(FIND-NODE-FOR-EXPR
 (13 1 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (4 1 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (3 2 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (2 2 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE ALISTP-WHEN-PSEUDO-DAGP-AUX))
 (2 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE USE-ALL-CONSP-2))
 (1 1 (:REWRITE USE-ALL-CONSP))
 (1 1 (:REWRITE USE-ALL-<-2))
 (1 1 (:REWRITE USE-ALL-<))
 (1 1 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (1 1 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (1 1 (:REWRITE ALISTP-WHEN-BOUNDED-NATP-ALISTP))
 )
(FIND-NODE-FOR-EXPR-TYPE
 (1055 25 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (985 10 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (960 15 (:DEFINITION NAT-LISTP))
 (908 57 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (756 30 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX-2))
 (582 30 (:DEFINITION TOP-NODENUM))
 (375 155 (:REWRITE DEFAULT-CAR))
 (280 30 (:REWRITE USE-ALL-<-FOR-CAR))
 (246 15 (:REWRITE BOUNDED-DAG-EXPRP-OF-CDR-OF-CAR-WHEN-WEAK-DAGP-AUX))
 (169 57 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (120 77 (:REWRITE DEFAULT-<-2))
 (120 10 (:REWRITE LEN-OF-CDR))
 (100 100 (:TYPE-PRESCRIPTION ALL-<))
 (93 93 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (93 93 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (93 93 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (90 30 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP))
 (85 5 (:REWRITE WEAK-DAGP-AUX-OF-CDR))
 (80 80 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (79 77 (:REWRITE DEFAULT-<-1))
 (77 77 (:REWRITE USE-ALL-<-2))
 (77 77 (:REWRITE USE-ALL-<))
 (77 66 (:REWRITE DEFAULT-CDR))
 (75 75 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (70 70 (:TYPE-PRESCRIPTION NAT-LISTP))
 (69 69 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (69 45 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (65 65 (:TYPE-PRESCRIPTION ALL-NATP))
 (60 30 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (60 30 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (60 30 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (57 57 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (50 25 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-CHEAP))
 (50 25 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-AUX-CHEAP))
 (50 10 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (43 43 (:REWRITE USE-ALL-CONSP-2))
 (43 43 (:REWRITE USE-ALL-CONSP))
 (43 43 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (40 5 (:REWRITE ALL-<-OF-CDR))
 (36 35 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (35 35 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (35 35 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (35 35 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (35 35 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (35 35 (:REWRITE ALL-<-TRANSITIVE))
 (35 5 (:REWRITE PSEUDO-DAGP-AUX-OF-CDR))
 (34 34 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (34 34 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (30 30 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (30 30 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (30 30 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (30 30 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (30 15 (:REWRITE DEFAULT-+-2))
 (30 15 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (30 10 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (27 27 (:REWRITE USE-ALL-NATP-2))
 (27 27 (:REWRITE USE-ALL-NATP))
 (25 25 (:TYPE-PRESCRIPTION WEAK-DAGP))
 (25 25 (:REWRITE INTEGERP-OF-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (25 25 (:REWRITE <-OF-0-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (20 20 (:TYPE-PRESCRIPTION ALL-CONSP))
 (20 20 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (20 10 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (20 10 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (19 19 (:REWRITE PSEUDO-DAGP-AUX-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (15 15 (:TYPE-PRESCRIPTION MYQUOTEP))
 (15 15 (:REWRITE DEFAULT-+-1))
 (15 15 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP-CHEAP))
 (15 15 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP-CHEAP))
 (15 15 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (15 15 (:REWRITE BOUNDED-DAG-EXPRP-MONOTONE))
 (14 14 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (10 10 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (10 10 (:REWRITE EQUAL-OF-LEN-AND-0))
 (10 10 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (10 10 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (10 10 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (10 10 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (10 10 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (10 10 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (10 10 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (8 4 (:REWRITE IFF-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (8 4 (:REWRITE CAR-WHEN-ALISTP-IFF-CHEAP))
 (7 7 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (1 1 (:DEFINITION NULL))
 )
(FIND-NODE-FOR-EXPR-BOUND-WHEN-PSEUDO-DAGP-AUX
 (11186 99 (:REWRITE BOUNDED-DAG-EXPRP-OF-CDR-OF-CAR-WHEN-WEAK-DAGP-AUX))
 (9828 51 (:DEFINITION WEAK-DAGP-AUX))
 (4785 123 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (4380 70 (:REWRITE WEAK-DAGP-AUX-OF-CDR))
 (4373 51 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (4251 74 (:DEFINITION NAT-LISTP))
 (4024 96 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX-2))
 (3441 127 (:DEFINITION NATP))
 (3268 144 (:REWRITE PSEUDO-DAGP-AUX-OF-CDR))
 (3134 199 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (1871 138 (:REWRITE USE-ALL-<-FOR-CAR))
 (1166 341 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (732 163 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (680 414 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (602 415 (:REWRITE DEFAULT-CDR))
 (466 233 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (466 233 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (464 464 (:TYPE-PRESCRIPTION ALL-<))
 (449 268 (:REWRITE DEFAULT-<-2))
 (416 416 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (416 208 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-CHEAP))
 (416 208 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-AUX-CHEAP))
 (414 414 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (407 407 (:TYPE-PRESCRIPTION ALL-NATP))
 (352 352 (:TYPE-PRESCRIPTION NAT-LISTP))
 (337 337 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (319 268 (:REWRITE DEFAULT-<-1))
 (305 253 (:REWRITE DEFAULT-+-2))
 (288 96 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP))
 (276 138 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (268 268 (:REWRITE USE-ALL-<-2))
 (268 268 (:REWRITE USE-ALL-<))
 (253 253 (:REWRITE DEFAULT-+-1))
 (235 235 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (233 233 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (233 233 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (233 32 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (222 111 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (208 208 (:TYPE-PRESCRIPTION WEAK-DAGP))
 (208 208 (:REWRITE INTEGERP-OF-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (202 101 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (184 23 (:REWRITE ALL-<-OF-CDR))
 (181 163 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (163 163 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (163 163 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (163 163 (:REWRITE ALL-<-TRANSITIVE))
 (160 114 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (152 56 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (138 138 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (130 130 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (127 127 (:REWRITE USE-ALL-NATP-2))
 (127 127 (:REWRITE USE-ALL-NATP))
 (124 124 (:TYPE-PRESCRIPTION ALISTP))
 (120 51 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (108 108 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (106 106 (:REWRITE USE-ALL-CONSP-2))
 (106 106 (:REWRITE USE-ALL-CONSP))
 (106 98 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (102 51 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (101 101 (:TYPE-PRESCRIPTION MYQUOTEP))
 (101 101 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP-CHEAP))
 (101 101 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (96 96 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (90 45 (:TYPE-PRESCRIPTION NATP-OF-TOP-NODENUM-WHEN-PSEUDO-DAGP))
 (88 88 (:TYPE-PRESCRIPTION ALL-CONSP))
 (86 86 (:REWRITE PSEUDO-DAGP-AUX-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (79 79 (:REWRITE <-OF-0-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (76 32 (:REWRITE +-OF-+-OF---SAME))
 (71 71 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP-CHEAP))
 (69 23 (:REWRITE FOLD-CONSTS-IN-+))
 (65 13 (:REWRITE ALL-CONSP-OF-CDR))
 (64 32 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (56 56 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (56 44 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (51 51 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (45 45 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (44 44 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (44 32 (:DEFINITION FIX))
 (32 32 (:TYPE-PRESCRIPTION NATP))
 (32 32 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (32 32 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (26 13 (:REWRITE IFF-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (26 13 (:REWRITE CAR-WHEN-ALISTP-IFF-CHEAP))
 (23 23 (:REWRITE LEN-OF-CDDR-WHEN-EQUAL-OF-LEN))
 (23 23 (:REWRITE EQUAL-OF-0-AND-+-OF---ALT))
 (16 1 (:LINEAR LEN-OF-CDR-LINEAR-STRONG))
 (14 1 (:LINEAR LEN-OF-CDR-LINEAR))
 (13 13 (:REWRITE EQUAL-OF-LEN-AND-0))
 (12 12 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (6 6 (:REWRITE EQUAL-OF-NON-NATP-AND-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (6 2 (:REWRITE NATP-OF-TOP-NODENUM-WHEN-PSEUDO-DAGP))
 )
(FIND-NODE-FOR-EXPR2-AUX
 (218 1 (:DEFINITION WEAK-DAGP-AUX))
 (144 5 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX-2))
 (107 5 (:DEFINITION TOP-NODENUM))
 (95 7 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (61 15 (:REWRITE DEFAULT-CAR))
 (58 2 (:DEFINITION NATP))
 (51 2 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (44 1 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (41 1 (:DEFINITION NAT-LISTP))
 (20 5 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (18 2 (:REWRITE LEN-OF-CDR))
 (17 1 (:REWRITE BOUNDED-DAG-EXPRP-OF-CDR-OF-CAR-WHEN-WEAK-DAGP-AUX))
 (16 2 (:REWRITE USE-ALL-<-FOR-CAR))
 (15 5 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP))
 (14 14 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (14 2 (:REWRITE PSEUDO-DAGP-AUX-OF-CDR))
 (13 13 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (13 13 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (13 13 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (12 12 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (10 8 (:REWRITE DEFAULT-<-2))
 (8 8 (:REWRITE USE-ALL-<-2))
 (8 8 (:REWRITE USE-ALL-<))
 (8 8 (:REWRITE DEFAULT-<-1))
 (8 8 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (7 7 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (7 7 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (6 6 (:TYPE-PRESCRIPTION NAT-LISTP))
 (6 6 (:TYPE-PRESCRIPTION ALL-<))
 (6 5 (:REWRITE DEFAULT-CDR))
 (6 4 (:REWRITE DEFAULT-+-2))
 (5 5 (:TYPE-PRESCRIPTION ALL-NATP))
 (5 5 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (5 1 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (4 4 (:REWRITE USE-ALL-CONSP-2))
 (4 4 (:REWRITE USE-ALL-CONSP))
 (4 4 (:REWRITE DEFAULT-+-1))
 (4 4 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (4 2 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (4 2 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (4 2 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-CHEAP))
 (4 2 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-AUX-CHEAP))
 (4 2 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (3 3 (:REWRITE PSEUDO-DAGP-AUX-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (3 3 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (3 1 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (2 2 (:TYPE-PRESCRIPTION WEAK-DAGP))
 (2 2 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (2 2 (:TYPE-PRESCRIPTION ALL-CONSP))
 (2 2 (:REWRITE USE-ALL-NATP-2))
 (2 2 (:REWRITE USE-ALL-NATP))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2 2 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (2 2 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (2 2 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (2 2 (:REWRITE INTEGERP-OF-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (2 2 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (2 2 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (2 2 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (2 2 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (2 2 (:REWRITE ALL-<-TRANSITIVE))
 (2 2 (:REWRITE <-OF-0-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (2 1 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (2 1 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (2 1 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (1 1 (:TYPE-PRESCRIPTION MYQUOTEP))
 (1 1 (:TYPE-PRESCRIPTION BOUNDED-DAG-EXPRP))
 (1 1 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (1 1 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (1 1 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (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-MONOTONE))
 (1 1 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (1 1 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 )
(FIND-NODE-FOR-EXPR2-AUX-TYPE
 (1157 29 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (1073 12 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (1042 17 (:DEFINITION NAT-LISTP))
 (961 61 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (798 33 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX-2))
 (609 33 (:DEFINITION TOP-NODENUM))
 (422 184 (:REWRITE DEFAULT-CAR))
 (312 34 (:REWRITE USE-ALL-<-FOR-CAR))
 (311 19 (:REWRITE BOUNDED-DAG-EXPRP-OF-CDR-OF-CAR-WHEN-WEAK-DAGP-AUX))
 (159 103 (:REWRITE DEFAULT-<-2))
 (124 103 (:REWRITE DEFAULT-<-1))
 (120 10 (:REWRITE LEN-OF-CDR))
 (112 112 (:TYPE-PRESCRIPTION ALL-<))
 (103 103 (:REWRITE USE-ALL-<-2))
 (103 103 (:REWRITE USE-ALL-<))
 (99 99 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (99 99 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (99 99 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (99 33 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP))
 (92 92 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (90 90 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (85 5 (:REWRITE WEAK-DAGP-AUX-OF-CDR))
 (83 72 (:REWRITE DEFAULT-CDR))
 (82 82 (:TYPE-PRESCRIPTION NAT-LISTP))
 (78 51 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (75 75 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (75 75 (:TYPE-PRESCRIPTION ALL-NATP))
 (68 34 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (68 34 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (68 34 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (61 61 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (60 12 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (58 29 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-CHEAP))
 (58 29 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-AUX-CHEAP))
 (46 46 (:REWRITE USE-ALL-CONSP-2))
 (46 46 (:REWRITE USE-ALL-CONSP))
 (46 46 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (40 5 (:REWRITE ALL-<-OF-CDR))
 (39 39 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (39 39 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (39 39 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (39 39 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (39 39 (:REWRITE ALL-<-TRANSITIVE))
 (39 38 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (38 38 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (38 38 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (38 19 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (36 36 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (36 12 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (35 5 (:REWRITE PSEUDO-DAGP-AUX-OF-CDR))
 (34 34 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (34 34 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (34 34 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (33 33 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (31 31 (:REWRITE USE-ALL-NATP-2))
 (31 31 (:REWRITE USE-ALL-NATP))
 (30 15 (:REWRITE DEFAULT-+-2))
 (29 29 (:TYPE-PRESCRIPTION WEAK-DAGP))
 (29 29 (:REWRITE INTEGERP-OF-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (29 29 (:REWRITE <-OF-0-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (24 24 (:TYPE-PRESCRIPTION ALL-CONSP))
 (24 24 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (24 12 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (24 12 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (22 22 (:REWRITE PSEUDO-DAGP-AUX-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (19 19 (:TYPE-PRESCRIPTION MYQUOTEP))
 (19 19 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP-CHEAP))
 (19 19 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP-CHEAP))
 (19 19 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (19 19 (:REWRITE BOUNDED-DAG-EXPRP-MONOTONE))
 (15 15 (:REWRITE DEFAULT-+-1))
 (12 12 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (12 12 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (12 12 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (12 12 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (12 12 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (12 12 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (12 12 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (12 12 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (10 10 (:REWRITE EQUAL-OF-LEN-AND-0))
 (10 10 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (1 1 (:DEFINITION NULL))
 )
(INTEGERP-OF-FIND-NODE-FOR-EXPR2-AUX)
(FIND-NODE-FOR-EXPR2-AUX-BOUND-WHEN-PSEUDO-DAGP-AUX
 (12071 109 (:REWRITE BOUNDED-DAG-EXPRP-OF-CDR-OF-CAR-WHEN-WEAK-DAGP-AUX))
 (10572 56 (:DEFINITION WEAK-DAGP-AUX))
 (4683 77 (:REWRITE WEAK-DAGP-AUX-OF-CDR))
 (4682 129 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (4391 106 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX-2))
 (4242 53 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (4106 76 (:DEFINITION NAT-LISTP))
 (3676 160 (:REWRITE PSEUDO-DAGP-AUX-OF-CDR))
 (3593 137 (:DEFINITION NATP))
 (3285 207 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (1821 139 (:REWRITE USE-ALL-<-FOR-CAR))
 (895 381 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (734 440 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (675 164 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (648 438 (:REWRITE DEFAULT-CDR))
 (535 323 (:REWRITE DEFAULT-<-2))
 (490 245 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (490 245 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (467 467 (:TYPE-PRESCRIPTION ALL-<))
 (444 222 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-CHEAP))
 (444 222 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-AUX-CHEAP))
 (442 442 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (440 440 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (427 427 (:TYPE-PRESCRIPTION ALL-NATP))
 (425 323 (:REWRITE DEFAULT-<-1))
 (392 392 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (364 364 (:TYPE-PRESCRIPTION NAT-LISTP))
 (332 277 (:REWRITE DEFAULT-+-2))
 (323 323 (:REWRITE USE-ALL-<-2))
 (323 323 (:REWRITE USE-ALL-<))
 (318 106 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP))
 (278 139 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (277 277 (:REWRITE DEFAULT-+-1))
 (253 35 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (251 251 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (249 203 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (245 245 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (245 245 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (232 116 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (222 222 (:TYPE-PRESCRIPTION WEAK-DAGP))
 (222 222 (:REWRITE INTEGERP-OF-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (222 111 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (184 23 (:REWRITE ALL-<-OF-CDR))
 (182 164 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (164 164 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (164 164 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (164 164 (:REWRITE ALL-<-TRANSITIVE))
 (152 76 (:TYPE-PRESCRIPTION NATP-OF-TOP-NODENUM-WHEN-PSEUDO-DAGP))
 (145 53 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (139 139 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (137 137 (:REWRITE USE-ALL-NATP-2))
 (137 137 (:REWRITE USE-ALL-NATP))
 (130 130 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (122 53 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (116 116 (:TYPE-PRESCRIPTION ALISTP))
 (112 112 (:REWRITE USE-ALL-CONSP-2))
 (112 112 (:REWRITE USE-ALL-CONSP))
 (112 112 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (112 106 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (111 111 (:TYPE-PRESCRIPTION MYQUOTEP))
 (111 111 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP-CHEAP))
 (111 111 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (106 106 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (106 53 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (97 97 (:REWRITE PSEUDO-DAGP-AUX-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (96 96 (:TYPE-PRESCRIPTION ALL-CONSP))
 (85 36 (:REWRITE +-OF-+-OF---SAME))
 (81 81 (:REWRITE <-OF-0-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (77 77 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP-CHEAP))
 (75 25 (:REWRITE FOLD-CONSTS-IN-+))
 (70 35 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (70 14 (:REWRITE ALL-CONSP-OF-CDR))
 (60 48 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (53 53 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (53 53 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (49 36 (:DEFINITION FIX))
 (48 48 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (35 35 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (35 35 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (35 35 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (29 29 (:TYPE-PRESCRIPTION NATP))
 (25 25 (:REWRITE LEN-OF-CDDR-WHEN-EQUAL-OF-LEN))
 (25 25 (:REWRITE EQUAL-OF-0-AND-+-OF---ALT))
 (18 6 (:REWRITE NATP-OF-TOP-NODENUM-WHEN-PSEUDO-DAGP))
 (16 1 (:LINEAR LEN-OF-CDR-LINEAR-STRONG))
 (14 1 (:LINEAR LEN-OF-CDR-LINEAR))
 (13 13 (:REWRITE EQUAL-OF-LEN-AND-0))
 (12 12 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (7 7 (:REWRITE EQUAL-OF-NON-NATP-AND-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 )
(FIND-NODE-FOR-EXPR2
 (248 1 (:DEFINITION WEAK-DAGP-AUX))
 (122 4 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX-2))
 (108 7 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (97 4 (:DEFINITION TOP-NODENUM))
 (58 2 (:DEFINITION NATP))
 (51 2 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (44 14 (:REWRITE DEFAULT-CAR))
 (44 1 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (41 1 (:DEFINITION NAT-LISTP))
 (37 37 (:TYPE-PRESCRIPTION LEN))
 (28 14 (:TYPE-PRESCRIPTION NATP-OF-LARGEST-NON-QUOTEP))
 (28 14 (:TYPE-PRESCRIPTION ACL2-NUMBERP-OF-LARGEST-NON-QUOTEP))
 (20 10 (:TYPE-PRESCRIPTION FIND-NODE-FOR-EXPR-TYPE))
 (20 7 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (17 1 (:REWRITE WEAK-DAGP-AUX-OF-CDR))
 (17 1 (:REWRITE BOUNDED-DAG-EXPRP-OF-CDR-OF-CAR-WHEN-WEAK-DAGP-AUX))
 (16 2 (:REWRITE USE-ALL-<-FOR-CAR))
 (12 7 (:REWRITE DEFAULT-<-2))
 (12 4 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP))
 (12 1 (:REWRITE LEN-OF-CDR))
 (11 11 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (11 11 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (11 11 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (10 10 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (10 10 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (10 5 (:TYPE-PRESCRIPTION FIND-NODE-FOR-EXPR2-AUX-TYPE))
 (7 7 (:REWRITE USE-ALL-<-2))
 (7 7 (:REWRITE USE-ALL-<))
 (7 7 (:REWRITE DEFAULT-<-1))
 (7 7 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (7 1 (:REWRITE PSEUDO-DAGP-AUX-OF-CDR))
 (6 6 (:TYPE-PRESCRIPTION NAT-LISTP))
 (6 6 (:TYPE-PRESCRIPTION ALL-<))
 (6 6 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (6 3 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (5 5 (:TYPE-PRESCRIPTION ALL-NATP))
 (5 5 (:REWRITE USE-ALL-CONSP-2))
 (5 5 (:REWRITE USE-ALL-CONSP))
 (5 5 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (5 5 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (5 1 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (4 4 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (4 2 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (4 2 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (4 2 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-CHEAP))
 (4 2 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-AUX-CHEAP))
 (4 2 (:REWRITE DEFAULT-+-2))
 (4 2 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 1 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (2 2 (:TYPE-PRESCRIPTION WEAK-DAGP))
 (2 2 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (2 2 (:TYPE-PRESCRIPTION ALL-CONSP))
 (2 2 (:REWRITE USE-ALL-NATP-2))
 (2 2 (:REWRITE USE-ALL-NATP))
 (2 2 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (2 2 (:REWRITE SYMBOLP-OF-CAR-WHEN-BOUNDED-DAG-EXPRP))
 (2 2 (:REWRITE PSEUDO-DAGP-AUX-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (2 2 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (2 2 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (2 2 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (2 2 (:REWRITE INTEGERP-OF-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (2 2 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (2 2 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (2 2 (:REWRITE ALL-<-TRANSITIVE))
 (2 2 (:REWRITE <-OF-0-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (2 1 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (2 1 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (2 1 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (1 1 (:TYPE-PRESCRIPTION MYQUOTEP))
 (1 1 (:TYPE-PRESCRIPTION BOUNDED-DAG-EXPRP))
 (1 1 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (1 1 (:REWRITE TRUE-LISTP-OF-DARGS-WHEN-BOUNDED-DAG-EXPRP-AND-CONSP))
 (1 1 (:REWRITE TRUE-LISTP-OF-DARGS-BETTER))
 (1 1 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (1 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (1 1 (:REWRITE EQUAL-OF-LEN-AND-0))
 (1 1 (:REWRITE DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (1 1 (:REWRITE DAG-EXPRP-WHEN-BOUNDED-DAG-EXPRP))
 (1 1 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (1 1 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (1 1 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (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-MONOTONE))
 (1 1 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (1 1 (:REWRITE ALL-DARGP-WHEN-BOUNDED-DARG-LISTP))
 (1 1 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 )
(FIND-NODE-FOR-EXPR2-TYPE
 (252 2 (:DEFINITION FIND-NODE-FOR-EXPR2-AUX))
 (248 1 (:DEFINITION WEAK-DAGP-AUX))
 (236 18 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (132 2 (:REWRITE <-OF-LARGEST-NON-QUOTEP))
 (122 4 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX-2))
 (104 4 (:DEFINITION FIND-NODE-FOR-EXPR))
 (97 4 (:DEFINITION TOP-NODENUM))
 (82 82 (:TYPE-PRESCRIPTION LEN))
 (61 25 (:REWRITE DEFAULT-CAR))
 (52 2 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-<))
 (51 2 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (44 1 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (41 1 (:DEFINITION NAT-LISTP))
 (40 4 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (35 19 (:REWRITE DEFAULT-<-2))
 (29 19 (:REWRITE DEFAULT-<-1))
 (29 16 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (26 26 (:TYPE-PRESCRIPTION ALL-DARGP))
 (26 13 (:TYPE-PRESCRIPTION NATP-OF-LARGEST-NON-QUOTEP))
 (26 13 (:TYPE-PRESCRIPTION ACL2-NUMBERP-OF-LARGEST-NON-QUOTEP))
 (21 15 (:REWRITE DEFAULT-CDR))
 (20 20 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (20 20 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (20 20 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (19 19 (:REWRITE USE-ALL-<-2))
 (19 19 (:REWRITE USE-ALL-<))
 (18 18 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (18 15 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (18 9 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (18 2 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DAG-EXPRP))
 (18 2 (:REWRITE BOUNDED-DARG-LISTP-OF-DARGS-WHEN-BOUNDED-DAG-EXPRP))
 (18 2 (:REWRITE BOUNDED-DARG-LISTP-OF-DARGS-WHEN-<-SIMPLE))
 (18 2 (:REWRITE <-OF-LARGEST-NON-QUOTEP-OF-DARGS))
 (17 17 (:TYPE-PRESCRIPTION BOUNDED-DAG-EXPRP))
 (17 1 (:REWRITE WEAK-DAGP-AUX-OF-CDR))
 (17 1 (:REWRITE BOUNDED-DAG-EXPRP-OF-CDR-OF-CAR-WHEN-WEAK-DAGP-AUX))
 (16 16 (:REWRITE USE-ALL-CONSP-2))
 (16 16 (:REWRITE USE-ALL-CONSP))
 (16 16 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (16 2 (:REWRITE USE-ALL-<-FOR-CAR))
 (12 12 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (12 4 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP))
 (12 2 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (12 1 (:REWRITE LEN-OF-CDR))
 (10 10 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (10 10 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (10 10 (:TYPE-PRESCRIPTION ALL-<))
 (9 9 (:TYPE-PRESCRIPTION MYQUOTEP))
 (9 9 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP-CHEAP))
 (9 9 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP-CHEAP))
 (9 9 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (9 9 (:REWRITE BOUNDED-DAG-EXPRP-MONOTONE))
 (7 1 (:REWRITE PSEUDO-DAGP-AUX-OF-CDR))
 (6 6 (:TYPE-PRESCRIPTION NAT-LISTP))
 (5 5 (:TYPE-PRESCRIPTION ALL-NATP))
 (5 5 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (5 1 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (4 4 (:TYPE-PRESCRIPTION BOUNDED-DARG-LISTP))
 (4 4 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (4 4 (:TYPE-PRESCRIPTION ALL-CONSP))
 (4 4 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (4 4 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (4 4 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (4 4 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (4 4 (:REWRITE ALL-<-TRANSITIVE))
 (4 2 (:REWRITE LARGEST-NON-QUOTEP-WHEN-ALL-MYQUOTEP-CHEAP))
 (4 2 (:REWRITE LARGEST-NON-QUOTEP-WHEN-ALL-CONSP-CHEAP))
 (4 2 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (4 2 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (4 2 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-CHEAP))
 (4 2 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-AUX-CHEAP))
 (4 2 (:REWRITE DEFAULT-+-2))
 (4 2 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (4 2 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (3 3 (:REWRITE USE-ALL-NATP-2))
 (3 3 (:REWRITE USE-ALL-NATP))
 (3 3 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (3 3 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (3 1 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (2 2 (:TYPE-PRESCRIPTION WEAK-DAGP))
 (2 2 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (2 2 (:REWRITE PSEUDO-DAGP-AUX-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (2 2 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (2 2 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (2 2 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (2 2 (:REWRITE INTEGERP-OF-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DAG-EXPRP-GEN))
 (2 2 (:REWRITE BOUNDED-DARG-LISTP-MONOTONE))
 (2 2 (:REWRITE <-OF-0-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (2 1 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (2 1 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (1 1 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (1 1 (:REWRITE EQUAL-OF-LEN-AND-0))
 (1 1 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (1 1 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (1 1 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (1 1 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (1 1 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 )
(INTEGERP-OF-FIND-NODE-FOR-EXPR2)
(NONNEG-OF-FIND-NODE-FOR-EXPR2)
(FIND-NODE-FOR-EXPR2-BOUND-WHEN-PSEUDO-DAGP-AUX
 (2204 37 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (1622 23 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (1411 10 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (1387 16 (:DEFINITION NAT-LISTP))
 (1196 23 (:DEFINITION NATP))
 (900 81 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (899 29 (:REWRITE USE-ALL-<-FOR-CAR))
 (734 31 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (312 312 (:TYPE-PRESCRIPTION LEN))
 (235 106 (:REWRITE DEFAULT-CAR))
 (190 26 (:REWRITE DEFAULT-CDR))
 (177 3 (:REWRITE PSEUDO-DAGP-AUX-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (149 59 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (148 10 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (144 72 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (137 83 (:REWRITE DEFAULT-<-2))
 (132 2 (:REWRITE <-OF-LARGEST-NON-QUOTEP))
 (117 65 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (96 96 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (93 83 (:REWRITE DEFAULT-<-1))
 (91 91 (:TYPE-PRESCRIPTION ALL-<))
 (83 83 (:REWRITE USE-ALL-<-2))
 (83 83 (:REWRITE USE-ALL-<))
 (81 81 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (78 78 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (78 78 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (78 78 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (74 74 (:TYPE-PRESCRIPTION ALISTP))
 (68 68 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (62 31 (:TYPE-PRESCRIPTION FIND-NODE-FOR-EXPR2-TYPE))
 (59 59 (:TYPE-PRESCRIPTION ALL-NATP))
 (59 59 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (58 58 (:TYPE-PRESCRIPTION NATP))
 (58 29 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (58 29 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (58 29 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-CHEAP))
 (58 29 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-AUX-CHEAP))
 (58 29 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (52 2 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-<))
 (48 48 (:TYPE-PRESCRIPTION NAT-LISTP))
 (46 23 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (31 31 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (31 31 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (31 31 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (31 31 (:REWRITE ALL-<-TRANSITIVE))
 (29 29 (:TYPE-PRESCRIPTION WEAK-DAGP))
 (29 29 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (29 29 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (29 29 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (29 29 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (29 29 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (29 29 (:REWRITE INTEGERP-OF-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (29 29 (:REWRITE <-OF-0-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (23 23 (:REWRITE USE-ALL-NATP-2))
 (23 23 (:REWRITE USE-ALL-NATP))
 (20 20 (:TYPE-PRESCRIPTION ALL-DARGP))
 (20 10 (:TYPE-PRESCRIPTION NATP-OF-LARGEST-NON-QUOTEP))
 (20 10 (:TYPE-PRESCRIPTION ACL2-NUMBERP-OF-LARGEST-NON-QUOTEP))
 (20 10 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (18 2 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DAG-EXPRP))
 (18 2 (:REWRITE BOUNDED-DARG-LISTP-OF-DARGS-WHEN-BOUNDED-DAG-EXPRP))
 (18 2 (:REWRITE BOUNDED-DARG-LISTP-OF-DARGS-WHEN-<-SIMPLE))
 (18 2 (:REWRITE <-OF-LARGEST-NON-QUOTEP-OF-DARGS))
 (16 16 (:TYPE-PRESCRIPTION BOUNDED-DAG-EXPRP))
 (16 8 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (12 6 (:TYPE-PRESCRIPTION NATP-OF-TOP-NODENUM-WHEN-PSEUDO-DAGP))
 (12 2 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (10 10 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (9 9 (:REWRITE USE-ALL-CONSP-2))
 (9 9 (:REWRITE USE-ALL-CONSP))
 (8 8 (:TYPE-PRESCRIPTION MYQUOTEP))
 (8 8 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP-CHEAP))
 (8 8 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP-CHEAP))
 (8 8 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (8 8 (:REWRITE BOUNDED-DAG-EXPRP-MONOTONE))
 (8 4 (:TYPE-PRESCRIPTION FIND-NODE-FOR-EXPR-TYPE))
 (6 3 (:REWRITE LARGEST-NON-QUOTEP-WHEN-ALL-MYQUOTEP-CHEAP))
 (6 3 (:REWRITE LARGEST-NON-QUOTEP-WHEN-ALL-CONSP-CHEAP))
 (5 5 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (4 4 (:TYPE-PRESCRIPTION BOUNDED-DARG-LISTP))
 (4 4 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (4 2 (:REWRITE IFF-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (4 2 (:REWRITE CAR-WHEN-ALISTP-IFF-CHEAP))
 (4 2 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (3 3 (:TYPE-PRESCRIPTION ALL-CONSP))
 (2 2 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2 2 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DAG-EXPRP-GEN))
 (2 2 (:REWRITE BOUNDED-DARG-LISTP-MONOTONE))
 )
(FIND-NODE-FOR-EXPR2-OF-NIL
 (14 1 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (5 5 (:TYPE-PRESCRIPTION LEN))
 (2 1 (:REWRITE LARGEST-NON-QUOTEP-WHEN-ALL-MYQUOTEP-CHEAP))
 (2 1 (:REWRITE LARGEST-NON-QUOTEP-WHEN-ALL-CONSP-CHEAP))
 (2 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (1 1 (:TYPE-PRESCRIPTION ALL-CONSP))
 (1 1 (:REWRITE USE-ALL-CONSP-2))
 (1 1 (:REWRITE USE-ALL-CONSP))
 (1 1 (:REWRITE USE-ALL-<-2))
 (1 1 (:REWRITE USE-ALL-<))
 (1 1 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (1 1 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (1 1 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (1 1 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 )
(ADD-TO-DAG
 (248 1 (:DEFINITION WEAK-DAGP-AUX))
 (122 4 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX-2))
 (108 7 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (58 2 (:DEFINITION NATP))
 (51 2 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (44 13 (:REWRITE DEFAULT-CAR))
 (44 1 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (41 1 (:DEFINITION NAT-LISTP))
 (39 34 (:TYPE-PRESCRIPTION NATP-OF-TOP-NODENUM-WHEN-PSEUDO-DAGP))
 (37 37 (:TYPE-PRESCRIPTION LEN))
 (20 7 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (17 1 (:REWRITE WEAK-DAGP-AUX-OF-CDR))
 (17 1 (:REWRITE BOUNDED-DAG-EXPRP-OF-CDR-OF-CAR-WHEN-WEAK-DAGP-AUX))
 (16 2 (:REWRITE USE-ALL-<-FOR-CAR))
 (15 15 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (12 7 (:REWRITE DEFAULT-<-2))
 (12 4 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP))
 (12 1 (:REWRITE LEN-OF-CDR))
 (11 11 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (11 11 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (11 11 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (10 10 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (7 7 (:REWRITE USE-ALL-<-2))
 (7 7 (:REWRITE USE-ALL-<))
 (7 7 (:REWRITE DEFAULT-<-1))
 (7 7 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (7 7 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (7 4 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (7 1 (:REWRITE PSEUDO-DAGP-AUX-OF-CDR))
 (6 6 (:TYPE-PRESCRIPTION NAT-LISTP))
 (6 6 (:TYPE-PRESCRIPTION ALL-<))
 (5 5 (:TYPE-PRESCRIPTION ALL-NATP))
 (5 5 (:REWRITE USE-ALL-CONSP-2))
 (5 5 (:REWRITE USE-ALL-CONSP))
 (5 5 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (5 5 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (5 1 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (4 4 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (4 2 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (4 2 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (4 2 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-CHEAP))
 (4 2 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-AUX-CHEAP))
 (4 2 (:REWRITE DEFAULT-+-2))
 (4 2 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 1 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (2 2 (:TYPE-PRESCRIPTION WEAK-DAGP))
 (2 2 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (2 2 (:TYPE-PRESCRIPTION ALL-CONSP))
 (2 2 (:REWRITE USE-ALL-NATP-2))
 (2 2 (:REWRITE USE-ALL-NATP))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2 2 (:REWRITE PSEUDO-DAGP-AUX-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (2 2 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (2 2 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (2 2 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (2 2 (:REWRITE INTEGERP-OF-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (2 2 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (2 2 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (2 2 (:REWRITE ALL-<-TRANSITIVE))
 (2 2 (:REWRITE <-OF-0-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (2 1 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (2 1 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (2 1 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (1 1 (:TYPE-PRESCRIPTION MYQUOTEP))
 (1 1 (:TYPE-PRESCRIPTION BOUNDED-DAG-EXPRP))
 (1 1 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (1 1 (:REWRITE EQUAL-OF-LEN-AND-0))
 (1 1 (:REWRITE DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (1 1 (:REWRITE DAG-EXPRP-WHEN-BOUNDED-DAG-EXPRP))
 (1 1 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (1 1 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (1 1 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (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-MONOTONE))
 (1 1 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (1 1 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (1 1 (:REWRITE ALISTP-WHEN-PSEUDO-DAGP-AUX))
 (1 1 (:REWRITE ALISTP-WHEN-BOUNDED-NATP-ALISTP))
 )
(NATP-OF-MV-NTH-0-OF-ADD-TO-DAG
 (220 9 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX-2))
 (175 12 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (125 5 (:DEFINITION NATP))
 (102 4 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (88 26 (:REWRITE DEFAULT-CAR))
 (88 2 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (82 2 (:DEFINITION NAT-LISTP))
 (35 11 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (34 2 (:REWRITE WEAK-DAGP-AUX-OF-CDR))
 (34 2 (:REWRITE BOUNDED-DAG-EXPRP-OF-CDR-OF-CAR-WHEN-WEAK-DAGP-AUX))
 (32 4 (:REWRITE USE-ALL-<-FOR-CAR))
 (27 9 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP))
 (22 22 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (21 21 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (21 2 (:REWRITE LEN-OF-CDR))
 (20 20 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (20 20 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (20 20 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (20 13 (:REWRITE DEFAULT-<-2))
 (14 14 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (14 8 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (14 2 (:REWRITE PSEUDO-DAGP-AUX-OF-CDR))
 (13 13 (:REWRITE USE-ALL-<-2))
 (13 13 (:REWRITE USE-ALL-<))
 (13 13 (:REWRITE DEFAULT-<-1))
 (12 12 (:TYPE-PRESCRIPTION NAT-LISTP))
 (12 12 (:TYPE-PRESCRIPTION ALL-<))
 (12 12 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (12 11 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (10 10 (:TYPE-PRESCRIPTION ALL-NATP))
 (10 6 (:REWRITE DEFAULT-+-2))
 (10 2 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (9 9 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (8 8 (:REWRITE USE-ALL-CONSP-2))
 (8 8 (:REWRITE USE-ALL-CONSP))
 (8 8 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (8 4 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (8 4 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (8 4 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-CHEAP))
 (8 4 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-AUX-CHEAP))
 (8 4 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (6 6 (:REWRITE DEFAULT-CDR))
 (6 6 (:REWRITE DEFAULT-+-1))
 (6 2 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (5 5 (:REWRITE USE-ALL-NATP-2))
 (5 5 (:REWRITE USE-ALL-NATP))
 (5 5 (:REWRITE PSEUDO-DAGP-AUX-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (5 5 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (5 5 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (4 4 (:TYPE-PRESCRIPTION WEAK-DAGP))
 (4 4 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (4 4 (:TYPE-PRESCRIPTION ALL-CONSP))
 (4 4 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (4 4 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (4 4 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (4 4 (:REWRITE INTEGERP-OF-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (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))
 (4 4 (:REWRITE <-OF-0-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (4 2 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (4 2 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (4 2 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (3 3 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2 2 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (2 2 (:TYPE-PRESCRIPTION MYQUOTEP))
 (2 2 (:TYPE-PRESCRIPTION BOUNDED-DAG-EXPRP))
 (2 2 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (2 2 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (2 2 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (2 2 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (2 2 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP-CHEAP))
 (2 2 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (2 2 (:REWRITE BOUNDED-DAG-EXPRP-MONOTONE))
 (2 2 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (2 2 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (1 1 (:REWRITE EQUAL-OF-LEN-AND-0))
 (1 1 (:DEFINITION NULL))
 )
(WEAK-DAGP-AUX-OF-MV-NTH-1-OF-ADD-TO-DAG
 (874 24 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-<))
 (817 362 (:REWRITE DEFAULT-CAR))
 (678 52 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (584 20 (:DEFINITION NATP))
 (554 24 (:REWRITE BOUNDED-DARG-LISTP-OF-DARGS-WHEN-<-SIMPLE))
 (527 17 (:REWRITE ALL-DARGP-WHEN-NOT-CONSP))
 (522 52 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (514 20 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (468 432 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (444 10 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (432 432 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (432 432 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (416 30 (:REWRITE DAG-EXPRP-OF-CDR-OF-CAR-WHEN-WEAK-DAGP-AUX))
 (414 10 (:DEFINITION NAT-LISTP))
 (374 153 (:REWRITE DEFAULT-CDR))
 (366 40 (:REWRITE BOUNDED-DAG-EXPRP-OF-CDR-OF-CAR-WHEN-WEAK-DAGP-AUX))
 (345 17 (:REWRITE ALL-DARGP-OF-DARGS-WHEN-DAG-EXPRP))
 (328 22 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DAG-EXPRP))
 (327 14 (:REWRITE TRUE-LISTP-OF-DARGS-WHEN-DAG-EXPRP))
 (307 164 (:REWRITE DEFAULT-<-2))
 (283 166 (:REWRITE DEFAULT-+-2))
 (265 95 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP))
 (234 234 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (210 30 (:REWRITE DAG-EXPRP-OF-CDR-OF-CAR-WHEN-WEAK-DAGP))
 (173 10 (:REWRITE WEAK-DAGP-AUX-OF-CDR))
 (172 172 (:REWRITE USE-ALL-CONSP-2))
 (172 172 (:REWRITE USE-ALL-CONSP))
 (172 172 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (166 166 (:REWRITE DEFAULT-+-1))
 (164 164 (:REWRITE USE-ALL-<-2))
 (164 164 (:REWRITE USE-ALL-<))
 (164 164 (:REWRITE DEFAULT-<-1))
 (160 20 (:REWRITE USE-ALL-<-FOR-CAR))
 (144 72 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (132 18 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (124 124 (:TYPE-PRESCRIPTION ALL-<))
 (113 113 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (105 91 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (93 93 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (91 55 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (90 30 (:REWRITE WEAK-DAGP-WHEN-PSEUDO-DAGP))
 (80 80 (:TYPE-PRESCRIPTION WEAK-DAGP))
 (77 10 (:REWRITE PSEUDO-DAGP-AUX-OF-CDR))
 (72 72 (:TYPE-PRESCRIPTION MYQUOTEP))
 (64 64 (:REWRITE PSEUDO-DAGP-AUX-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (64 4 (:LINEAR LEN-OF-CDR-LINEAR-STRONG))
 (62 62 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP-CHEAP))
 (62 62 (:REWRITE BOUNDED-DAG-EXPRP-MONOTONE))
 (60 60 (:TYPE-PRESCRIPTION NAT-LISTP))
 (60 14 (:REWRITE FOLD-CONSTS-IN-+))
 (57 57 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (56 4 (:LINEAR LEN-OF-CDR-LINEAR))
 (52 52 (:REWRITE DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (52 52 (:REWRITE DAG-EXPRP-WHEN-BOUNDED-DAG-EXPRP))
 (52 52 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (52 52 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (52 52 (:REWRITE ALL-<-TRANSITIVE))
 (52 10 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (50 50 (:TYPE-PRESCRIPTION ALL-NATP))
 (42 42 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (40 20 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (40 20 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (40 20 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-CHEAP))
 (40 20 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-AUX-CHEAP))
 (40 20 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (40 20 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (34 17 (:REWRITE ALL-DARGP-WHEN-ALL-MYQUOTEP-CHEAP))
 (30 30 (:REWRITE WEAK-DAGP-WHEN-PSEUDO-DAGP-AUX))
 (30 10 (:REWRITE EQUAL-OF-0-AND-+-OF---ALT))
 (30 10 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (27 27 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (26 23 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (25 25 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (25 25 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 (24 6 (:REWRITE ALL-MYQUOTEP-WHEN-NOT-CONSP))
 (22 22 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DAG-EXPRP-GEN))
 (20 20 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (20 20 (:TYPE-PRESCRIPTION ALL-CONSP))
 (20 20 (:REWRITE USE-ALL-NATP-2))
 (20 20 (:REWRITE USE-ALL-NATP))
 (20 20 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (20 20 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (20 20 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (20 20 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (20 20 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (20 20 (:REWRITE INTEGERP-OF-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (20 20 (:REWRITE <-OF-0-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (20 10 (:REWRITE SYMBOLP-OF-CDAR-WHEN-WEAK-DAGP-AUX-CHEAP))
 (20 10 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (20 10 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (17 17 (:REWRITE ALL-DARGP-WHEN-NOT-CONSP-CHEAP))
 (14 14 (:REWRITE TRUE-LISTP-OF-DARGS-WHEN-BOUNDED-DAG-EXPRP-AND-CONSP))
 (14 14 (:REWRITE TRUE-LISTP-OF-DARGS-BETTER))
 (12 12 (:REWRITE SYMBOLP-OF-CAR-WHEN-BOUNDED-DAG-EXPRP))
 (12 12 (:REWRITE LEN-OF-CDDR-WHEN-EQUAL-OF-LEN))
 (11 10 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (11 10 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (10 10 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (10 10 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (10 10 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (10 10 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (10 10 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (10 10 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (8 4 (:REWRITE UNICITY-OF-0))
 (4 4 (:DEFINITION FIX))
 (3 3 (:DEFINITION NULL))
 )
(PSEUDO-DAGP-AUX-OF-MV-NTH-1-OF-ADD-TO-DAG
 (2461 24 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP))
 (2048 39 (:REWRITE PSEUDO-DAGP-AUX-OF-CDR))
 (1543 40 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (1154 17 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (1103 17 (:DEFINITION NAT-LISTP))
 (909 24 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX-2))
 (837 242 (:REWRITE DEFAULT-CAR))
 (783 68 (:REWRITE USE-ALL-<-FOR-CAR))
 (307 68 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (288 18 (:REWRITE <-OF-+-OF---AND-0-ARG1))
 (285 17 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (266 29 (:REWRITE LEN-OF-CDR))
 (212 30 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (204 204 (:TYPE-PRESCRIPTION ALL-<))
 (177 134 (:REWRITE DEFAULT-<-2))
 (162 81 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (144 84 (:REWRITE DEFAULT-CDR))
 (142 136 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (136 68 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (134 134 (:REWRITE USE-ALL-<-2))
 (134 134 (:REWRITE USE-ALL-<))
 (134 134 (:REWRITE DEFAULT-<-1))
 (131 131 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (130 130 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (130 40 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (124 62 (:TYPE-PRESCRIPTION FIND-NODE-FOR-EXPR2-TYPE))
 (111 111 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (102 102 (:TYPE-PRESCRIPTION NAT-LISTP))
 (100 100 (:TYPE-PRESCRIPTION ALL-NATP))
 (100 96 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (91 64 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (90 45 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (90 45 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (90 45 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-CHEAP))
 (90 45 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-AUX-CHEAP))
 (88 77 (:REWRITE DEFAULT-+-2))
 (81 81 (:TYPE-PRESCRIPTION ALISTP))
 (77 77 (:REWRITE DEFAULT-+-1))
 (76 76 (:REWRITE USE-ALL-CONSP-2))
 (76 76 (:REWRITE USE-ALL-CONSP))
 (72 72 (:TYPE-PRESCRIPTION ALL-CONSP))
 (68 68 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (68 68 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (68 68 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (68 68 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (68 68 (:REWRITE ALL-<-TRANSITIVE))
 (65 13 (:REWRITE ALL-CONSP-OF-CDR))
 (64 32 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (61 36 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (60 30 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (58 58 (:REWRITE USE-ALL-NATP-2))
 (58 58 (:REWRITE USE-ALL-NATP))
 (51 51 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (50 50 (:REWRITE <-OF-0-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (45 45 (:TYPE-PRESCRIPTION WEAK-DAGP))
 (45 45 (:TYPE-PRESCRIPTION NATP))
 (45 45 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (45 45 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (45 45 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (45 45 (:REWRITE INTEGERP-OF-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (36 36 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (34 17 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (32 32 (:TYPE-PRESCRIPTION MYQUOTEP))
 (32 32 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP-CHEAP))
 (32 32 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (30 30 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (30 30 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (25 25 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (24 12 (:REWRITE +-OF-+-OF---SAME))
 (23 23 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP-CHEAP))
 (17 17 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (16 8 (:REWRITE WEAK-DAGP-AUX-OF-CDR))
 (8 8 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (3 3 (:REWRITE EQUAL-OF-LEN-AND-0))
 (2 2 (:REWRITE LEN-OF-CDDR-WHEN-EQUAL-OF-LEN))
 (2 2 (:REWRITE EQUAL-OF-0-AND-+-OF---ALT))
 )
(PSEUDO-DAGP-OF-MV-NTH-1-OF-ADD-TO-DAG
 (2557 46 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (1439 10 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (1409 10 (:DEFINITION NAT-LISTP))
 (1339 155 (:REWRITE DEFAULT-CAR))
 (1048 10 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (415 28 (:REWRITE USE-ALL-<-FOR-CAR))
 (265 46 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (238 87 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (219 28 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (201 201 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (186 93 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (166 166 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (151 89 (:REWRITE DEFAULT-<-2))
 (141 26 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (140 70 (:TYPE-PRESCRIPTION FIND-NODE-FOR-EXPR2-TYPE))
 (135 135 (:TYPE-PRESCRIPTION NATP))
 (129 129 (:TYPE-PRESCRIPTION WEAK-DAGP-AUX))
 (125 119 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (122 122 (:REWRITE USE-ALL-CONSP-2))
 (122 122 (:REWRITE USE-ALL-CONSP))
 (118 59 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (118 59 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (118 59 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-CHEAP))
 (118 59 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-AUX-CHEAP))
 (105 105 (:TYPE-PRESCRIPTION ALL-NATP))
 (93 93 (:TYPE-PRESCRIPTION ALISTP))
 (92 46 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (92 46 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (89 89 (:REWRITE USE-ALL-<-2))
 (89 89 (:REWRITE USE-ALL-<))
 (89 89 (:REWRITE DEFAULT-<-1))
 (84 84 (:TYPE-PRESCRIPTION ALL-<))
 (79 79 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (60 60 (:TYPE-PRESCRIPTION NAT-LISTP))
 (59 59 (:TYPE-PRESCRIPTION WEAK-DAGP))
 (59 59 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (59 59 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (59 59 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (59 59 (:REWRITE INTEGERP-OF-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (56 28 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (52 52 (:TYPE-PRESCRIPTION ALL-CONSP))
 (46 46 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (46 46 (:REWRITE USE-ALL-NATP-2))
 (46 46 (:REWRITE USE-ALL-NATP))
 (46 46 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (41 41 (:REWRITE DEFAULT-+-2))
 (41 41 (:REWRITE DEFAULT-+-1))
 (28 28 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (28 28 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (28 28 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (28 28 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (28 28 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (28 28 (:REWRITE ALL-<-TRANSITIVE))
 (28 28 (:REWRITE <-OF-0-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (26 26 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (20 10 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (20 6 (:REWRITE BOUNDED-DAG-EXPRP-MONOTONE))
 (17 12 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (12 6 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (10 10 (:REWRITE DEFAULT-CDR))
 (10 10 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (10 5 (:TYPE-PRESCRIPTION NATP-OF-TOP-NODENUM-WHEN-PSEUDO-DAGP))
 (6 6 (:TYPE-PRESCRIPTION MYQUOTEP))
 (6 6 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP-CHEAP))
 (6 6 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP-CHEAP))
 (6 6 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 )
(WEAK-DAGP-AUX-OF-MV-NTH-1-OF-ADD-TO-DAG-ALT
 (368 14 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX-2))
 (220 14 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (176 6 (:DEFINITION NATP))
 (157 45 (:REWRITE DEFAULT-CAR))
 (155 6 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (134 3 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (125 3 (:DEFINITION NAT-LISTP))
 (57 12 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (57 3 (:REWRITE WEAK-DAGP-AUX-OF-CDR))
 (57 3 (:REWRITE BOUNDED-DAG-EXPRP-OF-CDR-OF-CAR-WHEN-WEAK-DAGP-AUX))
 (48 6 (:REWRITE USE-ALL-<-FOR-CAR))
 (42 14 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP))
 (38 26 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (36 3 (:REWRITE LEN-OF-CDR))
 (35 3 (:REWRITE PSEUDO-DAGP-AUX-OF-CDR))
 (34 34 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (34 34 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (28 17 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (26 26 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (26 26 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (26 10 (:REWRITE DEFAULT-+-2))
 (23 23 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (22 13 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (20 14 (:REWRITE DEFAULT-<-2))
 (19 3 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (18 18 (:TYPE-PRESCRIPTION NAT-LISTP))
 (18 18 (:TYPE-PRESCRIPTION ALL-<))
 (15 15 (:TYPE-PRESCRIPTION ALL-NATP))
 (14 14 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (14 14 (:REWRITE USE-ALL-<-2))
 (14 14 (:REWRITE USE-ALL-<))
 (14 14 (:REWRITE DEFAULT-<-1))
 (14 14 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (12 10 (:REWRITE DEFAULT-CDR))
 (12 6 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (12 6 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (12 6 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-CHEAP))
 (12 6 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-AUX-CHEAP))
 (12 6 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (12 6 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (10 10 (:REWRITE PSEUDO-DAGP-AUX-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (10 10 (:REWRITE DEFAULT-+-1))
 (9 3 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (9 3 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (8 8 (:REWRITE USE-ALL-CONSP-2))
 (8 8 (:REWRITE USE-ALL-CONSP))
 (8 8 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (6 6 (:TYPE-PRESCRIPTION WEAK-DAGP))
 (6 6 (:TYPE-PRESCRIPTION MYQUOTEP))
 (6 6 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (6 6 (:TYPE-PRESCRIPTION ALL-CONSP))
 (6 6 (:REWRITE USE-ALL-NATP-2))
 (6 6 (:REWRITE USE-ALL-NATP))
 (6 6 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (6 6 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (6 6 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (6 6 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (6 6 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (6 6 (:REWRITE INTEGERP-OF-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (6 6 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP-CHEAP))
 (6 6 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (6 6 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (6 6 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (6 6 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (6 6 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (6 6 (:REWRITE ALL-<-TRANSITIVE))
 (6 6 (:REWRITE <-OF-0-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (6 3 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (6 3 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (5 5 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP-CHEAP))
 (5 3 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (5 3 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (3 3 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (3 3 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (3 3 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (3 3 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (3 3 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (3 3 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (3 3 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (3 1 (:REWRITE EQUAL-OF-LEN-AND-0))
 )
(ADD-TO-DAG-BOUND
 (1806 30 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (1002 6 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (984 6 (:DEFINITION NAT-LISTP))
 (768 96 (:REWRITE DEFAULT-CAR))
 (762 6 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (264 18 (:REWRITE USE-ALL-<-FOR-CAR))
 (147 26 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (142 71 (:TYPE-PRESCRIPTION FIND-NODE-FOR-EXPR2-TYPE))
 (138 18 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (137 54 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (123 123 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (116 58 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (110 110 (:TYPE-PRESCRIPTION WEAK-DAGP-AUX))
 (104 60 (:REWRITE DEFAULT-<-2))
 (98 98 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (93 93 (:TYPE-PRESCRIPTION NATP))
 (87 84 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (82 60 (:REWRITE DEFAULT-<-1))
 (79 14 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (78 39 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (78 39 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (78 39 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-CHEAP))
 (78 39 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-AUX-CHEAP))
 (69 69 (:TYPE-PRESCRIPTION ALL-NATP))
 (69 69 (:REWRITE USE-ALL-CONSP-2))
 (69 69 (:REWRITE USE-ALL-CONSP))
 (60 60 (:REWRITE USE-ALL-<-2))
 (60 60 (:REWRITE USE-ALL-<))
 (60 30 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (58 58 (:TYPE-PRESCRIPTION ALISTP))
 (58 58 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (56 25 (:REWRITE DEFAULT-+-2))
 (54 54 (:TYPE-PRESCRIPTION ALL-<))
 (52 26 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (39 39 (:TYPE-PRESCRIPTION WEAK-DAGP))
 (39 39 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (39 39 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (39 39 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (39 39 (:REWRITE INTEGERP-OF-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (36 36 (:TYPE-PRESCRIPTION NAT-LISTP))
 (36 18 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (30 30 (:REWRITE USE-ALL-NATP-2))
 (30 30 (:REWRITE USE-ALL-NATP))
 (28 28 (:TYPE-PRESCRIPTION ALL-CONSP))
 (28 3 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (26 26 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (26 26 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (25 25 (:REWRITE DEFAULT-+-1))
 (18 18 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (18 18 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (18 18 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (18 18 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (18 18 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (18 18 (:REWRITE ALL-<-TRANSITIVE))
 (18 18 (:REWRITE <-OF-0-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (14 14 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (12 6 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (6 6 (:REWRITE DEFAULT-CDR))
 (6 6 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 )
(ADD-TO-DAG-BOUND3
 (256 122 (:TYPE-PRESCRIPTION NATP-OF-TOP-NODENUM-WHEN-PSEUDO-DAGP))
 (187 15 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (150 3 (:REWRITE USE-ALL-<-FOR-CAR))
 (143 3 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (124 124 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (116 58 (:TYPE-PRESCRIPTION FIND-NODE-FOR-EXPR2-TYPE))
 (111 2 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (110 20 (:REWRITE DEFAULT-CAR))
 (109 1 (:DEFINITION PSEUDO-DAGP))
 (60 60 (:TYPE-PRESCRIPTION WEAK-DAGP-AUX))
 (58 2 (:DEFINITION NATP))
 (51 2 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (46 14 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (44 1 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (41 1 (:DEFINITION NAT-LISTP))
 (39 13 (:REWRITE DEFAULT-<-1))
 (24 22 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (24 13 (:REWRITE DEFAULT-<-2))
 (22 22 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (22 22 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (19 7 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (16 8 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (15 15 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (13 13 (:REWRITE USE-ALL-<-2))
 (13 13 (:REWRITE USE-ALL-<))
 (10 2 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (9 9 (:TYPE-PRESCRIPTION ALL-<))
 (9 9 (:REWRITE USE-ALL-CONSP-2))
 (9 9 (:REWRITE USE-ALL-CONSP))
 (9 9 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (9 9 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (8 8 (:TYPE-PRESCRIPTION ALISTP))
 (6 6 (:TYPE-PRESCRIPTION NAT-LISTP))
 (6 3 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (5 5 (:TYPE-PRESCRIPTION ALL-NATP))
 (4 4 (:TYPE-PRESCRIPTION ALL-CONSP))
 (4 2 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (4 2 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (4 2 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-CHEAP))
 (4 2 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-AUX-CHEAP))
 (4 2 (:REWRITE DEFAULT-+-2))
 (4 2 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (3 3 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (3 3 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (3 3 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (3 3 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (3 3 (:REWRITE ALL-<-TRANSITIVE))
 (2 2 (:TYPE-PRESCRIPTION WEAK-DAGP))
 (2 2 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (2 2 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (2 2 (:REWRITE USE-ALL-NATP-2))
 (2 2 (:REWRITE USE-ALL-NATP))
 (2 2 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (2 2 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (2 2 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (2 2 (:REWRITE INTEGERP-OF-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (2 2 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (2 2 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (2 2 (:REWRITE <-OF-0-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (2 1 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (1 1 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE PSEUDO-DAGP-AUX-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (1 1 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 )
(ADD-TO-DAG-BOUND2
 (554 10 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (380 57 (:REWRITE DEFAULT-CAR))
 (310 2 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (304 2 (:DEFINITION NAT-LISTP))
 (230 2 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (110 1 (:DEFINITION MYQUOTEP))
 (88 6 (:REWRITE USE-ALL-<-FOR-CAR))
 (78 39 (:TYPE-PRESCRIPTION FIND-NODE-FOR-EXPR2-TYPE))
 (67 67 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (64 32 (:TYPE-PRESCRIPTION NATP-OF-TOP-NODENUM-WHEN-PSEUDO-DAGP))
 (63 22 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (59 10 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (54 46 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (46 46 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (46 26 (:REWRITE DEFAULT-<-2))
 (46 23 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (46 6 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (33 33 (:REWRITE USE-ALL-CONSP-2))
 (33 33 (:REWRITE USE-ALL-CONSP))
 (31 26 (:REWRITE DEFAULT-<-1))
 (31 6 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (30 29 (:REWRITE DEFAULT-+-2))
 (29 29 (:REWRITE DEFAULT-+-1))
 (28 5 (:REWRITE DEFAULT-CDR))
 (28 1 (:DEFINITION QUOTEP))
 (27 27 (:TYPE-PRESCRIPTION NATP))
 (27 1 (:REWRITE LEN-OF-CDR))
 (26 26 (:REWRITE USE-ALL-<-2))
 (26 26 (:REWRITE USE-ALL-<))
 (26 13 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (26 13 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (26 13 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-CHEAP))
 (26 13 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-AUX-CHEAP))
 (23 23 (:TYPE-PRESCRIPTION ALL-NATP))
 (23 23 (:TYPE-PRESCRIPTION ALISTP))
 (22 22 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (20 10 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (20 10 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (18 18 (:TYPE-PRESCRIPTION ALL-<))
 (13 13 (:TYPE-PRESCRIPTION WEAK-DAGP))
 (13 13 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (13 13 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (13 13 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (13 13 (:REWRITE INTEGERP-OF-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (12 12 (:TYPE-PRESCRIPTION NAT-LISTP))
 (12 12 (:TYPE-PRESCRIPTION ALL-CONSP))
 (12 6 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (12 1 (:REWRITE EQUAL-OF-LEN-AND-0))
 (11 11 (:REWRITE USE-ALL-NATP-2))
 (11 11 (:REWRITE USE-ALL-NATP))
 (10 10 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (10 10 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (6 6 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (6 6 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (6 6 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (6 6 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (6 6 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (6 6 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (6 6 (:REWRITE ALL-<-TRANSITIVE))
 (6 6 (:REWRITE <-OF-0-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (4 2 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (3 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2 2 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION QUOTEP))
 (1 1 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 (1 1 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 )
(ADD-TO-DAG-OF-NIL)
(CONSP-OF-MV-NTH-1-OF-ADD-TO-DAG
 (814 64 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (333 41 (:REWRITE DEFAULT-CAR))
 (198 3 (:REWRITE <-OF-LARGEST-NON-QUOTEP))
 (153 18 (:REWRITE DEFAULT-CDR))
 (108 97 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (108 54 (:TYPE-PRESCRIPTION FIND-NODE-FOR-EXPR-TYPE))
 (97 97 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (97 97 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (88 88 (:TYPE-PRESCRIPTION ALL-DARGP))
 (88 44 (:TYPE-PRESCRIPTION NATP-OF-LARGEST-NON-QUOTEP))
 (88 44 (:TYPE-PRESCRIPTION ACL2-NUMBERP-OF-LARGEST-NON-QUOTEP))
 (78 3 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-<))
 (70 35 (:REWRITE DEFAULT-<-2))
 (64 64 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (57 3 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (50 35 (:REWRITE DEFAULT-<-1))
 (50 25 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (35 35 (:REWRITE USE-ALL-CONSP-2))
 (35 35 (:REWRITE USE-ALL-CONSP))
 (35 35 (:REWRITE USE-ALL-<-2))
 (35 35 (:REWRITE USE-ALL-<))
 (35 35 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (27 27 (:TYPE-PRESCRIPTION ALISTP))
 (27 3 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DAG-EXPRP))
 (27 3 (:REWRITE BOUNDED-DARG-LISTP-OF-DARGS-WHEN-BOUNDED-DAG-EXPRP))
 (27 3 (:REWRITE BOUNDED-DARG-LISTP-OF-DARGS-WHEN-<-SIMPLE))
 (27 3 (:REWRITE <-OF-LARGEST-NON-QUOTEP-OF-DARGS))
 (24 24 (:TYPE-PRESCRIPTION BOUNDED-DAG-EXPRP))
 (24 12 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (18 3 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (16 16 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (14 7 (:REWRITE DEFAULT-+-2))
 (12 12 (:TYPE-PRESCRIPTION MYQUOTEP))
 (12 12 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP-CHEAP))
 (12 12 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP-CHEAP))
 (12 12 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (12 12 (:REWRITE BOUNDED-DAG-EXPRP-MONOTONE))
 (10 10 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (8 4 (:REWRITE LARGEST-NON-QUOTEP-WHEN-ALL-MYQUOTEP-CHEAP))
 (8 4 (:REWRITE LARGEST-NON-QUOTEP-WHEN-ALL-CONSP-CHEAP))
 (7 7 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (7 7 (:REWRITE DEFAULT-+-1))
 (6 6 (:TYPE-PRESCRIPTION BOUNDED-DARG-LISTP))
 (6 6 (:TYPE-PRESCRIPTION ALL-<))
 (6 3 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (4 4 (:TYPE-PRESCRIPTION ALL-CONSP))
 (4 2 (:REWRITE IFF-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (4 2 (:REWRITE CAR-WHEN-ALISTP-IFF-CHEAP))
 (3 3 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DAG-EXPRP-GEN))
 (3 3 (:REWRITE BOUNDED-DARG-LISTP-MONOTONE))
 (3 3 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (3 3 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (3 3 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (3 3 (:REWRITE ALL-<-TRANSITIVE))
 (2 2 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 )
(COMPOSE-TERM-AND-DAG-AUX
 (1093 69 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (828 36 (:DEFINITION INTEGER-ABS))
 (567 3 (:REWRITE USE-ALL-<-FOR-CAR))
 (552 24 (:REWRITE LEN-OF-CDR))
 (524 224 (:REWRITE DEFAULT-+-2))
 (504 9 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (324 18 (:REWRITE EQUAL-OF-LEN-AND-0))
 (307 224 (:REWRITE DEFAULT-+-1))
 (282 6 (:REWRITE ALL-<-OF-CDR))
 (243 27 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (165 15 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (156 6 (:REWRITE ALL-CONSP-OF-CDR))
 (138 82 (:REWRITE DEFAULT-<-2))
 (108 18 (:DEFINITION LENGTH))
 (97 97 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (97 97 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (86 82 (:REWRITE DEFAULT-<-1))
 (82 82 (:REWRITE USE-ALL-<-2))
 (82 82 (:REWRITE USE-ALL-<))
 (69 69 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (66 66 (:REWRITE USE-ALL-CONSP-2))
 (66 66 (:REWRITE USE-ALL-CONSP))
 (66 66 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (60 30 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (57 27 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (54 27 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (42 42 (:TYPE-PRESCRIPTION ALL-CONSP))
 (36 36 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (36 36 (:REWRITE DEFAULT-UNARY-MINUS))
 (30 30 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (30 30 (:TYPE-PRESCRIPTION ALISTP))
 (27 27 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (27 27 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (27 27 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (27 27 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (21 21 (:TYPE-PRESCRIPTION ALL-<))
 (21 21 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (18 18 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (18 18 (:REWRITE DEFAULT-REALPART))
 (18 18 (:REWRITE DEFAULT-NUMERATOR))
 (18 18 (:REWRITE DEFAULT-IMAGPART))
 (18 18 (:REWRITE DEFAULT-DENOMINATOR))
 (18 18 (:REWRITE DEFAULT-COERCE-2))
 (18 18 (:REWRITE DEFAULT-COERCE-1))
 (15 15 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (9 9 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (9 9 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (9 9 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (9 9 (:REWRITE ALL-<-TRANSITIVE))
 (6 6 (:REWRITE LEN-OF-CDDR-WHEN-EQUAL-OF-LEN))
 (6 3 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (6 3 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (6 3 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (4 4 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (3 3 (:TYPE-PRESCRIPTION ALL-NATP))
 (3 3 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (3 3 (:REWRITE SYMBOLP-OF-CAR-WHEN-BOUNDED-DAG-EXPRP))
 (3 3 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (3 3 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (3 3 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 )
(FLAG-COMPOSE-TERM-AND-DAG-AUX
 (1429 93 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (1110 70 (:DEFINITION INTEGER-ABS))
 (831 374 (:REWRITE DEFAULT-+-2))
 (599 7 (:REWRITE USE-ALL-<-FOR-CAR))
 (597 29 (:REWRITE LEN-OF-CDR))
 (520 374 (:REWRITE DEFAULT-+-1))
 (508 13 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (324 18 (:REWRITE EQUAL-OF-LEN-AND-0))
 (282 6 (:REWRITE ALL-<-OF-CDR))
 (263 31 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (236 149 (:REWRITE DEFAULT-<-2))
 (210 35 (:DEFINITION LENGTH))
 (169 19 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (162 149 (:REWRITE DEFAULT-<-1))
 (156 6 (:REWRITE ALL-CONSP-OF-CDR))
 (152 152 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (152 152 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (149 149 (:REWRITE USE-ALL-<-2))
 (149 149 (:REWRITE USE-ALL-<))
 (93 93 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (90 90 (:REWRITE USE-ALL-CONSP-2))
 (90 90 (:REWRITE USE-ALL-CONSP))
 (90 90 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (70 70 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (70 70 (:REWRITE DEFAULT-UNARY-MINUS))
 (69 31 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (68 34 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (62 31 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (50 50 (:TYPE-PRESCRIPTION ALL-CONSP))
 (38 38 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (35 35 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (35 35 (:REWRITE DEFAULT-REALPART))
 (35 35 (:REWRITE DEFAULT-NUMERATOR))
 (35 35 (:REWRITE DEFAULT-IMAGPART))
 (35 35 (:REWRITE DEFAULT-DENOMINATOR))
 (35 35 (:REWRITE DEFAULT-COERCE-2))
 (35 35 (:REWRITE DEFAULT-COERCE-1))
 (34 34 (:TYPE-PRESCRIPTION ALISTP))
 (33 33 (:TYPE-PRESCRIPTION ALL-<))
 (31 31 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (31 31 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (31 31 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (31 31 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (26 26 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (19 19 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (14 7 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (14 7 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (14 7 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (13 13 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (13 13 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (13 13 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (13 13 (:REWRITE ALL-<-TRANSITIVE))
 (7 7 (:TYPE-PRESCRIPTION ALL-NATP))
 (7 7 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (7 7 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (7 7 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (7 7 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (6 6 (:REWRITE LEN-OF-CDDR-WHEN-EQUAL-OF-LEN))
 (4 4 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (3 3 (:REWRITE SYMBOLP-OF-CAR-WHEN-BOUNDED-DAG-EXPRP))
 )
(FLAG::FLAG-EQUIV-LEMMA)
(FLAG-COMPOSE-TERM-AND-DAG-AUX-EQUIVALENCES)
(FLAG-LEMMA-FOR-TRUE-LISTP-OF-MV-NTH-0-OF-COMPOSE-TERM-AND-DAG-AUX
 (992 4 (:DEFINITION COMPOSE-TERM-AND-DAG-AUX))
 (813 50 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (444 36 (:REWRITE DEFAULT-CAR))
 (407 19 (:REWRITE LEN-OF-CDR))
 (324 32 (:REWRITE DEFAULT-CDR))
 (228 12 (:REWRITE EQUAL-OF-LEN-AND-0))
 (160 4 (:DEFINITION ASSOC-EQUAL))
 (74 23 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (66 66 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (66 66 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (66 66 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (50 50 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (48 24 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (44 16 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (41 22 (:REWRITE DEFAULT-<-2))
 (38 38 (:REWRITE USE-ALL-CONSP-2))
 (38 38 (:REWRITE USE-ALL-CONSP))
 (38 38 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (36 16 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (32 16 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (31 19 (:REWRITE DEFAULT-+-2))
 (24 24 (:TYPE-PRESCRIPTION ALISTP))
 (22 22 (:REWRITE USE-ALL-<-2))
 (22 22 (:REWRITE USE-ALL-<))
 (22 22 (:REWRITE DEFAULT-<-1))
 (21 1 (:DEFINITION TRUE-LISTP))
 (20 20 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (20 20 (:TYPE-PRESCRIPTION ALL-CONSP))
 (19 19 (:REWRITE DEFAULT-+-1))
 (16 16 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (16 16 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (16 16 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (16 16 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (15 15 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (12 12 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (8 8 (:REWRITE EQUAL-OF-NON-NATP-AND-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (4 4 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (4 4 (:REWRITE SYMBOLP-OF-CAR-WHEN-BOUNDED-DAG-EXPRP))
 (4 4 (:REWRITE LEN-OF-CDDR-WHEN-EQUAL-OF-LEN))
 (4 4 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (2 2 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 )
(TRUE-LISTP-OF-MV-NTH-0-OF-COMPOSE-TERM-AND-DAG-AUX)
(TRUE-LISTP-OF-MV-NTH-0-OF-COMPOSE-TERM-AND-DAG-AUX-LST)
(FLAG-LEMMA-FOR-DUMMY1
 (992 4 (:DEFINITION COMPOSE-TERM-AND-DAG-AUX))
 (799 49 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (444 36 (:REWRITE DEFAULT-CAR))
 (326 34 (:REWRITE DEFAULT-CDR))
 (228 12 (:REWRITE EQUAL-OF-LEN-AND-0))
 (160 4 (:DEFINITION ASSOC-EQUAL))
 (80 29 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (76 76 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (76 76 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (49 49 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (48 24 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (44 16 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (39 21 (:REWRITE DEFAULT-<-2))
 (37 37 (:REWRITE USE-ALL-CONSP-2))
 (37 37 (:REWRITE USE-ALL-CONSP))
 (37 37 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (36 16 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (35 23 (:REWRITE DEFAULT-+-2))
 (32 16 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (24 24 (:TYPE-PRESCRIPTION ALISTP))
 (23 23 (:REWRITE DEFAULT-+-1))
 (21 21 (:REWRITE USE-ALL-<-2))
 (21 21 (:REWRITE USE-ALL-<))
 (21 21 (:REWRITE DEFAULT-<-1))
 (20 20 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (20 20 (:TYPE-PRESCRIPTION ALL-CONSP))
 (16 16 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (16 16 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (16 16 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (16 16 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (16 1 (:LINEAR LEN-OF-CDR-LINEAR-STRONG))
 (15 15 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (14 1 (:LINEAR LEN-OF-CDR-LINEAR))
 (12 12 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (8 8 (:REWRITE EQUAL-OF-NON-NATP-AND-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (4 4 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (4 4 (:REWRITE SYMBOLP-OF-CAR-WHEN-BOUNDED-DAG-EXPRP))
 (4 4 (:REWRITE LEN-OF-CDDR-WHEN-EQUAL-OF-LEN))
 (4 4 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 )
(DUMMY1)
(LEN-OF-MV-NTH-0-OF-COMPOSE-TERM-AND-DAG-AUX-LST)
(FLAG-LEMMA-FOR-DUMMY2
 (992 4 (:DEFINITION COMPOSE-TERM-AND-DAG-AUX))
 (818 50 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (444 36 (:REWRITE DEFAULT-CAR))
 (425 21 (:REWRITE LEN-OF-CDR))
 (324 32 (:REWRITE DEFAULT-CDR))
 (228 12 (:REWRITE EQUAL-OF-LEN-AND-0))
 (160 4 (:DEFINITION ASSOC-EQUAL))
 (68 68 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (68 68 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (50 50 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (48 24 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (44 16 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (39 22 (:REWRITE DEFAULT-<-2))
 (38 38 (:REWRITE USE-ALL-CONSP-2))
 (38 38 (:REWRITE USE-ALL-CONSP))
 (38 38 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (36 16 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (33 21 (:REWRITE DEFAULT-+-2))
 (32 16 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (24 24 (:TYPE-PRESCRIPTION ALISTP))
 (22 22 (:REWRITE USE-ALL-<-2))
 (22 22 (:REWRITE USE-ALL-<))
 (22 22 (:REWRITE DEFAULT-<-1))
 (21 21 (:REWRITE DEFAULT-+-1))
 (20 20 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (20 20 (:TYPE-PRESCRIPTION ALL-CONSP))
 (16 16 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (16 16 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (16 16 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (16 16 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (16 16 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (12 12 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (8 8 (:REWRITE EQUAL-OF-NON-NATP-AND-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (4 4 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (4 4 (:REWRITE SYMBOLP-OF-CAR-WHEN-BOUNDED-DAG-EXPRP))
 (4 4 (:REWRITE LEN-OF-CDDR-WHEN-EQUAL-OF-LEN))
 (4 4 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 )
(DUMMY2)
(CONSP-OF-MV-NTH-0-OF-COMPOSE-TERM-AND-DAG-AUX-LST)
(FLAG-LEMMA-FOR-COMPOSE-TERM-AND-DAG-AUX-RETURN-TYPE
 (10080 103 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (6439 6380 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (6380 6380 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (6380 6380 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (5305 1275 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (4506 4506 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (3908 1954 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (3534 1935 (:REWRITE DEFAULT-<-2))
 (3226 3226 (:REWRITE USE-ALL-CONSP-2))
 (3226 3226 (:REWRITE USE-ALL-CONSP))
 (3226 3226 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (3065 1798 (:REWRITE DEFAULT-+-2))
 (2917 1275 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (2886 78 (:DEFINITION STRIP-CDRS))
 (2550 1275 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (2508 8 (:REWRITE ALL-<-OF-CONS))
 (2016 1935 (:REWRITE DEFAULT-<-1))
 (1935 1935 (:REWRITE USE-ALL-<-2))
 (1935 1935 (:REWRITE USE-ALL-<))
 (1798 1798 (:REWRITE DEFAULT-+-1))
 (1786 1786 (:TYPE-PRESCRIPTION ALL-CONSP))
 (1785 439 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (1529 22 (:DEFINITION SYMBOL-LISTP))
 (1502 74 (:REWRITE CONSP-OF-MV-NTH-0-OF-COMPOSE-TERM-AND-DAG-AUX-LST))
 (1350 1350 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (1277 1277 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (1275 1275 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (1275 1275 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (1275 1275 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (1071 1071 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (960 72 (:REWRITE ALL-CONSP-OF-CDR))
 (635 635 (:REWRITE EQUAL-OF-NON-NATP-AND-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (576 72 (:REWRITE LEN-OF-NTH-WHEN-ALL-DARGP))
 (439 439 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (437 47 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (370 370 (:REWRITE LEN-OF-CDDR-WHEN-EQUAL-OF-LEN))
 (350 350 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (348 348 (:REWRITE SYMBOLP-OF-CAR-WHEN-BOUNDED-DAG-EXPRP))
 (214 2 (:REWRITE ALL-<-OF-REVERSE-LIST))
 (186 93 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (165 165 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (161 161 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (146 103 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (144 144 (:TYPE-PRESCRIPTION ALL-DARGP))
 (144 72 (:REWRITE ALL-DARGP-WHEN-ALL-MYQUOTEP-CHEAP))
 (112 4 (:REWRITE ALL-<-OF-TAKE))
 (106 106 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (106 106 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (106 106 (:REWRITE ALL-<-TRANSITIVE))
 (100 4 (:REWRITE CONSP-OF-TAKE))
 (98 98 (:REWRITE TERM-LISTP-IMPLIES-PSEUDO-TERM-LISTP))
 (85 85 (:REWRITE TERMP-IMPLIES-PSEUDO-TERMP))
 (80 80 (:TYPE-PRESCRIPTION PAIRLIS$-FAST-AUX))
 (72 72 (:REWRITE LEN-OF-NTH-WHEN-BOUNDED-DARG-LISTP))
 (72 72 (:REWRITE ALL-DARGP-WHEN-NOT-CONSP-CHEAP))
 (72 72 (:REWRITE ALL-DARGP-WHEN-NOT-CONSP))
 (72 72 (:REWRITE ALL-DARGP-WHEN-BOUNDED-DARG-LISTP))
 (41 41 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (40 4 (:REWRITE ZP-OPEN))
 (36 6 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (32 16 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (28 7 (:REWRITE FOLD-CONSTS-IN-+))
 (21 21 (:REWRITE DEFAULT-COERCE-2))
 (21 21 (:REWRITE DEFAULT-COERCE-1))
 (21 7 (:REWRITE EQUAL-OF-0-AND-+-OF---ALT))
 (18 18 (:TYPE-PRESCRIPTION MYQUOTEP))
 (16 16 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (16 16 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (16 16 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (11 11 (:REWRITE DARGP-LESS-THAN-WHEN-QUOTEP-CHEAP))
 (11 11 (:REWRITE DARGP-LESS-THAN-MONO))
 (8 8 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (8 8 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 (4 4 (:TYPE-PRESCRIPTION NATP))
 (4 4 (:REWRITE USE-ALL-NATP-2))
 (4 4 (:REWRITE USE-ALL-NATP))
 (4 4 (:REWRITE DARGP-LESS-THAN-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:REWRITE DARGP-LESS-THAN-WHEN-CONSP-CHEAP))
 (4 4 (:REWRITE ASSOC-EQUAL-WHEN-PSEUDO-DAGP-AUX))
 (4 2 (:REWRITE IFF-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (4 2 (:REWRITE CAR-WHEN-ALISTP-IFF-CHEAP))
 (4 2 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (2 2 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (1 1 (:REWRITE BOUNDED-DAG-EXPRP-MONOTONE))
 )
(COMPOSE-TERM-AND-DAG-AUX-RETURN-TYPE)
(COMPOSE-TERM-AND-DAG-AUX-LST-RETURN-TYPE)
(PSEUDO-DAGP-AUX-OF-MV-NTH-1-OF-COMPOSE-TERM-AND-DAG-AUX-LST
 (1159 22 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (664 5 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (649 5 (:DEFINITION NAT-LISTP))
 (606 88 (:REWRITE DEFAULT-CAR))
 (461 5 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (320 20 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (255 4 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-<))
 (222 6 (:DEFINITION STRIP-CDRS))
 (207 15 (:REWRITE USE-ALL-<-FOR-CAR))
 (147 7 (:DEFINITION COMPOSE-TERM-AND-DAG-AUX-LST))
 (123 21 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (120 120 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (118 66 (:REWRITE DEFAULT-<-2))
 (117 27 (:REWRITE DEFAULT-CDR))
 (104 104 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (98 49 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (95 41 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (82 82 (:REWRITE USE-ALL-CONSP-2))
 (82 82 (:REWRITE USE-ALL-CONSP))
 (79 76 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (66 66 (:REWRITE USE-ALL-<-2))
 (66 66 (:REWRITE USE-ALL-<))
 (66 66 (:REWRITE DEFAULT-<-1))
 (63 63 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (63 13 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (56 28 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (56 28 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (56 28 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-CHEAP))
 (56 28 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-AUX-CHEAP))
 (55 55 (:TYPE-PRESCRIPTION ALL-<))
 (54 54 (:TYPE-PRESCRIPTION NATP))
 (51 51 (:TYPE-PRESCRIPTION ALL-NATP))
 (49 49 (:TYPE-PRESCRIPTION ALISTP))
 (42 22 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (42 21 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (34 4 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (30 30 (:TYPE-PRESCRIPTION NAT-LISTP))
 (30 15 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (28 28 (:TYPE-PRESCRIPTION WEAK-DAGP-AUX))
 (28 28 (:TYPE-PRESCRIPTION WEAK-DAGP))
 (28 28 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (28 28 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (28 28 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (28 28 (:REWRITE INTEGERP-OF-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (26 26 (:TYPE-PRESCRIPTION ALL-CONSP))
 (26 20 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (25 2 (:REWRITE CONSP-OF-MV-NTH-0-OF-COMPOSE-TERM-AND-DAG-AUX-LST))
 (23 20 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (22 22 (:REWRITE USE-ALL-NATP-2))
 (22 22 (:REWRITE USE-ALL-NATP))
 (21 21 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (21 21 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (20 20 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (20 20 (:REWRITE ALL-<-TRANSITIVE))
 (18 4 (:REWRITE BOUNDED-DARG-LISTP-MONOTONE))
 (15 15 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (15 15 (:REWRITE DEFAULT-+-2))
 (15 15 (:REWRITE DEFAULT-+-1))
 (14 14 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (14 14 (:REWRITE <-OF-0-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (13 13 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (10 5 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (8 4 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (6 6 (:REWRITE TERM-LISTP-IMPLIES-PSEUDO-TERM-LISTP))
 (5 5 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (5 5 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (3 3 (:REWRITE TERMP-IMPLIES-PSEUDO-TERMP))
 )
(COMPOSE-TERM-AND-DAG-AUX
 (5880 168 (:DEFINITION STRIP-CDRS))
 (5229 1549 (:REWRITE DEFAULT-CDR))
 (4614 130 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-<))
 (4001 1805 (:REWRITE DEFAULT-CAR))
 (3995 70 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (3560 122 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (2662 2609 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (2593 85 (:DEFINITION COMPOSE-TERM-AND-DAG-AUX-LST))
 (2559 2559 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (2084 242 (:REWRITE NATP-OF-TOP-NODENUM-WHEN-PSEUDO-DAGP))
 (2064 1181 (:REWRITE DEFAULT-<-2))
 (1642 1642 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (1430 122 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (1224 558 (:REWRITE DEFAULT-+-2))
 (1181 1181 (:REWRITE USE-ALL-<-2))
 (1181 1181 (:REWRITE USE-ALL-<))
 (1181 1181 (:REWRITE DEFAULT-<-1))
 (1032 1032 (:REWRITE USE-ALL-CONSP-2))
 (1032 1032 (:REWRITE USE-ALL-CONSP))
 (1032 1032 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (732 170 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (631 122 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (630 58 (:REWRITE ALL-CONSP-OF-CDR))
 (568 296 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (558 558 (:REWRITE DEFAULT-+-1))
 (456 22 (:REWRITE CONSP-OF-MV-NTH-0-OF-COMPOSE-TERM-AND-DAG-AUX-LST))
 (348 348 (:TYPE-PRESCRIPTION ALL-CONSP))
 (311 311 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (304 152 (:REWRITE SYMBOL-ALISTP-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (282 282 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (274 274 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (267 267 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (267 267 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (262 2 (:REWRITE ALL-<-OF-REVERSE-LIST))
 (261 261 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (260 130 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (244 122 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (242 242 (:REWRITE USE-ALL-NATP-2))
 (242 242 (:REWRITE USE-ALL-NATP))
 (232 58 (:REWRITE PSEUDO-DAGP-AUX-OF-CDR))
 (219 33 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (216 216 (:REWRITE SYMBOLP-OF-CAR-WHEN-BOUNDED-DAG-EXPRP))
 (202 202 (:REWRITE TERM-LISTP-IMPLIES-PSEUDO-TERM-LISTP))
 (197 197 (:REWRITE TERMP-IMPLIES-PSEUDO-TERMP))
 (180 180 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (170 170 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (160 4 (:REWRITE ALL-<-OF-TAKE))
 (160 4 (:DEFINITION ASSOC-EQUAL))
 (142 142 (:REWRITE LEN-OF-CDDR-WHEN-EQUAL-OF-LEN))
 (140 140 (:TYPE-PRESCRIPTION ALL-<))
 (130 130 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (127 70 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (122 122 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (122 122 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (122 122 (:REWRITE EQUAL-OF-NON-NATP-AND-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (122 122 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (122 122 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (100 4 (:REWRITE CONSP-OF-TAKE))
 (80 80 (:REWRITE DEFAULT-COERCE-2))
 (80 80 (:REWRITE DEFAULT-COERCE-1))
 (72 72 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (72 72 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (72 72 (:REWRITE ALL-<-TRANSITIVE))
 (40 4 (:REWRITE ZP-OPEN))
 (18 9 (:REWRITE DARGP-LESS-THAN-WHEN-NATP-CHEAP))
 (18 9 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (9 9 (:REWRITE DARGP-LESS-THAN-WHEN-QUOTEP-CHEAP))
 (9 9 (:REWRITE DARGP-LESS-THAN-WHEN-NOT-CONSP-CHEAP))
 (9 9 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (9 9 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-CAR-AND-QUOTE))
 (9 9 (:REWRITE DARGP-LESS-THAN-WHEN-CONSP-CHEAP))
 (9 9 (:REWRITE DARGP-LESS-THAN-MONO))
 (8 8 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (8 8 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 (8 2 (:REWRITE FOLD-CONSTS-IN-+))
 (6 6 (:REWRITE DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (6 6 (:REWRITE DAG-EXPRP-WHEN-BOUNDED-DAG-EXPRP))
 (6 2 (:REWRITE EQUAL-OF-0-AND-+-OF---ALT))
 (4 4 (:REWRITE ALISTP-WHEN-BOUNDED-NATP-ALISTP))
 )
