(RENUMBERINGP)
(ALISTP-WHEN-RENUMBERINGP-CHEAP
 (497 18 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (418 9 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (391 9 (:DEFINITION NAT-LISTP))
 (232 25 (:REWRITE USE-ALL-<-FOR-CAR))
 (151 145 (:REWRITE DEFAULT-CAR))
 (141 135 (:REWRITE DEFAULT-CDR))
 (75 75 (:TYPE-PRESCRIPTION ALL-<))
 (59 59 (:REWRITE USE-ALL-CONSP-2))
 (59 59 (:REWRITE USE-ALL-CONSP))
 (57 25 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (55 11 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (54 54 (:TYPE-PRESCRIPTION NAT-LISTP))
 (53 53 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (52 52 (:TYPE-PRESCRIPTION ALL-NATP))
 (50 25 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (50 25 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (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 25 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (45 45 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (41 41 (:REWRITE USE-ALL-<-2))
 (41 41 (:REWRITE USE-ALL-<))
 (41 41 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (41 41 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (41 41 (:REWRITE DEFAULT-<-2))
 (41 41 (:REWRITE DEFAULT-<-1))
 (33 11 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (29 29 (:REWRITE USE-ALL-NATP-2))
 (29 29 (:REWRITE USE-ALL-NATP))
 (25 25 (:TYPE-PRESCRIPTION WEAK-DAGP-AUX))
 (25 25 (:TYPE-PRESCRIPTION WEAK-DAGP))
 (25 25 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (25 25 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (25 25 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (25 25 (:REWRITE INTEGERP-OF-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (25 25 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (25 25 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (25 25 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (25 25 (:REWRITE ALL-<-TRANSITIVE))
 (25 25 (:REWRITE <-OF-0-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (25 9 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (22 22 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (22 22 (:TYPE-PRESCRIPTION ALL-CONSP))
 (22 11 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (20 20 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (20 20 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 (18 18 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (18 18 (:REWRITE ALISTP-WHEN-PSEUDO-DAGP-AUX))
 (18 18 (:REWRITE ALISTP-WHEN-BOUNDED-NATP-ALISTP))
 (18 9 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (11 11 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (11 11 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (11 11 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (11 11 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (11 11 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-ALT))
 (11 11 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (11 11 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (9 9 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (6 6 (:REWRITE ALISTP-OF-CDR))
 )
(INTEGERP-OF-CDR-OF-ASSOC-EQUAL-WHEN-RENUMBERINGP
 (408 16 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (352 8 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (328 8 (:DEFINITION NAT-LISTP))
 (157 107 (:REWRITE DEFAULT-CAR))
 (128 16 (:REWRITE USE-ALL-<-FOR-CAR))
 (89 65 (:REWRITE DEFAULT-CDR))
 (86 18 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-ALT))
 (53 53 (:REWRITE USE-ALL-CONSP-2))
 (53 53 (:REWRITE USE-ALL-CONSP))
 (48 48 (:TYPE-PRESCRIPTION NAT-LISTP))
 (48 48 (:TYPE-PRESCRIPTION ALL-<))
 (48 48 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (40 40 (:TYPE-PRESCRIPTION ALL-NATP))
 (40 8 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (36 18 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (32 16 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (32 16 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (32 16 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-CHEAP))
 (32 16 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-AUX-CHEAP))
 (32 16 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (27 27 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (26 18 (:REWRITE ALISTP-WHEN-RENUMBERINGP-CHEAP))
 (24 24 (:REWRITE USE-ALL-NATP-2))
 (24 24 (:REWRITE USE-ALL-NATP))
 (24 24 (:REWRITE USE-ALL-<-2))
 (24 24 (:REWRITE USE-ALL-<))
 (24 24 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (24 24 (:REWRITE DEFAULT-<-2))
 (24 24 (:REWRITE DEFAULT-<-1))
 (24 8 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (16 16 (:TYPE-PRESCRIPTION WEAK-DAGP-AUX))
 (16 16 (:TYPE-PRESCRIPTION WEAK-DAGP))
 (16 16 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (16 16 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (16 16 (:TYPE-PRESCRIPTION ALL-CONSP))
 (16 16 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (16 16 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (16 16 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (16 16 (:REWRITE INTEGERP-OF-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (16 16 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (16 16 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (16 16 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (16 16 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (16 16 (:REWRITE ALL-<-TRANSITIVE))
 (16 16 (:REWRITE <-OF-0-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (16 8 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (16 8 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (13 13 (:REWRITE ASSOC-EQUAL-WHEN-PSEUDO-DAGP-AUX))
 (12 12 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (10 10 (:REWRITE EQUAL-OF-NON-NATP-AND-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (8 8 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (8 8 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (8 8 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 (8 8 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (8 8 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (8 8 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (8 8 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (8 8 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (8 8 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (8 8 (:REWRITE ALISTP-WHEN-PSEUDO-DAGP-AUX))
 (8 8 (:REWRITE ALISTP-WHEN-BOUNDED-NATP-ALISTP))
 (8 4 (:REWRITE IFF-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (8 4 (:REWRITE CAR-WHEN-ALISTP-IFF-CHEAP))
 )
(NON-NEG-OF-CDR-OF-ASSOC-EQUAL-WHEN-RENUMBERINGP
 (408 16 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (352 8 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (328 8 (:DEFINITION NAT-LISTP))
 (157 107 (:REWRITE DEFAULT-CAR))
 (128 16 (:REWRITE USE-ALL-<-FOR-CAR))
 (89 65 (:REWRITE DEFAULT-CDR))
 (86 18 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-ALT))
 (53 53 (:REWRITE USE-ALL-CONSP-2))
 (53 53 (:REWRITE USE-ALL-CONSP))
 (48 48 (:TYPE-PRESCRIPTION NAT-LISTP))
 (48 48 (:TYPE-PRESCRIPTION ALL-<))
 (48 48 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (40 40 (:TYPE-PRESCRIPTION ALL-NATP))
 (40 8 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (36 18 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (35 30 (:REWRITE DEFAULT-<-1))
 (32 16 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (32 16 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (32 16 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-CHEAP))
 (32 16 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-AUX-CHEAP))
 (32 16 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (30 30 (:REWRITE USE-ALL-<-2))
 (30 30 (:REWRITE USE-ALL-<))
 (30 30 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (30 30 (:REWRITE DEFAULT-<-2))
 (26 18 (:REWRITE ALISTP-WHEN-RENUMBERINGP-CHEAP))
 (24 24 (:REWRITE USE-ALL-NATP-2))
 (24 24 (:REWRITE USE-ALL-NATP))
 (24 24 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (24 8 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (16 16 (:TYPE-PRESCRIPTION WEAK-DAGP-AUX))
 (16 16 (:TYPE-PRESCRIPTION WEAK-DAGP))
 (16 16 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (16 16 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (16 16 (:TYPE-PRESCRIPTION ALL-CONSP))
 (16 16 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (16 16 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (16 16 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (16 16 (:REWRITE INTEGERP-OF-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (16 16 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (16 16 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (16 16 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (16 16 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (16 16 (:REWRITE ALL-<-TRANSITIVE))
 (16 16 (:REWRITE <-OF-0-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (16 8 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (16 8 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (13 13 (:REWRITE ASSOC-EQUAL-WHEN-PSEUDO-DAGP-AUX))
 (12 12 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (10 10 (:REWRITE EQUAL-OF-NON-NATP-AND-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (8 8 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (8 8 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (8 8 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 (8 8 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (8 8 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (8 8 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (8 8 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (8 8 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (8 8 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (8 8 (:REWRITE ALISTP-WHEN-PSEUDO-DAGP-AUX))
 (8 8 (:REWRITE ALISTP-WHEN-BOUNDED-NATP-ALISTP))
 (8 4 (:REWRITE IFF-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (8 4 (:REWRITE CAR-WHEN-ALISTP-IFF-CHEAP))
 (5 5 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(RENUMBER-DAG-EXPR-ARG
 (306 12 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (264 6 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (246 6 (:DEFINITION NAT-LISTP))
 (151 101 (:REWRITE DEFAULT-CAR))
 (112 14 (:REWRITE USE-ALL-<-FOR-CAR))
 (86 18 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-ALT))
 (51 51 (:REWRITE DEFAULT-CDR))
 (44 44 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (43 43 (:REWRITE USE-ALL-CONSP-2))
 (43 43 (:REWRITE USE-ALL-CONSP))
 (42 42 (:TYPE-PRESCRIPTION ALL-<))
 (40 8 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (36 36 (:TYPE-PRESCRIPTION NAT-LISTP))
 (36 18 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (32 32 (:TYPE-PRESCRIPTION ALL-NATP))
 (30 30 (:REWRITE USE-ALL-<-2))
 (30 30 (:REWRITE USE-ALL-<))
 (30 30 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (30 30 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (30 30 (:REWRITE DEFAULT-<-2))
 (30 30 (:REWRITE DEFAULT-<-1))
 (28 14 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (28 14 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (28 14 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-CHEAP))
 (28 14 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-AUX-CHEAP))
 (28 14 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (26 18 (:REWRITE ALISTP-WHEN-RENUMBERINGP-CHEAP))
 (24 8 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (20 20 (:REWRITE USE-ALL-NATP-2))
 (20 20 (:REWRITE USE-ALL-NATP))
 (16 16 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (16 16 (:TYPE-PRESCRIPTION ALL-CONSP))
 (16 8 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (14 14 (:TYPE-PRESCRIPTION WEAK-DAGP-AUX))
 (14 14 (:TYPE-PRESCRIPTION WEAK-DAGP))
 (14 14 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (14 14 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (14 14 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (14 14 (:REWRITE INTEGERP-OF-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (14 14 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (14 14 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (14 14 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (14 14 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (14 14 (:REWRITE ALL-<-TRANSITIVE))
 (14 14 (:REWRITE <-OF-0-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (13 13 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (13 13 (:REWRITE ASSOC-EQUAL-WHEN-PSEUDO-DAGP-AUX))
 (12 12 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (12 6 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (10 10 (:REWRITE EQUAL-OF-NON-NATP-AND-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (10 5 (:REWRITE IFF-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (10 5 (:REWRITE CAR-WHEN-ALISTP-IFF-CHEAP))
 (8 8 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (8 8 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (8 8 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 (8 8 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (8 8 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (8 8 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (8 8 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (8 8 (:REWRITE ALISTP-WHEN-PSEUDO-DAGP-AUX))
 (8 8 (:REWRITE ALISTP-WHEN-BOUNDED-NATP-ALISTP))
 (6 6 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (6 6 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 )
(DARGP-OF-RENUMBER-DAG-EXPR-ARG
 (787 489 (:REWRITE DEFAULT-CAR))
 (787 30 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (676 15 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (631 15 (:DEFINITION NAT-LISTP))
 (582 453 (:REWRITE DEFAULT-CDR))
 (350 65 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (329 329 (:REWRITE USE-ALL-CONSP-2))
 (329 329 (:REWRITE USE-ALL-CONSP))
 (320 37 (:REWRITE USE-ALL-<-FOR-CAR))
 (272 136 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (195 65 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (161 161 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (140 140 (:TYPE-PRESCRIPTION ALL-CONSP))
 (130 130 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (130 65 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (112 112 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (112 112 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 (111 111 (:TYPE-PRESCRIPTION ALL-<))
 (102 102 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (90 90 (:TYPE-PRESCRIPTION NAT-LISTP))
 (83 83 (:REWRITE USE-ALL-<-2))
 (83 83 (:REWRITE USE-ALL-<))
 (83 83 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (83 83 (:REWRITE DEFAULT-<-2))
 (83 83 (:REWRITE DEFAULT-<-1))
 (82 82 (:TYPE-PRESCRIPTION ALL-NATP))
 (80 40 (:REWRITE DARGP-WHEN-MYQUOTEP-CHEAP))
 (77 77 (:REWRITE USE-ALL-NATP-2))
 (77 77 (:REWRITE USE-ALL-NATP))
 (74 37 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (74 37 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (74 37 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-CHEAP))
 (74 37 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-AUX-CHEAP))
 (74 37 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (72 72 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (72 72 (:REWRITE ALISTP-WHEN-PSEUDO-DAGP-AUX))
 (70 70 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (70 70 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (70 70 (:REWRITE ALISTP-WHEN-BOUNDED-NATP-ALISTP))
 (66 40 (:REWRITE DARGP-WHEN-NATP-CHEAP))
 (65 65 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (65 65 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (65 65 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (61 37 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (57 57 (:REWRITE EQUAL-OF-NON-NATP-AND-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (46 46 (:REWRITE USE-ALL-DARGP-2))
 (46 46 (:REWRITE USE-ALL-DARGP))
 (46 46 (:REWRITE DARGP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (46 46 (:REWRITE DARGP-WHEN-DARGP-LESS-THAN))
 (41 7 (:REWRITE ALISTP-OF-CDR))
 (38 2 (:REWRITE MYQUOTEP-OF-CDR-OF-ASSOC-EQUAL))
 (37 37 (:TYPE-PRESCRIPTION WEAK-DAGP-AUX))
 (37 37 (:TYPE-PRESCRIPTION WEAK-DAGP))
 (37 37 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (37 37 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (37 37 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (37 37 (:REWRITE INTEGERP-OF-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (37 37 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (37 37 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (37 37 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (37 37 (:REWRITE ALL-<-TRANSITIVE))
 (37 37 (:REWRITE <-OF-0-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (37 1 (:REWRITE DARGP-OF-CDR-OF-ASSOC-EQUAL))
 (30 30 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (30 15 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (25 5 (:REWRITE ALL-CONSP-OF-CDR))
 (22 2 (:DEFINITION STRIP-CDRS))
 (21 15 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (18 1 (:REWRITE ALL-DARGP-WHEN-NOT-CONSP))
 (15 15 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (14 14 (:REWRITE ASSOC-EQUAL-WHEN-PSEUDO-DAGP-AUX))
 (14 7 (:REWRITE IFF-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (14 7 (:REWRITE CAR-WHEN-ALISTP-IFF-CHEAP))
 (9 9 (:TYPE-PRESCRIPTION QUOTEP))
 (4 4 (:TYPE-PRESCRIPTION STRIP-CDRS))
 (2 2 (:TYPE-PRESCRIPTION ALL-DARGP))
 (2 1 (:REWRITE ALL-DARGP-WHEN-NOT-CONSP-CHEAP))
 (2 1 (:REWRITE ALL-DARGP-WHEN-ALL-MYQUOTEP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (1 1 (:REWRITE ALL-DARGP-WHEN-BOUNDED-DARG-LISTP))
 )
(RENUMBER-DAG-EXPR-ARGS
 (137 1 (:DEFINITION RENUMBERINGP))
 (65 3 (:DEFINITION NATP))
 (51 2 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (44 1 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (41 1 (:DEFINITION NAT-LISTP))
 (16 2 (:REWRITE USE-ALL-<-FOR-CAR))
 (11 11 (:REWRITE DEFAULT-CDR))
 (10 1 (:DEFINITION MYQUOTEP))
 (7 1 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-ALT))
 (6 6 (:TYPE-PRESCRIPTION NAT-LISTP))
 (6 6 (:TYPE-PRESCRIPTION ALL-<))
 (6 6 (:REWRITE USE-ALL-CONSP-2))
 (6 6 (:REWRITE USE-ALL-CONSP))
 (5 5 (:TYPE-PRESCRIPTION ALL-NATP))
 (5 1 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (4 4 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (4 4 (:REWRITE DEFAULT-CAR))
 (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 ALL-DARGP-WHEN-ALL-MYQUOTEP-CHEAP))
 (4 2 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (4 1 (:DEFINITION QUOTEP))
 (3 3 (:TYPE-PRESCRIPTION ALISTP))
 (3 3 (:REWRITE USE-ALL-NATP-2))
 (3 3 (:REWRITE USE-ALL-NATP))
 (3 3 (:REWRITE USE-ALL-<-2))
 (3 3 (:REWRITE USE-ALL-<))
 (3 3 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (3 3 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 (3 1 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (2 2 (:TYPE-PRESCRIPTION WEAK-DAGP-AUX))
 (2 2 (:TYPE-PRESCRIPTION WEAK-DAGP))
 (2 2 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (2 2 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (2 2 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (2 2 (:TYPE-PRESCRIPTION ALL-CONSP))
 (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 CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (2 2 (:REWRITE ALL-DARGP-WHEN-BOUNDED-DARG-LISTP))
 (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 CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (2 1 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (2 1 (:REWRITE ALISTP-WHEN-RENUMBERINGP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (1 1 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (1 1 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 (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-DARGP-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE ALL-DARGP-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))
 )
(RENUMBER-DAG-EXPR
 (119 4 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (99 2 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (93 2 (:DEFINITION NAT-LISTP))
 (44 4 (:REWRITE USE-ALL-<-FOR-CAR))
 (26 21 (:REWRITE DEFAULT-CAR))
 (20 15 (:REWRITE DEFAULT-CDR))
 (16 8 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (16 4 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (12 12 (:TYPE-PRESCRIPTION NAT-LISTP))
 (12 12 (:TYPE-PRESCRIPTION ALL-<))
 (12 12 (:REWRITE USE-ALL-CONSP-2))
 (12 12 (:REWRITE USE-ALL-CONSP))
 (10 10 (:TYPE-PRESCRIPTION ALL-NATP))
 (9 3 (:REWRITE ALL-DARGP-WHEN-NOT-CONSP))
 (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))
 (8 2 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (6 6 (:REWRITE USE-ALL-NATP-2))
 (6 6 (:REWRITE USE-ALL-NATP))
 (6 6 (:REWRITE USE-ALL-<-2))
 (6 6 (:REWRITE USE-ALL-<))
 (6 6 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (6 6 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (6 6 (:REWRITE DEFAULT-<-2))
 (6 6 (:REWRITE DEFAULT-<-1))
 (6 3 (:REWRITE ALL-DARGP-WHEN-ALL-MYQUOTEP-CHEAP))
 (6 1 (:REWRITE TRUE-LISTP-OF-DARGS-WHEN-DAG-EXPRP))
 (5 5 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (5 5 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 (5 5 (:REWRITE DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (5 5 (:REWRITE DAG-EXPRP-WHEN-BOUNDED-DAG-EXPRP))
 (5 1 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (5 1 (:DEFINITION TRUE-LISTP))
 (4 4 (:TYPE-PRESCRIPTION WEAK-DAGP-AUX))
 (4 4 (:TYPE-PRESCRIPTION WEAK-DAGP))
 (4 4 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (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 CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (4 4 (:REWRITE ALL-DARGP-WHEN-BOUNDED-DARG-LISTP))
 (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 4 (:REWRITE <-OF-0-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (4 2 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (3 3 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (3 3 (:REWRITE ALL-DARGP-WHEN-NOT-CONSP-CHEAP))
 (3 1 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (2 2 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (2 2 (:TYPE-PRESCRIPTION ALL-CONSP))
 (2 2 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (2 2 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (2 1 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (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 SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (1 1 (:REWRITE SYMBOLP-OF-CAR-WHEN-BOUNDED-DAG-EXPRP))
 (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-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))
 )
(DAG-EXPRP-OF-RENUMBER-DAG-EXPR
 (1450 56 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (1248 28 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (1164 28 (:DEFINITION NAT-LISTP))
 (906 145 (:REWRITE ALL-DARGP-WHEN-NOT-CONSP))
 (610 583 (:REWRITE DEFAULT-CDR))
 (603 603 (:REWRITE USE-ALL-CONSP-2))
 (603 603 (:REWRITE USE-ALL-CONSP))
 (595 566 (:REWRITE DEFAULT-CAR))
 (536 64 (:REWRITE USE-ALL-<-FOR-CAR))
 (394 76 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (296 148 (:REWRITE ALL-DARGP-WHEN-ALL-MYQUOTEP-CHEAP))
 (220 76 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (216 144 (:REWRITE CAR-OF-DARGS-BECOMES-NTH-0-OF-DARGS))
 (214 145 (:REWRITE ALL-DARGP-WHEN-NOT-CONSP-CHEAP))
 (192 192 (:TYPE-PRESCRIPTION ALL-<))
 (188 94 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (168 168 (:TYPE-PRESCRIPTION NAT-LISTP))
 (156 156 (:TYPE-PRESCRIPTION ALL-CONSP))
 (154 154 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (152 76 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (150 150 (:REWRITE ALL-DARGP-WHEN-BOUNDED-DARG-LISTP))
 (148 148 (:TYPE-PRESCRIPTION ALL-NATP))
 (148 148 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (144 144 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (144 72 (:DEFINITION NTH))
 (130 130 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (130 130 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 (128 64 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (128 64 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (128 64 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-CHEAP))
 (128 64 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-AUX-CHEAP))
 (128 64 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (120 120 (:REWRITE USE-ALL-<-2))
 (120 120 (:REWRITE USE-ALL-<))
 (120 120 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (120 120 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (120 120 (:REWRITE DEFAULT-<-2))
 (120 120 (:REWRITE DEFAULT-<-1))
 (111 111 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (101 101 (:REWRITE DAG-EXPRP-WHEN-BOUNDED-DAG-EXPRP))
 (88 64 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (85 85 (:REWRITE USE-ALL-NATP-2))
 (85 85 (:REWRITE USE-ALL-NATP))
 (78 78 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (78 78 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (78 78 (:REWRITE ALISTP-WHEN-PSEUDO-DAGP-AUX))
 (78 78 (:REWRITE ALISTP-WHEN-BOUNDED-NATP-ALISTP))
 (76 76 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (76 76 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (76 76 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (76 76 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (64 64 (:TYPE-PRESCRIPTION WEAK-DAGP-AUX))
 (64 64 (:TYPE-PRESCRIPTION WEAK-DAGP))
 (64 64 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (64 64 (:REWRITE TRUE-LISTP-OF-DARGS-WHEN-BOUNDED-DAG-EXPRP-AND-CONSP))
 (64 64 (:REWRITE TRUE-LISTP-OF-DARGS-BETTER))
 (64 64 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (64 64 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (64 64 (:REWRITE INTEGERP-OF-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (64 64 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (64 64 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (64 64 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (64 64 (:REWRITE ALL-<-TRANSITIVE))
 (64 64 (:REWRITE <-OF-0-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (57 57 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (56 56 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (56 28 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (42 6 (:REWRITE ALISTP-OF-CDR))
 (35 7 (:REWRITE USE-ALL-DARGP))
 (34 28 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (30 30 (:REWRITE SYMBOLP-OF-CAR-WHEN-BOUNDED-DAG-EXPRP))
 (30 6 (:REWRITE ALL-CONSP-OF-CDR))
 (28 28 (:TYPE-PRESCRIPTION MEMBERP))
 (28 28 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (7 7 (:REWRITE USE-ALL-DARGP-2))
 (7 7 (:REWRITE DARGP-WHEN-DARGP-LESS-THAN))
 (2 2 (:TYPE-PRESCRIPTION QUOTEP))
 )
(WEAK-DAGP-AUX-FORWARD-TO-TRUE-LISTP)
(RENUMBERINGP-OF-ACONS
 (51 2 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (44 1 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (41 1 (:DEFINITION NAT-LISTP))
 (16 16 (:REWRITE DEFAULT-CDR))
 (16 2 (:REWRITE USE-ALL-<-FOR-CAR))
 (8 8 (:REWRITE USE-ALL-CONSP-2))
 (8 8 (:REWRITE USE-ALL-CONSP))
 (8 8 (:REWRITE DEFAULT-CAR))
 (7 7 (:REWRITE USE-ALL-NATP-2))
 (7 7 (:REWRITE USE-ALL-NATP))
 (7 7 (:REWRITE USE-ALL-<-2))
 (7 7 (:REWRITE USE-ALL-<))
 (7 7 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (7 7 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (7 7 (:REWRITE DEFAULT-<-2))
 (7 7 (:REWRITE DEFAULT-<-1))
 (7 1 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-ALT))
 (6 6 (:TYPE-PRESCRIPTION NAT-LISTP))
 (6 6 (:TYPE-PRESCRIPTION ALL-<))
 (5 5 (:TYPE-PRESCRIPTION ALL-NATP))
 (5 1 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (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 (:TYPE-PRESCRIPTION ALISTP))
 (3 3 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (3 3 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 (3 1 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (2 2 (:TYPE-PRESCRIPTION WEAK-DAGP-AUX))
 (2 2 (:TYPE-PRESCRIPTION WEAK-DAGP))
 (2 2 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (2 2 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (2 2 (:TYPE-PRESCRIPTION ALL-CONSP))
 (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 CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (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 DARGP-WHEN-NATP-CHEAP))
 (2 1 (:REWRITE DARGP-WHEN-MYQUOTEP-CHEAP))
 (2 1 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (2 1 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (2 1 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (2 1 (:REWRITE ALISTP-WHEN-RENUMBERINGP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (1 1 (:TYPE-PRESCRIPTION NATP))
 (1 1 (:TYPE-PRESCRIPTION MYQUOTEP))
 (1 1 (:REWRITE USE-ALL-DARGP-2))
 (1 1 (:REWRITE USE-ALL-DARGP))
 (1 1 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (1 1 (:REWRITE DARGP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (1 1 (:REWRITE DARGP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE DARGP-WHEN-CONSP-CHEAP))
 (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))
 (1 1 (:REWRITE ALISTP-WHEN-PSEUDO-DAGP-AUX))
 (1 1 (:REWRITE ALISTP-WHEN-BOUNDED-NATP-ALISTP))
 )
(WEAK-DAGP-AUX-OF-ACONS
 (1336 92 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX-2))
 (959 323 (:REWRITE DEFAULT-CAR))
 (906 55 (:DEFINITION TOP-NODENUM))
 (382 25 (:REWRITE BOUNDED-DARG-LISTP-OF-DARGS-WHEN-<-SIMPLE))
 (307 25 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-<))
 (303 25 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DAG-EXPRP))
 (303 25 (:REWRITE BOUNDED-DARG-LISTP-OF-DARGS-WHEN-BOUNDED-DAG-EXPRP))
 (252 19 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-ALT))
 (202 92 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP))
 (182 36 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (180 19 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (162 162 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (144 144 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (142 32 (:REWRITE BOUNDED-DAG-EXPRP-OF-CDR-OF-CAR-WHEN-WEAK-DAGP-AUX))
 (128 64 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (125 17 (:REWRITE ALL-DARGP-OF-DARGS-WHEN-DAG-EXPRP))
 (124 124 (:REWRITE USE-ALL-CONSP-2))
 (124 124 (:REWRITE USE-ALL-CONSP))
 (119 17 (:REWRITE PSEUDO-DAGP-AUX-OF-CDR))
 (119 17 (:REWRITE ALISTP-OF-CDR))
 (117 117 (:REWRITE DEFAULT-CDR))
 (112 17 (:REWRITE WEAK-DAGP-AUX-OF-CDR))
 (98 98 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (92 92 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (85 17 (:REWRITE ALL-CONSP-OF-CDR))
 (80 36 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (74 74 (:TYPE-PRESCRIPTION ALL-<))
 (73 73 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (72 72 (:TYPE-PRESCRIPTION ALL-CONSP))
 (72 72 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (72 36 (:REWRITE ALISTP-WHEN-RENUMBERINGP-CHEAP))
 (66 50 (:REWRITE DEFAULT-<-1))
 (64 64 (:TYPE-PRESCRIPTION MYQUOTEP))
 (62 7 (:REWRITE DAG-EXPRP-OF-CDR-OF-CAR-WHEN-WEAK-DAGP-AUX))
 (57 19 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (53 17 (:REWRITE ALL-DARGP-WHEN-NOT-CONSP))
 (53 5 (:REWRITE TRUE-LISTP-OF-DARGS-WHEN-DAG-EXPRP))
 (51 17 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (51 2 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (50 50 (:REWRITE USE-ALL-<-2))
 (50 50 (:REWRITE USE-ALL-<))
 (50 50 (:REWRITE DEFAULT-<-2))
 (50 33 (:REWRITE DEFAULT-+-2))
 (50 25 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (49 7 (:REWRITE DAG-EXPRP-OF-CDR-OF-CAR-WHEN-WEAK-DAGP))
 (48 48 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP-CHEAP))
 (48 48 (:REWRITE BOUNDED-DAG-EXPRP-MONOTONE))
 (47 47 (:REWRITE DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (47 47 (:REWRITE DAG-EXPRP-WHEN-BOUNDED-DAG-EXPRP))
 (44 1 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (42 42 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (41 1 (:DEFINITION NAT-LISTP))
 (38 19 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (38 19 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (36 36 (:TYPE-PRESCRIPTION RENUMBERINGP))
 (36 36 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (36 36 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (36 36 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (36 36 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (36 36 (:REWRITE ALL-<-TRANSITIVE))
 (36 36 (:REWRITE ALISTP-WHEN-PSEUDO-DAGP-AUX))
 (36 36 (:REWRITE ALISTP-WHEN-BOUNDED-NATP-ALISTP))
 (34 34 (:REWRITE USE-ALL-NATP-2))
 (34 34 (:REWRITE USE-ALL-NATP))
 (34 34 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (34 17 (:REWRITE ALL-DARGP-WHEN-ALL-MYQUOTEP-CHEAP))
 (33 33 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (33 33 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (33 33 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 (33 33 (:REWRITE DEFAULT-+-1))
 (32 16 (:REWRITE PSEUDO-DAGP-AUX-OF-CONS-OF-CONS))
 (25 25 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DAG-EXPRP-GEN))
 (25 5 (:DEFINITION TRUE-LISTP))
 (22 22 (:REWRITE PSEUDO-DAGP-AUX-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (21 7 (:REWRITE WEAK-DAGP-WHEN-PSEUDO-DAGP))
 (19 19 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (19 19 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (19 19 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (19 19 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (17 17 (:REWRITE ALL-DARGP-WHEN-NOT-CONSP-CHEAP))
 (16 16 (:TYPE-PRESCRIPTION WEAK-DAGP))
 (16 2 (:REWRITE USE-ALL-<-FOR-CAR))
 (10 10 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (10 10 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (7 7 (:REWRITE WEAK-DAGP-WHEN-PSEUDO-DAGP-AUX))
 (6 6 (:TYPE-PRESCRIPTION NAT-LISTP))
 (5 5 (:TYPE-PRESCRIPTION ALL-NATP))
 (5 5 (:REWRITE TRUE-LISTP-OF-DARGS-WHEN-BOUNDED-DAG-EXPRP-AND-CONSP))
 (5 5 (:REWRITE TRUE-LISTP-OF-DARGS-BETTER))
 (5 5 (:REWRITE SYMBOLP-OF-CAR-WHEN-BOUNDED-DAG-EXPRP))
 (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))
 (2 2 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (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 <-OF-0-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (2 1 (:REWRITE SYMBOLP-OF-CDAR-WHEN-WEAK-DAGP-AUX-CHEAP))
 (2 1 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (1 1 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 )
(INTEGERP-OF-+-OF-1-AND-CAR-OF-CAR-WHEN-WEAK-DAGP-AUX
 (34 1 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX-2))
 (30 1 (:DEFINITION TOP-NODENUM))
 (28 4 (:REWRITE DEFAULT-CAR))
 (14 2 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-ALT))
 (10 2 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (6 6 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (6 2 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (4 4 (:TYPE-PRESCRIPTION ALL-CONSP))
 (4 4 (:REWRITE USE-ALL-CONSP-2))
 (4 4 (:REWRITE USE-ALL-CONSP))
 (4 2 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (4 2 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (4 2 (:REWRITE ALISTP-WHEN-RENUMBERINGP-CHEAP))
 (3 1 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP))
 (2 2 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (2 2 (:TYPE-PRESCRIPTION RENUMBERINGP))
 (2 2 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (2 2 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (2 2 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (2 2 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (2 2 (:REWRITE CAR-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 ALISTP-WHEN-PSEUDO-DAGP-AUX))
 (2 2 (:REWRITE ALISTP-WHEN-BOUNDED-NATP-ALISTP))
 (1 1 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (1 1 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE DEFAULT-CDR))
 )
(<=-OF-0-AND-+-OF-1-AND-CAR-OF-CAR-WHEN-WEAK-DAGP-AUX
 (399 16 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX-2))
 (284 14 (:DEFINITION TOP-NODENUM))
 (261 45 (:REWRITE DEFAULT-CAR))
 (231 7 (:REWRITE BOUNDED-DAG-EXPRP-OF-CDR-OF-CAR-WHEN-WEAK-DAGP-AUX))
 (143 6 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (134 9 (:REWRITE WEAK-DAGP-AUX-OF-CDR))
 (122 3 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (115 3 (:DEFINITION NAT-LISTP))
 (112 9 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-ALT))
 (80 9 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (49 8 (:REWRITE PSEUDO-DAGP-AUX-OF-CDR))
 (49 7 (:REWRITE ALISTP-OF-CDR))
 (48 6 (:REWRITE USE-ALL-<-FOR-CAR))
 (46 46 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (44 16 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP))
 (43 43 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (35 7 (:REWRITE ALL-CONSP-OF-CDR))
 (32 32 (:TYPE-PRESCRIPTION ALL-CONSP))
 (32 16 (:REWRITE ALISTP-WHEN-RENUMBERINGP-CHEAP))
 (27 9 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (24 24 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (21 21 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (18 18 (:TYPE-PRESCRIPTION ALL-<))
 (18 18 (:REWRITE USE-ALL-CONSP-2))
 (18 18 (:REWRITE USE-ALL-CONSP))
 (18 9 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (18 9 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (16 16 (:TYPE-PRESCRIPTION RENUMBERINGP))
 (16 16 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (16 16 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (16 16 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (16 16 (:REWRITE ALISTP-WHEN-PSEUDO-DAGP-AUX))
 (16 16 (:REWRITE ALISTP-WHEN-BOUNDED-NATP-ALISTP))
 (15 15 (:TYPE-PRESCRIPTION ALL-NATP))
 (15 15 (:REWRITE DEFAULT-CDR))
 (14 7 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (12 7 (:REWRITE DEFAULT-+-2))
 (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 <-OF-CAR-WHEN-ALL-<-CHEAP))
 (10 10 (:TYPE-PRESCRIPTION NAT-LISTP))
 (9 9 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (9 9 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (9 9 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (9 9 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (8 8 (:REWRITE PSEUDO-DAGP-AUX-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (7 7 (:TYPE-PRESCRIPTION MYQUOTEP))
 (7 7 (:REWRITE DEFAULT-+-1))
 (7 7 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP-CHEAP))
 (7 7 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (7 7 (:REWRITE BOUNDED-DAG-EXPRP-MONOTONE))
 (6 6 (:TYPE-PRESCRIPTION WEAK-DAGP))
 (6 6 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (6 6 (:REWRITE USE-ALL-NATP-2))
 (6 6 (:REWRITE USE-ALL-NATP))
 (6 6 (:REWRITE USE-ALL-<-2))
 (6 6 (:REWRITE USE-ALL-<))
 (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 DEFAULT-<-2))
 (6 6 (:REWRITE DEFAULT-<-1))
 (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 ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (5 5 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (5 5 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP-CHEAP))
 (3 3 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (3 3 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 )
(BOUNDED-DAG-EXPRP-WHEN-SYMBOLP
 (2 1 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION MYQUOTEP))
 (1 1 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (1 1 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 )
(WEAK-DAGP-AUX-OF-ACONS-OF-0-AND-NIL-WHEN-SYMBOLP
 (10 1 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX-2))
 (5 1 (:DEFINITION TOP-NODENUM))
 (4 1 (:REWRITE WEAK-DAGP-AUX-OF-ACONS))
 (3 1 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP))
 (2 2 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (2 2 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (2 2 (:REWRITE DEFAULT-CAR))
 (2 1 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION BOUNDED-DAG-EXPRP))
 (1 1 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (1 1 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (1 1 (:REWRITE DEFAULT-CDR))
 )
(CONSP-WHEN-BOUNDED-DAG-EXPRP-WEAKEN
 (6 1 (:REWRITE TRUE-LISTP-OF-DARGS-WHEN-DAG-EXPRP))
 (6 1 (:REWRITE ALL-DARGP-OF-DARGS-WHEN-DAG-EXPRP))
 (5 5 (:REWRITE USE-ALL-CONSP-2))
 (5 5 (:REWRITE USE-ALL-CONSP))
 (5 1 (:DEFINITION TRUE-LISTP))
 (4 4 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (3 3 (:REWRITE DAG-EXPRP-WHEN-BOUNDED-DAG-EXPRP))
 (3 1 (:REWRITE ALL-DARGP-WHEN-NOT-CONSP))
 (2 2 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (2 2 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (2 1 (:REWRITE ALL-DARGP-WHEN-ALL-MYQUOTEP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (1 1 (:REWRITE TRUE-LISTP-OF-DARGS-WHEN-BOUNDED-DAG-EXPRP-AND-CONSP))
 (1 1 (:REWRITE TRUE-LISTP-OF-DARGS-BETTER))
 (1 1 (:REWRITE SYMBOLP-OF-CAR-WHEN-BOUNDED-DAG-EXPRP))
 (1 1 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 (1 1 (:REWRITE ALL-DARGP-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE ALL-DARGP-WHEN-BOUNDED-DARG-LISTP))
 )
(BINDS-ALL-NATS-UP-TO
 (49 2 (:DEFINITION ASSOC-EQUAL))
 (30 5 (:REWRITE DEFAULT-CAR))
 (7 7 (:REWRITE USE-ALL-<-2))
 (7 7 (:REWRITE USE-ALL-<))
 (7 7 (:REWRITE DEFAULT-<-2))
 (7 7 (:REWRITE DEFAULT-<-1))
 (7 6 (:REWRITE DEFAULT-+-2))
 (7 1 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-ALT))
 (6 6 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (6 6 (:REWRITE DEFAULT-+-1))
 (5 1 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (4 4 (:REWRITE ASSOC-EQUAL-WHEN-PSEUDO-DAGP-AUX))
 (4 2 (:REWRITE ALISTP-WHEN-RENUMBERINGP-CHEAP))
 (3 3 (:REWRITE USE-ALL-CONSP-2))
 (3 3 (:REWRITE USE-ALL-CONSP))
 (3 3 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (3 2 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (3 2 (:REWRITE CAR-WHEN-ALISTP-IFF-CHEAP))
 (3 1 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (2 2 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (2 2 (:TYPE-PRESCRIPTION RENUMBERINGP))
 (2 2 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (2 2 (:TYPE-PRESCRIPTION ALL-CONSP))
 (2 2 (:REWRITE EQUAL-OF-NON-NATP-AND-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (2 2 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (2 2 (:REWRITE ALISTP-WHEN-PSEUDO-DAGP-AUX))
 (2 2 (:REWRITE ALISTP-WHEN-BOUNDED-NATP-ALISTP))
 (2 1 (:REWRITE IFF-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (2 1 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (1 1 (:REWRITE USE-ALL-NATP-2))
 (1 1 (:REWRITE USE-ALL-NATP))
 (1 1 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (1 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (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-CONSP-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 )
(MAPS-EVERYTHING-TO-QUOTE-OR-NODENUM-LESS-THAN
 (4 2 (:REWRITE ALISTP-WHEN-RENUMBERINGP-CHEAP))
 (2 2 (:TYPE-PRESCRIPTION RENUMBERINGP))
 (2 2 (:REWRITE USE-ALL-CONSP-2))
 (2 2 (:REWRITE USE-ALL-CONSP))
 (2 2 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE ALISTP-WHEN-PSEUDO-DAGP-AUX))
 (2 2 (:REWRITE ALISTP-WHEN-BOUNDED-NATP-ALISTP))
 (1 1 (:REWRITE USE-ALL-<-2))
 (1 1 (:REWRITE USE-ALL-<))
 (1 1 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 )
(ASSOC-EQUAL-WHEN-BINDS-ALL-NATS-UP-TO
 (216 24 (:REWRITE DEFAULT-CAR))
 (56 8 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-ALT))
 (40 8 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (24 8 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (16 16 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (16 16 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (16 16 (:TYPE-PRESCRIPTION ALL-CONSP))
 (16 16 (:REWRITE USE-ALL-CONSP-2))
 (16 16 (:REWRITE USE-ALL-CONSP))
 (16 16 (:REWRITE ASSOC-EQUAL-WHEN-PSEUDO-DAGP-AUX))
 (16 8 (:REWRITE IFF-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (16 8 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (16 8 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (16 8 (:REWRITE CAR-WHEN-ALISTP-IFF-CHEAP))
 (16 8 (:REWRITE ALISTP-WHEN-RENUMBERINGP-CHEAP))
 (8 8 (:TYPE-PRESCRIPTION RENUMBERINGP))
 (8 8 (:REWRITE USE-ALL-<-2))
 (8 8 (:REWRITE USE-ALL-<))
 (8 8 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (8 8 (:REWRITE EQUAL-OF-NON-NATP-AND-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (8 8 (:REWRITE DEFAULT-CDR))
 (8 8 (:REWRITE DEFAULT-<-2))
 (8 8 (:REWRITE DEFAULT-<-1))
 (8 8 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (8 8 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (8 8 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (8 8 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (8 8 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (8 8 (:REWRITE ALISTP-WHEN-PSEUDO-DAGP-AUX))
 (8 8 (:REWRITE ALISTP-WHEN-BOUNDED-NATP-ALISTP))
 (6 6 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (6 6 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(<-OF-CDR-OF-ASSOC-EQUAL-WHEN-MAPS-EVERYTHING-TO-QUOTE-OR-NODENUM-LESS-THAN
 (1225 145 (:REWRITE DEFAULT-CAR))
 (378 60 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-ALT))
 (377 65 (:REWRITE DEFAULT-CDR))
 (272 60 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (166 60 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (120 60 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (120 60 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (115 115 (:REWRITE USE-ALL-CONSP-2))
 (115 115 (:REWRITE USE-ALL-CONSP))
 (106 106 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (106 106 (:TYPE-PRESCRIPTION ALL-CONSP))
 (106 53 (:REWRITE ALISTP-WHEN-RENUMBERINGP-CHEAP))
 (66 66 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (60 60 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (60 60 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (60 60 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (56 56 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (53 53 (:TYPE-PRESCRIPTION RENUMBERINGP))
 (53 53 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (53 53 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (53 53 (:REWRITE ALISTP-WHEN-PSEUDO-DAGP-AUX))
 (53 53 (:REWRITE ALISTP-WHEN-BOUNDED-NATP-ALISTP))
 (38 26 (:REWRITE DEFAULT-<-2))
 (33 26 (:REWRITE DEFAULT-<-1))
 (26 26 (:REWRITE USE-ALL-<-2))
 (26 26 (:REWRITE USE-ALL-<))
 (21 21 (:REWRITE ASSOC-EQUAL-WHEN-PSEUDO-DAGP-AUX))
 (21 21 (:REWRITE ASSOC-EQUAL-WHEN-BINDS-ALL-NATS-UP-TO))
 (19 19 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (12 6 (:REWRITE IFF-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (12 6 (:REWRITE CAR-WHEN-ALISTP-IFF-CHEAP))
 (10 10 (:REWRITE EQUAL-OF-NON-NATP-AND-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (8 8 (:REWRITE USE-ALL-NATP-2))
 (8 8 (:REWRITE USE-ALL-NATP))
 (8 8 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (8 8 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (8 8 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 (8 8 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 )
(NOT-OF-CDDDR-OF-ASSOC-EQUAL-WHEN-MAPS-EVERYTHING-TO-QUOTE-OR-NODENUM-LESS-THAN
 (182 26 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-ALT))
 (130 26 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (95 95 (:REWRITE USE-ALL-CONSP-2))
 (95 95 (:REWRITE USE-ALL-CONSP))
 (78 26 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (52 52 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (52 52 (:TYPE-PRESCRIPTION ALL-CONSP))
 (52 26 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (52 26 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (52 26 (:REWRITE ALISTP-WHEN-RENUMBERINGP-CHEAP))
 (26 26 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (26 26 (:TYPE-PRESCRIPTION RENUMBERINGP))
 (26 26 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (26 26 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (26 26 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (26 26 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (26 26 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (26 26 (:REWRITE ALISTP-WHEN-PSEUDO-DAGP-AUX))
 (26 26 (:REWRITE ALISTP-WHEN-BOUNDED-NATP-ALISTP))
 (24 16 (:REWRITE DEFAULT-<-2))
 (16 16 (:REWRITE USE-ALL-<-2))
 (16 16 (:REWRITE USE-ALL-<))
 (16 16 (:REWRITE DEFAULT-<-1))
 (14 14 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (8 8 (:REWRITE USE-ALL-NATP-2))
 (8 8 (:REWRITE USE-ALL-NATP))
 (8 8 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (8 8 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (8 8 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (8 8 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 (8 8 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (4 4 (:REWRITE EQUAL-OF-NON-NATP-AND-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 )
(NATP-OF-CDR-OF-ASSOC-EQUAL-WHEN-MAPS-EVERYTHING-TO-QUOTE-OR-NODENUM-LESS-THAN
 (1404 180 (:REWRITE DEFAULT-CAR))
 (617 115 (:REWRITE DEFAULT-CDR))
 (476 73 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-ALT))
 (342 73 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (246 4 (:REWRITE <-OF-CDR-OF-ASSOC-EQUAL-WHEN-MAPS-EVERYTHING-TO-QUOTE-OR-NODENUM-LESS-THAN))
 (205 73 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (157 157 (:REWRITE USE-ALL-CONSP-2))
 (157 157 (:REWRITE USE-ALL-CONSP))
 (146 73 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (146 73 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (134 134 (:TYPE-PRESCRIPTION ALL-CONSP))
 (134 67 (:REWRITE ALISTP-WHEN-RENUMBERINGP-CHEAP))
 (132 132 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (83 83 (:TYPE-PRESCRIPTION RENUMBERINGP))
 (82 82 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (73 73 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (73 73 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (73 73 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (67 67 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (67 67 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (67 67 (:REWRITE ALISTP-WHEN-PSEUDO-DAGP-AUX))
 (67 67 (:REWRITE ALISTP-WHEN-BOUNDED-NATP-ALISTP))
 (62 62 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (43 32 (:REWRITE DEFAULT-<-2))
 (34 32 (:REWRITE DEFAULT-<-1))
 (32 32 (:REWRITE USE-ALL-<-2))
 (32 32 (:REWRITE USE-ALL-<))
 (27 27 (:REWRITE ASSOC-EQUAL-WHEN-PSEUDO-DAGP-AUX))
 (27 27 (:REWRITE ASSOC-EQUAL-WHEN-BINDS-ALL-NATS-UP-TO))
 (18 9 (:REWRITE IFF-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (18 9 (:REWRITE CAR-WHEN-ALISTP-IFF-CHEAP))
 (17 17 (:REWRITE USE-ALL-NATP-2))
 (17 17 (:REWRITE USE-ALL-NATP))
 (17 17 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (17 17 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (16 16 (:REWRITE EQUAL-OF-NON-NATP-AND-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (15 15 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (15 15 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 (13 13 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (12 4 (:REWRITE NON-NEG-OF-CDR-OF-ASSOC-EQUAL-WHEN-RENUMBERINGP))
 (12 4 (:REWRITE INTEGERP-OF-CDR-OF-ASSOC-EQUAL-WHEN-RENUMBERINGP))
 (7 1 (:REWRITE ALISTP-OF-CDR))
 (5 1 (:REWRITE ALL-CONSP-OF-CDR))
 )
(CAR-OF-CAR-LINEAR-WHEN-WEAK-DAGP-AUX)
(CAR-OF-CAR-TYPE-WHEN-WEAK-DAGP-AUX-TYPE)
(BINDS-ALL-NATS-UP-TO-OF-ACONS-GREATER
 (231 39 (:REWRITE DEFAULT-CAR))
 (56 8 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-ALT))
 (40 8 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (32 16 (:TYPE-PRESCRIPTION CAR-OF-CAR-TYPE-WHEN-WEAK-DAGP-AUX-TYPE))
 (26 26 (:REWRITE ASSOC-EQUAL-WHEN-PSEUDO-DAGP-AUX))
 (26 26 (:REWRITE ASSOC-EQUAL-WHEN-BINDS-ALL-NATS-UP-TO))
 (26 13 (:REWRITE IFF-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (26 13 (:REWRITE CAR-WHEN-ALISTP-IFF-CHEAP))
 (24 8 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (21 21 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (19 13 (:REWRITE DEFAULT-<-2))
 (16 16 (:TYPE-PRESCRIPTION WEAK-DAGP-AUX))
 (16 16 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (16 16 (:TYPE-PRESCRIPTION ALL-CONSP))
 (16 16 (:REWRITE USE-ALL-CONSP-2))
 (16 16 (:REWRITE USE-ALL-CONSP))
 (16 13 (:REWRITE DEFAULT-<-1))
 (16 8 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (16 8 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (16 8 (:REWRITE ALISTP-WHEN-RENUMBERINGP-CHEAP))
 (13 13 (:REWRITE USE-ALL-<-2))
 (13 13 (:REWRITE USE-ALL-<))
 (13 13 (:REWRITE DEFAULT-CDR))
 (9 9 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (8 8 (:TYPE-PRESCRIPTION RENUMBERINGP))
 (8 8 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (8 8 (:REWRITE EQUAL-OF-NON-NATP-AND-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (8 8 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (8 8 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (8 8 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (8 8 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (8 8 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (8 8 (:REWRITE ALISTP-WHEN-PSEUDO-DAGP-AUX))
 (8 8 (:REWRITE ALISTP-WHEN-BOUNDED-NATP-ALISTP))
 (7 7 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (7 7 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (5 5 (:REWRITE USE-ALL-NATP-2))
 (5 5 (:REWRITE USE-ALL-NATP))
 (4 4 (:REWRITE DEFAULT-+-2))
 (4 4 (:REWRITE DEFAULT-+-1))
 )
(BINDS-ALL-NATS-UP-TO-OF-ACONS-OF-ONE-MORE
 (28 4 (:REWRITE DEFAULT-CAR))
 (7 7 (:REWRITE DEFAULT-+-2))
 (7 7 (:REWRITE DEFAULT-+-1))
 (7 1 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-ALT))
 (5 5 (:TYPE-PRESCRIPTION ALISTP))
 (5 1 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (4 2 (:TYPE-PRESCRIPTION CAR-OF-CAR-TYPE-WHEN-WEAK-DAGP-AUX-TYPE))
 (4 2 (:REWRITE CAR-WHEN-ALISTP-IFF-CHEAP))
 (3 3 (:REWRITE ASSOC-EQUAL-WHEN-PSEUDO-DAGP-AUX))
 (3 1 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (2 2 (:TYPE-PRESCRIPTION WEAK-DAGP-AUX))
 (2 2 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (2 2 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (2 2 (:TYPE-PRESCRIPTION ALL-CONSP))
 (2 2 (:REWRITE USE-ALL-CONSP-2))
 (2 2 (:REWRITE USE-ALL-CONSP))
 (2 2 (:REWRITE USE-ALL-<-2))
 (2 2 (:REWRITE USE-ALL-<))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 1 (:REWRITE IFF-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (2 1 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (2 1 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (2 1 (:REWRITE ALISTP-WHEN-RENUMBERINGP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION RENUMBERINGP))
 (1 1 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (1 1 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE EQUAL-OF-NON-NATP-AND-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (1 1 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (1 1 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (1 1 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (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))
 )
(CONSP-OF-RENUMBER-DAG-EXPR
 (11 11 (:TYPE-PRESCRIPTION RENUMBER-DAG-EXPR))
 (7 1 (:DEFINITION RENUMBER-DAG-EXPR-ARGS))
 (4 4 (:REWRITE USE-ALL-CONSP-2))
 (4 4 (:REWRITE USE-ALL-CONSP))
 (3 2 (:REWRITE CAR-OF-DARGS-BECOMES-NTH-0-OF-DARGS))
 (2 2 (:REWRITE DEFAULT-CAR))
 (2 1 (:DEFINITION NTH))
 (1 1 (:REWRITE DEFAULT-CDR))
 )
(QUOTEP-OF-RENUMBER-DAG-EXPR
 (11 11 (:TYPE-PRESCRIPTION RENUMBER-DAG-EXPR))
 (11 4 (:REWRITE DEFAULT-CAR))
 (7 1 (:DEFINITION RENUMBER-DAG-EXPR-ARGS))
 (4 4 (:REWRITE USE-ALL-CONSP-2))
 (4 4 (:REWRITE USE-ALL-CONSP))
 (3 2 (:REWRITE CAR-OF-DARGS-BECOMES-NTH-0-OF-DARGS))
 (2 1 (:DEFINITION NTH))
 (1 1 (:REWRITE DEFAULT-CDR))
 )
(RENUMBER-DAG-EXPR-WHEN-NOT-CONSP
 (1 1 (:REWRITE USE-ALL-CONSP-2))
 (1 1 (:REWRITE USE-ALL-CONSP))
 )
(RENUMBER-DAG-EXPR-WHEN-QUOTEP
 (19 19 (:TYPE-PRESCRIPTION RENUMBER-DAG-EXPR))
 (4 2 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE USE-ALL-CONSP-2))
 (3 3 (:REWRITE USE-ALL-CONSP))
 (3 1 (:REWRITE RENUMBER-DAG-EXPR-WHEN-NOT-CONSP))
 )
(PSEUDO-DAGP-AUX-OF-MINUS1
 (1 1 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 )
(MAPS-EVERYTHING-TO-QUOTE-OR-NODENUM-LESS-THAN-MONOTONIC
 (971 83 (:REWRITE DEFAULT-CDR))
 (259 37 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-ALT))
 (185 37 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (111 111 (:TYPE-PRESCRIPTION ALISTP))
 (111 37 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (74 74 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (74 74 (:TYPE-PRESCRIPTION ALL-CONSP))
 (74 37 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (74 37 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (74 37 (:REWRITE ALISTP-WHEN-RENUMBERINGP-CHEAP))
 (72 72 (:REWRITE USE-ALL-<-2))
 (72 72 (:REWRITE USE-ALL-<))
 (72 72 (:REWRITE DEFAULT-<-2))
 (72 72 (:REWRITE DEFAULT-<-1))
 (71 71 (:REWRITE USE-ALL-CONSP-2))
 (71 71 (:REWRITE USE-ALL-CONSP))
 (56 56 (:REWRITE DEFAULT-CAR))
 (37 37 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (37 37 (:TYPE-PRESCRIPTION RENUMBERINGP))
 (37 37 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (37 37 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (37 37 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 (37 37 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (37 37 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (37 37 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (37 37 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (37 37 (:REWRITE ALISTP-WHEN-PSEUDO-DAGP-AUX))
 (37 37 (:REWRITE ALISTP-WHEN-BOUNDED-NATP-ALISTP))
 (35 35 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (35 35 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (15 15 (:REWRITE USE-ALL-NATP-2))
 (15 15 (:REWRITE USE-ALL-NATP))
 )
(PSEUDO-DAGP-AUX-OF-ACONS
 (32 2 (:REWRITE BOUNDED-DAG-EXPRP-OF-CDR-OF-CAR-WHEN-WEAK-DAGP-AUX))
 (20 2 (:REWRITE PSEUDO-DAGP-AUX-OF-CDR))
 (18 2 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX-2))
 (14 2 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-ALT))
 (12 4 (:REWRITE FOLD-CONSTS-IN-+))
 (11 11 (:REWRITE DEFAULT-+-2))
 (11 11 (:REWRITE DEFAULT-+-1))
 (11 10 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (10 5 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (10 2 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (9 9 (:REWRITE DEFAULT-CAR))
 (8 8 (:TYPE-PRESCRIPTION WEAK-DAGP-AUX))
 (8 8 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (8 4 (:TYPE-PRESCRIPTION CAR-OF-CAR-TYPE-WHEN-WEAK-DAGP-AUX-TYPE))
 (8 2 (:DEFINITION TOP-NODENUM))
 (6 6 (:TYPE-PRESCRIPTION ALISTP))
 (6 2 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP))
 (6 2 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (5 5 (:TYPE-PRESCRIPTION MYQUOTEP))
 (5 5 (:REWRITE DEFAULT-CDR))
 (5 5 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP-CHEAP))
 (5 5 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP))
 (5 5 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP-CHEAP))
 (5 5 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (5 5 (:REWRITE BOUNDED-DAG-EXPRP-MONOTONE))
 (4 4 (:TYPE-PRESCRIPTION ALL-CONSP))
 (4 4 (:REWRITE USE-ALL-CONSP-2))
 (4 4 (:REWRITE USE-ALL-CONSP))
 (4 4 (:REWRITE USE-ALL-<-2))
 (4 4 (:REWRITE USE-ALL-<))
 (4 4 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (4 4 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (4 2 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (4 2 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (4 2 (:REWRITE ALISTP-WHEN-RENUMBERINGP-CHEAP))
 (2 2 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (2 2 (:TYPE-PRESCRIPTION RENUMBERINGP))
 (2 2 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (2 2 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (2 2 (:REWRITE EQUAL-OF-NON-NATP-AND-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (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 ALISTP-WHEN-PSEUDO-DAGP-AUX))
 (2 2 (:REWRITE ALISTP-WHEN-BOUNDED-NATP-ALISTP))
 (1 1 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 )
(CONSP-OF-CDDR-OF-ASSOC-EQUAL-WHEN-MAPS-EVERYTHING-TO-QUOTE-OR-NODENUM-LESS-THAN
 (1333 157 (:REWRITE DEFAULT-CAR))
 (453 93 (:REWRITE DEFAULT-CDR))
 (418 64 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-ALT))
 (382 191 (:TYPE-PRESCRIPTION CAR-OF-CAR-TYPE-WHEN-WEAK-DAGP-AUX-TYPE))
 (300 64 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (191 191 (:TYPE-PRESCRIPTION WEAK-DAGP-AUX))
 (182 64 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (142 142 (:REWRITE USE-ALL-CONSP-2))
 (142 142 (:REWRITE USE-ALL-CONSP))
 (128 64 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (128 64 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (118 118 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (118 118 (:TYPE-PRESCRIPTION ALL-CONSP))
 (118 59 (:REWRITE ALISTP-WHEN-RENUMBERINGP-CHEAP))
 (77 77 (:TYPE-PRESCRIPTION RENUMBERINGP))
 (72 72 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (64 64 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (64 64 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (64 64 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (59 59 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (59 59 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (59 59 (:REWRITE ALISTP-WHEN-PSEUDO-DAGP-AUX))
 (59 59 (:REWRITE ALISTP-WHEN-BOUNDED-NATP-ALISTP))
 (58 58 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (30 20 (:REWRITE DEFAULT-<-2))
 (27 9 (:REWRITE INTEGERP-OF-CDR-OF-ASSOC-EQUAL-WHEN-RENUMBERINGP))
 (25 25 (:REWRITE ASSOC-EQUAL-WHEN-PSEUDO-DAGP-AUX))
 (25 25 (:REWRITE ASSOC-EQUAL-WHEN-BINDS-ALL-NATS-UP-TO))
 (20 20 (:REWRITE USE-ALL-<-2))
 (20 20 (:REWRITE USE-ALL-<))
 (20 20 (:REWRITE DEFAULT-<-1))
 (19 19 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (16 16 (:REWRITE EQUAL-OF-NON-NATP-AND-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (16 8 (:REWRITE IFF-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (16 8 (:REWRITE CAR-WHEN-ALISTP-IFF-CHEAP))
 (14 14 (:REWRITE MAPS-EVERYTHING-TO-QUOTE-OR-NODENUM-LESS-THAN-MONOTONIC))
 (10 10 (:REWRITE USE-ALL-NATP-2))
 (10 10 (:REWRITE USE-ALL-NATP))
 (10 10 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (10 10 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (10 10 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (10 10 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 )
(QUOTEP-OF-CDR-OF-ASSOC-EQUAL-WHEN-MAPS-EVERYTHING-TO-QUOTE-OR-NODENUM-LESS-THAN
 (413 75 (:REWRITE DEFAULT-CDR))
 (406 64 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-ALT))
 (374 187 (:TYPE-PRESCRIPTION CAR-OF-CAR-TYPE-WHEN-WEAK-DAGP-AUX-TYPE))
 (292 64 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (187 187 (:TYPE-PRESCRIPTION WEAK-DAGP-AUX))
 (178 64 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (128 64 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (128 64 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (127 127 (:REWRITE USE-ALL-CONSP-2))
 (127 127 (:REWRITE USE-ALL-CONSP))
 (114 114 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (114 114 (:TYPE-PRESCRIPTION ALL-CONSP))
 (114 57 (:REWRITE ALISTP-WHEN-RENUMBERINGP-CHEAP))
 (71 71 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (65 65 (:TYPE-PRESCRIPTION RENUMBERINGP))
 (64 64 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (64 64 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (64 64 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (59 59 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (57 57 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (57 57 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (57 57 (:REWRITE ALISTP-WHEN-PSEUDO-DAGP-AUX))
 (57 57 (:REWRITE ALISTP-WHEN-BOUNDED-NATP-ALISTP))
 (27 18 (:REWRITE DEFAULT-<-2))
 (23 23 (:REWRITE ASSOC-EQUAL-WHEN-PSEUDO-DAGP-AUX))
 (23 23 (:REWRITE ASSOC-EQUAL-WHEN-BINDS-ALL-NATS-UP-TO))
 (18 18 (:REWRITE USE-ALL-<-2))
 (18 18 (:REWRITE USE-ALL-<))
 (18 18 (:REWRITE DEFAULT-<-1))
 (14 7 (:REWRITE IFF-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (14 7 (:REWRITE CAR-WHEN-ALISTP-IFF-CHEAP))
 (13 13 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (13 13 (:REWRITE EQUAL-OF-NON-NATP-AND-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (12 12 (:REWRITE MAPS-EVERYTHING-TO-QUOTE-OR-NODENUM-LESS-THAN-MONOTONIC))
 (12 4 (:REWRITE INTEGERP-OF-CDR-OF-ASSOC-EQUAL-WHEN-RENUMBERINGP))
 (9 9 (:REWRITE USE-ALL-NATP-2))
 (9 9 (:REWRITE USE-ALL-NATP))
 (9 9 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (9 9 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (9 9 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (9 9 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 )
(BOUNDED-DARG-LISTP-OF-RENUMBER-DAG-EXPR-ARGS
 (1514 75 (:DEFINITION ASSOC-EQUAL))
 (973 82 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (772 140 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-ALT))
 (748 369 (:REWRITE DEFAULT-CAR))
 (734 19 (:DEFINITION MAPS-EVERYTHING-TO-QUOTE-OR-NODENUM-LESS-THAN))
 (512 319 (:REWRITE DEFAULT-CDR))
 (436 218 (:TYPE-PRESCRIPTION CAR-OF-CAR-TYPE-WHEN-WEAK-DAGP-AUX-TYPE))
 (416 338 (:REWRITE USE-ALL-CONSP))
 (408 18 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (369 7 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (355 13 (:DEFINITION NAT-LISTP))
 (350 46 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (338 338 (:REWRITE USE-ALL-CONSP-2))
 (280 140 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (234 164 (:REWRITE ALISTP-WHEN-RENUMBERINGP-CHEAP))
 (218 218 (:TYPE-PRESCRIPTION WEAK-DAGP-AUX))
 (168 24 (:REWRITE ALISTP-OF-CDR))
 (138 46 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (120 24 (:REWRITE ALL-CONSP-OF-CDR))
 (107 106 (:REWRITE DEFAULT-<-1))
 (106 106 (:REWRITE USE-ALL-<-2))
 (106 106 (:REWRITE USE-ALL-<))
 (106 106 (:REWRITE DEFAULT-<-2))
 (104 30 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (96 6 (:REWRITE USE-ALL-<-FOR-CAR))
 (92 92 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (92 46 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (90 6 (:REWRITE INTEGERP-OF-CDR-OF-ASSOC-EQUAL-WHEN-RENUMBERINGP))
 (83 83 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (83 83 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (83 83 (:REWRITE ALL-<-TRANSITIVE))
 (78 78 (:TYPE-PRESCRIPTION MEMBERP))
 (78 78 (:REWRITE EQUAL-OF-NON-NATP-AND-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (78 78 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (71 8 (:REWRITE ALL-<-OF-CDR))
 (70 70 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (70 70 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (70 70 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (70 70 (:REWRITE ALISTP-WHEN-PSEUDO-DAGP-AUX))
 (70 70 (:REWRITE ALISTP-WHEN-BOUNDED-NATP-ALISTP))
 (66 33 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (64 64 (:REWRITE USE-ALL-NATP-2))
 (64 64 (:REWRITE USE-ALL-NATP))
 (62 62 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (54 54 (:REWRITE DEFAULT-+-2))
 (54 54 (:REWRITE DEFAULT-+-1))
 (50 50 (:TYPE-PRESCRIPTION NAT-LISTP))
 (48 48 (:REWRITE ASSOC-EQUAL-WHEN-PSEUDO-DAGP-AUX))
 (48 24 (:REWRITE IFF-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (48 24 (:REWRITE CAR-WHEN-ALISTP-IFF-CHEAP))
 (46 46 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (46 46 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (46 46 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (43 2 (:REWRITE ALL-<-OF-CONS))
 (30 18 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (30 5 (:REWRITE ALL-MYQUOTEP-WHEN-NOT-CONSP))
 (26 26 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (26 26 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 (24 1 (:REWRITE MYQUOTEP-OF-CDR-OF-ASSOC-EQUAL))
 (19 19 (:TYPE-PRESCRIPTION NATP))
 (18 18 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (14 7 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (12 6 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (12 6 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (12 6 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (12 6 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (9 6 (:REWRITE DARGP-LESS-THAN-WHEN-NATP-CHEAP))
 (6 6 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (6 6 (:REWRITE DARGP-LESS-THAN-WHEN-QUOTEP-CHEAP))
 (6 6 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (6 6 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-CAR-AND-QUOTE))
 (6 6 (:REWRITE DARGP-LESS-THAN-MONO))
 (6 6 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (2 2 (:TYPE-PRESCRIPTION QUOTEP))
 (1 1 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (1 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(ALL-DARGP-OF-RENUMBER-DAG-EXPR-ARGS
 (1080 55 (:DEFINITION ASSOC-EQUAL))
 (885 16 (:REWRITE ALL-DARGP-WHEN-NOT-CONSP))
 (606 106 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-ALT))
 (551 272 (:REWRITE DEFAULT-CAR))
 (514 14 (:DEFINITION MAPS-EVERYTHING-TO-QUOTE-OR-NODENUM-LESS-THAN))
 (394 244 (:REWRITE DEFAULT-CDR))
 (356 178 (:TYPE-PRESCRIPTION CAR-OF-CAR-TYPE-WHEN-WEAK-DAGP-AUX-TYPE))
 (285 37 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (247 247 (:REWRITE USE-ALL-CONSP-2))
 (247 247 (:REWRITE USE-ALL-CONSP))
 (212 106 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (201 9 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (183 126 (:REWRITE ALISTP-WHEN-RENUMBERINGP-CHEAP))
 (183 4 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (178 178 (:TYPE-PRESCRIPTION WEAK-DAGP-AUX))
 (175 7 (:DEFINITION NAT-LISTP))
 (140 20 (:REWRITE ALISTP-OF-CDR))
 (114 114 (:TYPE-PRESCRIPTION ALL-CONSP))
 (111 37 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (100 20 (:REWRITE ALL-CONSP-OF-CDR))
 (86 2 (:REWRITE <-OF-CDR-OF-ASSOC-EQUAL-WHEN-MAPS-EVERYTHING-TO-QUOTE-OR-NODENUM-LESS-THAN))
 (74 74 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (74 37 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (73 73 (:REWRITE USE-ALL-<-2))
 (73 73 (:REWRITE USE-ALL-<))
 (73 73 (:REWRITE DEFAULT-<-2))
 (73 73 (:REWRITE DEFAULT-<-1))
 (58 58 (:REWRITE EQUAL-OF-NON-NATP-AND-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (58 58 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (57 57 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (57 57 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (57 57 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (57 57 (:REWRITE ALISTP-WHEN-PSEUDO-DAGP-AUX))
 (57 57 (:REWRITE ALISTP-WHEN-BOUNDED-NATP-ALISTP))
 (52 52 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (48 3 (:REWRITE USE-ALL-<-FOR-CAR))
 (47 5 (:REWRITE ALL-<-OF-CDR))
 (46 4 (:REWRITE INTEGERP-OF-CDR-OF-ASSOC-EQUAL-WHEN-RENUMBERINGP))
 (45 45 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (43 43 (:REWRITE USE-ALL-NATP-2))
 (43 43 (:REWRITE USE-ALL-NATP))
 (39 39 (:REWRITE DEFAULT-+-2))
 (39 39 (:REWRITE DEFAULT-+-1))
 (37 37 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (37 37 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (37 37 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (36 33 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (34 34 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (34 34 (:REWRITE ALL-<-TRANSITIVE))
 (32 16 (:REWRITE ALL-DARGP-WHEN-NOT-CONSP-CHEAP))
 (32 16 (:REWRITE ALL-DARGP-WHEN-ALL-MYQUOTEP-CHEAP))
 (30 30 (:REWRITE ASSOC-EQUAL-WHEN-PSEUDO-DAGP-AUX))
 (30 15 (:REWRITE IFF-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (30 15 (:REWRITE CAR-WHEN-ALISTP-IFF-CHEAP))
 (28 28 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (26 26 (:TYPE-PRESCRIPTION NAT-LISTP))
 (24 12 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (24 1 (:REWRITE MYQUOTEP-OF-CDR-OF-ASSOC-EQUAL))
 (21 21 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (21 21 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 (16 16 (:REWRITE ALL-DARGP-WHEN-BOUNDED-DARG-LISTP))
 (15 9 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (12 12 (:REWRITE BOUNDED-DARG-LISTP-MONOTONE))
 (11 11 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (9 9 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (8 4 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (6 3 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (6 3 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (6 3 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (6 3 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (4 2 (:REWRITE USE-ALL-DARGP))
 (4 2 (:REWRITE DARGP-WHEN-NATP-CHEAP))
 (4 2 (:REWRITE DARGP-WHEN-MYQUOTEP-CHEAP))
 (3 3 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (3 3 (:REWRITE DARGP-LESS-THAN-WHEN-QUOTEP-CHEAP))
 (3 3 (:REWRITE DARGP-LESS-THAN-WHEN-NOT-CONSP-CHEAP))
 (3 3 (:REWRITE DARGP-LESS-THAN-WHEN-NATP-CHEAP))
 (3 3 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (3 3 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-CAR-AND-QUOTE))
 (3 3 (:REWRITE DARGP-LESS-THAN-MONO))
 (3 3 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (2 2 (:TYPE-PRESCRIPTION QUOTEP))
 (2 2 (:TYPE-PRESCRIPTION MEMBERP))
 (2 2 (:REWRITE USE-ALL-DARGP-2))
 (2 2 (:REWRITE DARGP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (2 2 (:REWRITE DARGP-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE DARGP-WHEN-CONSP-CHEAP))
 (1 1 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 )
(BOUNDED-DAG-EXPRP-OF-RENUMBER-DAG-EXPR
 (148 4 (:DEFINITION MAPS-EVERYTHING-TO-QUOTE-OR-NODENUM-LESS-THAN))
 (62 4 (:REWRITE BOUNDED-DARG-LISTP-OF-DARGS-WHEN-<-SIMPLE))
 (53 4 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DAG-EXPRP))
 (53 4 (:REWRITE BOUNDED-DARG-LISTP-OF-DARGS-WHEN-BOUNDED-DAG-EXPRP))
 (49 29 (:REWRITE DEFAULT-CDR))
 (35 30 (:REWRITE DEFAULT-CAR))
 (28 28 (:REWRITE USE-ALL-CONSP-2))
 (28 28 (:REWRITE USE-ALL-CONSP))
 (24 4 (:REWRITE ALL-DARGP-OF-DARGS-WHEN-DAG-EXPRP))
 (24 1 (:DEFINITION ASSOC-EQUAL))
 (22 4 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-<))
 (18 18 (:REWRITE USE-ALL-<-2))
 (18 18 (:REWRITE USE-ALL-<))
 (18 18 (:REWRITE DEFAULT-<-2))
 (18 18 (:REWRITE DEFAULT-<-1))
 (15 5 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-ALT))
 (12 12 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (12 4 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (12 4 (:REWRITE ALL-DARGP-WHEN-NOT-CONSP))
 (11 11 (:TYPE-PRESCRIPTION ALISTP))
 (10 5 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (9 9 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (9 9 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (9 9 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 (9 9 (:REWRITE DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (9 9 (:REWRITE DAG-EXPRP-WHEN-BOUNDED-DAG-EXPRP))
 (8 8 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (8 8 (:REWRITE MAPS-EVERYTHING-TO-QUOTE-OR-NODENUM-LESS-THAN-MONOTONIC))
 (8 4 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (8 4 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (8 4 (:REWRITE ALL-DARGP-WHEN-ALL-MYQUOTEP-CHEAP))
 (7 7 (:REWRITE USE-ALL-NATP-2))
 (7 7 (:REWRITE USE-ALL-NATP))
 (7 1 (:DEFINITION RENUMBER-DAG-EXPR-ARGS))
 (6 2 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (6 1 (:REWRITE TRUE-LISTP-OF-DARGS-WHEN-DAG-EXPRP))
 (5 5 (:REWRITE DEFAULT-+-2))
 (5 5 (:REWRITE DEFAULT-+-1))
 (5 5 (:REWRITE ALISTP-WHEN-RENUMBERINGP-CHEAP))
 (5 4 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP-CHEAP))
 (5 1 (:DEFINITION TRUE-LISTP))
 (4 4 (:TYPE-PRESCRIPTION MYQUOTEP))
 (4 4 (:TYPE-PRESCRIPTION ALL-<))
 (4 4 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DAG-EXPRP-GEN))
 (4 4 (:REWRITE BOUNDED-DARG-LISTP-MONOTONE))
 (4 4 (:REWRITE BOUNDED-DAG-EXPRP-MONOTONE))
 (4 4 (:REWRITE ALL-DARGP-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:REWRITE ALL-DARGP-WHEN-BOUNDED-DARG-LISTP))
 (4 2 (:TYPE-PRESCRIPTION CAR-OF-CAR-TYPE-WHEN-WEAK-DAGP-AUX-TYPE))
 (3 3 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP-CHEAP))
 (3 2 (:REWRITE CAR-OF-DARGS-BECOMES-NTH-0-OF-DARGS))
 (2 2 (:TYPE-PRESCRIPTION WEAK-DAGP-AUX))
 (2 2 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (2 2 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (2 2 (:REWRITE ASSOC-EQUAL-WHEN-PSEUDO-DAGP-AUX))
 (2 2 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (2 2 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (2 2 (:REWRITE ALL-<-TRANSITIVE))
 (2 1 (:REWRITE IFF-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (2 1 (:REWRITE CAR-WHEN-ALISTP-IFF-CHEAP))
 (2 1 (:DEFINITION NTH))
 (1 1 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (1 1 (:REWRITE TRUE-LISTP-OF-DARGS-WHEN-BOUNDED-DAG-EXPRP-AND-CONSP))
 (1 1 (:REWRITE TRUE-LISTP-OF-DARGS-BETTER))
 (1 1 (:REWRITE SYMBOLP-OF-CAR-WHEN-BOUNDED-DAG-EXPRP))
 (1 1 (:REWRITE EQUAL-OF-NON-NATP-AND-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (1 1 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 )
(BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP
 (2 2 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (2 1 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION MYQUOTEP))
 (1 1 (:REWRITE USE-ALL-CONSP-2))
 (1 1 (:REWRITE USE-ALL-CONSP))
 (1 1 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP-CHEAP))
 (1 1 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP))
 (1 1 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (1 1 (:REWRITE BOUNDED-DAG-EXPRP-MONOTONE))
 )
(BOUNDED-DAG-EXPRP-WHEN-QUOTEP
 (10 6 (:REWRITE DEFAULT-CDR))
 (8 8 (:REWRITE USE-ALL-CONSP-2))
 (8 8 (:REWRITE USE-ALL-CONSP))
 (4 2 (:REWRITE DEFAULT-CAR))
 (3 1 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP))
 (1 1 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 (1 1 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP))
 )
(DAG-EXPR-OF-CAAR-AND-CDAR-WHEN-WEAK-DAGP-AUX
 (185 3 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (178 1 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (176 2 (:DEFINITION NAT-LISTP))
 (60 4 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX-2))
 (44 18 (:REWRITE DEFAULT-CAR))
 (40 4 (:REWRITE USE-ALL-<-FOR-CAR))
 (40 4 (:DEFINITION TOP-NODENUM))
 (34 2 (:LINEAR CAR-OF-CAR-LINEAR-WHEN-WEAK-DAGP-AUX))
 (17 1 (:REWRITE BOUNDED-DAG-EXPRP-OF-CDR-OF-CAR-WHEN-WEAK-DAGP-AUX))
 (14 14 (:TYPE-PRESCRIPTION ALL-<))
 (14 2 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-ALT))
 (12 12 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (12 4 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP))
 (10 2 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (8 8 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (8 8 (:TYPE-PRESCRIPTION NAT-LISTP))
 (8 8 (:TYPE-PRESCRIPTION ALL-NATP))
 (8 8 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (8 4 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (8 4 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (8 4 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (8 1 (:REWRITE ALL-<-OF-CDR))
 (6 3 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-CHEAP))
 (6 3 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-AUX-CHEAP))
 (6 2 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (5 5 (:REWRITE USE-ALL-CONSP-2))
 (5 5 (:REWRITE USE-ALL-CONSP))
 (5 5 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (5 5 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (5 5 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (5 5 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (5 5 (:REWRITE ALL-<-TRANSITIVE))
 (5 1 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-QUOTEP))
 (4 4 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (4 4 (:TYPE-PRESCRIPTION ALL-CONSP))
 (4 4 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (4 4 (:REWRITE USE-ALL-<-2))
 (4 4 (:REWRITE USE-ALL-<))
 (4 4 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:REWRITE PSEUDO-DAGP-AUX-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (4 4 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (4 4 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (4 4 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (4 4 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (4 4 (:REWRITE DEFAULT-CDR))
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (4 2 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (4 2 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (4 2 (:REWRITE ALISTP-WHEN-RENUMBERINGP-CHEAP))
 (3 3 (:TYPE-PRESCRIPTION WEAK-DAGP))
 (3 3 (:REWRITE USE-ALL-NATP-2))
 (3 3 (:REWRITE USE-ALL-NATP))
 (3 3 (:REWRITE INTEGERP-OF-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (3 3 (:REWRITE <-OF-0-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (3 1 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP))
 (2 2 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (2 2 (:TYPE-PRESCRIPTION RENUMBERINGP))
 (2 2 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (2 2 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (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 ALISTP-WHEN-PSEUDO-DAGP-AUX))
 (2 2 (:REWRITE ALISTP-WHEN-BOUNDED-NATP-ALISTP))
 (2 1 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (2 1 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION MYQUOTEP))
 (1 1 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP-CHEAP))
 (1 1 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP))
 (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 (:DEFINITION EQ))
 )
(RENUMBER-DAG-EXPR-ARGS-WHEN-BOUNDED-DARG-LISTP-OF-0
 (29 11 (:REWRITE USE-ALL-CONSP))
 (21 3 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-ALT))
 (18 18 (:TYPE-PRESCRIPTION MEMBERP))
 (11 11 (:REWRITE USE-ALL-CONSP-2))
 (9 9 (:TYPE-PRESCRIPTION ALISTP))
 (9 3 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (7 3 (:REWRITE ALL-MYQUOTEP-WHEN-NOT-CONSP))
 (6 6 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (6 6 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (6 3 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (6 3 (:REWRITE ALISTP-WHEN-RENUMBERINGP-CHEAP))
 (5 5 (:REWRITE DEFAULT-CDR))
 (3 3 (:TYPE-PRESCRIPTION RENUMBERINGP))
 (3 3 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (3 3 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (3 3 (:REWRITE ALISTP-WHEN-PSEUDO-DAGP-AUX))
 (3 3 (:REWRITE ALISTP-WHEN-BOUNDED-NATP-ALISTP))
 )
(RENUMBER-DAG-EXPR-WHEN-BOUNDED-DAG-EXPRP-OF-0
 (156 10 (:REWRITE TRUE-LISTP-OF-DARGS-WHEN-DAG-EXPRP))
 (86 10 (:DEFINITION TRUE-LISTP))
 (59 5 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DAG-EXPRP))
 (59 5 (:REWRITE BOUNDED-DARG-LISTP-OF-DARGS-WHEN-BOUNDED-DAG-EXPRP))
 (55 31 (:REWRITE USE-ALL-CONSP))
 (51 51 (:REWRITE DEFAULT-CAR))
 (32 5 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-<))
 (31 31 (:REWRITE USE-ALL-CONSP-2))
 (28 12 (:REWRITE ALL-MYQUOTEP-WHEN-NOT-CONSP))
 (24 24 (:TYPE-PRESCRIPTION MEMBERP))
 (21 21 (:REWRITE DEFAULT-CDR))
 (20 20 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (15 15 (:REWRITE DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (15 15 (:REWRITE DAG-EXPRP-WHEN-BOUNDED-DAG-EXPRP))
 (12 4 (:REWRITE ALL-DARGP-WHEN-NOT-CONSP))
 (10 10 (:REWRITE TRUE-LISTP-OF-DARGS-WHEN-BOUNDED-DAG-EXPRP-AND-CONSP))
 (10 10 (:REWRITE TRUE-LISTP-OF-DARGS-BETTER))
 (10 10 (:REWRITE ALL-DARGP-WHEN-BOUNDED-DARG-LISTP))
 (9 9 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (9 9 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 (9 3 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (8 4 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (6 6 (:TYPE-PRESCRIPTION ALL-<))
 (5 5 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (5 5 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DAG-EXPRP-GEN))
 (4 4 (:TYPE-PRESCRIPTION MYQUOTEP))
 (4 4 (:REWRITE SYMBOLP-OF-CAR-WHEN-BOUNDED-DAG-EXPRP))
 (4 4 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP-CHEAP))
 (4 4 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP))
 (4 4 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-QUOTEP))
 (4 4 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP))
 (4 4 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (4 4 (:REWRITE BOUNDED-DAG-EXPRP-MONOTONE))
 (4 4 (:REWRITE ALL-DARGP-WHEN-NOT-CONSP-CHEAP))
 (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))
 )
(MERGE-DAG-INTO-DAG-AUX
 (8967 2484 (:REWRITE DEFAULT-CAR))
 (6852 143 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (6165 61 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (5982 61 (:DEFINITION NAT-LISTP))
 (2787 254 (:REWRITE PSEUDO-DAGP-AUX-OF-CDR))
 (1807 383 (:REWRITE DEFAULT-+-2))
 (1780 191 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (1465 573 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP))
 (1380 460 (:TYPE-PRESCRIPTION FIND-NODE-FOR-EXPR2-TYPE))
 (1342 118 (:REWRITE USE-ALL-<-FOR-CAR))
 (1226 214 (:REWRITE ALISTP-OF-CDR))
 (1132 821 (:REWRITE DEFAULT-CDR))
 (1115 615 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (1075 281 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-QUOTEP))
 (903 903 (:REWRITE USE-ALL-CONSP-2))
 (903 903 (:REWRITE USE-ALL-CONSP))
 (810 162 (:REWRITE ALL-CONSP-OF-CDR))
 (757 109 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (706 706 (:TYPE-PRESCRIPTION ALL-CONSP))
 (673 281 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP))
 (628 628 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (573 191 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (550 275 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (514 143 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (504 120 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (383 383 (:REWRITE DEFAULT-+-1))
 (382 191 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (368 353 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (366 366 (:TYPE-PRESCRIPTION NAT-LISTP))
 (358 358 (:TYPE-PRESCRIPTION ALL-<))
 (353 353 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (353 353 (:REWRITE ALISTP-WHEN-BOUNDED-NATP-ALISTP))
 (336 336 (:TYPE-PRESCRIPTION ALL-NATP))
 (317 61 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (280 277 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP))
 (278 275 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP-CHEAP))
 (278 275 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (277 277 (:TYPE-PRESCRIPTION MYQUOTEP))
 (272 136 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (272 136 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (272 136 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-CHEAP))
 (272 136 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-AUX-CHEAP))
 (257 235 (:REWRITE DEFAULT-<-1))
 (236 235 (:REWRITE DEFAULT-<-2))
 (236 118 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (235 235 (:REWRITE USE-ALL-<-2))
 (235 235 (:REWRITE USE-ALL-<))
 (208 208 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (208 190 (:DEFINITION EQ))
 (193 193 (:REWRITE USE-ALL-NATP-2))
 (193 193 (:REWRITE USE-ALL-NATP))
 (191 191 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (191 191 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (191 191 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (177 175 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP-CHEAP))
 (164 164 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (153 153 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (140 140 (:TYPE-PRESCRIPTION WEAK-DAGP))
 (136 136 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (136 136 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (136 136 (:REWRITE INTEGERP-OF-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (132 120 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (122 61 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (120 120 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (120 120 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (120 120 (:REWRITE ALL-<-TRANSITIVE))
 (116 116 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (116 116 (:REWRITE <-OF-0-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (67 23 (:REWRITE RENUMBER-DAG-EXPR-WHEN-NOT-CONSP))
 (62 62 (:REWRITE EQUAL-OF-NON-NATP-AND-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (61 61 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (52 52 (:REWRITE ASSOC-EQUAL-WHEN-PSEUDO-DAGP-AUX))
 (52 26 (:REWRITE CAR-WHEN-ALISTP-IFF-CHEAP))
 (45 23 (:REWRITE RENUMBER-DAG-EXPR-WHEN-QUOTEP))
 (34 17 (:REWRITE IFF-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (27 9 (:REWRITE CONSP-OF-RENUMBER-DAG-EXPR))
 (16 4 (:REWRITE DAG-EXPRP-OF-CDR-OF-CAR-WHEN-WEAK-DAGP))
 (15 15 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (15 15 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 (15 7 (:REWRITE NATP-OF-TOP-NODENUM-WHEN-PSEUDO-DAGP))
 (11 1 (:REWRITE WEAK-DAGP-AUX-OF-ACONS-OF-0-AND-NIL-WHEN-SYMBOLP))
 (10 4 (:REWRITE QUOTEP-OF-RENUMBER-DAG-EXPR))
 (8 1 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (6 2 (:REWRITE WEAK-DAGP-WHEN-PSEUDO-DAGP))
 (4 4 (:REWRITE USE-ALL-DARGP-2))
 (4 4 (:REWRITE USE-ALL-DARGP))
 (4 4 (:REWRITE DARGP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (4 4 (:REWRITE DARGP-WHEN-DARGP-LESS-THAN))
 (4 4 (:REWRITE DARGP-WHEN-CONSP-CHEAP))
 (4 2 (:REWRITE DARGP-WHEN-MYQUOTEP-CHEAP))
 (2 2 (:REWRITE WEAK-DAGP-WHEN-PSEUDO-DAGP-AUX))
 )
(CAR-OF-NTH-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX
 (304 11 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX-2))
 (250 16 (:REWRITE BOUNDED-DAG-EXPRP-OF-CDR-OF-CAR-WHEN-WEAK-DAGP-AUX))
 (115 81 (:REWRITE DEFAULT-CAR))
 (114 57 (:TYPE-PRESCRIPTION CAR-OF-CAR-TYPE-WHEN-WEAK-DAGP-AUX-TYPE))
 (89 89 (:TYPE-PRESCRIPTION WEAK-DAGP-AUX))
 (70 3 (:REWRITE DAG-EXPR-OF-CAAR-AND-CDAR-WHEN-WEAK-DAGP-AUX))
 (65 1 (:LINEAR CAR-OF-CAR-LINEAR-WHEN-WEAK-DAGP-AUX))
 (63 9 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-ALT))
 (60 16 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-QUOTEP))
 (47 47 (:REWRITE USE-ALL-CONSP-2))
 (47 47 (:REWRITE USE-ALL-CONSP))
 (45 9 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (40 10 (:DEFINITION TOP-NODENUM))
 (38 38 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (38 16 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP))
 (36 3 (:REWRITE PSEUDO-DAGP-AUX-OF-CDR))
 (32 16 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (31 11 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP))
 (29 29 (:REWRITE DEFAULT-CDR))
 (27 27 (:TYPE-PRESCRIPTION ALISTP))
 (27 9 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (22 22 (:REWRITE USE-ALL-<-2))
 (22 22 (:REWRITE USE-ALL-<))
 (22 22 (:REWRITE DEFAULT-<-2))
 (22 22 (:REWRITE DEFAULT-<-1))
 (19 19 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (18 18 (:TYPE-PRESCRIPTION ALL-CONSP))
 (18 9 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (18 9 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (18 9 (:REWRITE ALISTP-WHEN-RENUMBERINGP-CHEAP))
 (16 16 (:TYPE-PRESCRIPTION MYQUOTEP))
 (16 16 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP-CHEAP))
 (16 16 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP))
 (16 16 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (16 16 (:REWRITE BOUNDED-DAG-EXPRP-MONOTONE))
 (16 2 (:REWRITE USE-ALL-<-FOR-CAR))
 (15 15 (:REWRITE DEFAULT-+-2))
 (15 15 (:REWRITE DEFAULT-+-1))
 (15 15 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP-CHEAP))
 (15 3 (:REWRITE FOLD-CONSTS-IN-+))
 (14 2 (:REWRITE PSEUDO-DAGP-AUX-OF-NIL))
 (11 11 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (11 11 (:DEFINITION EQ))
 (9 9 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (9 9 (:TYPE-PRESCRIPTION RENUMBERINGP))
 (9 9 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (9 9 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (9 9 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (9 9 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (9 9 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (9 9 (:REWRITE ALISTP-WHEN-PSEUDO-DAGP-AUX))
 (9 9 (:REWRITE ALISTP-WHEN-BOUNDED-NATP-ALISTP))
 (8 8 (:REWRITE EQUAL-OF-NON-NATP-AND-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (6 6 (:TYPE-PRESCRIPTION ALL-<))
 (6 3 (:REWRITE UNICITY-OF-0))
 (4 4 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (4 2 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (3 3 (:DEFINITION FIX))
 (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 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 INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (2 1 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (2 1 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-CHEAP))
 (2 1 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-AUX-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION WEAK-DAGP))
 (1 1 (:TYPE-PRESCRIPTION ALL-NATP))
 (1 1 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (1 1 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (1 1 (:REWRITE INTEGERP-OF-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 )
(CAR-OF-CAR-OF-LAST-WHEN-PSEUDO-DAGP-AUX
 (2915 26 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX-2))
 (2757 16 (:LINEAR CAR-OF-CAR-LINEAR-WHEN-WEAK-DAGP-AUX))
 (987 151 (:REWRITE DEFAULT-CAR))
 (748 17 (:REWRITE USE-ALL-<-FOR-CAR))
 (721 25 (:DEFINITION TOP-NODENUM))
 (615 17 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (503 48 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (334 50 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-ALT))
 (290 25 (:REWRITE BOUNDED-DAG-EXPRP-OF-CDR-OF-CAR-WHEN-WEAK-DAGP-AUX))
 (264 264 (:TYPE-PRESCRIPTION ALL-CONSP))
 (247 39 (:REWRITE USE-ALL-CONSP-FOR-CAR-OF-LAST))
 (218 36 (:REWRITE DEFAULT-<-1))
 (197 37 (:REWRITE ALL-CONSP-OF-LAST))
 (169 132 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (169 132 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (154 28 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (144 144 (:TYPE-PRESCRIPTION ALISTP))
 (143 9 (:REWRITE PSEUDO-DAGP-AUX-OF-CDR))
 (142 142 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (142 30 (:REWRITE DEFAULT-+-2))
 (140 48 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (109 25 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-QUOTEP))
 (101 101 (:REWRITE USE-ALL-CONSP-2))
 (101 101 (:REWRITE USE-ALL-CONSP))
 (100 50 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (96 48 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (96 48 (:REWRITE ALISTP-WHEN-RENUMBERINGP-CHEAP))
 (84 10 (:REWRITE DAG-EXPR-OF-CAAR-AND-CDAR-WHEN-WEAK-DAGP-AUX))
 (77 69 (:REWRITE DEFAULT-CDR))
 (76 26 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP))
 (72 24 (:REWRITE ALL-CONSP-OF-CDR))
 (63 25 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP))
 (58 58 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (52 9 (:REWRITE FOLD-CONSTS-IN-+))
 (51 51 (:TYPE-PRESCRIPTION ALL-<))
 (50 25 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (48 48 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (48 48 (:TYPE-PRESCRIPTION RENUMBERINGP))
 (48 48 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (48 48 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (48 48 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (48 48 (:REWRITE ALISTP-WHEN-PSEUDO-DAGP-AUX))
 (46 46 (:REWRITE ALISTP-WHEN-BOUNDED-NATP-ALISTP))
 (36 36 (:REWRITE USE-ALL-<-2))
 (36 36 (:REWRITE USE-ALL-<))
 (36 36 (:REWRITE DEFAULT-<-2))
 (34 34 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (34 17 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (31 17 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (30 30 (:REWRITE DEFAULT-+-1))
 (27 19 (:DEFINITION EQ))
 (26 26 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (25 25 (:TYPE-PRESCRIPTION MYQUOTEP))
 (25 25 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP-CHEAP))
 (25 25 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP))
 (25 25 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (25 25 (:REWRITE BOUNDED-DAG-EXPRP-MONOTONE))
 (25 9 (:REWRITE UNICITY-OF-0))
 (24 24 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP-CHEAP))
 (17 17 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (17 17 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (17 17 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (17 17 (:REWRITE ALL-<-TRANSITIVE))
 (17 17 (:REWRITE <-OF-0-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (16 16 (:REWRITE PSEUDO-DAGP-AUX-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (16 9 (:DEFINITION FIX))
 (14 2 (:REWRITE PSEUDO-DAGP-AUX-OF-NIL))
 (11 11 (:REWRITE EQUAL-OF-NON-NATP-AND-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (5 5 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (2 1 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (2 1 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (2 1 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-CHEAP))
 (2 1 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-AUX-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION WEAK-DAGP))
 (1 1 (:TYPE-PRESCRIPTION ALL-NATP))
 (1 1 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (1 1 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (1 1 (:REWRITE INTEGERP-OF-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 )
(ALISTP-OF-MV-NTH-1-OF-MERGE-DAG-INTO-DAG-AUX
 (102 3 (:REWRITE RENUMBER-DAG-EXPR-WHEN-BOUNDED-DAG-EXPRP-OF-0))
 (96 18 (:REWRITE DEFAULT-CAR))
 (48 3 (:REWRITE BOUNDED-DAG-EXPRP-OF-CDR-OF-CAR-WHEN-WEAK-DAGP-AUX))
 (41 5 (:REWRITE DEFAULT-CDR))
 (27 3 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX-2))
 (24 12 (:REWRITE ALISTP-WHEN-RENUMBERINGP-CHEAP))
 (24 6 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-ALT))
 (19 19 (:REWRITE USE-ALL-CONSP-2))
 (19 19 (:REWRITE USE-ALL-CONSP))
 (18 6 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (15 3 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-QUOTEP))
 (12 12 (:TYPE-PRESCRIPTION RENUMBERINGP))
 (12 12 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (12 12 (:REWRITE ALISTP-WHEN-PSEUDO-DAGP-AUX))
 (12 12 (:REWRITE ALISTP-WHEN-BOUNDED-NATP-ALISTP))
 (12 6 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (12 6 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (12 6 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (12 3 (:DEFINITION TOP-NODENUM))
 (9 3 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP))
 (9 3 (:REWRITE RENUMBER-DAG-EXPR-WHEN-NOT-CONSP))
 (9 3 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP))
 (6 6 (:TYPE-PRESCRIPTION WEAK-DAGP-AUX))
 (6 6 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (6 6 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (6 6 (:TYPE-PRESCRIPTION BOUNDED-DAG-EXPRP))
 (6 6 (:TYPE-PRESCRIPTION ALL-CONSP))
 (6 6 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (6 6 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (6 6 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (6 6 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (6 3 (:REWRITE RENUMBER-DAG-EXPR-WHEN-QUOTEP))
 (6 3 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (3 3 (:TYPE-PRESCRIPTION MYQUOTEP))
 (3 3 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (3 3 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (3 3 (:REWRITE PSEUDO-DAGP-AUX-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (3 3 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP-CHEAP))
 (3 3 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP))
 (3 3 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP-CHEAP))
 (3 3 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-EQUAL-OF-QUOTE-AND-CAR-CHEAP))
 (3 3 (:REWRITE BOUNDED-DAG-EXPRP-MONOTONE))
 (3 3 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (3 3 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (3 3 (:DEFINITION EQ))
 )
(MERGE-DAG-INTO-DAG
 (2364 56 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (2086 1072 (:TYPE-PRESCRIPTION CAR-OF-CAR-TYPE-WHEN-WEAK-DAGP-AUX-TYPE))
 (1944 28 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (1860 28 (:DEFINITION NAT-LISTP))
 (1312 276 (:REWRITE DEFAULT-CAR))
 (672 42 (:REWRITE USE-ALL-<-FOR-CAR))
 (454 227 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (430 215 (:REWRITE ALISTP-WHEN-RENUMBERINGP-CHEAP))
 (378 42 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (372 28 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (252 28 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (232 34 (:REWRITE DEFAULT-CDR))
 (215 215 (:TYPE-PRESCRIPTION RENUMBERINGP))
 (204 56 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (168 168 (:TYPE-PRESCRIPTION NAT-LISTP))
 (154 154 (:TYPE-PRESCRIPTION ALL-NATP))
 (142 28 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (140 70 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (140 70 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (140 70 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-CHEAP))
 (135 70 (:REWRITE INTEGERP-OF-CAR-OF-CAR-WHEN-WEAK-DAGP-AUX-CHEAP))
 (126 126 (:TYPE-PRESCRIPTION ALL-<))
 (112 112 (:TYPE-PRESCRIPTION NATP))
 (86 85 (:TYPE-PRESCRIPTION NATP-OF-TOP-NODENUM-WHEN-PSEUDO-DAGP))
 (84 42 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (78 1 (:DEFINITION MERGE-DAG-INTO-DAG-AUX))
 (70 70 (:TYPE-PRESCRIPTION WEAK-DAGP))
 (70 70 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (70 70 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (70 70 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (70 70 (:REWRITE INTEGERP-OF-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (56 56 (:TYPE-PRESCRIPTION ALL-CONSP))
 (56 56 (:REWRITE USE-ALL-NATP-2))
 (56 56 (:REWRITE USE-ALL-NATP))
 (56 28 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (56 28 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (49 49 (:REWRITE USE-ALL-CONSP-2))
 (49 49 (:REWRITE USE-ALL-CONSP))
 (47 47 (:REWRITE USE-ALL-<-2))
 (47 47 (:REWRITE USE-ALL-<))
 (47 47 (:REWRITE DEFAULT-<-2))
 (47 47 (:REWRITE DEFAULT-<-1))
 (44 4 (:DEFINITION NTH))
 (42 42 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (42 42 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (42 42 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (42 42 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (42 42 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (42 42 (:REWRITE ALL-<-TRANSITIVE))
 (42 42 (:REWRITE <-OF-0-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (33 1 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX-2))
 (32 30 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (30 28 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (30 5 (:REWRITE ZP-OPEN))
 (28 28 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (28 28 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (28 28 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (28 28 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (28 28 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (28 28 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (24 1 (:REWRITE CDR-OF-REVERSE-LIST))
 (21 21 (:REWRITE DEFAULT-+-2))
 (21 21 (:REWRITE DEFAULT-+-1))
 (18 1 (:REWRITE RENUMBER-DAG-EXPR-WHEN-BOUNDED-DAG-EXPRP-OF-0))
 (15 15 (:REWRITE ALISTP-WHEN-BOUNDED-NATP-ALISTP))
 (11 1 (:DEFINITION TAKE))
 (5 5 (:TYPE-PRESCRIPTION REVERSE-LIST))
 (5 1 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-QUOTEP))
 (3 3 (:REWRITE CONSP-OF-REVERSE-LIST))
 (3 1 (:REWRITE RENUMBER-DAG-EXPR-WHEN-NOT-CONSP))
 (3 1 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-NOT-CONSP))
 (2 2 (:TYPE-PRESCRIPTION BOUNDED-DAG-EXPRP))
 (2 1 (:REWRITE RENUMBER-DAG-EXPR-WHEN-QUOTEP))
 (2 1 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-MYQUOTEP-CHEAP))
 (1 1 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (1 1 (:REWRITE MAPS-EVERYTHING-TO-QUOTE-OR-NODENUM-LESS-THAN-MONOTONIC))
 (1 1 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP-CHEAP))
 (1 1 (:REWRITE BOUNDED-DAG-EXPRP-WHEN-SYMBOLP))
 (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 (:DEFINITION EQ))
 )
(COMPOSE-TERM-AND-DAGS-AUX)
(COMPOSE-TERM-AND-DAGS-FN
 (12 6 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (6 6 (:TYPE-PRESCRIPTION TRUE-LISTP))
 )
(SPLIT-DAG-AT-NODE
 (70 2 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX-2))
 (42 2 (:DEFINITION TOP-NODENUM))
 (40 7 (:REWRITE DEFAULT-CAR))
 (19 3 (:REWRITE USE-ALL-<-FOR-CAR))
 (19 1 (:REWRITE PSEUDO-DAGP-AUX-OF-CDR))
 (14 1 (:REWRITE DEFAULT-+-2))
 (13 2 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-ALT))
 (10 2 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (7 7 (:TYPE-PRESCRIPTION ALL-<))
 (7 4 (:REWRITE DEFAULT-<-1))
 (7 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (6 6 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (6 6 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (6 4 (:REWRITE CONSP-OF-CAR-WHEN-ALISTP-CHEAP))
 (6 3 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (6 2 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP))
 (5 1 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (4 4 (:REWRITE USE-ALL-<-2))
 (4 4 (:REWRITE USE-ALL-<))
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 2 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (4 2 (:REWRITE ALISTP-WHEN-RENUMBERINGP-CHEAP))
 (3 3 (:REWRITE USE-ALL-CONSP-2))
 (3 3 (:REWRITE USE-ALL-CONSP))
 (3 3 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (3 3 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (3 3 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (3 1 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (2 2 (:TYPE-PRESCRIPTION RENUMBERINGP))
 (2 2 (:TYPE-PRESCRIPTION ALL-CONSP))
 (2 2 (:REWRITE WEAK-DAGP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (2 2 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (2 2 (:REWRITE ALL-<-TRANSITIVE))
 (2 2 (:REWRITE ALISTP-WHEN-PSEUDO-DAGP-AUX))
 (2 1 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (1 1 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (1 1 (:REWRITE PSEUDO-DAGP-AUX-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (1 1 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE DEFAULT-+-1))
 (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-CONSP-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (1 1 (:REWRITE ALISTP-WHEN-BOUNDED-NATP-ALISTP))
 (1 1 (:REWRITE ALISTP-OF-CDR))
 )
