(M1::OK-INPUTS)
(M1::THETA
 (5 5 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (5 5 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (5 5 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (5 5 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (5 5 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (5 5 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (5 5 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (5 5 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (5 5 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (5 5 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (5 5 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (5 5 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 )
(M1::HELPER
 (149 149 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (149 149 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (149 149 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (149 149 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (130 26 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (130 26 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (122 26 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (122 26 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (122 26 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (33 3 (:REWRITE DEFAULT-MOD-RATIO))
 (26 26 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (26 26 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (26 26 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (26 26 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (26 26 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (22 1 (:LINEAR MOD-BOUNDS-3))
 (19 19 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (19 19 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (19 19 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (19 19 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (18 18 (:REWRITE DEFAULT-TIMES-2))
 (18 18 (:REWRITE DEFAULT-TIMES-1))
 (10 2 (:LINEAR MOD-BOUNDS-2))
 (8 8 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (5 5 (:REWRITE REDUCE-INTEGERP-+))
 (5 5 (:REWRITE INTEGERP-MINUS-X))
 (5 5 (:META META-INTEGERP-CORRECT))
 (5 4 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (5 4 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (4 4 (:REWRITE THE-FLOOR-BELOW))
 (4 4 (:REWRITE THE-FLOOR-ABOVE))
 (4 4 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (4 4 (:REWRITE DEFAULT-LESS-THAN-2))
 (4 4 (:REWRITE DEFAULT-LESS-THAN-1))
 (3 3 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (3 3 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (3 3 (:REWRITE INTEGERP-<-CONSTANT))
 (3 3 (:REWRITE DEFAULT-MOD-2))
 (3 3 (:REWRITE DEFAULT-MOD-1))
 (3 3 (:REWRITE CONSTANT-<-INTEGERP))
 (3 3 (:REWRITE |(mod x 2)| . 2))
 (3 3 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (3 3 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (3 3 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (3 3 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (3 3 (:REWRITE |(< c (- x))|))
 (3 3 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (3 3 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (3 3 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (3 3 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (3 3 (:REWRITE |(< (/ x) (/ y))|))
 (3 3 (:REWRITE |(< (- x) c)|))
 (3 3 (:REWRITE |(< (- x) (- y))|))
 (2 2 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (2 2 (:TYPE-PRESCRIPTION ABS))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (2 2 (:REWRITE SIMPLIFY-SUMS-<))
 (2 2 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (2 2 (:REWRITE |(< (/ x) 0)|))
 (2 2 (:REWRITE |(< (* x y) 0)|))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE |(<= (/ x) y) with (< x 0)|))
 (1 1 (:REWRITE |(<= (/ x) y) with (< 0 x)|))
 (1 1 (:REWRITE |(< x (/ y)) with (< y 0)|))
 (1 1 (:REWRITE |(< 0 (* x y))|))
 (1 1 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 )
(M1::FINAL-N
 (149 149 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (149 149 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (149 149 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (149 149 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (130 26 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (130 26 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (122 26 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (122 26 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (122 26 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (33 3 (:REWRITE DEFAULT-MOD-RATIO))
 (26 26 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (26 26 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (26 26 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (26 26 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (26 26 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (22 1 (:LINEAR MOD-BOUNDS-3))
 (19 19 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (19 19 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (19 19 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (19 19 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (18 18 (:REWRITE DEFAULT-TIMES-2))
 (18 18 (:REWRITE DEFAULT-TIMES-1))
 (10 2 (:LINEAR MOD-BOUNDS-2))
 (8 8 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (5 5 (:REWRITE REDUCE-INTEGERP-+))
 (5 5 (:REWRITE INTEGERP-MINUS-X))
 (5 5 (:META META-INTEGERP-CORRECT))
 (5 4 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (5 4 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (4 4 (:REWRITE THE-FLOOR-BELOW))
 (4 4 (:REWRITE THE-FLOOR-ABOVE))
 (4 4 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (4 4 (:REWRITE DEFAULT-LESS-THAN-2))
 (4 4 (:REWRITE DEFAULT-LESS-THAN-1))
 (3 3 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (3 3 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (3 3 (:REWRITE INTEGERP-<-CONSTANT))
 (3 3 (:REWRITE DEFAULT-MOD-2))
 (3 3 (:REWRITE DEFAULT-MOD-1))
 (3 3 (:REWRITE CONSTANT-<-INTEGERP))
 (3 3 (:REWRITE |(mod x 2)| . 2))
 (3 3 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (3 3 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (3 3 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (3 3 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (3 3 (:REWRITE |(< c (- x))|))
 (3 3 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (3 3 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (3 3 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (3 3 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (3 3 (:REWRITE |(< (/ x) (/ y))|))
 (3 3 (:REWRITE |(< (- x) c)|))
 (3 3 (:REWRITE |(< (- x) (- y))|))
 (2 2 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (2 2 (:TYPE-PRESCRIPTION ABS))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (2 2 (:REWRITE SIMPLIFY-SUMS-<))
 (2 2 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (2 2 (:REWRITE |(< (/ x) 0)|))
 (2 2 (:REWRITE |(< (* x y) 0)|))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE |(<= (/ x) y) with (< x 0)|))
 (1 1 (:REWRITE |(<= (/ x) y) with (< 0 x)|))
 (1 1 (:REWRITE |(< x (/ y)) with (< y 0)|))
 (1 1 (:REWRITE |(< 0 (* x y))|))
 (1 1 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 )
(M1::FN)
(M1::HELPER-IS-THETA
 (342 330 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (342 330 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (330 330 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (330 330 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (330 330 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (243 243 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (243 243 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (243 243 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (243 243 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (188 81 (:REWRITE DEFAULT-TIMES-2))
 (181 37 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (181 37 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (173 37 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (124 12 (:REWRITE DEFAULT-MOD-RATIO))
 (90 90 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (90 90 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (90 90 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (90 90 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (85 81 (:REWRITE DEFAULT-TIMES-1))
 (52 7 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (52 7 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (50 7 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (44 2 (:LINEAR MOD-BOUNDS-3))
 (38 38 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (38 38 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (38 5 (:REWRITE ZP-OPEN))
 (37 37 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (37 37 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (37 37 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (36 36 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (36 36 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (27 27 (:REWRITE REDUCE-INTEGERP-+))
 (27 27 (:REWRITE INTEGERP-MINUS-X))
 (27 27 (:META META-INTEGERP-CORRECT))
 (24 3 (:REWRITE |(* x (+ y z))|))
 (22 12 (:REWRITE DEFAULT-EXPT-1))
 (20 4 (:LINEAR MOD-BOUNDS-2))
 (17 17 (:REWRITE THE-FLOOR-BELOW))
 (17 17 (:REWRITE THE-FLOOR-ABOVE))
 (17 17 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (17 17 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (17 17 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (17 17 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (17 17 (:REWRITE INTEGERP-<-CONSTANT))
 (17 17 (:REWRITE DEFAULT-LESS-THAN-2))
 (17 17 (:REWRITE DEFAULT-LESS-THAN-1))
 (17 17 (:REWRITE CONSTANT-<-INTEGERP))
 (17 17 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (17 17 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (17 17 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (17 17 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (17 17 (:REWRITE |(< c (- x))|))
 (17 17 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (17 17 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (17 17 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (17 17 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (17 17 (:REWRITE |(< (/ x) (/ y))|))
 (17 17 (:REWRITE |(< (- x) c)|))
 (17 17 (:REWRITE |(< (- x) (- y))|))
 (16 16 (:REWRITE DEFAULT-PLUS-2))
 (16 16 (:REWRITE DEFAULT-PLUS-1))
 (16 16 (:REWRITE |(< (/ x) 0)|))
 (16 16 (:REWRITE |(< (* x y) 0)|))
 (14 14 (:REWRITE SIMPLIFY-SUMS-<))
 (14 14 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (14 14 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (13 13 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (13 13 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (12 12 (:REWRITE DEFAULT-MOD-2))
 (12 12 (:REWRITE DEFAULT-MOD-1))
 (12 12 (:REWRITE DEFAULT-EXPT-2))
 (12 12 (:REWRITE |(mod x 2)| . 2))
 (11 11 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (11 11 (:REWRITE NORMALIZE-ADDENDS))
 (11 11 (:REWRITE |(expt 1/c n)|))
 (11 11 (:REWRITE |(expt (- x) n)|))
 (9 1 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (7 7 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (7 7 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (7 7 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (7 7 (:REWRITE |(equal c (/ x))|))
 (7 7 (:REWRITE |(equal c (- x))|))
 (7 7 (:REWRITE |(equal (/ x) c)|))
 (7 7 (:REWRITE |(equal (/ x) (/ y))|))
 (7 7 (:REWRITE |(equal (- x) c)|))
 (7 7 (:REWRITE |(equal (- x) (- y))|))
 (4 4 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (4 1 (:REWRITE EVEN-AND-ODD-ALTERNATE))
 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (2 2 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (1 1 (:REWRITE |(< y (+ (- c) x))|))
 (1 1 (:REWRITE |(< x (+ c/d y))|))
 (1 1 (:REWRITE |(< 0 (/ x))|))
 (1 1 (:REWRITE |(< 0 (* x y))|))
 (1 1 (:REWRITE |(* c (expt d n))|))
 )
(M1::FN-IS-THETA
 (24 24 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (24 24 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (24 24 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (24 24 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (24 24 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (24 24 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (24 24 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (24 24 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (11 1 (:REWRITE DEFAULT-TIMES-2))
 (2 2 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (2 2 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (2 2 (:REWRITE THE-FLOOR-BELOW))
 (2 2 (:REWRITE THE-FLOOR-ABOVE))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (2 2 (:REWRITE SIMPLIFY-SUMS-<))
 (2 2 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (2 2 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (2 2 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (2 2 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (2 2 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (2 2 (:REWRITE REDUCE-INTEGERP-+))
 (2 2 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (2 2 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (2 2 (:REWRITE INTEGERP-MINUS-X))
 (2 2 (:REWRITE INTEGERP-<-CONSTANT))
 (2 2 (:REWRITE DEFAULT-LESS-THAN-2))
 (2 2 (:REWRITE DEFAULT-LESS-THAN-1))
 (2 2 (:REWRITE DEFAULT-EXPT-2))
 (2 2 (:REWRITE DEFAULT-EXPT-1))
 (2 2 (:REWRITE CONSTANT-<-INTEGERP))
 (2 2 (:REWRITE |(expt 1/c n)|))
 (2 2 (:REWRITE |(expt (- x) n)|))
 (2 2 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (2 2 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (2 2 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (2 2 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (2 2 (:REWRITE |(< c (- x))|))
 (2 2 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (2 2 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (2 2 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (2 2 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (2 2 (:REWRITE |(< (/ x) 0)|))
 (2 2 (:REWRITE |(< (/ x) (/ y))|))
 (2 2 (:REWRITE |(< (- x) c)|))
 (2 2 (:REWRITE |(< (- x) (- y))|))
 (2 2 (:REWRITE |(< (* x y) 0)|))
 (2 2 (:META META-INTEGERP-CORRECT))
 (1 1 (:REWRITE DEFAULT-TIMES-1))
 )
(M1::EVEN-LOOP-CLK
 (18 14 (:REWRITE DEFAULT-PLUS-1))
 (14 14 (:REWRITE DEFAULT-PLUS-2))
 (6 6 (:REWRITE THE-FLOOR-BELOW))
 (6 6 (:REWRITE THE-FLOOR-ABOVE))
 (6 6 (:REWRITE DEFAULT-LESS-THAN-2))
 (6 6 (:REWRITE DEFAULT-LESS-THAN-1))
 (6 5 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (6 5 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (5 5 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (5 5 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (5 5 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (5 5 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (5 5 (:REWRITE INTEGERP-<-CONSTANT))
 (5 5 (:REWRITE CONSTANT-<-INTEGERP))
 (5 5 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (5 5 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (5 5 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (5 5 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (5 5 (:REWRITE |(< c (- x))|))
 (5 5 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (5 5 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (5 5 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (5 5 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (5 5 (:REWRITE |(< (/ x) (/ y))|))
 (5 5 (:REWRITE |(< (- x) c)|))
 (5 5 (:REWRITE |(< (- x) (- y))|))
 (4 4 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (3 3 (:REWRITE |(< (+ c/d x) y)|))
 (3 3 (:REWRITE |(< (+ (- c) x) y)|))
 (2 2 (:TYPE-PRESCRIPTION ABS))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (2 2 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (2 2 (:REWRITE DEFAULT-MINUS))
 (2 2 (:REWRITE |(< (/ x) 0)|))
 (2 2 (:REWRITE |(< (* x y) 0)|))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (1 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (1 1 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1 1 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (1 1 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (1 1 (:REWRITE DEFAULT-TIMES-2))
 (1 1 (:REWRITE DEFAULT-TIMES-1))
 (1 1 (:REWRITE |(equal c (/ x))|))
 (1 1 (:REWRITE |(equal c (- x))|))
 (1 1 (:REWRITE |(equal (/ x) c)|))
 (1 1 (:REWRITE |(equal (/ x) (/ y))|))
 (1 1 (:REWRITE |(equal (- x) c)|))
 (1 1 (:REWRITE |(equal (- x) (- y))|))
 )
(M1::EVEN-CLK)
(M1::LOOP-CLK
 (140 140 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (140 140 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (140 140 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (140 140 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (125 25 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (125 25 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (117 25 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (117 25 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (117 25 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (33 3 (:REWRITE DEFAULT-MOD-RATIO))
 (25 25 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (25 25 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (25 25 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (25 25 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (25 25 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (22 1 (:LINEAR MOD-BOUNDS-3))
 (20 20 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (20 20 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (20 20 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (20 20 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (17 17 (:REWRITE DEFAULT-TIMES-2))
 (17 17 (:REWRITE DEFAULT-TIMES-1))
 (10 2 (:LINEAR MOD-BOUNDS-2))
 (8 8 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (5 5 (:REWRITE REDUCE-INTEGERP-+))
 (5 5 (:REWRITE INTEGERP-MINUS-X))
 (5 5 (:META META-INTEGERP-CORRECT))
 (5 4 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (5 4 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (4 4 (:REWRITE THE-FLOOR-BELOW))
 (4 4 (:REWRITE THE-FLOOR-ABOVE))
 (4 4 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (4 4 (:REWRITE DEFAULT-LESS-THAN-2))
 (4 4 (:REWRITE DEFAULT-LESS-THAN-1))
 (3 3 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (3 3 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (3 3 (:REWRITE INTEGERP-<-CONSTANT))
 (3 3 (:REWRITE DEFAULT-MOD-2))
 (3 3 (:REWRITE DEFAULT-MOD-1))
 (3 3 (:REWRITE CONSTANT-<-INTEGERP))
 (3 3 (:REWRITE |(mod x 2)| . 2))
 (3 3 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (3 3 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (3 3 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (3 3 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (3 3 (:REWRITE |(< c (- x))|))
 (3 3 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (3 3 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (3 3 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (3 3 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (3 3 (:REWRITE |(< (/ x) (/ y))|))
 (3 3 (:REWRITE |(< (- x) c)|))
 (3 3 (:REWRITE |(< (- x) (- y))|))
 (2 2 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (2 2 (:TYPE-PRESCRIPTION ABS))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (2 2 (:REWRITE SIMPLIFY-SUMS-<))
 (2 2 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (2 2 (:REWRITE |(< (/ x) 0)|))
 (2 2 (:REWRITE |(< (* x y) 0)|))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE |(<= (/ x) y) with (< x 0)|))
 (1 1 (:REWRITE |(<= (/ x) y) with (< 0 x)|))
 (1 1 (:REWRITE |(< x (/ y)) with (< y 0)|))
 (1 1 (:REWRITE |(< 0 (* x y))|))
 (1 1 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 )
(M1::CLK)
(M1::TEST)
(M1::EVEN-LOOP-IS-MOD=0
 (144 12 (:REWRITE ZP-OPEN))
 (140 140 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (140 140 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (133 133 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (133 133 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (133 133 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (133 133 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (125 26 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (121 33 (:REWRITE ACL2-NUMBERP-X))
 (59 47 (:REWRITE DEFAULT-PLUS-2))
 (59 5 (:REWRITE DEFAULT-MOD-RATIO))
 (47 47 (:REWRITE DEFAULT-PLUS-1))
 (44 11 (:REWRITE RATIONALP-X))
 (37 26 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (37 26 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (32 5 (:REWRITE |(* y x)|))
 (29 29 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (29 29 (:REWRITE NORMALIZE-ADDENDS))
 (28 28 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (26 26 (:REWRITE REDUCE-INTEGERP-+))
 (26 26 (:REWRITE INTEGERP-MINUS-X))
 (26 26 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (26 26 (:REWRITE |(equal c (/ x))|))
 (26 26 (:REWRITE |(equal c (- x))|))
 (26 26 (:REWRITE |(equal (/ x) c)|))
 (26 26 (:REWRITE |(equal (/ x) (/ y))|))
 (26 26 (:REWRITE |(equal (- x) c)|))
 (26 26 (:REWRITE |(equal (- x) (- y))|))
 (26 26 (:META META-INTEGERP-CORRECT))
 (23 23 (:REWRITE DEFAULT-TIMES-2))
 (23 23 (:REWRITE DEFAULT-TIMES-1))
 (19 19 (:REWRITE DEFAULT-CDR))
 (18 18 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (15 15 (:REWRITE THE-FLOOR-BELOW))
 (15 15 (:REWRITE THE-FLOOR-ABOVE))
 (15 15 (:REWRITE SIMPLIFY-SUMS-<))
 (15 15 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (15 15 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (15 15 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (15 15 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (15 15 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (15 15 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (15 15 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (15 15 (:REWRITE INTEGERP-<-CONSTANT))
 (15 15 (:REWRITE DEFAULT-LESS-THAN-2))
 (15 15 (:REWRITE DEFAULT-LESS-THAN-1))
 (15 15 (:REWRITE DEFAULT-CAR))
 (15 15 (:REWRITE CONSTANT-<-INTEGERP))
 (15 15 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (15 15 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (15 15 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (15 15 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (15 15 (:REWRITE |(< c (- x))|))
 (15 15 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (15 15 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (15 15 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (15 15 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (15 15 (:REWRITE |(< (/ x) (/ y))|))
 (15 15 (:REWRITE |(< (- x) c)|))
 (15 15 (:REWRITE |(< (- x) (- y))|))
 (11 11 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (11 11 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (11 11 (:REWRITE REDUCE-RATIONALP-+))
 (11 11 (:REWRITE REDUCE-RATIONALP-*))
 (11 11 (:REWRITE RATIONALP-MINUS-X))
 (11 11 (:REWRITE |(< (/ x) 0)|))
 (11 11 (:REWRITE |(< (* x y) 0)|))
 (11 11 (:META META-RATIONALP-CORRECT))
 (7 7 (:REWRITE |(equal (+ (- c) x) y)|))
 (5 5 (:REWRITE DEFAULT-MOD-2))
 (5 5 (:REWRITE DEFAULT-MOD-1))
 (5 5 (:REWRITE |(mod x 2)| . 2))
 (4 4 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (4 4 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (4 4 (:REWRITE |(< y (+ (- c) x))|))
 (4 4 (:REWRITE |(< x (+ c/d y))|))
 (4 4 (:REWRITE |(< 0 (/ x))|))
 (4 4 (:REWRITE |(< 0 (* x y))|))
 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (1 1 (:REWRITE |(< (+ c/d x) y)|))
 (1 1 (:REWRITE |(< (+ (- c) x) y)|))
 )
(M1::EVEN-IS-MOD=0
 (24 24 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (24 24 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (24 24 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (24 24 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (22 2 (:REWRITE DEFAULT-MOD-RATIO))
 (14 14 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (14 14 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (14 14 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (14 14 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (8 2 (:REWRITE |(* y x)|))
 (6 6 (:REWRITE DEFAULT-TIMES-2))
 (6 6 (:REWRITE DEFAULT-TIMES-1))
 (5 5 (:REWRITE REDUCE-INTEGERP-+))
 (5 5 (:REWRITE INTEGERP-MINUS-X))
 (5 5 (:META META-INTEGERP-CORRECT))
 (4 4 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (2 2 (:REWRITE DEFAULT-MOD-2))
 (2 2 (:REWRITE DEFAULT-MOD-1))
 (2 2 (:REWRITE |(mod x 2)| . 2))
 (1 1 (:REWRITE THE-FLOOR-BELOW))
 (1 1 (:REWRITE THE-FLOOR-ABOVE))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (1 1 (:REWRITE SIMPLIFY-SUMS-<))
 (1 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (1 1 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (1 1 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (1 1 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (1 1 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (1 1 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (1 1 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (1 1 (:REWRITE INTEGERP-<-CONSTANT))
 (1 1 (:REWRITE DEFAULT-LESS-THAN-2))
 (1 1 (:REWRITE DEFAULT-LESS-THAN-1))
 (1 1 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE CONSTANT-<-INTEGERP))
 (1 1 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (1 1 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (1 1 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (1 1 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (1 1 (:REWRITE |(< c (- x))|))
 (1 1 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (1 1 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (1 1 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (1 1 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (1 1 (:REWRITE |(< (/ x) 0)|))
 (1 1 (:REWRITE |(< (/ x) (/ y))|))
 (1 1 (:REWRITE |(< (- x) c)|))
 (1 1 (:REWRITE |(< (- x) (- y))|))
 (1 1 (:REWRITE |(< (* x y) 0)|))
 )
(M1::HELPER-IS-FN
 (401 34 (:REWRITE DEFAULT-MOD-RATIO))
 (351 254 (:REWRITE DEFAULT-TIMES-1))
 (334 254 (:REWRITE DEFAULT-TIMES-2))
 (192 192 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (192 192 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (192 192 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (192 192 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (175 175 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (175 175 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (175 175 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (175 175 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (156 32 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (156 32 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (148 32 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (130 10 (:REWRITE |(* (* x y) z)|))
 (93 3 (:REWRITE |(* (expt x n) (expt y n))|))
 (84 21 (:REWRITE |(* c (* d x))|))
 (79 13 (:REWRITE ZP-OPEN))
 (66 18 (:REWRITE ACL2-NUMBERP-X))
 (61 61 (:REWRITE REDUCE-INTEGERP-+))
 (61 61 (:REWRITE INTEGERP-MINUS-X))
 (61 61 (:META META-INTEGERP-CORRECT))
 (60 6 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (53 23 (:REWRITE DEFAULT-EXPT-1))
 (48 6 (:REWRITE |(* x (+ y z))|))
 (47 17 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (44 2 (:LINEAR MOD-BOUNDS-3))
 (34 34 (:REWRITE DEFAULT-MOD-2))
 (34 34 (:REWRITE DEFAULT-MOD-1))
 (34 34 (:REWRITE |(mod x 2)| . 2))
 (32 32 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (32 32 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (32 32 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (32 32 (:REWRITE DEFAULT-PLUS-2))
 (32 32 (:REWRITE DEFAULT-PLUS-1))
 (31 31 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (31 31 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (31 31 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (31 31 (:REWRITE NORMALIZE-ADDENDS))
 (24 6 (:REWRITE RATIONALP-X))
 (23 23 (:REWRITE DEFAULT-EXPT-2))
 (22 22 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (22 22 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (22 22 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (22 22 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (22 22 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (22 22 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (22 22 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (22 22 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (22 22 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (22 22 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (20 20 (:REWRITE |(expt 1/c n)|))
 (20 20 (:REWRITE |(expt (- x) n)|))
 (20 4 (:LINEAR MOD-BOUNDS-2))
 (18 18 (:REWRITE THE-FLOOR-BELOW))
 (18 18 (:REWRITE THE-FLOOR-ABOVE))
 (18 18 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (18 18 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (18 18 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (18 18 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (18 18 (:REWRITE INTEGERP-<-CONSTANT))
 (18 18 (:REWRITE DEFAULT-LESS-THAN-2))
 (18 18 (:REWRITE DEFAULT-LESS-THAN-1))
 (18 18 (:REWRITE CONSTANT-<-INTEGERP))
 (18 18 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (18 18 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (18 18 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (18 18 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (18 18 (:REWRITE |(< c (- x))|))
 (18 18 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (18 18 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (18 18 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (18 18 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (18 18 (:REWRITE |(< (/ x) (/ y))|))
 (18 18 (:REWRITE |(< (- x) c)|))
 (18 18 (:REWRITE |(< (- x) (- y))|))
 (18 2 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (17 17 (:REWRITE DEFAULT-CDR))
 (16 16 (:REWRITE SIMPLIFY-SUMS-<))
 (16 16 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (16 16 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (16 16 (:REWRITE |(< (/ x) 0)|))
 (16 16 (:REWRITE |(< (* x y) 0)|))
 (15 3 (:REWRITE |(expt (expt x m) n)|))
 (14 14 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (14 14 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (14 14 (:REWRITE DEFAULT-CAR))
 (12 6 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (12 6 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (8 2 (:REWRITE EVEN-AND-ODD-ALTERNATE))
 (6 6 (:REWRITE REDUCE-RATIONALP-+))
 (6 6 (:REWRITE REDUCE-RATIONALP-*))
 (6 6 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (6 6 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (6 6 (:REWRITE RATIONALP-MINUS-X))
 (6 6 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (6 6 (:REWRITE |(equal c (/ x))|))
 (6 6 (:REWRITE |(equal c (- x))|))
 (6 6 (:REWRITE |(equal (/ x) c)|))
 (6 6 (:REWRITE |(equal (/ x) (/ y))|))
 (6 6 (:REWRITE |(equal (- x) c)|))
 (6 6 (:REWRITE |(equal (- x) (- y))|))
 (6 6 (:META META-RATIONALP-CORRECT))
 (2 2 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (2 2 (:REWRITE |(< y (+ (- c) x))|))
 (2 2 (:REWRITE |(< x (+ c/d y))|))
 (2 2 (:REWRITE |(< 0 (/ x))|))
 (2 2 (:REWRITE |(< 0 (* x y))|))
 (2 2 (:REWRITE |(* a (/ a) b)|))
 )
(M1::PROGRAM-IS-FN
 (320 4 (:DEFINITION M1::HELPER))
 (148 2 (:DEFINITION M1::FINAL-N))
 (90 6 (:REWRITE |(mod x 2)| . 1))
 (84 24 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (72 6 (:REWRITE |(equal (if a b c) x)|))
 (66 6 (:REWRITE DEFAULT-MOD-RATIO))
 (64 16 (:REWRITE |(* y x)|))
 (56 50 (:REWRITE DEFAULT-TIMES-1))
 (50 50 (:REWRITE DEFAULT-TIMES-2))
 (42 42 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (42 42 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (42 42 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (42 42 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (36 6 (:REWRITE BUBBLE-DOWN-*-MATCH-1))
 (30 6 (:REWRITE |(* x x)|))
 (14 14 (:REWRITE REDUCE-INTEGERP-+))
 (14 14 (:REWRITE INTEGERP-MINUS-X))
 (14 14 (:META META-INTEGERP-CORRECT))
 (6 6 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (6 6 (:REWRITE ZP-OPEN))
 (6 6 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (6 6 (:REWRITE NORMALIZE-ADDENDS))
 (6 6 (:REWRITE DEFAULT-PLUS-2))
 (6 6 (:REWRITE DEFAULT-PLUS-1))
 (6 6 (:REWRITE DEFAULT-MOD-2))
 (6 6 (:REWRITE DEFAULT-MOD-1))
 (6 6 (:REWRITE DEFAULT-EXPT-2))
 (6 6 (:REWRITE DEFAULT-EXPT-1))
 (6 6 (:REWRITE |(mod x 2)| . 2))
 (6 6 (:REWRITE |(expt 1/c n)|))
 (6 6 (:REWRITE |(expt (- x) n)|))
 (6 6 (:DEFINITION FIX))
 (4 4 (:REWRITE |(* 1 x)|))
 (2 2 (:REWRITE THE-FLOOR-BELOW))
 (2 2 (:REWRITE THE-FLOOR-ABOVE))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (2 2 (:REWRITE SIMPLIFY-SUMS-<))
 (2 2 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (2 2 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (2 2 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (2 2 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (2 2 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (2 2 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (2 2 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (2 2 (:REWRITE INTEGERP-<-CONSTANT))
 (2 2 (:REWRITE DEFAULT-LESS-THAN-2))
 (2 2 (:REWRITE DEFAULT-LESS-THAN-1))
 (2 2 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE CONSTANT-<-INTEGERP))
 (2 2 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (2 2 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (2 2 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (2 2 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (2 2 (:REWRITE |(< c (- x))|))
 (2 2 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (2 2 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (2 2 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (2 2 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (2 2 (:REWRITE |(< (/ x) 0)|))
 (2 2 (:REWRITE |(< (/ x) (/ y))|))
 (2 2 (:REWRITE |(< (- x) c)|))
 (2 2 (:REWRITE |(< (- x) (- y))|))
 (2 2 (:REWRITE |(< (* x y) 0)|))
 )
(M1::PROGRAM-CORRECT
 (148 2 (:DEFINITION M1::FINAL-N))
 (30 2 (:REWRITE |(mod x 2)| . 1))
 (28 8 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (24 2 (:REWRITE |(equal (if a b c) x)|))
 (22 2 (:REWRITE DEFAULT-MOD-RATIO))
 (16 14 (:REWRITE DEFAULT-TIMES-1))
 (16 4 (:REWRITE |(* y x)|))
 (14 14 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (14 14 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (14 14 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (14 14 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (14 14 (:REWRITE DEFAULT-TIMES-2))
 (12 2 (:REWRITE BUBBLE-DOWN-*-MATCH-1))
 (10 2 (:REWRITE |(* x x)|))
 (6 6 (:REWRITE REDUCE-INTEGERP-+))
 (6 6 (:REWRITE INTEGERP-MINUS-X))
 (6 6 (:REWRITE DEFAULT-EXPT-2))
 (6 6 (:REWRITE DEFAULT-EXPT-1))
 (6 6 (:REWRITE |(expt 1/c n)|))
 (6 6 (:REWRITE |(expt (- x) n)|))
 (6 6 (:META META-INTEGERP-CORRECT))
 (2 2 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (2 2 (:REWRITE ZP-OPEN))
 (2 2 (:REWRITE THE-FLOOR-BELOW))
 (2 2 (:REWRITE THE-FLOOR-ABOVE))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (2 2 (:REWRITE SIMPLIFY-SUMS-<))
 (2 2 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (2 2 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (2 2 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (2 2 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (2 2 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (2 2 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (2 2 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (2 2 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (2 2 (:REWRITE NORMALIZE-ADDENDS))
 (2 2 (:REWRITE INTEGERP-<-CONSTANT))
 (2 2 (:REWRITE DEFAULT-PLUS-2))
 (2 2 (:REWRITE DEFAULT-PLUS-1))
 (2 2 (:REWRITE DEFAULT-MOD-2))
 (2 2 (:REWRITE DEFAULT-MOD-1))
 (2 2 (:REWRITE DEFAULT-LESS-THAN-2))
 (2 2 (:REWRITE DEFAULT-LESS-THAN-1))
 (2 2 (:REWRITE CONSTANT-<-INTEGERP))
 (2 2 (:REWRITE |(mod x 2)| . 2))
 (2 2 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (2 2 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (2 2 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (2 2 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (2 2 (:REWRITE |(< c (- x))|))
 (2 2 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (2 2 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
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 (2 2 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (2 2 (:REWRITE |(< (/ x) 0)|))
 (2 2 (:REWRITE |(< (/ x) (/ y))|))
 (2 2 (:REWRITE |(< (- x) c)|))
 (2 2 (:REWRITE |(< (- x) (- y))|))
 (2 2 (:REWRITE |(< (* x y) 0)|))
 (2 2 (:DEFINITION FIX))
 )
(M1::TOTAL-CORRECTNESS
 (148 2 (:DEFINITION M1::FINAL-N))
 (30 2 (:REWRITE |(mod x 2)| . 1))
 (28 8 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (24 2 (:REWRITE |(equal (if a b c) x)|))
 (22 2 (:REWRITE DEFAULT-MOD-RATIO))
 (16 14 (:REWRITE DEFAULT-TIMES-1))
 (16 4 (:REWRITE |(* y x)|))
 (14 14 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (14 14 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (14 14 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (14 14 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (14 14 (:REWRITE DEFAULT-TIMES-2))
 (12 2 (:REWRITE BUBBLE-DOWN-*-MATCH-1))
 (10 10 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (10 10 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (10 10 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (10 10 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (10 10 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (10 10 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (10 10 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (10 10 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (10 2 (:REWRITE |(* x x)|))
 (7 7 (:REWRITE DEFAULT-EXPT-2))
 (7 7 (:REWRITE DEFAULT-EXPT-1))
 (7 7 (:REWRITE |(expt 1/c n)|))
 (7 7 (:REWRITE |(expt (- x) n)|))
 (6 6 (:REWRITE REDUCE-INTEGERP-+))
 (6 6 (:REWRITE INTEGERP-MINUS-X))
 (6 6 (:META META-INTEGERP-CORRECT))
 (2 2 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (2 2 (:REWRITE ZP-OPEN))
 (2 2 (:REWRITE THE-FLOOR-BELOW))
 (2 2 (:REWRITE THE-FLOOR-ABOVE))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (2 2 (:REWRITE SIMPLIFY-SUMS-<))
 (2 2 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (2 2 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (2 2 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (2 2 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (2 2 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (2 2 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (2 2 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (2 2 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (2 2 (:REWRITE NORMALIZE-ADDENDS))
 (2 2 (:REWRITE INTEGERP-<-CONSTANT))
 (2 2 (:REWRITE DEFAULT-PLUS-2))
 (2 2 (:REWRITE DEFAULT-PLUS-1))
 (2 2 (:REWRITE DEFAULT-MOD-2))
 (2 2 (:REWRITE DEFAULT-MOD-1))
 (2 2 (:REWRITE DEFAULT-LESS-THAN-2))
 (2 2 (:REWRITE DEFAULT-LESS-THAN-1))
 (2 2 (:REWRITE CONSTANT-<-INTEGERP))
 (2 2 (:REWRITE |(mod x 2)| . 2))
 (2 2 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (2 2 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (2 2 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (2 2 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (2 2 (:REWRITE |(< c (- x))|))
 (2 2 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (2 2 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (2 2 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (2 2 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (2 2 (:REWRITE |(< (/ x) 0)|))
 (2 2 (:REWRITE |(< (/ x) (/ y))|))
 (2 2 (:REWRITE |(< (- x) c)|))
 (2 2 (:REWRITE |(< (- x) (- y))|))
 (2 2 (:REWRITE |(< (* x y) 0)|))
 (2 2 (:DEFINITION FIX))
 (1 1 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (1 1 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 )
