+-1))
 (4 4 (:LINEAR LEN-WHEN-PREFIXP))
 (2 2 (:REWRITE REV-WHEN-NOT-CONSP))
 (2 2 (:LINEAR ADE::V-<-CORRECT-2))
 (2 2 (:LINEAR ADE::V-<-CORRECT-1))
 (2 2 (:LINEAR ADE::A-HELPFUL-LEMMA-FOR-TREE-INDUCTIONS))
 (2 1 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (2 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (2 1 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-A+AB-=-0))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-A+AB))
 (1 1 (:REWRITE SIMPLIFY-SUMS-<))
 (1 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (1 1 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (1 1 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (1 1 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE |(equal (- x) 0)|))
 (1 1 (:REWRITE |(equal (- x) (- y))|))
 (1 1 (:REWRITE |(< 0 (- x))|))
 (1 1 (:REWRITE |(< (- x) (- y))|))
 )
(ADE::V-ADDER-OUTPUT-LEMMA
 (5 1 (:REWRITE TAKE-OF-TOO-MANY))
 (2 1 (:REWRITE TAKE-WHEN-ATOM))
 (2 1 (:REWRITE ADE::LEN-OF-V-ADDER))
 (1 1 (:TYPE-PRESCRIPTION ADE::V-ADDER))
 (1 1 (:TYPE-PRESCRIPTION NFIX))
 (1 1 (:TYPE-PRESCRIPTION LEN))
 )
(ADE::GCD$OP-LEMMA
 (9922 52 (:REWRITE |(< (if a b c) x)|))
 (7839 1002 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (3540 2015 (:REWRITE DEFAULT-+-2))
 (2305 478 (:REWRITE TAKE-WHEN-ATOM))
 (2015 2015 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (2015 2015 (:REWRITE DEFAULT-+-1))
 (1744 1744 (:LINEAR LEN-WHEN-PREFIXP))
 (1417 1417 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (1417 1417 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (1417 1417 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (1409 204 (:DEFINITION BINARY-APPEND))
 (1314 435 (:REWRITE DEFAULT-CAR))
 (1262 1254 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (1112 1112 (:REWRITE |(< (- x) (- y))|))
 (1063 771 (:REWRITE SIMPLIFY-SUMS-<))
 (1062 771 (:REWRITE DEFAULT-<-2))
 (945 410 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (872 872 (:LINEAR ADE::A-HELPFUL-LEMMA-FOR-TREE-INDUCTIONS))
 (849 410 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (778 771 (:REWRITE DEFAULT-<-1))
 (516 481 (:REWRITE DEFAULT-*-2))
 (481 481 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (481 481 (:REWRITE DEFAULT-*-1))
 (462 231 (:REWRITE |(< d (+ c x))|))
 (462 231 (:REWRITE |(+ c (+ d x))|))
 (422 422 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (422 422 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (422 422 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (422 422 (:REWRITE |(equal (- x) (- y))|))
 (310 84 (:REWRITE APPEND-ATOM-UNDER-LIST-EQUIV))
 (295 295 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-A+AB))
 (295 295 (:REWRITE |(< 0 (- x))|))
 (244 244 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (244 244 (:REWRITE DEFAULT-UNARY-/))
 (241 241 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-A+AB-=-0))
 (241 241 (:REWRITE |(equal (- x) 0)|))
 (232 232 (:REWRITE REDUCE-INTEGERP-+))
 (232 232 (:REWRITE INTEGERP-MINUS-X))
 (232 232 (:META META-INTEGERP-CORRECT))
 (231 231 (:REWRITE |(< (+ c x) d)|))
 (177 177 (:REWRITE |(integerp (* c x))|))
 (136 136 (:LINEAR ADE::V-<-CORRECT-2))
 (136 136 (:LINEAR ADE::V-<-CORRECT-1))
 (87 87 (:REWRITE |(* (- x) y)|))
 (82 82 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-A+AB-<-0))
 (82 82 (:REWRITE |(< (- x) 0)|))
 (72 9 (:REWRITE REPEAT-WHEN-ZP))
 (62 6 (:REWRITE ADE::V-<-CORRECT-2))
 (56 28 (:TYPE-PRESCRIPTION NOT-INTEGERP-4E))
 (50 6 (:REWRITE ADE::V-<-CORRECT-1))
 (42 6 (:REWRITE |(< x (if a b c))|))
 (41 41 (:REWRITE INSERT-0-*))
 (40 40 (:TYPE-PRESCRIPTION REV))
 (37 37 (:TYPE-PRESCRIPTION NOT-INTEGERP-4D))
 (37 37 (:TYPE-PRESCRIPTION NOT-INTEGERP-3D))
 (37 37 (:TYPE-PRESCRIPTION NOT-INTEGERP-2D))
 (37 37 (:TYPE-PRESCRIPTION NOT-INTEGERP-1D))
 (31 11 (:REWRITE CONSP-OF-REPEAT))
 (28 28 (:TYPE-PRESCRIPTION NOT-INTEGERP-3E))
 (28 28 (:TYPE-PRESCRIPTION NOT-INTEGERP-2E))
 (28 28 (:TYPE-PRESCRIPTION NOT-INTEGERP-1E))
 (20 5 (:REWRITE CAR-OF-TAKE))
 (17 15 (:REWRITE DEFAULT-UNARY-MINUS))
 (16 16 (:REWRITE CONSP-OF-REV))
 (2 2 (:REWRITE LIST-FIX-UNDER-LIST-EQUIV))
 )
(ADE::V-TO-NAT-OF-GCD$OP-IS-GCD-ALG
 (4604 50 (:DEFINITION POSP))
 (3891 2265 (:REWRITE DEFAULT-+-2))
 (2265 2265 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (2265 2265 (:REWRITE DEFAULT-+-1))
 (2149 67 (:DEFINITION NATP))
 (1927 1837 (:REWRITE DEFAULT-CDR))
 (1374 1339 (:REWRITE DEFAULT-*-2))
 (1339 1339 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (1339 1339 (:REWRITE DEFAULT-*-1))
 (1283 1283 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (1283 1283 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (1283 1283 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (1212 1198 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (1160 1160 (:LINEAR LEN-WHEN-PREFIXP))
 (1153 1153 (:REWRITE |(< (- x) (- y))|))
 (1009 737 (:REWRITE SIMPLIFY-SUMS-<))
 (930 687 (:REWRITE DEFAULT-<-2))
 (828 352 (:REWRITE TAKE-WHEN-ATOM))
 (722 687 (:REWRITE DEFAULT-<-1))
 (703 149 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (629 473 (:REWRITE |(+ c (+ d x))|))
 (626 26 (:DEFINITION NFIX))
 (599 363 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (580 580 (:LINEAR ADE::A-HELPFUL-LEMMA-FOR-TREE-INDUCTIONS))
 (465 465 (:REWRITE |(equal (- x) (- y))|))
 (462 6 (:REWRITE |(< (if a b c) x)|))
 (455 455 (:REWRITE |(* (- x) y)|))
 (432 276 (:REWRITE |(< d (+ c x))|))
 (374 61 (:DEFINITION BINARY-APPEND))
 (361 361 (:REWRITE |(< 0 (- x))|))
 (328 55 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (310 82 (:REWRITE CONSP-OF-TAKE))
 (300 300 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (300 300 (:REWRITE DEFAULT-UNARY-/))
 (294 294 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-A+AB))
 (287 122 (:REWRITE APPEND-WHEN-NOT-CONSP))
 (277 149 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (262 217 (:REWRITE DEFAULT-CAR))
 (244 244 (:REWRITE DEFAULT-UNARY-MINUS))
 (240 240 (:LINEAR ADE::V-<-CORRECT-2))
 (240 240 (:LINEAR ADE::V-<-CORRECT-1))
 (215 215 (:REWRITE REDUCE-INTEGERP-+))
 (215 215 (:REWRITE INTEGERP-MINUS-X))
 (215 215 (:META META-INTEGERP-CORRECT))
 (191 32 (:REWRITE CONSP-OF-APPEND))
 (190 190 (:REWRITE |(< (+ c x) d)|))
 (180 180 (:REWRITE |(integerp (* c x))|))
 (144 9 (:REWRITE |(+ x (if a b c))|))
 (143 143 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (143 143 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (143 143 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (108 9 (:REWRITE |(- (if a b c))|))
 (102 6 (:TYPE-PRESCRIPTION ADE::BVP-TAKE))
 (102 6 (:TYPE-PRESCRIPTION ADE::BVP-NTHCDR))
 (95 95 (:REWRITE |(equal (- x) 0)|))
 (88 88 (:REWRITE |(equal (+ c x) d)|))
 (84 84 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-A+AB-=-0))
 (56 28 (:TYPE-PRESCRIPTION NOT-INTEGERP-4E))
 (50 10 (:DEFINITION TRUE-LISTP))
 (45 9 (:REWRITE BUBBLE-DOWN-+-BUBBLE-DOWN))
 (40 40 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-A+AB-<-0))
 (40 40 (:REWRITE |(< (- x) 0)|))
 (37 37 (:TYPE-PRESCRIPTION NOT-INTEGERP-4D))
 (37 37 (:TYPE-PRESCRIPTION NOT-INTEGERP-3D))
 (37 37 (:TYPE-PRESCRIPTION NOT-INTEGERP-2D))
 (37 37 (:TYPE-PRESCRIPTION NOT-INTEGERP-1D))
 (28 28 (:TYPE-PRESCRIPTION NOT-INTEGERP-3E))
 (28 28 (:TYPE-PRESCRIPTION NOT-INTEGERP-2E))
 (28 28 (:TYPE-PRESCRIPTION NOT-INTEGERP-1E))
 (27 27 (:REWRITE INSERT-0-*))
 (25 25 (:TYPE-PRESCRIPTION POSP))
 (20 20 (:REWRITE FOLD-CONSTS-IN-+))
 (19 19 (:REWRITE ADE::BVP-V-ADDER-OUTPUT))
 (19 4 (:REWRITE APPEND-ATOM-UNDER-LIST-EQUIV))
 )
(ADE::GCD$OP-COMMUTATIVE
 (293 2 (:REWRITE PREFIXP-OF-APPEND-ARG1))
 (233 6 (:REWRITE TAKE-OF-TOO-MANY))
 (230 2 (:DEFINITION ADE::GCD-ALG))
 (161 83 (:REWRITE DEFAULT-+-2))
 (91 5 (:REWRITE ZP-OPEN))
 (85 85 (:REWRITE DEFAULT-CDR))
 (83 83 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (83 83 (:REWRITE DEFAULT-+-1))
 (52 2 (:REWRITE ADE::LEN-NTHCDR))
 (46 2 (:REWRITE ADE::V-<-CORRECT-2))
 (46 2 (:REWRITE ADE::V-<-CORRECT-1))
 (44 22 (:REWRITE DEFAULT-*-2))
 (29 1 (:DEFINITION NTHCDR))
 (24 6 (:DEFINITION BINARY-APPEND))
 (23 23 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (23 23 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (23 23 (:REWRITE |(< (- x) (- y))|))
 (23 16 (:REWRITE DEFAULT-<-2))
 (22 22 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (22 22 (:REWRITE DEFAULT-*-1))
 (22 16 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (20 16 (:REWRITE SIMPLIFY-SUMS-<))
 (18 9 (:REWRITE LIST-EQUIV-WHEN-ATOM-RIGHT))
 (18 6 (:TYPE-PRESCRIPTION TRUE-LISTP-NTHCDR-TYPE-PRESCRIPTION))
 (18 6 (:REWRITE |(* y (* x z))|))
 (17 3 (:REWRITE TAKE-WHEN-ATOM))
 (16 16 (:REWRITE DEFAULT-<-1))
 (16 10 (:REWRITE DEFAULT-UNARY-MINUS))
 (15 14 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (15 14 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (15 14 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (15 3 (:REWRITE |(+ y x)|))
 (14 14 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-A+AB))
 (14 14 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (14 14 (:REWRITE DEFAULT-UNARY-/))
 (14 14 (:REWRITE |(equal (- x) (- y))|))
 (14 14 (:REWRITE |(< 0 (- x))|))
 (12 12 (:REWRITE APPEND-WHEN-NOT-CONSP))
 (10 10 (:REWRITE PREFIXP-TRANSITIVE . 2))
 (10 10 (:REWRITE PREFIXP-TRANSITIVE . 1))
 (10 10 (:REWRITE PREFIXP-ONE-WAY-OR-ANOTHER . 2))
 (10 10 (:REWRITE PREFIXP-ONE-WAY-OR-ANOTHER . 1))
 (10 1 (:REWRITE PREFIXP-WHEN-NOT-CONSP-LEFT))
 (9 9 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-A+AB-=-0))
 (9 9 (:REWRITE LIST-EQUIV-WHEN-ATOM-LEFT))
 (9 9 (:REWRITE |(equal (- x) 0)|))
 (8 8 (:TYPE-PRESCRIPTION ADE::BOOLEANP-V-<))
 (8 8 (:REWRITE REV-WHEN-NOT-CONSP))
 (8 4 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (6 6 (:TYPE-PRESCRIPTION NFIX))
 (6 6 (:REWRITE INSERT-0-*))
 (6 6 (:REWRITE DEFAULT-CAR))
 (4 4 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (4 4 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (4 4 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (4 4 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (4 4 (:LINEAR LEN-WHEN-PREFIXP))
 (2 2 (:REWRITE CONSP-OF-APPEND))
 (2 2 (:LINEAR ADE::A-HELPFUL-LEMMA-FOR-TREE-INDUCTIONS))
 (1 1 (:REWRITE PREFIXP-WHEN-NOT-CONSP-RIGHT))
 )
(ADE::GCD$OP-MAP)
(ADE::LEN-OF-GCD$OP-MAP
 (28 28 (:LINEAR LEN-WHEN-PREFIXP))
 (14 14 (:LINEAR ADE::A-HELPFUL-LEMMA-FOR-TREE-INDUCTIONS))
 (14 7 (:REWRITE DEFAULT-+-2))
 (9 8 (:REWRITE DEFAULT-CDR))
 (9 3 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (9 3 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (9 3 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (7 7 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (7 7 (:REWRITE NORMALIZE-ADDENDS))
 (7 7 (:REWRITE DEFAULT-+-1))
 (3 3 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE |(equal (- x) (- y))|))
 )
(ADE::GCD$OP-MAP-OF-APPEND
 (50 19 (:REWRITE DEFAULT-CDR))
 (29 26 (:REWRITE DEFAULT-CAR))
 (15 15 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (12 4 (:REWRITE CAR-OF-APPEND))
 (8 8 (:REWRITE CONSP-OF-APPEND))
 (6 3 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (6 3 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (6 3 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (4 4 (:REWRITE CDR-OF-APPEND-WHEN-CONSP))
 (3 3 (:REWRITE |(equal (- x) (- y))|))
 )
