(LOOKUP-LST-ARRAY
 (2419 5 (:REWRITE NOT-ALL-NATP-WHEN-NOT-NATP-AND-MEMBER-EQUAL))
 (2198 120 (:DEFINITION MEMBER-EQUAL))
 (1195 59 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (576 576 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (555 21 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (542 7 (:DEFINITION NAT-LISTP))
 (374 34 (:REWRITE LEN-OF-CDR))
 (306 34 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (234 6 (:DEFINITION NATP))
 (185 94 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (140 140 (:REWRITE DEFAULT-CAR))
 (139 139 (:REWRITE DEFAULT-CDR))
 (96 96 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (96 96 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (96 96 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (96 96 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (91 66 (:REWRITE DEFAULT-<-2))
 (82 9 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (79 79 (:TYPE-PRESCRIPTION BOOLEANP))
 (75 75 (:TYPE-PRESCRIPTION NAT-LISTP))
 (69 67 (:REWRITE USE-ALL-<))
 (67 67 (:REWRITE USE-ALL-<-2))
 (67 67 (:REWRITE <-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (66 66 (:REWRITE DEFAULT-<-1))
 (62 7 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (59 59 (:REWRITE USE-ALL-CONSP-2))
 (59 59 (:REWRITE USE-ALL-CONSP))
 (59 59 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (59 59 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (59 59 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (59 59 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (42 21 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (41 19 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (34 34 (:REWRITE DEFAULT-+-2))
 (34 34 (:REWRITE DEFAULT-+-1))
 (34 34 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (30 4 (:REWRITE ALL-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (19 19 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (19 13 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (19 13 (:REWRITE ALL-<-TRANSITIVE))
 (18 9 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (18 9 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (17 9 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (14 14 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (13 13 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (12 12 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (12 12 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (9 9 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (9 9 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (9 9 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-DARGP-LESS-THAN))
 (9 7 (:REWRITE USE-ALL-NATP))
 (8 8 (:REWRITE USE-ALL-<=-2))
 (8 8 (:REWRITE USE-ALL-<=))
 (8 8 (:REWRITE NOT-<-OF-CAR-WHEN-ALL-DARGP-LESS-THAN-2))
 (8 8 (:LINEAR ARRAY2P-LINEAR))
 (7 7 (:REWRITE USE-ALL-NATP-2))
 (7 7 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-ALL-DARGP-LESS-THAN-SPECIAL-ALT))
 (7 7 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-ALL-DARGP-LESS-THAN-SPECIAL))
 (7 7 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-ALL-DARGP-LESS-THAN))
 (7 7 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (7 7 (:REWRITE NATP-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (6 1 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-OF-CDR))
 (6 1 (:REWRITE <-OF-CAR-AND-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (6 1 (:REWRITE <-OF-CAR-AND-ALEN1))
 (4 4 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (4 4 (:TYPE-PRESCRIPTION MEMBERP))
 (4 4 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (4 4 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (4 4 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (4 4 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (1 1 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 )
(SUM-LIST-TAIL-AUX)
(INTEGERP-OF-SUM-LIST-TAIL-AUX
 (124 7 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (24 3 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (18 9 (:REWRITE ALL-NATP-IMPLIES-ALL-INTEGERP-CHEAP))
 (15 7 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (15 3 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (14 7 (:REWRITE DEFAULT-<-2))
 (14 2 (:REWRITE ALL-INTEGERP-OF-CDR))
 (12 12 (:TYPE-PRESCRIPTION ALL-NATP))
 (11 11 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (9 9 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (9 9 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (9 9 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (9 9 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (7 7 (:REWRITE USE-ALL-CONSP-2))
 (7 7 (:REWRITE USE-ALL-CONSP))
 (7 7 (:REWRITE USE-ALL-<-2))
 (7 7 (:REWRITE USE-ALL-<))
 (7 7 (:REWRITE DEFAULT-CAR))
 (7 7 (:REWRITE DEFAULT-<-1))
 (7 7 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (7 7 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (7 7 (:REWRITE <-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (7 7 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (7 7 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (6 6 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (6 6 (:REWRITE DEFAULT-+-2))
 (6 6 (:REWRITE DEFAULT-+-1))
 (6 3 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (6 3 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (4 4 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE USE-ALL-RATIONALP-2))
 (3 3 (:REWRITE USE-ALL-RATIONALP))
 (3 3 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-DARGP-LESS-THAN))
 (3 3 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (3 3 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 )
(SUM-LIST-TAIL)
(INTEGERP-OF-SUM-LIST-TAIL)
(ARRAY-HAS-INTEGER-VALUESP
 (140 140 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (76 76 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (11 9 (:REWRITE DEFAULT-<-2))
 (11 7 (:REWRITE DEFAULT-+-2))
 (10 4 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (9 9 (:REWRITE USE-ALL-<=-2))
 (9 9 (:REWRITE USE-ALL-<=))
 (9 9 (:REWRITE USE-ALL-<-2))
 (9 9 (:REWRITE USE-ALL-<))
 (9 9 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (9 9 (:REWRITE <-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (7 7 (:REWRITE DEFAULT-+-1))
 (5 2 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (4 4 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (3 3 (:REWRITE USE-ALL-RATIONALP-2))
 (3 3 (:REWRITE USE-ALL-RATIONALP))
 (2 2 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (2 2 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (2 2 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (2 2 (:LINEAR ARRAY2P-LINEAR))
 (1 1 (:REWRITE USE-ALL-NATP-2))
 (1 1 (:REWRITE USE-ALL-NATP))
 (1 1 (:REWRITE NATP-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (1 1 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 )
(ARRAY-HAS-INTEGER-VALUESP-OF-ASET1
 (613 613 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (67 27 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (43 35 (:REWRITE DEFAULT-<-2))
 (35 35 (:REWRITE USE-ALL-<=-2))
 (35 35 (:REWRITE USE-ALL-<=))
 (35 35 (:REWRITE USE-ALL-<-2))
 (35 35 (:REWRITE USE-ALL-<))
 (35 35 (:REWRITE DEFAULT-<-1))
 (35 35 (:REWRITE <-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (33 33 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (18 18 (:LINEAR ARRAY2P-LINEAR))
 (18 2 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (16 16 (:REWRITE DEFAULT-+-2))
 (16 16 (:REWRITE DEFAULT-+-1))
 (14 14 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (8 8 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (8 2 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (7 7 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (6 6 (:REWRITE USE-ALL-NATP-2))
 (6 6 (:REWRITE USE-ALL-NATP))
 (6 6 (:REWRITE NATP-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (6 2 (:REWRITE +-COMBINE-CONSTANTS))
 (2 2 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (1 1 (:REWRITE EQUAL-OF-+-COMBINE-CONSTANTS))
 (1 1 (:REWRITE EQUAL-OF-+-CANCEL-SAME-3))
 (1 1 (:DEFINITION FIX))
 )
(INTEGERP-OF-AREF1-WHEN-ARRAY-HAS-INTEGER-VALUESP
 (196 196 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (32 8 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (16 8 (:TYPE-PRESCRIPTION ALEN1-TYPE))
 (12 12 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (8 8 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (8 8 (:TYPE-PRESCRIPTION ARRAY1P))
 (8 8 (:REWRITE USE-ALL-<=-2))
 (8 8 (:REWRITE USE-ALL-<=))
 (8 8 (:REWRITE USE-ALL-<-2))
 (8 8 (:REWRITE USE-ALL-<))
 (8 8 (:REWRITE DEFAULT-<-2))
 (8 8 (:REWRITE DEFAULT-<-1))
 (8 8 (:REWRITE <-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (6 6 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(ALL-INTEGERP-OF-LOOKUP-LST-ARRAY
 (392 3 (:REWRITE NOT-ALL-NATP-WHEN-NOT-NATP-AND-MEMBER-EQUAL))
 (362 18 (:DEFINITION MEMBER-EQUAL))
 (277 13 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (260 12 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (253 4 (:DEFINITION NAT-LISTP))
 (121 11 (:REWRITE LEN-OF-CDR))
 (109 3 (:DEFINITION NATP))
 (99 11 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (85 3 (:REWRITE USE-ALL-<-FOR-CAR))
 (72 72 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (45 4 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (38 38 (:TYPE-PRESCRIPTION NAT-LISTP))
 (25 25 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (25 25 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (25 25 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (25 25 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (24 12 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (23 23 (:REWRITE DEFAULT-CDR))
 (23 23 (:REWRITE DEFAULT-CAR))
 (20 12 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (19 17 (:REWRITE DEFAULT-<-2))
 (19 1 (:REWRITE ALL-<-OF-CDR))
 (18 18 (:REWRITE <-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (17 17 (:REWRITE USE-ALL-<-2))
 (17 17 (:REWRITE USE-ALL-<))
 (17 17 (:REWRITE DEFAULT-<-1))
 (16 4 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (14 14 (:REWRITE DEFAULT-+-2))
 (14 14 (:REWRITE DEFAULT-+-1))
 (13 13 (:REWRITE USE-ALL-CONSP-2))
 (13 13 (:REWRITE USE-ALL-CONSP))
 (13 13 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (13 13 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (13 13 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (13 13 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (11 11 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (11 5 (:REWRITE USE-ALL-NATP))
 (10 10 (:TYPE-PRESCRIPTION MEMBERP))
 (9 9 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (9 5 (:REWRITE USE-ALL-<=))
 (8 8 (:TYPE-PRESCRIPTION BOOLEANP))
 (8 8 (:TYPE-PRESCRIPTION ALL-<))
 (8 4 (:TYPE-PRESCRIPTION ALEN1-TYPE))
 (8 4 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (7 7 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (6 6 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (6 3 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (6 3 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (6 3 (:REWRITE ALL-NATP-IMPLIES-ALL-INTEGERP-CHEAP))
 (6 3 (:REWRITE ALL-INTEGERP-WHEN-NOT-CONSP-CHEAP))
 (5 5 (:REWRITE USE-ALL-NATP-2))
 (5 5 (:REWRITE USE-ALL-<=-2))
 (5 5 (:REWRITE NATP-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (4 4 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (4 4 (:TYPE-PRESCRIPTION ARRAY1P))
 (4 4 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (4 4 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (4 4 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (4 4 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (4 4 (:REWRITE ALL-<-TRANSITIVE))
 (3 3 (:REWRITE NOT-ALL-<=-WHEN-<-AND-MEMBER-EQUAL))
 (3 3 (:REWRITE NOT-<-OF-CAR-WHEN-ALL-DARGP-LESS-THAN-2))
 (3 3 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-DARGP-LESS-THAN))
 (3 3 (:REWRITE ALL-<=-MONOTONE))
 (2 1 (:REWRITE IFF-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (1 1 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 )
(SIZE-ARRAY-FOR-NODES-AUX
 (9366 18 (:REWRITE NOT-ALL-NATP-WHEN-NOT-NATP-AND-MEMBER-EQUAL))
 (8032 688 (:DEFINITION MEMBER-EQUAL))
 (3380 3380 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (1466 726 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (1450 1450 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (1417 64 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (1373 20 (:DEFINITION NAT-LISTP))
 (1253 39 (:DEFINITION NATP))
 (1036 921 (:REWRITE DEFAULT-CAR))
 (1034 353 (:REWRITE DEFAULT-+-2))
 (998 860 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (851 776 (:REWRITE DEFAULT-CDR))
 (820 31 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (798 27 (:REWRITE NOT-EQUAL-OF-CAR-AND-QUOTE-WHEN-LEN-WRONG-AND-PSEUDO-DAG-ARRAYP-AUX))
 (620 30 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-OF-CAR))
 (577 89 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (562 562 (:TYPE-PRESCRIPTION BOOLEANP))
 (534 267 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (423 9 (:REWRITE AREF1-OF-ASET1-BOTH))
 (414 353 (:REWRITE DEFAULT-+-1))
 (411 411 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (406 406 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (400 400 (:REWRITE USE-ALL-CONSP-2))
 (400 400 (:REWRITE USE-ALL-CONSP))
 (373 134 (:REWRITE DEFAULT-<-1))
 (351 9 (:REWRITE NUM-EXAMINED-NODES-OF-ASET1-IRREL))
 (273 90 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (267 267 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (260 52 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (252 4 (:REWRITE TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (243 9 (:REWRITE AREF1-OF-ASET1-DIFF))
 (235 23 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (231 173 (:REWRITE USE-ALL-<))
 (229 31 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (226 64 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (224 224 (:TYPE-PRESCRIPTION NAT-LISTP))
 (217 91 (:REWRITE USE-ALL-NATP))
 (212 134 (:REWRITE DEFAULT-<-2))
 (201 19 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (201 5 (:REWRITE ALL-DARGP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (194 194 (:REWRITE <-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (190 7 (:DEFINITION BINARY-APPEND))
 (184 184 (:TYPE-PRESCRIPTION MEMBERP))
 (173 173 (:REWRITE USE-ALL-<-2))
 (139 24 (:REWRITE <-OF-CAR-AND-ALEN1))
 (130 98 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (129 129 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (128 64 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (124 31 (:REWRITE NOT-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP))
 (120 30 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (116 58 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (116 58 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-SIMPLE))
 (110 22 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (108 15 (:REWRITE ALL-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (101 101 (:REWRITE USE-ALL-<=-2))
 (101 101 (:REWRITE USE-ALL-<=))
 (98 98 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (98 98 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (98 98 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (93 48 (:REWRITE ALL-<-TRANSITIVE))
 (91 91 (:REWRITE USE-ALL-NATP-2))
 (91 91 (:REWRITE NATP-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (90 43 (:REWRITE DEFAULT-UNARY-MINUS))
 (82 60 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (81 11 (:REWRITE INTEGERP-OF-+-WHEN-INTEGERP-1-CHEAP))
 (72 72 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-ALL-DARGP-LESS-THAN-SPECIAL))
 (72 72 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-ALL-DARGP-LESS-THAN))
 (71 71 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (68 44 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (67 6 (:REWRITE CONSP-OF-MERGE-SORT-<))
 (66 66 (:REWRITE USE-ALL-RATIONALP-2))
 (66 66 (:REWRITE USE-ALL-RATIONALP))
 (66 22 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (63 60 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (60 60 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (58 58 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (52 52 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (52 52 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (47 47 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (47 44 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (44 44 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (44 44 (:TYPE-PRESCRIPTION ALL-CONSP))
 (44 22 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (44 22 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (44 10 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (41 41 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-DARGP-LESS-THAN))
 (36 18 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (35 35 (:REWRITE NOT-<-OF-CAR-WHEN-ALL-DARGP-LESS-THAN-2))
 (34 1 (:REWRITE DAG-EXPRP0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (33 33 (:REWRITE FOLD-CONSTS-IN-+))
 (33 33 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (33 27 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (33 27 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (31 31 (:REWRITE QUOTE-LEMMA-FOR-ALL-DARGP-LESS-THAN-GEN-ALT))
 (30 30 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (30 30 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (30 30 (:LINEAR ARRAY2P-LINEAR))
 (24 6 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (22 22 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (22 22 (:REWRITE EQUAL-OF-+-COMBINE-CONSTANTS))
 (22 22 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (22 22 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (22 22 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (22 22 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (18 18 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (18 3 (:REWRITE USE-ALL-<=-FOR-CAR))
 (18 3 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-OF-CDR))
 (17 17 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (17 17 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (16 4 (:REWRITE INTEGERP-OF-ALEN1))
 (16 1 (:REWRITE ALL-<-OF-KEEP-ATOMS-OF-DARGS-WHEN-BOUNDED-DAG-EXPRP))
 (13 4 (:REWRITE PERM-OF-APPEND-WHEN-NOT-CONSP))
 (12 12 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (6 6 (:TYPE-PRESCRIPTION ALL-<=))
 (6 3 (:REWRITE IFF-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (6 1 (:REWRITE DAG-EXPRP0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (6 1 (:REWRITE BOUNDED-DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (4 4 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (4 4 (:REWRITE TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (4 4 (:REWRITE INTEGERP-OF-ALEN1-GEN))
 (3 3 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (3 3 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (3 3 (:REWRITE ALL-<=-MONOTONE))
 (2 1 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION MYQUOTEP))
 (1 1 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP-CHEAP))
 (1 1 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (1 1 (:REWRITE BOUNDED-DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-GEN))
 (1 1 (:REWRITE BOUNDED-DAG-EXPRP-MONOTONE))
 )
(ALEN1-OF-SIZE-ARRAY-FOR-NODES-AUX
 (12978 372 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (4278 228 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (3877 3877 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (3514 596 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (3375 225 (:REWRITE LEN-OF-CDR))
 (2627 78 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (2543 44 (:DEFINITION NAT-LISTP))
 (1806 77 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (1228 1075 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (1168 479 (:REWRITE DEFAULT-<-2))
 (1075 1075 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (1075 1075 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (1075 1075 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (1029 999 (:REWRITE DEFAULT-CAR))
 (967 937 (:REWRITE DEFAULT-CDR))
 (918 644 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (881 16 (:DEFINITION NATP))
 (737 479 (:REWRITE DEFAULT-<-1))
 (717 72 (:REWRITE ALL-<-TRANSITIVE))
 (651 651 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (598 299 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (591 483 (:REWRITE USE-ALL-<))
 (543 253 (:REWRITE DEFAULT-+-2))
 (488 488 (:REWRITE <-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (483 483 (:REWRITE USE-ALL-<-2))
 (431 65 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (377 13 (:REWRITE NOT-EQUAL-OF-CAR-AND-QUOTE-WHEN-LEN-WRONG-AND-PSEUDO-DAG-ARRAYP-AUX))
 (375 30 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (372 372 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (366 352 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (366 352 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (353 353 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (351 351 (:REWRITE USE-ALL-CONSP-2))
 (351 351 (:REWRITE USE-ALL-CONSP))
 (329 329 (:TYPE-PRESCRIPTION NAT-LISTP))
 (299 299 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (274 253 (:REWRITE DEFAULT-+-1))
 (273 13 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-OF-CAR))
 (262 44 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (253 40 (:REWRITE ALL-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (238 238 (:TYPE-PRESCRIPTION BOOLEANP))
 (225 225 (:REWRITE EQUAL-OF-LEN-AND-0))
 (225 225 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (200 65 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (188 188 (:TYPE-PRESCRIPTION MEMBERP))
 (184 21 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (172 6 (:DEFINITION BINARY-APPEND))
 (168 84 (:REWRITE IFF-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (156 78 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (155 59 (:REWRITE NOT-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP))
 (148 1 (:REWRITE ALL-DARGP-LESS-THAN-OF-DARGS-WHEN-<-SIMPLE))
 (146 3 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (140 3 (:REWRITE BOUNDED-DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (131 51 (:REWRITE USE-ALL-NATP))
 (129 129 (:REWRITE USE-ALL-<=-2))
 (129 129 (:REWRITE USE-ALL-<=))
 (122 2 (:REWRITE ALL-DARGP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (97 97 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (84 73 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (81 55 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-ALL-DARGP-LESS-THAN-SPECIAL-ALT))
 (81 14 (:REWRITE ALL-DARGP-LESS-THAN-WHEN-ALL-<))
 (79 65 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (77 20 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (69 65 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (52 13 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (52 2 (:REWRITE CONSP-OF-MERGE-SORT-<))
 (51 51 (:REWRITE USE-ALL-NATP-2))
 (51 51 (:REWRITE NATP-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (46 23 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (46 23 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-SIMPLE))
 (44 4 (:REWRITE PERM-OF-APPEND-WHEN-NOT-CONSP))
 (42 42 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-ALL-DARGP-LESS-THAN-SPECIAL))
 (42 42 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-ALL-DARGP-LESS-THAN))
 (40 40 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (38 19 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (33 19 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (32 16 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (30 6 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (29 29 (:REWRITE USE-ALL-RATIONALP-2))
 (29 29 (:REWRITE USE-ALL-RATIONALP))
 (28 28 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (28 28 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (28 28 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (28 14 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (27 3 (:REWRITE NOT-<-OF-+-1-AND-CAR-WHEN-ALL-<))
 (26 26 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (24 24 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (23 23 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (23 1 (:REWRITE ALL-DARGP-LESS-THAN-WHEN-NOT-CONSP))
 (22 22 (:LINEAR ARRAY2P-LINEAR))
 (20 20 (:REWRITE QUOTE-LEMMA-FOR-ALL-DARGP-LESS-THAN-GEN-ALT))
 (19 19 (:REWRITE NOT-<-OF-CAR-WHEN-ALL-DARGP-LESS-THAN-2))
 (19 19 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-DARGP-LESS-THAN))
 (18 3 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-OF-CDR))
 (16 16 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (16 16 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (13 13 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (13 13 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (12 12 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (12 12 (:REWRITE FOLD-CONSTS-IN-+))
 (12 12 (:REWRITE +-COMBINE-CONSTANTS))
 (12 3 (:REWRITE INTEGERP-OF-+-WHEN-INTEGERP-1-CHEAP))
 (12 2 (:REWRITE USE-ALL-<=-FOR-CAR))
 (11 1 (:REWRITE ALL-DARGP-LESS-THAN-WHEN-BOUNDED-DAG-EXPRP))
 (11 1 (:REWRITE ALL-DARGP-LESS-THAN-OF-DARGS-WHEN-BOUNDED-DAG-EXPRP))
 (10 5 (:REWRITE DEFAULT-UNARY-MINUS))
 (9 9 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (6 6 (:TYPE-PRESCRIPTION BOUNDED-DAG-EXPRP))
 (6 6 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (6 6 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (6 3 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (6 3 (:DEFINITION FIX))
 (6 1 (:REWRITE ALL-DARGP-LESS-THAN-WHEN-NOT-CONSP-CHEAP))
 (5 2 (:REWRITE INTEGERP-OF-ALEN1))
 (4 4 (:TYPE-PRESCRIPTION ALL-<=))
 (3 3 (:TYPE-PRESCRIPTION MYQUOTEP))
 (3 3 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP-CHEAP))
 (3 3 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP-CHEAP))
 (3 3 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (3 3 (:REWRITE BOUNDED-DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-GEN))
 (3 3 (:REWRITE BOUNDED-DAG-EXPRP-MONOTONE))
 (3 3 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (3 3 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (2 2 (:REWRITE INTEGERP-OF-ALEN1-GEN))
 (2 2 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (2 2 (:REWRITE ALL-<=-MONOTONE))
 (2 1 (:REWRITE ALL-DARGP-LESS-THAN-WHEN-ALL-MYQUOTEP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (1 1 (:REWRITE ALL-DARGP-LESS-THAN-WHEN-BOUNDED-DAG-EXPRP-GEN))
 (1 1 (:REWRITE ALL-DARGP-LESS-THAN-OF-DARGS-OF-AREF1))
 (1 1 (:REWRITE ALL-DARGP-LESS-THAN-MONOTONE))
 )
(ARRAY1P-OF-SIZE-ARRAY-FOR-NODES-AUX
 (27402 765 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (9312 492 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (7350 490 (:REWRITE LEN-OF-CDR))
 (3725 121 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (3610 65 (:DEFINITION NAT-LISTP))
 (3330 2044 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (2726 2657 (:REWRITE DEFAULT-CAR))
 (2649 2649 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (2619 2574 (:REWRITE DEFAULT-CDR))
 (2548 2283 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (2283 2283 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (2283 2283 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (2283 2283 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (1707 856 (:REWRITE DEFAULT-<-2))
 (1262 1262 (:TYPE-PRESCRIPTION BOOLEANP))
 (1098 530 (:REWRITE DEFAULT-+-2))
 (1013 23 (:DEFINITION NATP))
 (983 865 (:REWRITE USE-ALL-<))
 (962 856 (:REWRITE DEFAULT-<-1))
 (919 919 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (868 868 (:REWRITE <-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (865 865 (:REWRITE USE-ALL-<-2))
 (842 421 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (765 765 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (758 737 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (758 737 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (737 737 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (734 734 (:REWRITE USE-ALL-CONSP-2))
 (734 734 (:REWRITE USE-ALL-CONSP))
 (703 81 (:REWRITE ALL-<-TRANSITIVE))
 (632 18 (:REWRITE NOT-EQUAL-OF-CAR-AND-QUOTE-WHEN-LEN-WRONG-AND-PSEUDO-DAG-ARRAYP-AUX))
 (562 530 (:REWRITE DEFAULT-+-1))
 (512 19 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-OF-CAR))
 (497 497 (:TYPE-PRESCRIPTION NAT-LISTP))
 (490 490 (:REWRITE EQUAL-OF-LEN-AND-0))
 (490 490 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (421 421 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (390 195 (:REWRITE IFF-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (361 73 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (325 37 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (319 49 (:REWRITE ALL-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (252 7 (:DEFINITION BINARY-APPEND))
 (242 121 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (236 85 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-ALL-DARGP-LESS-THAN-SPECIAL-ALT))
 (234 234 (:TYPE-PRESCRIPTION MEMBERP))
 (234 99 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (192 76 (:REWRITE USE-ALL-NATP))
 (175 64 (:REWRITE NOT-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP))
 (151 151 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (151 51 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (132 19 (:REWRITE ALL-DARGP-LESS-THAN-WHEN-ALL-<))
 (128 2 (:REWRITE ALL-DARGP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (128 1 (:REWRITE AREF1-OF-ASET1-BOTH))
 (120 120 (:REWRITE USE-ALL-<=-2))
 (120 120 (:REWRITE USE-ALL-<=))
 (117 98 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (103 99 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (78 24 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (78 3 (:REWRITE CONSP-OF-MERGE-SORT-<))
 (77 73 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (76 76 (:REWRITE USE-ALL-NATP-2))
 (76 76 (:REWRITE NATP-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (76 76 (:LINEAR ARRAY2P-LINEAR))
 (76 19 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (70 12 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (66 66 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-ALL-DARGP-LESS-THAN-SPECIAL))
 (66 66 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-ALL-DARGP-LESS-THAN))
 (66 33 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (62 62 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (58 2 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (54 29 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (54 27 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (44 4 (:REWRITE PERM-OF-APPEND-WHEN-NOT-CONSP))
 (42 42 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (42 6 (:REWRITE <-OF-CAR-AND-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (40 40 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (40 40 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (40 20 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (40 20 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX-SIMPLE))
 (38 38 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (37 6 (:REWRITE <-OF-CAR-AND-ALEN1))
 (35 35 (:REWRITE QUOTE-LEMMA-FOR-ALL-DARGP-LESS-THAN-GEN-ALT))
 (32 7 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-OF-CDR))
 (31 31 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (29 29 (:REWRITE NOT-<-OF-CAR-WHEN-ALL-DARGP-LESS-THAN-2))
 (29 29 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-DARGP-LESS-THAN))
 (27 27 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (27 27 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (20 20 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (20 4 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (19 19 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (19 19 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (18 18 (:REWRITE FOLD-CONSTS-IN-+))
 (18 18 (:REWRITE +-COMBINE-CONSTANTS))
 (16 8 (:REWRITE DEFAULT-UNARY-MINUS))
 (12 12 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (12 2 (:REWRITE NOT-<-OF-+-1-AND-CAR-WHEN-ALL-<))
 (10 10 (:REWRITE USE-ALL-RATIONALP-2))
 (10 10 (:REWRITE USE-ALL-RATIONALP))
 (8 8 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (8 2 (:REWRITE INTEGERP-OF-+-WHEN-INTEGERP-1-CHEAP))
 (6 1 (:REWRITE USE-ALL-<=-FOR-CAR))
 (4 4 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (4 2 (:DEFINITION FIX))
 (2 2 (:TYPE-PRESCRIPTION ALL-<=))
 (2 2 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (2 2 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (1 1 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (1 1 (:REWRITE ALL-<=-MONOTONE))
 )
(SIZE-ARRAY-FOR-SORTED-NODES
 (1016 5 (:REWRITE NOT-ALL-NATP-WHEN-NOT-NATP-AND-MEMBER-EQUAL))
 (907 52 (:DEFINITION MEMBER-EQUAL))
 (609 34 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (492 492 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (321 13 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (306 5 (:DEFINITION NAT-LISTP))
 (260 260 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (156 4 (:DEFINITION NATP))
 (92 4 (:REWRITE USE-ALL-<-FOR-CAR))
 (81 47 (:REWRITE DEFAULT-<-2))
 (79 13 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (57 57 (:REWRITE DEFAULT-CDR))
 (57 57 (:REWRITE DEFAULT-CAR))
 (53 47 (:REWRITE USE-ALL-<))
 (50 50 (:TYPE-PRESCRIPTION NAT-LISTP))
 (47 47 (:REWRITE USE-ALL-<-2))
 (47 47 (:REWRITE DEFAULT-<-1))
 (47 47 (:REWRITE <-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (45 27 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (39 39 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (39 39 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (39 39 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (39 39 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (37 5 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (34 34 (:REWRITE USE-ALL-CONSP-2))
 (34 34 (:REWRITE USE-ALL-CONSP))
 (34 34 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (34 34 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (34 34 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (34 34 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (26 13 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (18 18 (:TYPE-PRESCRIPTION BOOLEANP))
 (14 5 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (13 13 (:REWRITE USE-ALL-<=-2))
 (13 13 (:REWRITE USE-ALL-<=))
 (13 13 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (12 5 (:REWRITE ALL-<-TRANSITIVE))
 (8 8 (:TYPE-PRESCRIPTION MEMBERP))
 (8 4 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (8 4 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (8 4 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (7 5 (:REWRITE USE-ALL-NATP))
 (5 5 (:REWRITE USE-ALL-NATP-2))
 (5 5 (:REWRITE NATP-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (5 5 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (5 5 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (4 4 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (4 4 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (4 4 (:REWRITE NOT-<-OF-CAR-WHEN-ALL-DARGP-LESS-THAN-2))
 (4 4 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (4 4 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (4 4 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-DARGP-LESS-THAN))
 (3 3 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (1 1 (:REWRITE USE-ALL-RATIONALP-2))
 (1 1 (:REWRITE USE-ALL-RATIONALP))
 (1 1 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (1 1 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (1 1 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 )
(ALEN1-OF-SIZE-ARRAY-FOR-SORTED-NODES
 (342 1 (:REWRITE NOT-ALL-NATP-WHEN-NOT-NATP-AND-MEMBER-EQUAL))
 (319 11 (:DEFINITION MEMBER-EQUAL))
 (252 14 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (114 114 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (78 3 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (75 1 (:DEFINITION NAT-LISTP))
 (70 70 (:TYPE-PRESCRIPTION LEN))
 (55 55 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (35 1 (:DEFINITION NATP))
 (30 16 (:REWRITE DEFAULT-<-2))
 (25 3 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (24 2 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (19 1 (:REWRITE USE-ALL-<-FOR-CAR))
 (18 16 (:REWRITE USE-ALL-<))
 (16 16 (:REWRITE USE-ALL-<-2))
 (16 16 (:REWRITE DEFAULT-<-1))
 (16 16 (:REWRITE <-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (14 14 (:REWRITE USE-ALL-CONSP-2))
 (14 14 (:REWRITE USE-ALL-CONSP))
 (14 14 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (14 14 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (14 14 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (14 14 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (14 14 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (14 14 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (14 14 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (14 14 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (14 14 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (12 12 (:REWRITE DEFAULT-CDR))
 (12 12 (:REWRITE DEFAULT-CAR))
 (11 11 (:TYPE-PRESCRIPTION NAT-LISTP))
 (11 6 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (9 1 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (9 1 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (6 3 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (5 5 (:TYPE-PRESCRIPTION BOOLEANP))
 (3 3 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:TYPE-PRESCRIPTION MEMBERP))
 (2 2 (:REWRITE USE-ALL-<=-2))
 (2 2 (:REWRITE USE-ALL-<=))
 (2 2 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (2 2 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (2 2 (:REWRITE ALL-<-TRANSITIVE))
 (2 1 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (2 1 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (2 1 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (1 1 (:TYPE-PRESCRIPTION ALL-INTEGERP))
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(ARRAY1P-OF-SIZE-ARRAY-FOR-SORTED-NODES
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 )
(SIZE-ARRAY-FOR-NODES
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 (33 33 (:TYPE-PRESCRIPTION NAT-LISTP))
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 )
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 )
(ARRAY1P-OF-SIZE-ARRAY-FOR-NODES
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(SIZE-OF-NODE
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 (2 2 (:LINEAR ARRAY2P-LINEAR))
 (1 1 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 )
