(FLOOR-SUM-CASES-HELPER-A
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 (185 185 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (163 163 (:REWRITE NORMALIZE-FACTORS-SCATTER-EXPONENTS))
 (134 53 (:REWRITE SIMPLIFY-SUMS-<))
 (88 61 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (86 12 (:REWRITE PREFER-POSITIVE-EXPONENTS-SCATTER-EXPONENTS-<-2))
 (66 61 (:REWRITE |(< (- x) (- y))|))
 (61 61 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (61 61 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (61 61 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (61 61 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (61 61 (:REWRITE INTEGERP-<-CONSTANT))
 (61 61 (:REWRITE CONSTANT-<-INTEGERP))
 (61 61 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (61 61 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
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 (54 34 (:META META-RATIONALP-CORRECT))
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 (49 49 (:REWRITE INTEGERP-MINUS-X))
 (49 49 (:META META-INTEGERP-CORRECT))
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 (35 35 (:REWRITE |(< (+ (- c) x) y)|))
 (34 34 (:REWRITE REDUCE-RATIONALP-+))
 (34 34 (:REWRITE RATIONALP-MINUS-X))
 (34 34 (:REWRITE |(+ c (+ d x))|))
 (32 32 (:REWRITE FOLD-CONSTS-IN-+))
 (32 12 (:REWRITE SIMPLIFY-PRODUCTS-SCATTER-EXPONENTS-<))
 (32 12 (:REWRITE PREFER-POSITIVE-EXPONENTS-SCATTER-EXPONENTS-<))
 (28 28 (:REWRITE ARITH-NORMALIZE-ADDENDS))
 (18 18 (:REWRITE |(< y (+ (- c) x))|))
 (18 18 (:REWRITE |(< x (+ c/d y))|))
 (17 17 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (16 8 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
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 (14 14 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (14 14 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (14 14 (:REWRITE |(< 0 (/ x))|))
 (14 14 (:REWRITE |(< 0 (* x y))|))
 (8 8 (:REWRITE |arith (* c (* d x))|))
 (8 8 (:REWRITE |arith (* (- x) y)|))
 (8 8 (:REWRITE DEFAULT-MOD-2))
 (8 4 (:REWRITE DEFAULT-MINUS))
 (5 5 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (5 5 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (5 5 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (5 5 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (5 5 (:REWRITE |(equal c (/ x))|))
 (5 5 (:REWRITE |(equal c (- x))|))
 (5 5 (:REWRITE |(equal (/ x) c)|))
 (5 5 (:REWRITE |(equal (/ x) (/ y))|))
 (5 5 (:REWRITE |(equal (- x) c)|))
 (5 5 (:REWRITE |(equal (- x) (- y))|))
 (4 4 (:REWRITE |arith (- (* c x))|))
 (4 4 (:REWRITE |(- (* c x))|))
 (3 3 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (2 2 (:REWRITE |arith (+ c (+ d x))|))
 (2 2 (:REWRITE SIMPLIFY-PRODUCTS-SCATTER-EXPONENTS-EQUAL))
 (2 2 (:REWRITE PREFER-POSITIVE-EXPONENTS-SCATTER-EXPONENTS-EQUAL))
 (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 |(< (/ x) 0)|))
 (1 1 (:REWRITE |(< (* x y) 0)|))
 )
(FLOOR-SUM-CASES-HELPER-B
 (872 872 (:REWRITE NORMALIZE-FACTORS-SCATTER-EXPONENTS))
 (519 519 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (303 144 (:REWRITE SIMPLIFY-PRODUCTS-SCATTER-EXPONENTS-<))
 (265 227 (:META META-RATIONALP-CORRECT))
 (243 243 (:REWRITE RATIONALP-MINUS-X))
 (232 232 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (229 224 (:REWRITE |(< (- x) (- y))|))
 (225 225 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (225 225 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (224 224 (:REWRITE INTEGERP-<-CONSTANT))
 (224 224 (:REWRITE CONSTANT-<-INTEGERP))
 (224 224 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (224 224 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (224 224 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (224 224 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (224 224 (:REWRITE |(< c (- x))|))
 (224 224 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (224 224 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (224 224 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (224 224 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (224 224 (:REWRITE |(< (/ x) (/ y))|))
 (224 224 (:REWRITE |(< (- x) c)|))
 (222 144 (:REWRITE PREFER-POSITIVE-EXPONENTS-SCATTER-EXPONENTS-<))
 (172 120 (:REWRITE |(equal (/ x) c)|))
 (161 145 (:META META-INTEGERP-CORRECT))
 (150 107 (:REWRITE PREFER-POSITIVE-EXPONENTS-SCATTER-EXPONENTS-EQUAL))
 (149 149 (:REWRITE INTEGERP-MINUS-X))
 (138 138 (:REWRITE FOLD-CONSTS-IN-+))
 (137 120 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (129 129 (:REWRITE |arith (* c (* d x))|))
 (121 121 (:REWRITE ARITH-NORMALIZE-ADDENDS))
 (120 120 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (120 120 (:REWRITE |(equal c (/ x))|))
 (120 120 (:REWRITE |(equal (/ x) (/ y))|))
 (120 120 (:REWRITE |(equal (- x) (- y))|))
 (116 116 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (116 116 (:REWRITE |(equal c (- x))|))
 (116 116 (:REWRITE |(equal (- x) c)|))
 (95 95 (:REWRITE |arith (* (- x) y)|))
 (81 81 (:REWRITE |(< 0 (/ x))|))
 (81 81 (:REWRITE |(< 0 (* x y))|))
 (80 80 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (80 80 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (66 66 (:REWRITE |(< y (+ (- c) x))|))
 (66 66 (:REWRITE |(< x (+ c/d y))|))
 (63 63 (:REWRITE |arith (- (* c x))|))
 (51 51 (:REWRITE |(equal (+ (- c) x) y)|))
 (49 49 (:REWRITE |(< (+ c/d x) y)|))
 (48 48 (:REWRITE |(< (+ (- c) x) y)|))
 (41 41 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (28 28 (:REWRITE |(< (* x y) 0)|))
 (27 27 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (27 27 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (27 27 (:REWRITE |(< (/ x) 0)|))
 (16 4 (:REWRITE RATIONALP-/))
 (16 4 (:REWRITE DEFAULT-MOD-RATIO))
 (15 15 (:REWRITE |arith (+ c (+ d x))|))
 (13 8 (:REWRITE DEFAULT-MINUS))
 (9 9 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (8 8 (:REWRITE DEFAULT-MOD-2))
 (5 5 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (5 5 (:REWRITE |(- (* c x))|))
 (4 4 (:REWRITE |(not (equal x (/ y)))|))
 (4 4 (:REWRITE |(equal x (/ y))|))
 (4 4 (:REWRITE |(/ (/ x))|))
 (4 1 (:REWRITE |(<= 1 (* x (/ y))) with (< y 0)|))
 (4 1 (:REWRITE |(<= 1 (* x (/ y))) with (< 0 y)|))
 (4 1 (:REWRITE |(< (* x (/ y)) 1) with (< y 0)|))
 (4 1 (:REWRITE |(< (* x (/ y)) 1) with (< 0 y)|))
 )
(|(floor (+ x y) z)|
 (211 102 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (190 190 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (176 44 (:REWRITE DEFAULT-MOD-RATIO))
 (150 150 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (124 12 (:LINEAR LINEAR-FLOOR-BOUNDS-2))
 (108 12 (:LINEAR MOD-BOUNDS-2))
 (102 102 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (102 102 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (102 102 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (102 102 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (102 102 (:REWRITE INTEGERP-<-CONSTANT))
 (102 102 (:REWRITE CONSTANT-<-INTEGERP))
 (102 102 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
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 (102 102 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
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 (34 34 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (34 34 (:REWRITE |(< 0 (/ x))|))
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 (17 5 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
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 (16 16 (:REWRITE RATIONALP-MINUS-X))
 (16 16 (:META META-RATIONALP-CORRECT))
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 (13 13 (:REWRITE |(< x (+ c/d y))|))
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 (10 10 (:REWRITE FOLD-CONSTS-IN-+))
 (10 10 (:REWRITE |(+ c (+ d x))|))
 (8 8 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (8 8 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (8 8 (:REWRITE |(< (/ x) 0)|))
 (8 8 (:REWRITE |(< (* x y) 0)|))
 (5 5 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
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 (5 5 (:REWRITE |(equal c (/ x))|))
 (5 5 (:REWRITE |(equal c (- x))|))
 (5 5 (:REWRITE |(equal (/ x) c)|))
 (5 5 (:REWRITE |(equal (/ x) (/ y))|))
 (5 5 (:REWRITE |(equal (- x) c)|))
 (5 5 (:REWRITE |(equal (- x) (- y))|))
 (4 4 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (4 4 (:REWRITE |(equal (+ (- c) x) y)|))
 )
(|(mod (+ x y) z)|
 (455 455 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (343 55 (:REWRITE DEFAULT-MOD-RATIO))
 (268 268 (:REWRITE |(+ c (+ d x))|))
 (259 259 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (240 60 (:REWRITE PREFER-POSITIVE-EXPONENTS-SCATTER-EXPONENTS-<-2))
 (234 22 (:LINEAR MOD-BOUNDS-3))
 (226 162 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (212 212 (:REWRITE FOLD-CONSTS-IN-+))
 (209 198 (:REWRITE |(< (- x) (- y))|))
 (198 198 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (198 198 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (198 198 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (198 198 (:REWRITE INTEGERP-<-CONSTANT))
 (198 198 (:REWRITE CONSTANT-<-INTEGERP))
 (198 198 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
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 (198 198 (:REWRITE |(< (/ x) (/ y))|))
 (198 198 (:REWRITE |(< (- x) c)|))
 (186 186 (:REWRITE NORMALIZE-FACTORS-SCATTER-EXPONENTS))
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 (166 166 (:REWRITE DEFAULT-FLOOR-1))
 (163 69 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (151 123 (:REWRITE |(equal (- x) (- y))|))
 (149 123 (:REWRITE |(equal (/ x) c)|))
 (126 18 (:LINEAR LINEAR-FLOOR-BOUNDS-2))
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 (123 123 (:REWRITE |(equal c (/ x))|))
 (123 123 (:REWRITE |(equal (/ x) (/ y))|))
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 (121 121 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (121 121 (:REWRITE |(equal c (- x))|))
 (121 121 (:REWRITE |(equal (- x) c)|))
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 (79 79 (:REWRITE |(equal (+ (- c) x) y)|))
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 (64 52 (:REWRITE PREFER-POSITIVE-EXPONENTS-SCATTER-EXPONENTS-EQUAL))
 (62 62 (:REWRITE |(< (/ x) 0)|))
 (62 62 (:REWRITE |(< (* x y) 0)|))
 (60 60 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (60 60 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (53 53 (:REWRITE |(< y (+ (- c) x))|))
 (53 53 (:REWRITE |(< x (+ c/d y))|))
 (53 53 (:REWRITE |(< (+ c/d x) y)|))
 (53 53 (:REWRITE |(< (+ (- c) x) y)|))
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 (48 48 (:META META-INTEGERP-CORRECT))
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 (40 40 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (40 40 (:REWRITE |(< 0 (/ x))|))
 (40 40 (:REWRITE |(< 0 (* x y))|))
 (28 28 (:REWRITE |arith (* c (* d x))|))
 (28 28 (:REWRITE |arith (* (- x) y)|))
 (26 26 (:REWRITE ARITH-NORMALIZE-ADDENDS))
 (14 14 (:REWRITE |arith (- (* c x))|))
 (10 10 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
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 (2 2 (:REWRITE |(equal x (/ y))|))
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 (2 2 (:REWRITE |(< (* x (/ y)) 0) rationalp (* x (/ y))|))
 (2 2 (:REWRITE |(/ (/ x))|))
 )
(CROCK-XXX33-HELPER
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 (18 9 (:REWRITE RATIONALP-X))
 (10 10 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (10 10 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (10 10 (:REWRITE |(equal c (/ x))|))
 (10 10 (:REWRITE |(equal c (- x))|))
 (10 10 (:REWRITE |(equal (/ x) c)|))
 (10 10 (:REWRITE |(equal (/ x) (/ y))|))
 (10 10 (:REWRITE |(equal (- x) c)|))
 (10 10 (:REWRITE |(equal (- x) (- y))|))
 (9 9 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (9 9 (:REWRITE REDUCE-RATIONALP-+))
 (9 9 (:REWRITE REDUCE-INTEGERP-+))
 (9 9 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (9 9 (:META META-RATIONALP-CORRECT))
 (6 6 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (4 4 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (4 4 (:REWRITE DEFAULT-MINUS))
 (3 3 (:REWRITE SIMPLIFY-PRODUCTS-SCATTER-EXPONENTS-EQUAL))
 (3 3 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (3 3 (:REWRITE NORMALIZE-FACTORS-SCATTER-EXPONENTS))
 (3 3 (:REWRITE NORMALIZE-ADDENDS))
 (3 3 (:REWRITE DEFAULT-DIVIDE))
 (3 3 (:REWRITE |(equal (+ (- c) x) y)|))
 (1 1 (:REWRITE |(- (* c x))|))
 )
(CROCK-XXX33A)
(REWRITE-FLOOR-MOD
 (19106 19106 (:REWRITE NORMALIZE-FACTORS-SCATTER-EXPONENTS))
 (7425 2256 (:REWRITE PREFER-POSITIVE-EXPONENTS-SCATTER-EXPONENTS-<))
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 (2697 2256 (:REWRITE SIMPLIFY-PRODUCTS-SCATTER-EXPONENTS-<))
 (2662 39 (:REWRITE FLOOR-=-X/Y . 4))
 (1721 478 (:REWRITE DEFAULT-FLOOR-RATIO))
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 (497 497 (:REWRITE |(equal (+ (- c) x) y)|))
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 (424 167 (:REWRITE FLOOR-X-Y-=--1 . 3))
 (420 420 (:REWRITE |(< y (+ (- c) x))|))
 (420 420 (:REWRITE |(< x (+ c/d y))|))
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 (38 6 (:LINEAR MOD-BOUNDS-2))
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 (35 35 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (30 30 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (26 26 (:REWRITE |(< 0 (* x (/ y))) rationalp (* x (/ y))|))
 (24 24 (:REWRITE |(not (equal x (/ y)))|))
 (24 24 (:REWRITE |(equal x (/ y))|))
 (22 22 (:REWRITE ARITH-NORMALIZE-FACTORS-SCATTER-EXPONENTS))
 (22 22 (:REWRITE |(* x (- y))|))
 (22 22 (:REWRITE |(* (- x) y)|))
 (20 20 (:REWRITE |(< (* x (/ y)) 0) rationalp (* x (/ y))|))
 (12 12 (:REWRITE |(equal (* x y) 0)|))
 (10 10 (:REWRITE ARITH-NORMALIZE-ADDENDS))
 (9 3 (:LINEAR MOD-BOUNDS-3))
 (1 1 (:REWRITE FLOOR-MOD-ELIM))
 (1 1 (:REWRITE |(- (* c x))|))
 )
(REWRITE-MOD-MOD
 (18335 18335 (:REWRITE NORMALIZE-FACTORS-SCATTER-EXPONENTS))
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 (9192 8502 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (8503 8503 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (7581 2050 (:REWRITE PREFER-POSITIVE-EXPONENTS-SCATTER-EXPONENTS-<))
 (6529 1011 (:REWRITE MOD-ZERO . 4))
 (6478 6478 (:REWRITE |(+ c (+ d x))|))
 (5584 5584 (:REWRITE FOLD-CONSTS-IN-+))
 (2845 2050 (:REWRITE SIMPLIFY-PRODUCTS-SCATTER-EXPONENTS-<))
 (2656 80 (:LINEAR MOD-BOUNDS-2))
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 (1325 1325 (:REWRITE INTEGERP-/))
 (738 40 (:LINEAR MOD-BOUNDS-3))
 (640 512 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (517 517 (:REWRITE |(equal (* x y) 0)|))
 (409 13 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (372 372 (:REWRITE |(< y (+ (- c) x))|))
 (372 372 (:REWRITE |(< x (+ c/d y))|))
 (269 269 (:REWRITE |(equal (+ (- c) x) y)|))
 (240 240 (:REWRITE DEFAULT-MINUS))
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 (70 70 (:REWRITE |(* (- x) y)|))
 (32 32 (:REWRITE |(not (equal x (/ y)))|))
 (32 32 (:REWRITE |(equal x (/ y))|))
 (18 9 (:REWRITE |(* (if a b c) x)|))
 (15 15 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (14 14 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (6 6 (:REWRITE |(< 0 (* x (/ y))) rationalp (* x (/ y))|))
 (4 4 (:REWRITE |(< (* x (/ y)) 0) rationalp (* x (/ y))|))
 )
