(FIXEDPOINT)
(LOCALFIXEDPOINT)
(ABSTRACT-LOCALFIXEDPOINT
 (2157 12 (:DEFINITION REMOVE-EQUAL))
 (1705 9 (:REWRITE LIST::WEAK-RIGHT-NORMALIZATION-CONS))
 (1450 38 (:REWRITE BAG::MEMBERP-CAR-WHEN-DISJOINT))
 (1164 42 (:REWRITE LIST::REMOVE-REDUCTON))
 (911 6 (:DEFINITION LIST::DISJOINT-REMOVE-DEFINITION))
 (622 6 (:REWRITE LIST::MEMBERP-REMOVE))
 (494 38 (:REWRITE BAG::SUBBAGP-IMPLIES-MEMBERSHIP))
 (469 6 (:DEFINITION LIST::DISJOINT))
 (419 101 (:REWRITE <<-TRICHOTOMY))
 (369 97 (:REWRITE LIST::MEMBERP-OF-CDR-CHEAP))
 (369 97 (:REWRITE LIST::MEMBERP-FROM-MEMBERP-OF-CDR-CHEAP))
 (358 358 (:TYPE-PRESCRIPTION ALIST::KEYS))
 (313 59 (:REWRITE <<-ASYMMETRIC))
 (289 285 (:REWRITE DEFAULT-CAR))
 (188 184 (:REWRITE DEFAULT-CDR))
 (138 138 (:TYPE-PRESCRIPTION LIST::DISJOINT))
 (120 4 (:REWRITE LIST::MEMBERP-OF-CONS))
 (115 115 (:REWRITE BAG::MEMBERP-OF-REMOVE-ALL))
 (113 97 (:REWRITE <<-TRANSITIVE))
 (112 82 (:REWRITE LIST::MEMBERP-OF-NON-CONSP-CHEAP))
 (107 107 (:REWRITE BAG::NON-MEMBERP-FROM-MEMBERP-OF-OTHER-CHEAP))
 (107 107 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINTNESS))
 (107 107 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-TWO))
 (107 107 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-ONE))
 (103 103 (:REWRITE BAG::MEMBERP-SUBBAGP))
 (103 103 (:REWRITE BAG::MEMBERP-OF-REMOVE-BAG-MEANS-MEMBERP))
 (103 103 (:REWRITE BAG::MEMBERP-OF-REMOVE-1))
 (97 97 (:REWRITE LIST::SUBSET-MEMBERSHIP-FREE-SUBSETP))
 (97 97 (:REWRITE LIST::SUBSET-MEMBERSHIP-FREE-MEMBERP))
 (96 96 (:TYPE-PRESCRIPTION BAG::SUBBAGP))
 (95 95 (:REWRITE LIST::MEMBERP-DISJOINT-NON-MEMBERP))
 (76 38 (:REWRITE BAG::MEMBERP-CAR-WHEN-DISJOINT-CHEAP))
 (72 36 (:REWRITE BAG::SUBBAGP-FROM-SUBBAGP-OF-CDR-CHEAP))
 (62 6 (:REWRITE LIST::MEMBERP-OF-CONS-IRREL))
 (60 24 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-TWO))
 (56 20 (:REWRITE BAG::DISJOINT-OF-NON-CONSP-TWO))
 (54 26 (:REWRITE WFKEYED-IMPLIES-NOT-NIL-MEMBERP))
 (52 12 (:REWRITE BAG::UNIQUE-MEANS-CAR-NOT-MEMBERP-OF-CDR))
 (48 8 (:REWRITE LIST::EQUAL-CAR-DIFFERENTIAL))
 (38 20 (:REWRITE LIST::NOT-CONSP-DISJOINT))
 (38 20 (:REWRITE BAG::DISJOINT-OF-NON-CONSP-ONE))
 (36 36 (:REWRITE BAG::SUBBAGP-REMOVE-BAG))
 (36 36 (:REWRITE BAG::SUBBAGP-REMOVE))
 (36 36 (:REWRITE BAG::SUBBAGP-CHAINING))
 (36 36 (:REWRITE BAG::PERM-SUBBAGP-SUBBAGP))
 (36 24 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-TWO-CHEAP))
 (28 28 (:TYPE-PRESCRIPTION WFKEYED))
 (28 28 (:REWRITE BAG::DISJOINT-FROM-COMMON-UNIQUENSS))
 (28 28 (:LINEAR BAG::COUNT-WITH-SUBBAGP-LINEAR))
 (24 24 (:REWRITE BAG::SUBBAGP-OF-REMOVE-1-IMPLIES-SUBBAGP))
 (24 24 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-ONE-CHEAP))
 (24 24 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-ONE))
 (20 20 (:TYPE-PRESCRIPTION BAG::UNIQUE))
 (20 20 (:REWRITE BAG::SUBBAGP-DISJOINT-COMMUTE))
 (20 20 (:REWRITE BAG::SUBBAGP-DISJOINT))
 (20 20 (:REWRITE LIST::DISJOINT-BY-MULTIPLICITY))
 (16 2 (:REWRITE LIST::SUBSETP-REMOVE-BY-SUBSET))
 (12 12 (:REWRITE BAG::SUBBAGP-SELF))
 (12 12 (:REWRITE CLR-DIFFERENTIAL))
 (12 8 (:REWRITE EQUAL-BOOLEANS-REDUCTON))
 (12 6 (:REWRITE BAG::DISJOINT-CDR-FROM-DISJOINT-CHEAP))
 (12 6 (:REWRITE BAG::DISJOINT-CDR-FROM-DISJOINT))
 (10 10 (:REWRITE BAG::UNIQUE-OF-NON-CONSP-CHEAP))
 (10 10 (:REWRITE BAG::SUBBAGP-UNIQUENESS))
 (10 8 (:REWRITE BAG::DISJOINT-SELF-MEANS-NOT-CONSP))
 (9 9 (:REWRITE LIST::MEMBERP-OF-CONS-CHEAP))
 (9 3 (:REWRITE WFR-CANCELLATIONS))
 (8 8 (:REWRITE LIST::CARS-MATCH-FROM-FIRSTN-FACT-2))
 (8 8 (:REWRITE LIST::CARS-MATCH-FROM-FIRSTN-FACT))
 (6 6 (:TYPE-PRESCRIPTION WFR))
 (4 4 (:TYPE-PRESCRIPTION BOOLEANP))
 (4 4 (:REWRITE LIST::SUBSET-BY-MULTIPLICITY))
 (4 4 (:REWRITE BAG::COUNT-0-FOR-NON-MEMBERP))
 (4 4 (:REWRITE LIST::CDR-DOES-NOTHING-REWRITE))
 (4 4 (:REWRITE <<-IRREFLEXIVE))
 (4 2 (:REWRITE LIST::SUBSET-REMOVE-REDUCTION-1))
 (3 3 (:TYPE-PRESCRIPTION RKEYS-NON-NIL-TP))
 )
(LEAF-MEASURE-AUX
 (2237 1082 (:REWRITE DEFAULT-+-2))
 (1512 1082 (:REWRITE DEFAULT-+-1))
 (1498 107 (:DEFINITION LENGTH))
 (1059 7 (:LINEAR ACL2-COUNT-CAR-CDR-LINEAR))
 (856 214 (:DEFINITION INTEGER-ABS))
 (856 107 (:DEFINITION LEN))
 (428 214 (:REWRITE LIST::LEN-WHEN-AT-MOST-1))
 (427 40 (:REWRITE LIST::WEAK-RIGHT-NORMALIZATION-CONS))
 (387 365 (:REWRITE <<-TRANSITIVE))
 (274 238 (:REWRITE DEFAULT-<-2))
 (250 238 (:REWRITE DEFAULT-<-1))
 (214 214 (:REWRITE LIST::LEN-OF-NON-CONSP))
 (214 214 (:REWRITE DEFAULT-UNARY-MINUS))
 (156 39 (:REWRITE LIST::MEMBERP-OF-CDR-CHEAP))
 (156 39 (:REWRITE LIST::MEMBERP-FROM-MEMBERP-OF-CDR-CHEAP))
 (132 6 (:REWRITE BAG::MEMBERP-CAR-WHEN-DISJOINT))
 (108 6 (:REWRITE BAG::SUBBAGP-IMPLIES-MEMBERSHIP))
 (107 107 (:TYPE-PRESCRIPTION LEN))
 (107 107 (:REWRITE DEFAULT-REALPART))
 (107 107 (:REWRITE DEFAULT-NUMERATOR))
 (107 107 (:REWRITE DEFAULT-IMAGPART))
 (107 107 (:REWRITE DEFAULT-DENOMINATOR))
 (107 107 (:REWRITE DEFAULT-COERCE-2))
 (107 107 (:REWRITE DEFAULT-COERCE-1))
 (99 3 (:DEFINITION LIST::DISJOINT-REMOVE-DEFINITION))
 (50 2 (:REWRITE LIST::MEMBERP-OF-CONS-IRREL))
 (45 45 (:REWRITE BAG::MEMBERP-SUBBAGP))
 (45 45 (:REWRITE BAG::MEMBERP-OF-REMOVE-BAG-MEANS-MEMBERP))
 (45 45 (:REWRITE BAG::MEMBERP-OF-REMOVE-ALL))
 (45 45 (:REWRITE BAG::MEMBERP-OF-REMOVE-1))
 (40 21 (:REWRITE EQUAL-BOOLEANS-REDUCTON))
 (39 39 (:REWRITE LIST::SUBSET-MEMBERSHIP-FREE-SUBSETP))
 (39 39 (:REWRITE LIST::SUBSET-MEMBERSHIP-FREE-MEMBERP))
 (30 30 (:REWRITE BAG::NON-MEMBERP-FROM-MEMBERP-OF-OTHER-CHEAP))
 (30 30 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINTNESS))
 (30 30 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-TWO))
 (30 30 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-ONE))
 (26 13 (:REWRITE LIST::MEMBERP-OF-NON-CONSP-CHEAP))
 (24 24 (:REWRITE LIST::MEMBERP-DISJOINT-NON-MEMBERP))
 (24 6 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-TWO))
 (23 23 (:REWRITE CLR-DIFFERENTIAL))
 (18 18 (:TYPE-PRESCRIPTION BAG::SUBBAGP))
 (16 4 (:REWRITE LIST::EQUAL-CAR-DIFFERENTIAL))
 (12 12 (:TYPE-PRESCRIPTION LIST::DISJOINT))
 (12 12 (:TYPE-PRESCRIPTION BOOLEANP))
 (12 6 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-TWO-CHEAP))
 (12 6 (:REWRITE BAG::SUBBAGP-FROM-SUBBAGP-OF-CDR-CHEAP))
 (12 6 (:REWRITE BAG::MEMBERP-CAR-WHEN-DISJOINT-CHEAP))
 (12 3 (:REWRITE BAG::DISJOINT-OF-NON-CONSP-TWO))
 (9 9 (:REWRITE LIST::MEMBERP-OF-CONS-CHEAP))
 (6 6 (:REWRITE BAG::SUBBAGP-REMOVE-BAG))
 (6 6 (:REWRITE BAG::SUBBAGP-REMOVE))
 (6 6 (:REWRITE BAG::SUBBAGP-OF-REMOVE-1-IMPLIES-SUBBAGP))
 (6 6 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-ONE-CHEAP))
 (6 6 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-ONE))
 (6 6 (:REWRITE BAG::SUBBAGP-CHAINING))
 (6 6 (:REWRITE BAG::PERM-SUBBAGP-SUBBAGP))
 (6 6 (:REWRITE ALIST::MEMBERP-CONS))
 (4 4 (:REWRITE LIST::CARS-MATCH-FROM-FIRSTN-FACT-2))
 (4 4 (:REWRITE LIST::CARS-MATCH-FROM-FIRSTN-FACT))
 (3 3 (:REWRITE BAG::SUBBAGP-DISJOINT-COMMUTE))
 (3 3 (:REWRITE BAG::SUBBAGP-DISJOINT))
 (3 3 (:REWRITE BAG::DISJOINT-OF-NON-CONSP-ONE))
 (3 3 (:REWRITE BAG::DISJOINT-FROM-COMMON-UNIQUENSS))
 (3 3 (:REWRITE LIST::DISJOINT-BY-MULTIPLICITY))
 (3 1 (:REWRITE WFKEYED-IMPLIES-NOT-NIL-MEMBERP))
 (2 2 (:TYPE-PRESCRIPTION WFKEYED))
 (2 2 (:REWRITE LIST::CDR-DOES-NOTHING-REWRITE))
 )
(LEAF-MEASURE-IFRP
 (266 2 (:DEFINITION G-AUX))
 (264 4 (:REWRITE NOT-MEMBERP-G-AUX))
 (228 4 (:DEFINITION ACL2-COUNT))
 (184 6 (:DEFINITION RCDP))
 (140 4 (:DEFINITION ALIST::KEYS))
 (124 32 (:REWRITE <<-TRICHOTOMY))
 (124 4 (:REWRITE G-AUX-IS-NIL-FOR-<<))
 (116 8 (:REWRITE LIST::WEAK-RIGHT-NORMALIZATION-CONS))
 (92 16 (:REWRITE <<-ASYMMETRIC))
 (74 74 (:REWRITE DEFAULT-CAR))
 (64 32 (:REWRITE DEFAULT-+-2))
 (56 4 (:DEFINITION LENGTH))
 (54 54 (:REWRITE DEFAULT-CDR))
 (44 32 (:REWRITE DEFAULT-+-1))
 (40 8 (:REWRITE LIST::MEMBERP-OF-CDR-CHEAP))
 (40 8 (:REWRITE LIST::MEMBERP-FROM-MEMBERP-OF-CDR-CHEAP))
 (32 32 (:REWRITE <<-TRANSITIVE))
 (32 8 (:REWRITE COMMUTATIVITY-OF-+))
 (32 8 (:DEFINITION INTEGER-ABS))
 (32 4 (:DEFINITION LEN))
 (16 8 (:REWRITE LIST::LEN-WHEN-AT-MOST-1))
 (10 9 (:REWRITE DEFAULT-<-2))
 (10 9 (:REWRITE DEFAULT-<-1))
 (8 8 (:REWRITE LIST::SUBSET-MEMBERSHIP-FREE-SUBSETP))
 (8 8 (:REWRITE LIST::SUBSET-MEMBERSHIP-FREE-MEMBERP))
 (8 8 (:REWRITE BAG::MEMBERP-SUBBAGP))
 (8 8 (:REWRITE BAG::MEMBERP-OF-REMOVE-BAG-MEANS-MEMBERP))
 (8 8 (:REWRITE BAG::MEMBERP-OF-REMOVE-ALL))
 (8 8 (:REWRITE BAG::MEMBERP-OF-REMOVE-1))
 (8 8 (:REWRITE LIST::LEN-OF-NON-CONSP))
 (8 8 (:REWRITE FOLD-CONSTS-IN-+))
 (8 8 (:REWRITE DEFAULT-UNARY-MINUS))
 (8 4 (:REWRITE LIST::MEMBERP-OF-NON-CONSP-CHEAP))
 (4 4 (:TYPE-PRESCRIPTION LEN))
 (4 4 (:REWRITE BAG::NON-MEMBERP-FROM-MEMBERP-OF-OTHER-CHEAP))
 (4 4 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINTNESS))
 (4 4 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-TWO))
 (4 4 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-ONE))
 (4 4 (:REWRITE LIST::MEMBERP-DISJOINT-NON-MEMBERP))
 (4 4 (:REWRITE DEFAULT-REALPART))
 (4 4 (:REWRITE DEFAULT-NUMERATOR))
 (4 4 (:REWRITE DEFAULT-IMAGPART))
 (4 4 (:REWRITE DEFAULT-DENOMINATOR))
 (4 4 (:REWRITE DEFAULT-COERCE-2))
 (4 4 (:REWRITE DEFAULT-COERCE-1))
 (4 2 (:REWRITE EQUAL-BOOLEANS-REDUCTON))
 (3 3 (:TYPE-PRESCRIPTION ACL2->RCD))
 (3 1 (:REWRITE WFR-CANCELLATIONS))
 (2 2 (:TYPE-PRESCRIPTION WFR))
 (2 2 (:TYPE-PRESCRIPTION BOOLEANP))
 (2 2 (:REWRITE CLR-DIFFERENTIAL))
 (1 1 (:REWRITE ACL2->RCD-RETURNS-RCDP))
 )
(G-AUX-IMPLIES-INEQUALITY
 (118 2 (:REWRITE NOT-MEMBERP-G-AUX))
 (114 2 (:DEFINITION ACL2-COUNT))
 (92 3 (:DEFINITION RCDP))
 (62 16 (:REWRITE <<-TRICHOTOMY))
 (62 2 (:REWRITE G-AUX-IS-NIL-FOR-<<))
 (62 2 (:DEFINITION ALIST::KEYS))
 (50 4 (:REWRITE LIST::WEAK-RIGHT-NORMALIZATION-CONS))
 (46 8 (:REWRITE <<-ASYMMETRIC))
 (35 35 (:REWRITE DEFAULT-CAR))
 (32 16 (:REWRITE DEFAULT-+-2))
 (28 2 (:DEFINITION LENGTH))
 (26 26 (:REWRITE DEFAULT-CDR))
 (22 16 (:REWRITE DEFAULT-+-1))
 (16 16 (:REWRITE <<-TRANSITIVE))
 (16 4 (:REWRITE LIST::MEMBERP-OF-CDR-CHEAP))
 (16 4 (:REWRITE LIST::MEMBERP-FROM-MEMBERP-OF-CDR-CHEAP))
 (16 4 (:REWRITE COMMUTATIVITY-OF-+))
 (16 4 (:DEFINITION INTEGER-ABS))
 (16 2 (:DEFINITION LEN))
 (8 4 (:REWRITE LIST::LEN-WHEN-AT-MOST-1))
 (4 4 (:REWRITE LIST::SUBSET-MEMBERSHIP-FREE-SUBSETP))
 (4 4 (:REWRITE LIST::SUBSET-MEMBERSHIP-FREE-MEMBERP))
 (4 4 (:REWRITE BAG::MEMBERP-SUBBAGP))
 (4 4 (:REWRITE BAG::MEMBERP-OF-REMOVE-BAG-MEANS-MEMBERP))
 (4 4 (:REWRITE BAG::MEMBERP-OF-REMOVE-ALL))
 (4 4 (:REWRITE BAG::MEMBERP-OF-REMOVE-1))
 (4 4 (:REWRITE LIST::LEN-OF-NON-CONSP))
 (4 4 (:REWRITE FOLD-CONSTS-IN-+))
 (4 4 (:REWRITE DEFAULT-UNARY-MINUS))
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (4 2 (:REWRITE LIST::MEMBERP-OF-NON-CONSP-CHEAP))
 (2 2 (:TYPE-PRESCRIPTION LEN))
 (2 2 (:REWRITE BAG::NON-MEMBERP-FROM-MEMBERP-OF-OTHER-CHEAP))
 (2 2 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINTNESS))
 (2 2 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-TWO))
 (2 2 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-ONE))
 (2 2 (:REWRITE LIST::MEMBERP-DISJOINT-NON-MEMBERP))
 (2 2 (:REWRITE DEFAULT-REALPART))
 (2 2 (:REWRITE DEFAULT-NUMERATOR))
 (2 2 (:REWRITE DEFAULT-IMAGPART))
 (2 2 (:REWRITE DEFAULT-DENOMINATOR))
 (2 2 (:REWRITE DEFAULT-COERCE-2))
 (2 2 (:REWRITE DEFAULT-COERCE-1))
 (2 1 (:REWRITE EQUAL-BOOLEANS-REDUCTON))
 (1 1 (:TYPE-PRESCRIPTION BOOLEANP))
 (1 1 (:REWRITE CLR-DIFFERENTIAL))
 )
(FIXEDPOINT-TO-IFRP
 (1030 35 (:DEFINITION RCDP))
 (792 18 (:REWRITE NOT-MEMBERP-G-AUX))
 (611 157 (:REWRITE <<-TRICHOTOMY))
 (534 18 (:REWRITE G-AUX-IS-NIL-FOR-<<))
 (433 75 (:REWRITE <<-ASYMMETRIC))
 (342 342 (:REWRITE DEFAULT-CAR))
 (262 18 (:DEFINITION ALIST::KEYS))
 (248 8 (:REWRITE MEMBERP-G-AUX))
 (182 182 (:REWRITE DEFAULT-CDR))
 (157 157 (:REWRITE <<-TRANSITIVE))
 (144 32 (:REWRITE LIST::WEAK-RIGHT-NORMALIZATION-CONS))
 (72 16 (:REWRITE LIST::MEMBERP-OF-CDR-CHEAP))
 (72 16 (:REWRITE LIST::MEMBERP-FROM-MEMBERP-OF-CDR-CHEAP))
 (48 16 (:REWRITE WFKEYED-IMPLIES-NOT-NIL-MEMBERP))
 (32 32 (:TYPE-PRESCRIPTION WFKEYED))
 (32 16 (:REWRITE LIST::MEMBERP-OF-NON-CONSP-CHEAP))
 (16 16 (:REWRITE LIST::SUBSET-MEMBERSHIP-FREE-SUBSETP))
 (16 16 (:REWRITE LIST::SUBSET-MEMBERSHIP-FREE-MEMBERP))
 (16 16 (:REWRITE BAG::NON-MEMBERP-FROM-MEMBERP-OF-OTHER-CHEAP))
 (16 16 (:REWRITE BAG::MEMBERP-SUBBAGP))
 (16 16 (:REWRITE BAG::MEMBERP-OF-REMOVE-BAG-MEANS-MEMBERP))
 (16 16 (:REWRITE BAG::MEMBERP-OF-REMOVE-ALL))
 (16 16 (:REWRITE BAG::MEMBERP-OF-REMOVE-1))
 (16 16 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINTNESS))
 (16 16 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-TWO))
 (16 16 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-ONE))
 (16 16 (:REWRITE LIST::MEMBERP-DISJOINT-NON-MEMBERP))
 (6 2 (:REWRITE WFR-CANCELLATIONS))
 (4 4 (:TYPE-PRESCRIPTION WFR))
 (4 2 (:REWRITE EQUAL-BOOLEANS-REDUCTON))
 (2 2 (:TYPE-PRESCRIPTION BOOLEANP))
 (2 2 (:REWRITE CLR-DIFFERENTIAL))
 )
(ABSTRACT-FIXEDPOINT-HELPER
 (387 99 (:REWRITE <<-TRICHOTOMY))
 (324 58 (:REWRITE <<-ASYMMETRIC))
 (241 241 (:REWRITE DEFAULT-CAR))
 (140 140 (:REWRITE DEFAULT-CDR))
 (126 5 (:REWRITE NOT-MEMBERP-G-AUX))
 (101 5 (:REWRITE G-AUX-IS-NIL-FOR-<<))
 (99 99 (:REWRITE <<-TRANSITIVE))
 (49 5 (:DEFINITION ALIST::KEYS))
 (16 4 (:REWRITE LIST::WEAK-RIGHT-NORMALIZATION-CONS))
 (9 2 (:REWRITE LIST::EQUAL-CAR-DIFFERENTIAL))
 (8 2 (:REWRITE LIST::MEMBERP-OF-CDR-CHEAP))
 (8 2 (:REWRITE LIST::MEMBERP-FROM-MEMBERP-OF-CDR-CHEAP))
 (7 1 (:REWRITE MEMBERP-G-AUX))
 (6 2 (:REWRITE WFKEYED-IMPLIES-NOT-NIL-MEMBERP))
 (4 4 (:TYPE-PRESCRIPTION WFKEYED))
 (4 4 (:REWRITE CLR-DIFFERENTIAL))
 (4 2 (:REWRITE LIST::MEMBERP-OF-NON-CONSP-CHEAP))
 (3 1 (:REWRITE WFR-CANCELLATIONS))
 (2 2 (:TYPE-PRESCRIPTION WFR))
 (2 2 (:TYPE-PRESCRIPTION BOOLEANP))
 (2 2 (:REWRITE LIST::SUBSET-MEMBERSHIP-FREE-SUBSETP))
 (2 2 (:REWRITE LIST::SUBSET-MEMBERSHIP-FREE-MEMBERP))
 (2 2 (:REWRITE BAG::NON-MEMBERP-FROM-MEMBERP-OF-OTHER-CHEAP))
 (2 2 (:REWRITE BAG::MEMBERP-SUBBAGP))
 (2 2 (:REWRITE BAG::MEMBERP-OF-REMOVE-BAG-MEANS-MEMBERP))
 (2 2 (:REWRITE BAG::MEMBERP-OF-REMOVE-ALL))
 (2 2 (:REWRITE BAG::MEMBERP-OF-REMOVE-1))
 (2 2 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINTNESS))
 (2 2 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-TWO))
 (2 2 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-ONE))
 (2 2 (:REWRITE LIST::MEMBERP-DISJOINT-NON-MEMBERP))
 (2 2 (:REWRITE LIST::CARS-MATCH-FROM-FIRSTN-FACT-2))
 (2 2 (:REWRITE LIST::CARS-MATCH-FROM-FIRSTN-FACT))
 (1 1 (:REWRITE LIST::CDR-DOES-NOTHING-REWRITE))
 )
(ABSTRACT-FIXEDPOINT
 (2433 5 (:DEFINITION REMOVE-EQUAL))
 (1668 4 (:REWRITE LIST::WEAK-RIGHT-NORMALIZATION-CONS))
 (1344 32 (:REWRITE BAG::MEMBERP-CAR-WHEN-DISJOINT))
 (800 8 (:DEFINITION LIST::DISJOINT-REMOVE-DEFINITION))
 (742 23 (:REWRITE LIST::WEAK-RIGHT-NORMALIZATION-REMOVE))
 (732 12 (:REWRITE LIST::MEMBERP-REMOVE))
 (692 23 (:REWRITE LIST::REMOVE-REDUCTON))
 (544 32 (:REWRITE BAG::SUBBAGP-IMPLIES-MEMBERSHIP))
 (400 8 (:DEFINITION LIST::DISJOINT))
 (170 34 (:REWRITE LIST::MEMBERP-OF-CDR-CHEAP))
 (170 34 (:REWRITE LIST::MEMBERP-FROM-MEMBERP-OF-CDR-CHEAP))
 (124 124 (:TYPE-PRESCRIPTION LIST::DISJOINT))
 (102 34 (:REWRITE DEFAULT-CAR))
 (90 30 (:REWRITE LIST::MEMBERP-OF-NON-CONSP-CHEAP))
 (84 20 (:REWRITE LIST::NOT-CONSP-DISJOINT))
 (84 20 (:REWRITE BAG::DISJOINT-OF-NON-CONSP-ONE))
 (80 80 (:TYPE-PRESCRIPTION BAG::SUBBAGP))
 (76 16 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-TWO))
 (64 32 (:REWRITE BAG::SUBBAGP-FROM-SUBBAGP-OF-CDR-CHEAP))
 (64 32 (:REWRITE BAG::MEMBERP-CAR-WHEN-DISJOINT-CHEAP))
 (62 62 (:REWRITE BAG::MEMBERP-OF-REMOVE-ALL))
 (56 20 (:REWRITE BAG::DISJOINT-OF-NON-CONSP-TWO))
 (56 12 (:REWRITE BAG::DISJOINT-SELF-MEANS-NOT-CONSP))
 (54 54 (:REWRITE BAG::NON-MEMBERP-FROM-MEMBERP-OF-OTHER-CHEAP))
 (54 54 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINTNESS))
 (54 54 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-TWO))
 (54 54 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-ONE))
 (54 18 (:REWRITE DEFAULT-CDR))
 (48 16 (:REWRITE BAG::UNIQUE-MEANS-CAR-NOT-MEMBERP-OF-CDR))
 (48 16 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-ONE-CHEAP))
 (48 16 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-ONE))
 (46 46 (:REWRITE BAG::MEMBERP-SUBBAGP))
 (46 46 (:REWRITE BAG::MEMBERP-OF-REMOVE-BAG-MEANS-MEMBERP))
 (46 46 (:REWRITE BAG::MEMBERP-OF-REMOVE-1))
 (38 38 (:REWRITE LIST::MEMBERP-DISJOINT-NON-MEMBERP))
 (36 16 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-TWO-CHEAP))
 (34 34 (:REWRITE LIST::SUBSET-MEMBERSHIP-FREE-SUBSETP))
 (34 34 (:REWRITE LIST::SUBSET-MEMBERSHIP-FREE-MEMBERP))
 (32 32 (:REWRITE BAG::SUBBAGP-REMOVE-BAG))
 (32 32 (:REWRITE BAG::SUBBAGP-REMOVE))
 (32 32 (:REWRITE BAG::SUBBAGP-CHAINING))
 (32 32 (:REWRITE BAG::PERM-SUBBAGP-SUBBAGP))
 (32 32 (:REWRITE BAG::DISJOINT-FROM-COMMON-UNIQUENSS))
 (24 4 (:REWRITE LIST::SUBSETP-REMOVE-BY-SUBSET))
 (20 20 (:REWRITE BAG::SUBBAGP-DISJOINT-COMMUTE))
 (20 20 (:REWRITE BAG::SUBBAGP-DISJOINT))
 (20 20 (:REWRITE LIST::DISJOINT-BY-MULTIPLICITY))
 (20 10 (:REWRITE WFR-IMPLIES-NOT-NIL-MEMBERP))
 (16 16 (:TYPE-PRESCRIPTION BAG::UNIQUE))
 (16 16 (:REWRITE UNIQUE-RKEYS))
 (16 16 (:REWRITE BAG::SUBBAGP-SELF))
 (16 16 (:REWRITE BAG::SUBBAGP-OF-REMOVE-1-IMPLIES-SUBBAGP))
 (16 8 (:REWRITE BAG::DISJOINT-CDR-FROM-DISJOINT-CHEAP))
 (16 8 (:REWRITE BAG::DISJOINT-CDR-FROM-DISJOINT))
 (10 10 (:TYPE-PRESCRIPTION WFR))
 (8 8 (:REWRITE LIST::SUBSET-BY-MULTIPLICITY))
 (8 4 (:REWRITE LIST::SUBSET-REMOVE-REDUCTION-1))
 (5 5 (:REWRITE RKEYS-WHEN-NOT-CONSP))
 (2 2 (:LINEAR BAG::COUNT-WITH-SUBBAGP-LINEAR))
 (2 1 (:LINEAR BAG::COUNT-LINEAR))
 (1 1 (:REWRITE BAG::COUNT-0-FOR-NON-MEMBERP))
 )
(FIXEDPOINT-IMPACT-ON-KEYS
 (72 2 (:DEFINITION RCDP))
 (38 10 (:REWRITE <<-TRICHOTOMY))
 (34 6 (:REWRITE <<-ASYMMETRIC))
 (23 23 (:REWRITE DEFAULT-CAR))
 (22 22 (:TYPE-PRESCRIPTION <<))
 (13 13 (:REWRITE DEFAULT-CDR))
 (10 10 (:REWRITE <<-TRANSITIVE))
 (3 3 (:TYPE-PRESCRIPTION RKEYS-NON-NIL-TP))
 (3 1 (:REWRITE WFR-CANCELLATIONS))
 (2 2 (:TYPE-PRESCRIPTION WFR))
 (1 1 (:REWRITE LIST::EQUAL-CONS-CASES))
 (1 1 (:REWRITE EQUAL-BOOLEANS-REDUCTON))
 (1 1 (:REWRITE CLR-DIFFERENTIAL))
 )
(FIXEDPOINT-MEASURE
 (160 80 (:REWRITE DEFAULT-+-2))
 (124 3 (:DEFINITION IFRP))
 (110 80 (:REWRITE DEFAULT-+-1))
 (92 3 (:DEFINITION RCDP))
 (80 10 (:DEFINITION LEN))
 (56 56 (:REWRITE DEFAULT-CDR))
 (43 11 (:REWRITE <<-TRICHOTOMY))
 (40 40 (:REWRITE DEFAULT-CAR))
 (40 20 (:REWRITE LIST::LEN-WHEN-AT-MOST-1))
 (29 5 (:REWRITE <<-ASYMMETRIC))
 (25 25 (:TYPE-PRESCRIPTION <<))
 (20 20 (:REWRITE LIST::LEN-OF-NON-CONSP))
 (20 20 (:REWRITE FOLD-CONSTS-IN-+))
 (20 20 (:REWRITE DEFAULT-UNARY-MINUS))
 (20 20 (:REWRITE DEFAULT-<-2))
 (20 20 (:REWRITE DEFAULT-<-1))
 (14 14 (:TYPE-PRESCRIPTION RCDP))
 (11 11 (:REWRITE <<-TRANSITIVE))
 (10 10 (:TYPE-PRESCRIPTION LEN))
 (10 10 (:REWRITE DEFAULT-REALPART))
 (10 10 (:REWRITE DEFAULT-NUMERATOR))
 (10 10 (:REWRITE DEFAULT-IMAGPART))
 (10 10 (:REWRITE DEFAULT-DENOMINATOR))
 (10 10 (:REWRITE DEFAULT-COERCE-2))
 (10 10 (:REWRITE DEFAULT-COERCE-1))
 (6 2 (:LINEAR ACL2-COUNT-G-DECREASES))
 (4 4 (:TYPE-PRESCRIPTION WFR))
 (2 1 (:REWRITE EQUAL-BOOLEANS-REDUCTON))
 (1 1 (:REWRITE CLR-DIFFERENTIAL))
 )
(FIXEDPOINT-NIL)
(FIXEDPOINT-IMPLIES-FIXEDPOINT-GAR
 (118 4 (:DEFINITION RCDP))
 (76 20 (:REWRITE <<-TRICHOTOMY))
 (68 12 (:REWRITE <<-ASYMMETRIC))
 (40 40 (:REWRITE DEFAULT-CAR))
 (23 23 (:REWRITE DEFAULT-CDR))
 (20 20 (:REWRITE <<-TRANSITIVE))
 (12 1 (:REWRITE G-AUX-IS-NIL-FOR-<<))
 (9 1 (:DEFINITION ALIST::KEYS))
 (4 3 (:REWRITE FIXEDPOINT-NIL))
 (4 2 (:REWRITE LIST::MEMBERP-OF-CDR-CHEAP))
 (4 2 (:REWRITE LIST::MEMBERP-FROM-MEMBERP-OF-CDR-CHEAP))
 (3 1 (:REWRITE WFR-CANCELLATIONS))
 (2 2 (:TYPE-PRESCRIPTION WFR))
 (2 2 (:REWRITE LIST::SUBSET-MEMBERSHIP-FREE-SUBSETP))
 (2 2 (:REWRITE LIST::SUBSET-MEMBERSHIP-FREE-MEMBERP))
 (2 2 (:REWRITE BAG::NON-MEMBERP-FROM-MEMBERP-OF-OTHER-CHEAP))
 (2 2 (:REWRITE BAG::MEMBERP-SUBBAGP))
 (2 2 (:REWRITE BAG::MEMBERP-OF-REMOVE-BAG-MEANS-MEMBERP))
 (2 2 (:REWRITE BAG::MEMBERP-OF-REMOVE-ALL))
 (2 2 (:REWRITE BAG::MEMBERP-OF-REMOVE-1))
 (2 2 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINTNESS))
 (2 2 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-TWO))
 (2 2 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-ONE))
 (2 2 (:REWRITE LIST::MEMBERP-DISJOINT-NON-MEMBERP))
 (2 1 (:REWRITE LIST::MEMBERP-OF-CONS-REDUCE-CHEAP))
 (1 1 (:REWRITE LIST::MEMBERP-OF-CONS-CHEAP))
 )
(FIXEDPOINT-GAR-REWRITE
 (82 3 (:DEFINITION RCDP))
 (57 15 (:REWRITE <<-TRICHOTOMY))
 (51 9 (:REWRITE <<-ASYMMETRIC))
 (30 30 (:REWRITE DEFAULT-CAR))
 (17 17 (:REWRITE DEFAULT-CDR))
 (15 15 (:REWRITE <<-TRANSITIVE))
 (12 1 (:REWRITE G-AUX-IS-NIL-FOR-<<))
 (9 1 (:DEFINITION ALIST::KEYS))
 (4 2 (:REWRITE LIST::MEMBERP-OF-CDR-CHEAP))
 (4 2 (:REWRITE LIST::MEMBERP-FROM-MEMBERP-OF-CDR-CHEAP))
 (3 1 (:REWRITE WFR-CANCELLATIONS))
 (3 1 (:REWRITE EQUAL-BOOLEANS-REDUCTON))
 (2 2 (:TYPE-PRESCRIPTION WFR))
 (2 2 (:REWRITE LIST::SUBSET-MEMBERSHIP-FREE-SUBSETP))
 (2 2 (:REWRITE LIST::SUBSET-MEMBERSHIP-FREE-MEMBERP))
 (2 2 (:REWRITE BAG::NON-MEMBERP-FROM-MEMBERP-OF-OTHER-CHEAP))
 (2 2 (:REWRITE BAG::MEMBERP-SUBBAGP))
 (2 2 (:REWRITE BAG::MEMBERP-OF-REMOVE-BAG-MEANS-MEMBERP))
 (2 2 (:REWRITE BAG::MEMBERP-OF-REMOVE-ALL))
 (2 2 (:REWRITE BAG::MEMBERP-OF-REMOVE-1))
 (2 2 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINTNESS))
 (2 2 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-TWO))
 (2 2 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-ONE))
 (2 2 (:REWRITE LIST::MEMBERP-DISJOINT-NON-MEMBERP))
 (2 1 (:REWRITE LIST::MEMBERP-OF-CONS-REDUCE-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION BOOLEANP))
 (1 1 (:REWRITE LIST::MEMBERP-OF-CONS-CHEAP))
 (1 1 (:REWRITE FIXEDPOINT-NIL))
 (1 1 (:REWRITE CLR-DIFFERENTIAL))
 )
(<<-CONVERSE)
(IFRP-S-AUX)
(IFRP-S-AUX-TO-IFRP-S-AUX
 (2402 2402 (:REWRITE DEFAULT-CDR))
 (924 116 (:REWRITE LIST::EQUAL-CAR-DIFFERENTIAL))
 (332 332 (:REWRITE CLR-DIFFERENTIAL))
 (237 237 (:TYPE-PRESCRIPTION BOOLEANP))
 (116 116 (:REWRITE LIST::CARS-MATCH-FROM-FIRSTN-FACT-2))
 (116 116 (:REWRITE LIST::CARS-MATCH-FROM-FIRSTN-FACT))
 (42 42 (:REWRITE LIST::CDR-DOES-NOTHING-REWRITE))
 )
(IFRP-S-AUX-MEMBER
 (8 8 (:TYPE-PRESCRIPTION LIST::MEMBERP-TYPE-1))
 )
(IFRP-S-AUX-REFORMULATION
 (36759 708 (:REWRITE LIST::WEAK-RIGHT-NORMALIZATION-CONS))
 (29127 745 (:REWRITE BAG::MEMBERP-CAR-WHEN-DISJOINT))
 (19834 103 (:DEFINITION LIST::DISJOINT-REMOVE-DEFINITION))
 (14458 183 (:REWRITE NOT-MEMBERP-G-AUX))
 (10726 745 (:REWRITE BAG::SUBBAGP-IMPLIES-MEMBERSHIP))
 (7827 103 (:DEFINITION REMOVE-EQUAL))
 (7414 103 (:DEFINITION LIST::DISJOINT))
 (7245 6540 (:REWRITE DEFAULT-CDR))
 (6963 206 (:REWRITE LIST::WEAK-RIGHT-NORMALIZATION-REMOVE))
 (6724 183 (:REWRITE G-AUX-IS-NIL-FOR-<<))
 (4972 206 (:REWRITE LIST::REMOVE-REDUCTON))
 (4796 1104 (:REWRITE LIST::MEMBERP-OF-CDR-CHEAP))
 (4796 1104 (:REWRITE LIST::MEMBERP-FROM-MEMBERP-OF-CDR-CHEAP))
 (3120 130 (:LINEAR LIST::LEN-NON-NEGATIVE-LINEAR))
 (2220 222 (:DEFINITION LEN))
 (1956 8 (:REWRITE BAG::SUBBAGP-OF-X-AND-CONS-CAR-X))
 (1751 1751 (:TYPE-PRESCRIPTION BAG::SUBBAGP))
 (1632 9 (:REWRITE BAG::SUBBAGP-OF-CONS-IRREL))
 (1490 745 (:REWRITE BAG::MEMBERP-CAR-WHEN-DISJOINT-CHEAP))
 (1332 184 (:REWRITE LIST::EQUAL-CAR-DIFFERENTIAL))
 (1328 664 (:REWRITE BAG::SUBBAGP-FROM-SUBBAGP-OF-CDR-CHEAP))
 (1322 1322 (:REWRITE BAG::MEMBERP-OF-REMOVE-ALL))
 (1299 431 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-TWO))
 (1175 323 (:REWRITE BAG::DISJOINT-OF-NON-CONSP-TWO))
 (1159 11 (:REWRITE BAG::DISJOINT-OF-CONS-TWO))
 (1110 444 (:REWRITE LIST::LEN-OF-NON-CONSP))
 (1104 1104 (:REWRITE LIST::SUBSET-MEMBERSHIP-FREE-SUBSETP))
 (1104 1104 (:REWRITE LIST::SUBSET-MEMBERSHIP-FREE-MEMBERP))
 (1104 1104 (:REWRITE BAG::MEMBERP-SUBBAGP))
 (1104 1104 (:REWRITE BAG::MEMBERP-OF-REMOVE-BAG-MEANS-MEMBERP))
 (1104 1104 (:REWRITE BAG::MEMBERP-OF-REMOVE-1))
 (1089 661 (:REWRITE LIST::MEMBERP-OF-NON-CONSP-CHEAP))
 (1080 8 (:REWRITE BAG::SUBBAGP-OF-CDR))
 (1046 1046 (:REWRITE BAG::NON-MEMBERP-FROM-MEMBERP-OF-OTHER-CHEAP))
 (1046 1046 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINTNESS))
 (1046 1046 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-TWO))
 (1046 1046 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-ONE))
 (828 828 (:REWRITE LIST::MEMBERP-DISJOINT-NON-MEMBERP))
 (765 3 (:REWRITE BAG::DISJOINT-COMMUTATIVE))
 (744 372 (:REWRITE DEFAULT-+-2))
 (733 431 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-TWO-CHEAP))
 (649 649 (:REWRITE BAG::SUBBAGP-REMOVE-BAG))
 (649 649 (:REWRITE BAG::SUBBAGP-REMOVE))
 (649 649 (:REWRITE BAG::SUBBAGP-CHAINING))
 (649 649 (:REWRITE BAG::PERM-SUBBAGP-SUBBAGP))
 (632 323 (:REWRITE BAG::DISJOINT-OF-NON-CONSP-ONE))
 (621 312 (:REWRITE LIST::NOT-CONSP-DISJOINT))
 (618 618 (:TYPE-PRESCRIPTION REMOVE-EQUAL))
 (600 200 (:REWRITE BAG::UNIQUE-MEANS-CAR-NOT-MEMBERP-OF-CDR))
 (594 99 (:REWRITE BAG::UNIQUE-MEMBERP-MEANS-COUNT-IS-ONE))
 (520 130 (:LINEAR LIST::LEN-WHEN-CONSP-LINEAR))
 (486 486 (:REWRITE CLR-DIFFERENTIAL))
 (444 148 (:REWRITE WFKEYED-IMPLIES-NOT-NIL-MEMBERP))
 (438 438 (:REWRITE BAG::DISJOINT-FROM-COMMON-UNIQUENSS))
 (431 431 (:REWRITE BAG::SUBBAGP-OF-REMOVE-1-IMPLIES-SUBBAGP))
 (431 431 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-ONE-CHEAP))
 (431 431 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-ONE))
 (398 398 (:TYPE-PRESCRIPTION BAG::UNIQUE))
 (372 372 (:REWRITE DEFAULT-+-1))
 (326 326 (:REWRITE BAG::SUBBAGP-DISJOINT-COMMUTE))
 (326 326 (:REWRITE BAG::SUBBAGP-DISJOINT))
 (312 312 (:REWRITE LIST::DISJOINT-BY-MULTIPLICITY))
 (298 199 (:REWRITE BAG::UNIQUE-OF-NON-CONSP-CHEAP))
 (296 296 (:TYPE-PRESCRIPTION WFKEYED))
 (236 103 (:REWRITE BAG::DISJOINT-CDR-FROM-DISJOINT))
 (235 9 (:REWRITE BAG::SUBBAGP-IMPLIES-SUBBAGP-CONS))
 (223 223 (:TYPE-PRESCRIPTION BOOLEANP))
 (218 218 (:REWRITE BAG::SUBBAGP-SELF))
 (206 103 (:REWRITE BAG::DISJOINT-CDR-FROM-DISJOINT-CHEAP))
 (199 199 (:REWRITE BAG::SUBBAGP-UNIQUENESS))
 (198 198 (:LINEAR BAG::COUNT-WITH-SUBBAGP-LINEAR))
 (187 187 (:REWRITE LIST::CARS-MATCH-FROM-FIRSTN-FACT-2))
 (187 187 (:REWRITE LIST::CARS-MATCH-FROM-FIRSTN-FACT))
 (170 7 (:REWRITE BAG::SUBBAGP-OF-SINGLETON))
 (167 167 (:REWRITE LIST::MEMBERP-OF-CONS-CHEAP))
 (160 14 (:REWRITE LIST::OPEN-EQUIV))
 (108 108 (:REWRITE BAG::DISJOINT-SELF-MEANS-NOT-CONSP))
 (99 99 (:REWRITE BAG::COUNT-WHEN-NON-MEMBER))
 (99 99 (:REWRITE BAG::COUNT-0-FOR-NON-MEMBERP))
 (81 4 (:REWRITE BAG::DISJOINT-OF-SINGLETON-TWO))
 (78 78 (:REWRITE LIST::CDR-DOES-NOTHING-REWRITE))
 (61 7 (:REWRITE LIST::EQUIV-OF-TWO-TRUE-LISTPS))
 (36 6 (:DEFINITION TRUE-LISTP))
 (30 30 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (22 11 (:REWRITE BAG::DISJOINT-OF-CONS-REDUCE-CHEAP))
 (14 7 (:REWRITE LIST::EQUIV-OF-NON-CONSP-TWO))
 (12 12 (:REWRITE LIST::TRUE-LISTP-OF-NON-CONSP))
 (7 7 (:REWRITE LIST::EQUIV-OF-NON-CONSP-ONE))
 (7 7 (:REWRITE LIST::EQUIV-OF-CONSTANT))
 )
(IFRP-S-MEMBER
 (8 8 (:TYPE-PRESCRIPTION LIST::MEMBERP-TYPE-1))
 (6 6 (:TYPE-PRESCRIPTION RKEYS-NON-NIL-TP))
 )
(IFRP-S
 (6 6 (:TYPE-PRESCRIPTION RKEYS-NON-NIL-TP))
 )
(IFRP-S-TO-IFRP-S-MEMBER)
(IFRP-RCD->ACL2
 (114 30 (:REWRITE <<-TRICHOTOMY))
 (102 18 (:REWRITE <<-ASYMMETRIC))
 (66 66 (:TYPE-PRESCRIPTION <<))
 (53 53 (:REWRITE DEFAULT-CAR))
 (33 33 (:REWRITE DEFAULT-CDR))
 (30 30 (:REWRITE <<-TRANSITIVE))
 (3 1 (:REWRITE WFR-CANCELLATIONS))
 (2 2 (:TYPE-PRESCRIPTION WFR))
 (1 1 (:REWRITE CLR-DIFFERENTIAL))
 )
(IFRP-S-TO-IFRP-S
 (1590 6 (:DEFINITION G-AUX))
 (1280 12 (:REWRITE NOT-MEMBERP-G-AUX))
 (832 24 (:REWRITE LIST::SUBSET-MEMBERSHIP-FREE-MEMBERP))
 (784 4 (:DEFINITION SUBSETP-EQUAL))
 (624 4 (:REWRITE LIST::MEMBER-EQ-IS-MEMBERP-PROPOSITIONALLY))
 (534 16 (:DEFINITION RCDP))
 (481 125 (:REWRITE <<-TRICHOTOMY))
 (480 20 (:REWRITE BAG::MEMBERP-CAR-WHEN-DISJOINT))
 (440 10 (:DEFINITION IFRP))
 (432 4 (:DEFINITION LIST::DISJOINT-REMOVE-DEFINITION))
 (371 69 (:REWRITE <<-ASYMMETRIC))
 (324 12 (:REWRITE G-AUX-IS-NIL-FOR-<<))
 (278 120 (:TYPE-PRESCRIPTION LIST::MEMBERP-TYPE-1))
 (271 235 (:REWRITE DEFAULT-CAR))
 (196 20 (:REWRITE BAG::SUBBAGP-IMPLIES-MEMBERSHIP))
 (148 10 (:DEFINITION ALIST::KEYS))
 (139 133 (:REWRITE DEFAULT-CDR))
 (125 125 (:REWRITE <<-TRANSITIVE))
 (106 24 (:REWRITE LIST::MEMBERP-OF-CDR-CHEAP))
 (106 24 (:REWRITE LIST::MEMBERP-FROM-MEMBERP-OF-CDR-CHEAP))
 (100 8 (:REWRITE LIST::WEAK-RIGHT-NORMALIZATION-REMOVE))
 (92 24 (:REWRITE BAG::MEMBERP-SUBBAGP))
 (80 16 (:REWRITE LIST::WEAK-RIGHT-NORMALIZATION-CONS))
 (80 4 (:REWRITE LIST::REMOVE-REDUCTON))
 (64 64 (:TYPE-PRESCRIPTION ACL2->RCD))
 (52 52 (:TYPE-PRESCRIPTION BAG::SUBBAGP))
 (40 20 (:REWRITE BAG::SUBBAGP-FROM-SUBBAGP-OF-CDR-CHEAP))
 (40 20 (:REWRITE BAG::MEMBERP-CAR-WHEN-DISJOINT-CHEAP))
 (39 1 (:DEFINITION S-AUX))
 (32 32 (:TYPE-PRESCRIPTION LIST::DISJOINT))
 (32 32 (:REWRITE BAG::MEMBERP-OF-REMOVE-ALL))
 (32 8 (:REWRITE LIST::SUBSETP-NOT-CONSP-2))
 (32 8 (:REWRITE BAG::DISJOINT-OF-NON-CONSP-TWO))
 (30 10 (:REWRITE WFKEYED-IMPLIES-NOT-NIL-MEMBERP))
 (26 16 (:REWRITE LIST::MEMBERP-OF-NON-CONSP-CHEAP))
 (24 24 (:REWRITE LIST::SUBSET-MEMBERSHIP-FREE-SUBSETP))
 (24 24 (:REWRITE BAG::NON-MEMBERP-FROM-MEMBERP-OF-OTHER-CHEAP))
 (24 24 (:REWRITE BAG::MEMBERP-OF-REMOVE-BAG-MEANS-MEMBERP))
 (24 24 (:REWRITE BAG::MEMBERP-OF-REMOVE-1))
 (24 24 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINTNESS))
 (24 24 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-TWO))
 (24 24 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-ONE))
 (24 12 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-TWO-CHEAP))
 (24 12 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-TWO))
 (20 20 (:TYPE-PRESCRIPTION WFKEYED))
 (20 20 (:REWRITE BAG::SUBBAGP-REMOVE-BAG))
 (20 20 (:REWRITE BAG::SUBBAGP-REMOVE))
 (20 20 (:REWRITE BAG::SUBBAGP-CHAINING))
 (20 20 (:REWRITE BAG::PERM-SUBBAGP-SUBBAGP))
 (20 4 (:REWRITE LIST::LEN-WHEN-AT-MOST-1))
 (20 4 (:DEFINITION REMOVE-EQUAL))
 (20 2 (:DEFINITION LEN))
 (16 16 (:REWRITE LIST::MEMBERP-DISJOINT-NON-MEMBERP))
 (16 6 (:REWRITE WFR-CANCELLATIONS))
 (12 12 (:REWRITE BAG::SUBBAGP-OF-REMOVE-1-IMPLIES-SUBBAGP))
 (12 12 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-ONE-CHEAP))
 (12 12 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-ONE))
 (12 12 (:REWRITE BAG::DISJOINT-FROM-COMMON-UNIQUENSS))
 (10 10 (:TYPE-PRESCRIPTION WFR))
 (10 4 (:REWRITE LIST::LEN-OF-NON-CONSP))
 (8 8 (:REWRITE LIST::SUBSETP-NOT-CONSP-1))
 (8 8 (:REWRITE LIST::SUBSET-BY-MULTIPLICITY))
 (8 8 (:REWRITE BAG::SUBBAGP-SELF))
 (8 8 (:REWRITE BAG::SUBBAGP-DISJOINT-COMMUTE))
 (8 8 (:REWRITE BAG::SUBBAGP-DISJOINT))
 (8 8 (:REWRITE BAG::DISJOINT-OF-NON-CONSP-ONE))
 (7 7 (:REWRITE CLR-DIFFERENTIAL))
 (4 4 (:TYPE-PRESCRIPTION SUBSETP-EQUAL))
 (4 4 (:REWRITE LIST::SUBSET-CHAINING-2))
 (4 4 (:REWRITE LIST::SUBSET-CHAINING-1))
 (4 4 (:REWRITE BAG::DISJOINT-SELF-MEANS-NOT-CONSP))
 (4 4 (:REWRITE LIST::DISJOINT-BY-MULTIPLICITY))
 (4 3 (:REWRITE EQUAL-BOOLEANS-REDUCTON))
 (4 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE BAG::LEN-1-AND-MEMBERP-MEANS-YOU-KNOW-X))
 (2 2 (:REWRITE DEFAULT-+-1))
 (1 1 (:TYPE-PRESCRIPTION BOOLEANP))
 (1 1 (:REWRITE RKEYS-WHEN-NOT-CONSP))
 )
(CONSP-KEYS
 (21 21 (:REWRITE DEFAULT-CAR))
 (8 8 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE CLR-DIFFERENTIAL))
 )
(IFF-S-AUX-ALT
 (2318 9 (:REWRITE LIST::WEAK-RIGHT-NORMALIZATION-CONS))
 (1869 30 (:REWRITE BAG::MEMBERP-CAR-WHEN-DISJOINT))
 (1319 4 (:DEFINITION LIST::DISJOINT-REMOVE-DEFINITION))
 (677 172 (:REWRITE <<-TRICHOTOMY))
 (656 4 (:DEFINITION REMOVE-EQUAL))
 (607 426 (:REWRITE DEFAULT-CDR))
 (549 101 (:REWRITE <<-ASYMMETRIC))
 (483 4 (:DEFINITION LIST::DISJOINT))
 (448 8 (:REWRITE LIST::WEAK-RIGHT-NORMALIZATION-REMOVE))
 (368 8 (:REWRITE LIST::REMOVE-REDUCTON))
 (336 28 (:REWRITE BAG::SUBBAGP-IMPLIES-MEMBERSHIP))
 (221 68 (:REWRITE LIST::MEMBERP-OF-CDR-CHEAP))
 (221 68 (:REWRITE LIST::MEMBERP-FROM-MEMBERP-OF-CDR-CHEAP))
 (204 25 (:REWRITE LIST::EQUAL-CAR-DIFFERENTIAL))
 (195 167 (:REWRITE <<-TRANSITIVE))
 (154 94 (:REWRITE LIST::LEN-OF-NON-CONSP))
 (145 75 (:REWRITE EQUAL-BOOLEANS-REDUCTON))
 (144 72 (:REWRITE DEFAULT-+-2))
 (110 2 (:LINEAR LIST::LEN-OF-CDR-LINEAR))
 (100 100 (:REWRITE CLR-DIFFERENTIAL))
 (94 2 (:LINEAR LIST::LEN-OF-CDR-BOUND-WEAK-LINEAR))
 (90 2 (:LINEAR LIST::LEN-OF-CDR-BOUND-TIGHT-LINEAR))
 (78 78 (:REWRITE BAG::MEMBERP-OF-REMOVE-ALL))
 (72 72 (:REWRITE DEFAULT-+-1))
 (68 68 (:REWRITE LIST::SUBSET-MEMBERSHIP-FREE-SUBSETP))
 (68 68 (:REWRITE LIST::SUBSET-MEMBERSHIP-FREE-MEMBERP))
 (68 68 (:REWRITE BAG::MEMBERP-SUBBAGP))
 (68 68 (:REWRITE BAG::MEMBERP-OF-REMOVE-BAG-MEANS-MEMBERP))
 (68 68 (:REWRITE BAG::MEMBERP-OF-REMOVE-1))
 (66 44 (:REWRITE LIST::MEMBERP-OF-NON-CONSP-CHEAP))
 (64 64 (:TYPE-PRESCRIPTION BAG::SUBBAGP))
 (63 63 (:REWRITE BAG::NON-MEMBERP-FROM-MEMBERP-OF-OTHER-CHEAP))
 (63 63 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINTNESS))
 (63 63 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-TWO))
 (63 63 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-ONE))
 (60 30 (:REWRITE BAG::MEMBERP-CAR-WHEN-DISJOINT-CHEAP))
 (59 59 (:TYPE-PRESCRIPTION BOOLEANP))
 (55 55 (:REWRITE LIST::MEMBERP-DISJOINT-NON-MEMBERP))
 (48 24 (:REWRITE BAG::SUBBAGP-FROM-SUBBAGP-OF-CDR-CHEAP))
 (47 14 (:REWRITE BAG::DISJOINT-OF-NON-CONSP-TWO))
 (43 16 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-TWO))
 (29 29 (:REWRITE LIST::CARS-MATCH-FROM-FIRSTN-FACT-2))
 (29 29 (:REWRITE LIST::CARS-MATCH-FROM-FIRSTN-FACT))
 (25 16 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-TWO-CHEAP))
 (24 24 (:TYPE-PRESCRIPTION REMOVE-EQUAL))
 (24 24 (:REWRITE BAG::SUBBAGP-REMOVE-BAG))
 (24 24 (:REWRITE BAG::SUBBAGP-REMOVE))
 (24 24 (:REWRITE BAG::SUBBAGP-CHAINING))
 (24 24 (:REWRITE BAG::PERM-SUBBAGP-SUBBAGP))
 (24 12 (:REWRITE LIST::NOT-CONSP-DISJOINT))
 (24 12 (:REWRITE BAG::DISJOINT-OF-NON-CONSP-ONE))
 (24 8 (:REWRITE BAG::UNIQUE-MEANS-CAR-NOT-MEMBERP-OF-CDR))
 (19 19 (:REWRITE LIST::CDR-DOES-NOTHING-REWRITE))
 (19 5 (:REWRITE LIST::MEMBERP-OF-CONS-REDUCE-CHEAP))
 (18 18 (:REWRITE BAG::DISJOINT-FROM-COMMON-UNIQUENSS))
 (16 16 (:REWRITE BAG::SUBBAGP-OF-REMOVE-1-IMPLIES-SUBBAGP))
 (16 16 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-ONE-CHEAP))
 (16 16 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-ONE))
 (14 14 (:REWRITE BAG::SUBBAGP-DISJOINT-COMMUTE))
 (14 14 (:REWRITE BAG::SUBBAGP-DISJOINT))
 (12 12 (:REWRITE LIST::DISJOINT-BY-MULTIPLICITY))
 (10 10 (:TYPE-PRESCRIPTION BAG::UNIQUE))
 (8 8 (:REWRITE BAG::SUBBAGP-SELF))
 (8 4 (:REWRITE BAG::DISJOINT-CDR-FROM-DISJOINT-CHEAP))
 (8 4 (:REWRITE BAG::DISJOINT-CDR-FROM-DISJOINT))
 (6 6 (:REWRITE BAG::LEN-1-AND-MEMBERP-MEANS-YOU-KNOW-X))
 (6 2 (:REWRITE UNICITY-OF-0))
 (5 5 (:REWRITE BAG::UNIQUE-OF-NON-CONSP-CHEAP))
 (5 5 (:REWRITE BAG::SUBBAGP-UNIQUENESS))
 (5 5 (:REWRITE LIST::MEMBERP-OF-CONS-IRREL))
 (5 5 (:REWRITE LIST::MEMBERP-OF-CONS-CHEAP))
 (5 1 (:REWRITE BAG::UNIQUE-MEMBERP-MEANS-COUNT-IS-ONE))
 (4 4 (:REWRITE BAG::DISJOINT-SELF-MEANS-NOT-CONSP))
 (4 2 (:DEFINITION FIX))
 (2 2 (:LINEAR BAG::COUNT-WITH-SUBBAGP-LINEAR))
 (1 1 (:REWRITE BAG::COUNT-WHEN-NON-MEMBER))
 (1 1 (:REWRITE BAG::COUNT-0-FOR-NON-MEMBERP))
 )
(IFF-RCD->ACL2
 (114 30 (:REWRITE <<-TRICHOTOMY))
 (102 18 (:REWRITE <<-ASYMMETRIC))
 (83 83 (:REWRITE DEFAULT-CAR))
 (49 49 (:REWRITE DEFAULT-CDR))
 (30 30 (:REWRITE <<-TRANSITIVE))
 (26 2 (:REWRITE NOT-MEMBERP-G-AUX))
 (24 2 (:REWRITE MEMBERP-G-AUX))
 (24 2 (:REWRITE G-AUX-IS-NIL-FOR-<<))
 (18 2 (:DEFINITION ALIST::KEYS))
 (9 3 (:REWRITE WFR-CANCELLATIONS))
 (6 6 (:TYPE-PRESCRIPTION WFR))
 (1 1 (:REWRITE RCD->ACL2-OF-RECORD-NON-NIL))
 )
(G-AUX-NIL-IFRP
 (92 4 (:DEFINITION RCDP))
 (38 10 (:REWRITE <<-TRICHOTOMY))
 (34 6 (:REWRITE <<-ASYMMETRIC))
 (32 32 (:REWRITE DEFAULT-CAR))
 (18 18 (:REWRITE DEFAULT-CDR))
 (14 1 (:REWRITE NOT-MEMBERP-G-AUX))
 (12 1 (:REWRITE MEMBERP-G-AUX))
 (12 1 (:REWRITE G-AUX-IS-NIL-FOR-<<))
 (10 10 (:REWRITE <<-TRANSITIVE))
 (9 1 (:DEFINITION ALIST::KEYS))
 (3 1 (:REWRITE WFR-CANCELLATIONS))
 (2 2 (:TYPE-PRESCRIPTION WFR))
 )
(IFF-ACL2->RCD
 (88 2 (:DEFINITION IFRP))
 (72 2 (:DEFINITION RCDP))
 (38 10 (:REWRITE <<-TRICHOTOMY))
 (34 6 (:REWRITE <<-ASYMMETRIC))
 (22 22 (:TYPE-PRESCRIPTION <<))
 (20 20 (:REWRITE DEFAULT-CAR))
 (12 12 (:REWRITE DEFAULT-CDR))
 (10 10 (:REWRITE <<-TRANSITIVE))
 (7 7 (:TYPE-PRESCRIPTION ACL2->RCD))
 (4 4 (:TYPE-PRESCRIPTION RCDP))
 (3 1 (:REWRITE WFR-CANCELLATIONS))
 (2 2 (:TYPE-PRESCRIPTION WFR))
 )
(IFF-S-MEMBER)
(IFF-S-IFRP)
(IFF-S-IFRP-TO-IFF-S-MEMBER)
(IFF-S-TO-IFF-S-IFRP
 (12580 118 (:REWRITE LIST::WEAK-RIGHT-NORMALIZATION-CONS))
 (9818 234 (:REWRITE BAG::MEMBERP-CAR-WHEN-DISJOINT))
 (6815 33 (:DEFINITION LIST::DISJOINT-REMOVE-DEFINITION))
 (2772 33 (:DEFINITION REMOVE-EQUAL))
 (2558 33 (:DEFINITION LIST::DISJOINT))
 (2376 66 (:REWRITE LIST::WEAK-RIGHT-NORMALIZATION-REMOVE))
 (1716 66 (:REWRITE LIST::REMOVE-REDUCTON))
 (1621 47 (:DEFINITION RCDP))
 (1405 13 (:DEFINITION G-AUX))
 (1333 1194 (:REWRITE DEFAULT-CAR))
 (1304 1117 (:REWRITE DEFAULT-CDR))
 (1273 26 (:REWRITE NOT-MEMBERP-G-AUX))
 (1211 325 (:REWRITE <<-TRICHOTOMY))
 (1060 271 (:REWRITE LIST::MEMBERP-FROM-MEMBERP-OF-CDR-CHEAP))
 (1006 244 (:REWRITE LIST::MEMBERP-OF-CDR-CHEAP))
 (997 184 (:REWRITE <<-ASYMMETRIC))
 (641 26 (:REWRITE G-AUX-IS-NIL-FOR-<<))
 (468 234 (:REWRITE BAG::MEMBERP-CAR-WHEN-DISJOINT-CHEAP))
 (446 160 (:REWRITE WFR-CANCELLATIONS))
 (429 132 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-TWO))
 (402 201 (:REWRITE BAG::SUBBAGP-FROM-SUBBAGP-OF-CDR-CHEAP))
 (396 99 (:REWRITE BAG::DISJOINT-OF-NON-CONSP-TWO))
 (366 282 (:REWRITE LIST::LEN-OF-NON-CONSP))
 (366 10 (:LINEAR LIST::LEN-OF-CDR-LINEAR))
 (360 180 (:REWRITE DEFAULT-+-2))
 (343 325 (:REWRITE <<-TRANSITIVE))
 (340 340 (:REWRITE BAG::MEMBERP-OF-REMOVE-ALL))
 (340 10 (:LINEAR LIST::LEN-OF-CDR-BOUND-WEAK-LINEAR))
 (326 10 (:LINEAR LIST::LEN-OF-CDR-BOUND-TIGHT-LINEAR))
 (286 286 (:TYPE-PRESCRIPTION WFR))
 (272 272 (:REWRITE BAG::NON-MEMBERP-FROM-MEMBERP-OF-OTHER-CHEAP))
 (272 272 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINTNESS))
 (272 272 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-TWO))
 (272 272 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-ONE))
 (271 271 (:REWRITE LIST::SUBSET-MEMBERSHIP-FREE-SUBSETP))
 (271 271 (:REWRITE LIST::SUBSET-MEMBERSHIP-FREE-MEMBERP))
 (271 271 (:REWRITE BAG::MEMBERP-SUBBAGP))
 (271 271 (:REWRITE BAG::MEMBERP-OF-REMOVE-BAG-MEANS-MEMBERP))
 (271 271 (:REWRITE BAG::MEMBERP-OF-REMOVE-1))
 (259 177 (:REWRITE LIST::MEMBERP-OF-NON-CONSP-CHEAP))
 (231 132 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-TWO-CHEAP))
 (203 203 (:REWRITE LIST::MEMBERP-DISJOINT-NON-MEMBERP))
 (201 201 (:REWRITE BAG::SUBBAGP-REMOVE-BAG))
 (201 201 (:REWRITE BAG::SUBBAGP-REMOVE))
 (201 201 (:REWRITE BAG::SUBBAGP-CHAINING))
 (201 201 (:REWRITE BAG::PERM-SUBBAGP-SUBBAGP))
 (198 198 (:TYPE-PRESCRIPTION REMOVE-EQUAL))
 (198 99 (:REWRITE LIST::NOT-CONSP-DISJOINT))
 (198 99 (:REWRITE BAG::DISJOINT-OF-NON-CONSP-ONE))
 (198 66 (:REWRITE BAG::UNIQUE-MEANS-CAR-NOT-MEMBERP-OF-CDR))
 (180 180 (:REWRITE DEFAULT-+-1))
 (135 135 (:REWRITE BAG::DISJOINT-FROM-COMMON-UNIQUENSS))
 (132 132 (:REWRITE BAG::SUBBAGP-OF-REMOVE-1-IMPLIES-SUBBAGP))
 (132 132 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-ONE-CHEAP))
 (132 132 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-ONE))
 (99 99 (:REWRITE BAG::SUBBAGP-DISJOINT-COMMUTE))
 (99 99 (:REWRITE BAG::SUBBAGP-DISJOINT))
 (99 99 (:REWRITE LIST::DISJOINT-BY-MULTIPLICITY))
 (99 33 (:REWRITE WFKEYED-IMPLIES-NOT-NIL-MEMBERP))
 (66 66 (:TYPE-PRESCRIPTION WFKEYED))
 (66 66 (:TYPE-PRESCRIPTION BAG::UNIQUE))
 (66 33 (:REWRITE BAG::DISJOINT-CDR-FROM-DISJOINT-CHEAP))
 (66 33 (:REWRITE BAG::DISJOINT-CDR-FROM-DISJOINT))
 (50 27 (:REWRITE EQUAL-BOOLEANS-REDUCTON))
 (43 43 (:REWRITE CLR-DIFFERENTIAL))
 (40 36 (:REWRITE BAG::DISJOINT-SELF-MEANS-NOT-CONSP))
 (39 1 (:DEFINITION S-AUX))
 (33 33 (:REWRITE BAG::UNIQUE-OF-NON-CONSP-CHEAP))
 (33 33 (:REWRITE BAG::SUBBAGP-UNIQUENESS))
 (28 4 (:REWRITE FOLD-CONSTS-IN-+))
 (13 13 (:REWRITE BAG::LEN-1-AND-MEMBERP-MEANS-YOU-KNOW-X))
 (12 4 (:REWRITE UNICITY-OF-0))
 (9 9 (:TYPE-PRESCRIPTION BOOLEANP))
 (8 8 (:REWRITE RKEYS-WHEN-NOT-CONSP))
 (8 4 (:DEFINITION FIX))
 (4 4 (:LINEAR BAG::COUNT-WITH-SUBBAGP-LINEAR))
 )
(IFRP-TO-FIXEDPOINT
 (144 4 (:DEFINITION RCDP))
 (76 20 (:REWRITE <<-TRICHOTOMY))
 (68 12 (:REWRITE <<-ASYMMETRIC))
 (44 44 (:TYPE-PRESCRIPTION <<))
 (40 40 (:REWRITE DEFAULT-CAR))
 (24 24 (:REWRITE DEFAULT-CDR))
 (20 20 (:REWRITE <<-TRANSITIVE))
 (1 1 (:REWRITE FIXEDPOINT-NIL))
 (1 1 (:REWRITE CLR-DIFFERENTIAL))
 )
(FIXEDPOINT-S-FN)
(FIXEDPOINT-S-TO-FIXEDPOINT-S-FN
 (3300 91 (:DEFINITION RCDP))
 (1900 500 (:REWRITE <<-TRICHOTOMY))
 (1700 300 (:REWRITE <<-ASYMMETRIC))
 (1336 1110 (:REWRITE DEFAULT-CDR))
 (1020 974 (:REWRITE DEFAULT-CAR))
 (500 500 (:REWRITE <<-TRANSITIVE))
 (478 332 (:REWRITE LIST::LEN-OF-NON-CONSP))
 (438 18 (:REWRITE FIXEDPOINT-NIL))
 (420 210 (:REWRITE DEFAULT-+-2))
 (354 6 (:REWRITE FIXEDPOINT-IMPLIES-FIXEDPOINT-GAR))
 (334 10 (:LINEAR LIST::LEN-OF-CDR-LINEAR))
 (308 10 (:LINEAR LIST::LEN-OF-CDR-BOUND-WEAK-LINEAR))
 (294 10 (:LINEAR LIST::LEN-OF-CDR-BOUND-TIGHT-LINEAR))
 (210 210 (:REWRITE DEFAULT-+-1))
 (135 135 (:REWRITE RKEYS-WHEN-NOT-CONSP))
 (48 48 (:REWRITE CLR-DIFFERENTIAL))
 (46 22 (:REWRITE EQUAL-BOOLEANS-REDUCTON))
 (28 4 (:REWRITE FOLD-CONSTS-IN-+))
 (22 22 (:REWRITE BAG::LEN-1-AND-MEMBERP-MEANS-YOU-KNOW-X))
 (12 4 (:REWRITE UNICITY-OF-0))
 (8 4 (:DEFINITION FIX))
 (1 1 (:TYPE-PRESCRIPTION BOOLEANP))
 )
(IFF-S-FIXEDPOINT)
(IFF-S-IFRP-TO-IFF-S-FIXEDPOINT
 (132 3 (:DEFINITION IFRP))
 (108 3 (:DEFINITION RCDP))
 (102 4 (:DEFINITION LEN))
 (88 40 (:REWRITE DEFAULT-CDR))
 (88 8 (:REWRITE LIST::LEN-WHEN-AT-MOST-1))
 (58 40 (:REWRITE DEFAULT-CAR))
 (57 15 (:REWRITE <<-TRICHOTOMY))
 (51 9 (:REWRITE <<-ASYMMETRIC))
 (38 8 (:REWRITE LIST::LEN-OF-NON-CONSP))
 (33 33 (:TYPE-PRESCRIPTION <<))
 (15 15 (:REWRITE <<-TRANSITIVE))
 (8 4 (:REWRITE DEFAULT-+-2))
 (6 6 (:TYPE-PRESCRIPTION RCDP))
 (5 5 (:REWRITE CLR-DIFFERENTIAL))
 (4 4 (:REWRITE RKEYS-WHEN-NOT-CONSP))
 (4 4 (:REWRITE BAG::LEN-1-AND-MEMBERP-MEANS-YOU-KNOW-X))
 (4 4 (:REWRITE DEFAULT-+-1))
 (1 1 (:REWRITE FIXEDPOINT-NIL))
 )
(IFF-S-TO-IFF-S-FIXEDPOINT)
(OPEN-ABSTRACT-FIXEDPOINT-ON-S
 (3573 7 (:DEFINITION REMOVE-EQUAL))
 (2502 6 (:REWRITE LIST::WEAK-RIGHT-NORMALIZATION-CONS))
 (2016 48 (:REWRITE BAG::MEMBERP-CAR-WHEN-DISJOINT))
 (1349 10 (:REWRITE FIXEDPOINT-IMPLIES-FIXEDPOINT-GAR))
 (1200 12 (:DEFINITION LIST::DISJOINT-REMOVE-DEFINITION))
 (1098 18 (:REWRITE LIST::MEMBERP-REMOVE))
 (1062 33 (:REWRITE LIST::WEAK-RIGHT-NORMALIZATION-REMOVE))
 (988 33 (:REWRITE LIST::REMOVE-REDUCTON))
 (816 48 (:REWRITE BAG::SUBBAGP-IMPLIES-MEMBERSHIP))
 (600 12 (:DEFINITION LIST::DISJOINT))
 (240 48 (:REWRITE LIST::MEMBERP-OF-CDR-CHEAP))
 (240 48 (:REWRITE LIST::MEMBERP-FROM-MEMBERP-OF-CDR-CHEAP))
 (186 186 (:TYPE-PRESCRIPTION LIST::DISJOINT))
 (150 50 (:REWRITE DEFAULT-CAR))
 (126 42 (:REWRITE LIST::MEMBERP-OF-NON-CONSP-CHEAP))
 (126 30 (:REWRITE LIST::NOT-CONSP-DISJOINT))
 (126 30 (:REWRITE BAG::DISJOINT-OF-NON-CONSP-ONE))
 (120 120 (:TYPE-PRESCRIPTION BAG::SUBBAGP))
 (114 24 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-TWO))
 (96 48 (:REWRITE BAG::SUBBAGP-FROM-SUBBAGP-OF-CDR-CHEAP))
 (96 48 (:REWRITE BAG::MEMBERP-CAR-WHEN-DISJOINT-CHEAP))
 (90 90 (:REWRITE BAG::MEMBERP-OF-REMOVE-ALL))
 (84 30 (:REWRITE BAG::DISJOINT-OF-NON-CONSP-TWO))
 (84 18 (:REWRITE BAG::DISJOINT-SELF-MEANS-NOT-CONSP))
 (78 78 (:REWRITE BAG::NON-MEMBERP-FROM-MEMBERP-OF-OTHER-CHEAP))
 (78 78 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINTNESS))
 (78 78 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-TWO))
 (78 78 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-ONE))
 (78 26 (:REWRITE DEFAULT-CDR))
 (72 24 (:REWRITE BAG::UNIQUE-MEANS-CAR-NOT-MEMBERP-OF-CDR))
 (72 24 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-ONE-CHEAP))
 (72 24 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-ONE))
 (66 66 (:REWRITE BAG::MEMBERP-SUBBAGP))
 (66 66 (:REWRITE BAG::MEMBERP-OF-REMOVE-BAG-MEANS-MEMBERP))
 (66 66 (:REWRITE BAG::MEMBERP-OF-REMOVE-1))
 (54 54 (:REWRITE LIST::MEMBERP-DISJOINT-NON-MEMBERP))
 (54 24 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-TWO-CHEAP))
 (48 48 (:REWRITE LIST::SUBSET-MEMBERSHIP-FREE-SUBSETP))
 (48 48 (:REWRITE LIST::SUBSET-MEMBERSHIP-FREE-MEMBERP))
 (48 48 (:REWRITE BAG::SUBBAGP-REMOVE-BAG))
 (48 48 (:REWRITE BAG::SUBBAGP-REMOVE))
 (48 48 (:REWRITE BAG::SUBBAGP-CHAINING))
 (48 48 (:REWRITE BAG::PERM-SUBBAGP-SUBBAGP))
 (48 48 (:REWRITE BAG::DISJOINT-FROM-COMMON-UNIQUENSS))
 (30 30 (:REWRITE BAG::SUBBAGP-DISJOINT-COMMUTE))
 (30 30 (:REWRITE BAG::SUBBAGP-DISJOINT))
 (30 30 (:REWRITE LIST::DISJOINT-BY-MULTIPLICITY))
 (30 5 (:REWRITE LIST::SUBSETP-REMOVE-BY-SUBSET))
 (28 14 (:REWRITE WFR-IMPLIES-NOT-NIL-MEMBERP))
 (24 24 (:TYPE-PRESCRIPTION BAG::UNIQUE))
 (24 24 (:REWRITE UNIQUE-RKEYS))
 (24 24 (:REWRITE BAG::SUBBAGP-SELF))
 (24 24 (:REWRITE BAG::SUBBAGP-OF-REMOVE-1-IMPLIES-SUBBAGP))
 (24 12 (:REWRITE BAG::DISJOINT-CDR-FROM-DISJOINT-CHEAP))
 (24 12 (:REWRITE BAG::DISJOINT-CDR-FROM-DISJOINT))
 (16 16 (:REWRITE FIXEDPOINT-NIL))
 (14 14 (:TYPE-PRESCRIPTION WFR))
 (10 10 (:REWRITE LIST::SUBSET-BY-MULTIPLICITY))
 (10 5 (:REWRITE LIST::SUBSET-REMOVE-REDUCTION-1))
 (7 7 (:REWRITE RKEYS-WHEN-NOT-CONSP))
 (2 2 (:LINEAR BAG::COUNT-WITH-SUBBAGP-LINEAR))
 (2 1 (:LINEAR BAG::COUNT-LINEAR))
 (1 1 (:REWRITE BAG::COUNT-0-FOR-NON-MEMBERP))
 )
(GAR-AS-MEMBERP
 (12 12 (:TYPE-PRESCRIPTION RKEYS-NON-NIL-TP))
 )
(IFF-S
 (850 2 (:REWRITE LIST::WEAK-RIGHT-NORMALIZATION-CONS))
 (672 16 (:REWRITE BAG::MEMBERP-CAR-WHEN-DISJOINT))
 (508 20 (:REWRITE LIST::REMOVE-REDUCTON))
 (400 4 (:DEFINITION LIST::DISJOINT-REMOVE-DEFINITION))
 (378 6 (:REWRITE LIST::MEMBERP-REMOVE))
 (272 16 (:REWRITE BAG::SUBBAGP-IMPLIES-MEMBERSHIP))
 (200 4 (:DEFINITION LIST::DISJOINT))
 (147 39 (:REWRITE LIST::MEMBERP-OF-CDR-CHEAP))
 (147 39 (:REWRITE LIST::MEMBERP-FROM-MEMBERP-OF-CDR-CHEAP))
 (87 33 (:REWRITE DEFAULT-CAR))
 (85 31 (:REWRITE DEFAULT-CDR))
 (73 35 (:REWRITE LIST::MEMBERP-OF-NON-CONSP-CHEAP))
 (53 53 (:REWRITE BAG::MEMBERP-OF-REMOVE-ALL))
 (49 49 (:REWRITE BAG::NON-MEMBERP-FROM-MEMBERP-OF-OTHER-CHEAP))
 (49 49 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINTNESS))
 (49 49 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-TWO))
 (49 49 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-ONE))
 (45 45 (:REWRITE BAG::MEMBERP-SUBBAGP))
 (45 45 (:REWRITE BAG::MEMBERP-OF-REMOVE-BAG-MEANS-MEMBERP))
 (45 45 (:REWRITE BAG::MEMBERP-OF-REMOVE-1))
 (42 10 (:REWRITE LIST::NOT-CONSP-DISJOINT))
 (42 10 (:REWRITE BAG::DISJOINT-OF-NON-CONSP-ONE))
 (41 41 (:REWRITE LIST::MEMBERP-DISJOINT-NON-MEMBERP))
 (40 40 (:TYPE-PRESCRIPTION BAG::SUBBAGP))
 (40 39 (:REWRITE LIST::SUBSET-MEMBERSHIP-FREE-SUBSETP))
 (39 39 (:REWRITE LIST::SUBSET-MEMBERSHIP-FREE-MEMBERP))
 (38 8 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-TWO))
 (32 16 (:REWRITE BAG::SUBBAGP-FROM-SUBBAGP-OF-CDR-CHEAP))
 (32 16 (:REWRITE BAG::MEMBERP-CAR-WHEN-DISJOINT-CHEAP))
 (30 1 (:DEFINITION LEN))
 (28 10 (:REWRITE BAG::DISJOINT-OF-NON-CONSP-TWO))
 (28 6 (:REWRITE BAG::DISJOINT-SELF-MEANS-NOT-CONSP))
 (24 24 (:REWRITE RKEYS-WHEN-NOT-CONSP))
 (24 8 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-ONE-CHEAP))
 (24 8 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-ONE))
 (24 2 (:REWRITE LIST::LEN-WHEN-AT-MOST-1))
 (18 18 (:LINEAR BAG::COUNT-WITH-SUBBAGP-LINEAR))
 (18 8 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-TWO-CHEAP))
 (16 16 (:REWRITE BAG::SUBBAGP-REMOVE-BAG))
 (16 16 (:REWRITE BAG::SUBBAGP-REMOVE))
 (16 16 (:REWRITE BAG::SUBBAGP-CHAINING))
 (16 16 (:REWRITE BAG::PERM-SUBBAGP-SUBBAGP))
 (16 16 (:REWRITE BAG::DISJOINT-FROM-COMMON-UNIQUENSS))
 (16 8 (:REWRITE EQUAL-BOOLEANS-REDUCTON))
 (12 2 (:REWRITE LIST::SUBSETP-REMOVE-BY-SUBSET))
 (10 10 (:REWRITE BAG::SUBBAGP-DISJOINT-COMMUTE))
 (10 10 (:REWRITE BAG::SUBBAGP-DISJOINT))
 (10 10 (:REWRITE LIST::DISJOINT-BY-MULTIPLICITY))
 (10 2 (:REWRITE LIST::LEN-OF-NON-CONSP))
 (9 9 (:REWRITE FIXEDPOINT-NIL))
 (9 9 (:REWRITE CLR-DIFFERENTIAL))
 (8 8 (:TYPE-PRESCRIPTION BOOLEANP))
 (8 8 (:REWRITE BAG::SUBBAGP-SELF))
 (8 8 (:REWRITE BAG::SUBBAGP-OF-REMOVE-1-IMPLIES-SUBBAGP))
 (8 4 (:REWRITE BAG::DISJOINT-CDR-FROM-DISJOINT-CHEAP))
 (8 4 (:REWRITE BAG::DISJOINT-CDR-FROM-DISJOINT))
 (4 4 (:REWRITE LIST::SUBSET-BY-MULTIPLICITY))
 (4 2 (:REWRITE LIST::SUBSET-REMOVE-REDUCTION-1))
 (2 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE LIST::MEMBERP-OF-CONS-CHEAP))
 (1 1 (:REWRITE BAG::LEN-1-AND-MEMBERP-MEANS-YOU-KNOW-X))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(FIXEDPOINT-S
 (5333 20 (:REWRITE LIST::WEAK-RIGHT-NORMALIZATION-CONS))
 (4252 112 (:REWRITE BAG::MEMBERP-CAR-WHEN-DISJOINT))
 (2706 87 (:REWRITE LIST::WEAK-RIGHT-NORMALIZATION-REMOVE))
 (2586 87 (:REWRITE LIST::REMOVE-REDUCTON))
 (2578 26 (:DEFINITION LIST::DISJOINT-REMOVE-DEFINITION))
 (2572 44 (:REWRITE LIST::MEMBERP-REMOVE))
 (1688 112 (:REWRITE BAG::SUBBAGP-IMPLIES-MEMBERSHIP))
 (1290 26 (:DEFINITION LIST::DISJOINT))
 (750 150 (:REWRITE LIST::MEMBERP-OF-CDR-CHEAP))
 (750 150 (:REWRITE LIST::MEMBERP-FROM-MEMBERP-OF-CDR-CHEAP))
 (431 431 (:TYPE-PRESCRIPTION LIST::DISJOINT))
 (284 284 (:TYPE-PRESCRIPTION BAG::SUBBAGP))
 (262 124 (:REWRITE LIST::MEMBERP-OF-NON-CONSP-CHEAP))
 (248 248 (:REWRITE BAG::MEMBERP-OF-REMOVE-ALL))
 (244 152 (:REWRITE LIST::SUBSET-MEMBERSHIP-FREE-SUBSETP))
 (228 116 (:REWRITE DEFAULT-CAR))
 (224 112 (:REWRITE BAG::SUBBAGP-FROM-SUBBAGP-OF-CDR-CHEAP))
 (224 112 (:REWRITE BAG::MEMBERP-CAR-WHEN-DISJOINT-CHEAP))
 (219 60 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-TWO))
 (217 69 (:REWRITE LIST::NOT-CONSP-DISJOINT))
 (217 69 (:REWRITE BAG::DISJOINT-OF-NON-CONSP-ONE))
 (214 214 (:REWRITE BAG::NON-MEMBERP-FROM-MEMBERP-OF-OTHER-CHEAP))
 (214 214 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINTNESS))
 (214 214 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-TWO))
 (214 214 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-ONE))
 (196 196 (:REWRITE BAG::MEMBERP-SUBBAGP))
 (196 196 (:REWRITE BAG::MEMBERP-OF-REMOVE-BAG-MEANS-MEMBERP))
 (196 196 (:REWRITE BAG::MEMBERP-OF-REMOVE-1))
 (172 52 (:REWRITE BAG::UNIQUE-MEANS-CAR-NOT-MEMBERP-OF-CDR))
 (162 162 (:REWRITE LIST::MEMBERP-DISJOINT-NON-MEMBERP))
 (162 69 (:REWRITE BAG::DISJOINT-OF-NON-CONSP-TWO))
 (152 152 (:REWRITE LIST::SUBSET-MEMBERSHIP-FREE-MEMBERP))
 (126 2 (:REWRITE LIST::MEMBERP-OF-CONS))
 (122 39 (:REWRITE BAG::DISJOINT-SELF-MEANS-NOT-CONSP))
 (120 64 (:REWRITE DEFAULT-CDR))
 (116 60 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-ONE-CHEAP))
 (116 60 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-ONE))
 (113 60 (:REWRITE BAG::SUBBAGP-OF-NON-CONSP-TWO-CHEAP))
 (112 112 (:REWRITE BAG::SUBBAGP-REMOVE-BAG))
 (112 112 (:REWRITE BAG::SUBBAGP-REMOVE))
 (112 112 (:REWRITE BAG::SUBBAGP-CHAINING))
 (112 112 (:REWRITE BAG::PERM-SUBBAGP-SUBBAGP))
 (108 108 (:REWRITE BAG::DISJOINT-FROM-COMMON-UNIQUENSS))
 (72 4 (:REWRITE LIST::MEMBERP-OF-CONS-IRREL))
 (69 69 (:REWRITE BAG::SUBBAGP-DISJOINT-COMMUTE))
 (69 69 (:REWRITE BAG::SUBBAGP-DISJOINT))
 (69 69 (:REWRITE LIST::DISJOINT-BY-MULTIPLICITY))
 (65 8 (:REWRITE LIST::SUBSETP-REMOVE-BY-SUBSET))
 (60 60 (:TYPE-PRESCRIPTION BAG::UNIQUE))
 (60 60 (:REWRITE BAG::SUBBAGP-OF-REMOVE-1-IMPLIES-SUBBAGP))
 (52 52 (:REWRITE BAG::SUBBAGP-SELF))
 (52 26 (:REWRITE BAG::DISJOINT-CDR-FROM-DISJOINT-CHEAP))
 (52 26 (:REWRITE BAG::DISJOINT-CDR-FROM-DISJOINT))
 (50 50 (:LINEAR BAG::COUNT-WITH-SUBBAGP-LINEAR))
 (44 44 (:REWRITE UNIQUE-RKEYS))
 (42 20 (:REWRITE WFR-IMPLIES-NOT-NIL-MEMBERP))
 (24 4 (:REWRITE LIST::MEMBERP-OF-CONS-REDUCE-CHEAP))
 (22 22 (:TYPE-PRESCRIPTION WFR))
 (18 18 (:REWRITE RKEYS-WHEN-NOT-CONSP))
 (17 17 (:REWRITE FIXEDPOINT-NIL))
 (16 16 (:REWRITE LIST::SUBSET-BY-MULTIPLICITY))
 (16 8 (:REWRITE LIST::SUBSET-REMOVE-REDUCTION-1))
 (11 11 (:REWRITE CLR-DIFFERENTIAL))
 (10 10 (:TYPE-PRESCRIPTION BOOLEANP))
 (8 8 (:REWRITE BAG::UNIQUE-OF-NON-CONSP-CHEAP))
 (8 8 (:REWRITE BAG::SUBBAGP-UNIQUENESS))
 (8 8 (:REWRITE LIST::MEMBERP-OF-CONS-CHEAP))
 (5 1 (:REWRITE FIXEDPOINT-IMPLIES-FIXEDPOINT-GAR))
 )
