(M1::OK-INPUTS)
(M1::THETA
 (30 6 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (30 6 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (12 12 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (12 12 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (12 12 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (12 12 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (6 6 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (6 6 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (6 6 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (6 6 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (6 6 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (6 6 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (6 6 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (6 6 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (6 6 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (6 6 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (6 6 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 )
(M1::HELPER)
(M1::FN)
(M1::HELPER-IS-THETA
 (150 21 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (134 134 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (134 134 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (134 134 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (134 134 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (126 18 (:REWRITE ACL2-NUMBERP-X))
 (73 7 (:REWRITE DEFAULT-MOD-RATIO))
 (42 21 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (40 7 (:REWRITE |(* y x)|))
 (36 9 (:REWRITE RATIONALP-X))
 (36 9 (:REWRITE M1::INTEGERP-IMPLIES-RATIONALP))
 (33 33 (:REWRITE REDUCE-INTEGERP-+))
 (33 33 (:REWRITE INTEGERP-MINUS-X))
 (33 33 (:META META-INTEGERP-CORRECT))
 (32 28 (:REWRITE DEFAULT-TIMES-2))
 (28 28 (:REWRITE DEFAULT-TIMES-1))
 (27 15 (:REWRITE DEFAULT-PLUS-2))
 (21 21 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (21 21 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (21 21 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (21 21 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (21 21 (:REWRITE |(equal c (/ x))|))
 (21 21 (:REWRITE |(equal c (- x))|))
 (21 21 (:REWRITE |(equal (/ x) c)|))
 (21 21 (:REWRITE |(equal (/ x) (/ y))|))
 (21 21 (:REWRITE |(equal (- x) c)|))
 (21 21 (:REWRITE |(equal (- x) (- y))|))
 (20 20 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (15 15 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (15 15 (:REWRITE NORMALIZE-ADDENDS))
 (15 15 (:REWRITE DEFAULT-PLUS-1))
 (11 11 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (9 9 (:REWRITE THE-FLOOR-BELOW))
 (9 9 (:REWRITE THE-FLOOR-ABOVE))
 (9 9 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (9 9 (:REWRITE REDUCE-RATIONALP-+))
 (9 9 (:REWRITE REDUCE-RATIONALP-*))
 (9 9 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (9 9 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (9 9 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (9 9 (:REWRITE RATIONALP-MINUS-X))
 (9 9 (:REWRITE INTEGERP-<-CONSTANT))
 (9 9 (:REWRITE DEFAULT-LESS-THAN-2))
 (9 9 (:REWRITE DEFAULT-LESS-THAN-1))
 (9 9 (:REWRITE CONSTANT-<-INTEGERP))
 (9 9 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (9 9 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (9 9 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (9 9 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (9 9 (:REWRITE |(< c (- x))|))
 (9 9 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (9 9 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (9 9 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (9 9 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (9 9 (:REWRITE |(< (/ x) 0)|))
 (9 9 (:REWRITE |(< (/ x) (/ y))|))
 (9 9 (:REWRITE |(< (- x) c)|))
 (9 9 (:REWRITE |(< (- x) (- y))|))
 (9 9 (:REWRITE |(< (* x y) 0)|))
 (9 9 (:META META-RATIONALP-CORRECT))
 (7 7 (:REWRITE ZP-OPEN))
 (7 7 (:REWRITE DEFAULT-MOD-2))
 (7 7 (:REWRITE DEFAULT-MOD-1))
 (7 7 (:REWRITE |(mod x 2)| . 2))
 (5 5 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (5 5 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (5 5 (:REWRITE SIMPLIFY-SUMS-<))
 (5 5 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (5 5 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 )
(M1::FN-IS-THETA
 (22 2 (:REWRITE DEFAULT-MOD-RATIO))
 (17 17 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (17 17 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (17 17 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (17 17 (: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 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::LOOP-CLK)
(M1::CLK)
(M1::TEST)
(M1::LOOP-IS-HELPER
 (263 32 (:REWRITE ZP-OPEN))
 (219 39 (:REWRITE ACL2-NUMBERP-X))
 (212 17 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (60 15 (:REWRITE RATIONALP-X))
 (60 15 (:REWRITE M1::INTEGERP-IMPLIES-RATIONALP))
 (59 59 (:REWRITE DEFAULT-PLUS-2))
 (59 59 (:REWRITE DEFAULT-PLUS-1))
 (49 49 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (49 49 (:REWRITE NORMALIZE-ADDENDS))
 (40 8 (:REWRITE |(+ c (+ d x))|))
 (37 37 (:REWRITE REDUCE-INTEGERP-+))
 (37 37 (:REWRITE INTEGERP-MINUS-X))
 (37 37 (:META META-INTEGERP-CORRECT))
 (32 17 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (26 17 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (17 17 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (17 17 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (17 17 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (17 17 (:REWRITE |(equal c (/ x))|))
 (17 17 (:REWRITE |(equal c (- x))|))
 (17 17 (:REWRITE |(equal (/ x) c)|))
 (17 17 (:REWRITE |(equal (/ x) (/ y))|))
 (17 17 (:REWRITE |(equal (- x) c)|))
 (17 17 (:REWRITE |(equal (- x) (- y))|))
 (16 16 (:REWRITE THE-FLOOR-BELOW))
 (16 16 (:REWRITE THE-FLOOR-ABOVE))
 (16 16 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (16 16 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (16 16 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (16 16 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (16 16 (:REWRITE INTEGERP-<-CONSTANT))
 (16 16 (:REWRITE DEFAULT-LESS-THAN-2))
 (16 16 (:REWRITE DEFAULT-LESS-THAN-1))
 (16 16 (:REWRITE CONSTANT-<-INTEGERP))
 (16 16 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (16 16 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (16 16 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (16 16 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (16 16 (:REWRITE |(< c (- x))|))
 (16 16 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (16 16 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (16 16 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (16 16 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (16 16 (:REWRITE |(< (/ x) (/ y))|))
 (16 16 (:REWRITE |(< (- x) c)|))
 (16 16 (:REWRITE |(< (- x) (- y))|))
 (15 15 (:REWRITE REDUCE-RATIONALP-+))
 (15 15 (:REWRITE REDUCE-RATIONALP-*))
 (15 15 (:REWRITE RATIONALP-MINUS-X))
 (15 15 (:META META-RATIONALP-CORRECT))
 (14 14 (:REWRITE SIMPLIFY-SUMS-<))
 (14 14 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (14 14 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (9 9 (:REWRITE |(< (/ x) 0)|))
 (9 9 (:REWRITE |(< (* x y) 0)|))
 (7 7 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (7 7 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (7 7 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (7 7 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (7 7 (:REWRITE |(< y (+ (- c) x))|))
 (7 7 (:REWRITE |(< x (+ c/d y))|))
 (7 7 (:REWRITE |(< 0 (/ x))|))
 (7 7 (:REWRITE |(< 0 (* x y))|))
 (6 6 (:REWRITE DEFAULT-CDR))
 (6 6 (:REWRITE DEFAULT-CAR))
 (5 5 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 )
(M1::PROGRAM-IS-FN
 (24 4 (:DEFINITION M1::HELPER))
 (4 4 (:REWRITE ZP-OPEN))
 (4 4 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (4 4 (:REWRITE NORMALIZE-ADDENDS))
 (4 4 (:REWRITE DEFAULT-PLUS-2))
 (4 4 (:REWRITE DEFAULT-PLUS-1))
 (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-INTEGERP-+))
 (1 1 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (1 1 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (1 1 (:REWRITE INTEGERP-MINUS-X))
 (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)|))
 (1 1 (:META META-INTEGERP-CORRECT))
 )
(M1::PROGRAM-CORRECT
 (44 4 (:REWRITE DEFAULT-MOD-RATIO))
 (28 28 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (28 28 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (28 28 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (28 28 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (16 4 (:REWRITE |(* y x)|))
 (12 12 (:REWRITE DEFAULT-TIMES-2))
 (12 12 (:REWRITE DEFAULT-TIMES-1))
 (9 9 (:REWRITE REDUCE-INTEGERP-+))
 (9 9 (:REWRITE INTEGERP-MINUS-X))
 (9 9 (:META META-INTEGERP-CORRECT))
 (8 8 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (4 4 (:REWRITE DEFAULT-MOD-2))
 (4 4 (:REWRITE DEFAULT-MOD-1))
 (4 4 (: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 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::TOTAL-CORRECTNESS
 (61 61 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (61 61 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (61 61 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (61 61 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (55 5 (:REWRITE DEFAULT-MOD-RATIO))
 (54 54 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (54 54 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (54 54 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (54 54 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (40 8 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (40 8 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (36 8 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (36 8 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (20 5 (:REWRITE |(* y x)|))
 (17 17 (:REWRITE REDUCE-INTEGERP-+))
 (17 17 (:REWRITE INTEGERP-MINUS-X))
 (17 17 (:REWRITE DEFAULT-TIMES-2))
 (17 17 (:REWRITE DEFAULT-TIMES-1))
 (17 17 (:META META-INTEGERP-CORRECT))
 (15 2 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (14 2 (:REWRITE ACL2-NUMBERP-X))
 (12 12 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (8 8 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (8 8 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (8 8 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (8 8 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (8 8 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (8 8 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (5 5 (:REWRITE DEFAULT-MOD-2))
 (5 5 (:REWRITE DEFAULT-MOD-1))
 (5 5 (:REWRITE |(mod x 2)| . 2))
 (4 1 (:REWRITE RATIONALP-X))
 (4 1 (:REWRITE M1::INTEGERP-IMPLIES-RATIONALP))
 (3 3 (:REWRITE THE-FLOOR-BELOW))
 (3 3 (:REWRITE THE-FLOOR-ABOVE))
 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (3 3 (:REWRITE SIMPLIFY-SUMS-<))
 (3 3 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (3 3 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (3 3 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (3 3 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (3 3 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (3 3 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (3 3 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (3 3 (:REWRITE INTEGERP-<-CONSTANT))
 (3 3 (:REWRITE DEFAULT-LESS-THAN-2))
 (3 3 (:REWRITE DEFAULT-LESS-THAN-1))
 (3 3 (:REWRITE CONSTANT-<-INTEGERP))
 (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) 0)|))
 (3 3 (:REWRITE |(< (/ x) (/ y))|))
 (3 3 (:REWRITE |(< (- x) c)|))
 (3 3 (:REWRITE |(< (- x) (- y))|))
 (3 3 (:REWRITE |(< (* x y) 0)|))
 (3 2 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (2 2 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (2 2 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (2 2 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (2 2 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (2 2 (:REWRITE |(equal c (/ x))|))
 (2 2 (:REWRITE |(equal c (- x))|))
 (2 2 (:REWRITE |(equal (/ x) c)|))
 (2 2 (:REWRITE |(equal (/ x) (/ y))|))
 (2 2 (:REWRITE |(equal (- x) c)|))
 (2 2 (:REWRITE |(equal (- x) (- y))|))
 (1 1 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (1 1 (:REWRITE REDUCE-RATIONALP-+))
 (1 1 (:REWRITE REDUCE-RATIONALP-*))
 (1 1 (:REWRITE RATIONALP-MINUS-X))
 (1 1 (:META META-RATIONALP-CORRECT))
 )
