(NATP-OF-IF)
(MAKE-SIZE-ARRAY-FOR-DAG-ARRAY-WITH-NAME-AUX
 (1536 2 (:REWRITE NATP-OF-IF))
 (1417 1417 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (1263 4 (:LINEAR LARGEST-NON-QUOTEP-BOUND))
 (1247 4 (:LINEAR LARGEST-NON-QUOTEP-BOUND-ALT))
 (1240 8 (:REWRITE NATP-OF-NTH-FROM-ALL-NATP))
 (1003 50 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (812 8 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (788 8 (:DEFINITION NAT-LISTP))
 (782 1 (:REWRITE SIZE-ARRAYP-OF-ASET1-AT-END))
 (608 16 (:REWRITE NATP-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (412 24 (:DEFINITION NTH))
 (404 202 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (366 8 (:REWRITE NATP-OF-NTH-OF-DARGS))
 (356 8 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (252 8 (:REWRITE NATP-OF-NTH-WHEN-ALL-DARGP))
 (239 84 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (230 36 (:REWRITE CAR-OF-DARGS-BECOMES-NTH-0-OF-DARGS))
 (208 208 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (206 116 (:REWRITE DEFAULT-<-1))
 (199 116 (:REWRITE DEFAULT-<-2))
 (198 24 (:REWRITE CONSP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE-IFF))
 (120 120 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (116 116 (:REWRITE USE-ALL-<-2))
 (116 116 (:REWRITE USE-ALL-<))
 (98 66 (:REWRITE DEFAULT-+-2))
 (94 8 (:REWRITE DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (84 84 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (84 84 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (84 84 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (84 14 (:REWRITE ACL2-NUMBERP-WHEN-NATP))
 (75 66 (:REWRITE DEFAULT-+-1))
 (74 65 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (74 65 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (72 36 (:TYPE-PRESCRIPTION NATP-OF-LARGEST-NON-QUOTEP))
 (64 8 (:REWRITE NOT-EQUAL-OF-CAR-AND-QUOTE-WHEN-LEN-WRONG-AND-PSEUDO-DAG-ARRAYP-AUX))
 (60 15 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (53 53 (:REWRITE USE-ALL-<=-2))
 (53 53 (:REWRITE USE-ALL-<=))
 (52 52 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (50 50 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (49 49 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (48 48 (:TYPE-PRESCRIPTION NAT-LISTP))
 (48 6 (:REWRITE DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (43 43 (:REWRITE USE-ALL-CONSP-2))
 (43 43 (:REWRITE USE-ALL-CONSP))
 (42 14 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (39 39 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (36 18 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (35 35 (:REWRITE USE-ALL-NATP-2))
 (35 35 (:REWRITE USE-ALL-NATP))
 (34 10 (:REWRITE DEFAULT-CAR))
 (32 8 (:REWRITE NOT-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP))
 (32 8 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (30 30 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (30 12 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (24 12 (:REWRITE LARGEST-NON-QUOTEP-WHEN-ALL-MYQUOTEP-CHEAP))
 (24 12 (:REWRITE LARGEST-NON-QUOTEP-WHEN-ALL-CONSP-CHEAP))
 (24 6 (:REWRITE DAG-EXPRP-OF-AREF1-WHEN-BOUNDED-DAG-EXPRP-OF-AREF1))
 (22 22 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (20 20 (:LINEAR ARRAY2P-LINEAR))
 (18 18 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (18 3 (:REWRITE <=-OF-0-WHEN-0-NATP))
 (16 16 (:TYPE-PRESCRIPTION DAG-EXPRP))
 (16 16 (:TYPE-PRESCRIPTION ALL-NATP))
 (16 8 (:REWRITE LEN-OF-NTH-WHEN-ALL-DARGP))
 (16 8 (:REWRITE LEN-OF-NTH-OF-DARGS))
 (16 8 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (15 15 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (15 15 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (14 14 (:REWRITE USE-ALL-RATIONALP-2))
 (14 14 (:REWRITE USE-ALL-RATIONALP))
 (12 12 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (12 12 (:TYPE-PRESCRIPTION ALL-CONSP))
 (12 3 (:REWRITE DEFAULT-UNARY-MINUS))
 (12 1 (:REWRITE SIZE-ARRAYP-OF-ASET1))
 (8 8 (:REWRITE QUOTE-LEMMA-FOR-BOUNDED-DARG-LISTP-GEN-ALT))
 (8 8 (:REWRITE NATP-OF-NTH-WHEN-BOUNDED-DARG-LISTP-GEN))
 (8 8 (:REWRITE LEN-OF-NTH-WHEN-BOUNDED-DARG-LISTP))
 (8 8 (:REWRITE DEFAULT-CDR))
 (6 6 (:TYPE-PRESCRIPTION BOUNDED-DAG-EXPRP))
 (6 6 (:REWRITE BOUNDED-DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-BETTER))
 (6 1 (:REWRITE INTEGERP-WHEN-NATP))
 (4 4 (:LINEAR <-OF-LARGEST-NON-QUOTEP))
 (3 3 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE FOLD-CONSTS-IN-+))
 (1 1 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE ARRAY1P-WHEN-SIZE-ARRAYP))
 )
(ARRAY1P-OF-MAKE-SIZE-ARRAY-FOR-DAG-ARRAY-WITH-NAME-AUX
 (355 15 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (152 76 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (148 148 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (143 143 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (96 12 (:REWRITE NOT-EQUAL-OF-CAR-AND-QUOTE-WHEN-LEN-WRONG-AND-PSEUDO-DAG-ARRAYP-AUX))
 (88 22 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (76 76 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (70 35 (:REWRITE DEFAULT-<-2))
 (52 13 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (40 17 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (40 16 (:REWRITE DEFAULT-CAR))
 (35 35 (:REWRITE USE-ALL-<-2))
 (35 35 (:REWRITE USE-ALL-<))
 (35 35 (:REWRITE DEFAULT-<-1))
 (35 35 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (33 17 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (28 28 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (28 28 (:REWRITE DEFAULT-+-2))
 (28 28 (:REWRITE DEFAULT-+-1))
 (28 14 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (28 14 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (26 26 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (21 21 (:REWRITE USE-ALL-<=-2))
 (21 21 (:REWRITE USE-ALL-<=))
 (21 7 (:REWRITE FOLD-CONSTS-IN-+))
 (19 19 (:REWRITE ARRAY1P-WHEN-SIZE-ARRAYP))
 (19 19 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (17 17 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (17 17 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (17 17 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (16 16 (:LINEAR ARRAY2P-LINEAR))
 (15 15 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (14 14 (:REWRITE USE-ALL-CONSP-2))
 (14 14 (:REWRITE USE-ALL-CONSP))
 (14 14 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (13 13 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (13 13 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (12 12 (:REWRITE QUOTE-LEMMA-FOR-BOUNDED-DARG-LISTP-GEN-ALT))
 (7 7 (:REWRITE USE-ALL-NATP-2))
 (7 7 (:REWRITE USE-ALL-NATP))
 (7 7 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 )
(ALEN1-OF-MAKE-SIZE-ARRAY-FOR-DAG-ARRAY-WITH-NAME-AUX
 (488 488 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (379 16 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (156 78 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (155 155 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (104 13 (:REWRITE NOT-EQUAL-OF-CAR-AND-QUOTE-WHEN-LEN-WRONG-AND-PSEUDO-DAG-ARRAYP-AUX))
 (92 23 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (78 78 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (72 36 (:REWRITE DEFAULT-<-2))
 (56 14 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (42 18 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (41 17 (:REWRITE DEFAULT-CAR))
 (36 36 (:REWRITE USE-ALL-<-2))
 (36 36 (:REWRITE USE-ALL-<))
 (36 36 (:REWRITE DEFAULT-<-1))
 (36 36 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (35 18 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (30 30 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (30 15 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (30 15 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (28 28 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (28 28 (:REWRITE DEFAULT-+-2))
 (28 28 (:REWRITE DEFAULT-+-1))
 (21 21 (:REWRITE USE-ALL-<=-2))
 (21 21 (:REWRITE USE-ALL-<=))
 (21 7 (:REWRITE FOLD-CONSTS-IN-+))
 (18 18 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (18 18 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (18 18 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (16 16 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (15 15 (:REWRITE USE-ALL-CONSP-2))
 (15 15 (:REWRITE USE-ALL-CONSP))
 (15 15 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (14 14 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (14 14 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (13 13 (:REWRITE QUOTE-LEMMA-FOR-BOUNDED-DARG-LISTP-GEN-ALT))
 (10 10 (:LINEAR ARRAY2P-LINEAR))
 (8 8 (:REWRITE ARRAY1P-WHEN-SIZE-ARRAYP))
 (8 8 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (7 7 (:REWRITE USE-ALL-NATP-2))
 (7 7 (:REWRITE USE-ALL-NATP))
 (7 7 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 )
(SIZE-ARRAYP-OF-MAKE-SIZE-ARRAY-FOR-DAG-ARRAY-WITH-NAME-AUX
 (1808 1808 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (1536 2 (:REWRITE NATP-OF-IF))
 (1027 49 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (938 3 (:LINEAR LARGEST-NON-QUOTEP-BOUND))
 (928 6 (:REWRITE NATP-OF-NTH-FROM-ALL-NATP))
 (926 3 (:LINEAR LARGEST-NON-QUOTEP-BOUND-ALT))
 (782 1 (:REWRITE SIZE-ARRAYP-OF-ASET1-AT-END))
 (608 6 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (590 6 (:DEFINITION NAT-LISTP))
 (456 12 (:REWRITE NATP-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (304 18 (:DEFINITION NTH))
 (300 150 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (283 283 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (266 6 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (264 6 (:REWRITE NATP-OF-NTH-OF-DARGS))
 (203 75 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (198 138 (:REWRITE DEFAULT-<-2))
 (188 6 (:REWRITE NATP-OF-NTH-WHEN-ALL-DARGP))
 (170 27 (:REWRITE CAR-OF-DARGS-BECOMES-NTH-0-OF-DARGS))
 (146 18 (:REWRITE CONSP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE-IFF))
 (141 141 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (138 138 (:REWRITE USE-ALL-<-2))
 (138 138 (:REWRITE USE-ALL-<))
 (138 138 (:REWRITE DEFAULT-<-1))
 (122 61 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (112 14 (:REWRITE NOT-EQUAL-OF-CAR-AND-QUOTE-WHEN-LEN-WRONG-AND-PSEUDO-DAG-ARRAYP-AUX))
 (97 73 (:REWRITE DEFAULT-+-2))
 (79 79 (:REWRITE USE-ALL-<=-2))
 (79 79 (:REWRITE USE-ALL-<=))
 (78 60 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (78 60 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (76 19 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (75 75 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (75 75 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (75 75 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (73 73 (:REWRITE DEFAULT-+-1))
 (66 6 (:REWRITE DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (63 63 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (54 27 (:TYPE-PRESCRIPTION NATP-OF-LARGEST-NON-QUOTEP))
 (49 49 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (48 48 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (48 21 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (46 22 (:REWRITE DEFAULT-CAR))
 (44 11 (:REWRITE NOT-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP))
 (42 42 (:REWRITE USE-ALL-CONSP-2))
 (42 42 (:REWRITE USE-ALL-CONSP))
 (38 38 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (36 36 (:TYPE-PRESCRIPTION SYMBOLP-OF-NTH-0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (36 36 (:TYPE-PRESCRIPTION NAT-LISTP))
 (32 4 (:REWRITE DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (28 28 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (26 26 (:LINEAR ARRAY2P-LINEAR))
 (25 25 (:REWRITE USE-ALL-NATP-2))
 (25 25 (:REWRITE USE-ALL-NATP))
 (24 6 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (21 7 (:REWRITE FOLD-CONSTS-IN-+))
 (19 19 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (19 19 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (18 9 (:REWRITE LARGEST-NON-QUOTEP-WHEN-ALL-MYQUOTEP-CHEAP))
 (18 9 (:REWRITE LARGEST-NON-QUOTEP-WHEN-ALL-CONSP-CHEAP))
 (16 4 (:REWRITE DAG-EXPRP-OF-AREF1-WHEN-BOUNDED-DAG-EXPRP-OF-AREF1))
 (14 14 (:REWRITE QUOTE-LEMMA-FOR-BOUNDED-DARG-LISTP-GEN-ALT))
 (14 14 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (12 12 (:TYPE-PRESCRIPTION DAG-EXPRP))
 (12 12 (:TYPE-PRESCRIPTION ALL-NATP))
 (12 6 (:REWRITE LEN-OF-NTH-WHEN-ALL-DARGP))
 (12 6 (:REWRITE LEN-OF-NTH-OF-DARGS))
 (12 6 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (12 1 (:REWRITE SIZE-ARRAYP-OF-ASET1))
 (9 9 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (9 9 (:TYPE-PRESCRIPTION ALL-CONSP))
 (6 6 (:REWRITE NATP-OF-NTH-WHEN-BOUNDED-DARG-LISTP-GEN))
 (6 6 (:REWRITE LEN-OF-NTH-WHEN-BOUNDED-DARG-LISTP))
 (6 6 (:REWRITE DEFAULT-CDR))
 (6 6 (:REWRITE ALL-DARGP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (4 4 (:TYPE-PRESCRIPTION BOUNDED-DAG-EXPRP))
 (4 4 (:REWRITE BOUNDED-DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-BETTER))
 (3 3 (:LINEAR <-OF-LARGEST-NON-QUOTEP))
 )
(MAKE-SIZE-ARRAY-FOR-DAG-ARRAY-WITH-NAME
 (156 156 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (3 3 (:REWRITE USE-ALL-<=-2))
 (3 3 (:REWRITE USE-ALL-<=))
 (3 3 (:REWRITE USE-ALL-<-2))
 (3 3 (:REWRITE USE-ALL-<))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 (3 3 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (2 2 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (2 2 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 )
(ARRAY1P-OF-MAKE-SIZE-ARRAY-FOR-DAG-ARRAY-WITH-NAME
 (6 1 (:REWRITE INTEGERP-WHEN-NATP))
 (3 3 (:REWRITE USE-ALL-<=-2))
 (3 3 (:REWRITE USE-ALL-<=))
 (3 3 (:REWRITE USE-ALL-<-2))
 (3 3 (:REWRITE USE-ALL-<))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 (3 3 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 (1 1 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (1 1 (:REWRITE USE-ALL-NATP-2))
 (1 1 (:REWRITE USE-ALL-NATP))
 (1 1 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (1 1 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (1 1 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE ARRAY1P-WHEN-SIZE-ARRAYP))
 (1 1 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 )
(SIZE-ARRAYP-OF-MAKE-SIZE-ARRAY-FOR-DAG-ARRAY-WITH-NAME
 (74 74 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (3 3 (:REWRITE USE-ALL-<=-2))
 (3 3 (:REWRITE USE-ALL-<=))
 (3 3 (:REWRITE USE-ALL-<-2))
 (3 3 (:REWRITE USE-ALL-<))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 (3 3 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (1 1 (:REWRITE USE-ALL-NATP-2))
 (1 1 (:REWRITE USE-ALL-NATP))
 (1 1 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (1 1 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (1 1 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 )
(ALEN1-OF-MAKE-SIZE-ARRAY-FOR-DAG-ARRAY-WITH-NAME
 (32 32 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (6 1 (:REWRITE INTEGERP-WHEN-NATP))
 (3 3 (:REWRITE USE-ALL-<=-2))
 (3 3 (:REWRITE USE-ALL-<=))
 (3 3 (:REWRITE USE-ALL-<-2))
 (3 3 (:REWRITE USE-ALL-<))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 (3 3 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 (1 1 (:REWRITE USE-ALL-NATP-2))
 (1 1 (:REWRITE USE-ALL-NATP))
 (1 1 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (1 1 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (1 1 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE ARRAY1P-WHEN-SIZE-ARRAYP))
 (1 1 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 )
(DAG-SIZE
 (1052 36 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (577 94 (:REWRITE DEFAULT-CAR))
 (542 4 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (530 4 (:DEFINITION NAT-LISTP))
 (474 4 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (162 40 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (131 3 (:REWRITE USE-ALL-<-FOR-CAR))
 (111 111 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (104 104 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (104 3 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (99 14 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (92 36 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (88 88 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (85 47 (:REWRITE DEFAULT-<-2))
 (81 81 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (67 1 (:REWRITE BOUNDED-NATP-ALISTP-WHEN-PSEUDO-DAGP-AUX))
 (55 55 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (55 10 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (52 52 (:REWRITE USE-ALL-CONSP-2))
 (52 52 (:REWRITE USE-ALL-CONSP))
 (47 47 (:REWRITE USE-ALL-<-2))
 (47 47 (:REWRITE USE-ALL-<))
 (47 47 (:REWRITE DEFAULT-<-1))
 (47 47 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (44 44 (:REWRITE DEFAULT-+-2))
 (44 44 (:REWRITE DEFAULT-+-1))
 (36 36 (:REWRITE USE-ALL-NATP-2))
 (36 36 (:REWRITE USE-ALL-NATP))
 (36 36 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (36 36 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (36 36 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (28 28 (:TYPE-PRESCRIPTION ALL-NATP))
 (28 14 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (27 27 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (24 24 (:TYPE-PRESCRIPTION NAT-LISTP))
 (20 20 (:TYPE-PRESCRIPTION ALL-CONSP))
 (15 5 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (14 14 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (14 14 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (10 10 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (10 10 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (9 9 (:TYPE-PRESCRIPTION ALL-<))
 (9 9 (:REWRITE USE-ALL-<=-2))
 (9 9 (:REWRITE USE-ALL-<=))
 (8 4 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (6 6 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (6 3 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (6 1 (:REWRITE ALL-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (6 1 (:REWRITE <-OF-CAR-AND-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (6 1 (:REWRITE <-OF-CAR-AND-ALEN1))
 (5 5 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:REWRITE NOT-<-OF-+-1-AND-CAR-WHEN-ALL-<))
 (4 4 (:REWRITE DEFAULT-CDR))
 (4 4 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (3 3 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (3 3 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL))
 (3 3 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP))
 (3 3 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (3 3 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (3 3 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (3 3 (:REWRITE ALL-<-TRANSITIVE))
 (2 2 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (1 1 (:REWRITE BOUNDED-NATP-ALISTP-MONOTONE))
 (1 1 (:REWRITE ARRAY1P-WHEN-SIZE-ARRAYP))
 (1 1 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 )
(NATP-OF-DAG-SIZE
 (19 19 (:TYPE-PRESCRIPTION NATP-OF-TOP-NODENUM-OF-DAG))
 (8 1 (:REWRITE LEN-OF-NTH-WHEN-ALL-DARGP))
 (7 7 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (7 7 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (7 7 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (7 7 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (5 1 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (3 3 (:REWRITE DEFAULT-+-2))
 (3 3 (:REWRITE DEFAULT-+-1))
 (3 1 (:TYPE-PRESCRIPTION ALEN1-TYPE))
 (2 2 (:TYPE-PRESCRIPTION ALL-DARGP))
 (2 1 (:REWRITE ALL-DARGP-WHEN-ALL-MYQUOTEP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (1 1 (:TYPE-PRESCRIPTION ARRAY1P))
 (1 1 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (1 1 (:REWRITE USE-ALL-<=-2))
 (1 1 (:REWRITE USE-ALL-<=))
 (1 1 (:REWRITE USE-ALL-<-2))
 (1 1 (:REWRITE USE-ALL-<))
 (1 1 (:REWRITE LEN-OF-NTH-WHEN-BOUNDED-DARG-LISTP))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE ALL-DARGP-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE ALL-DARGP-WHEN-NOT-CONSP))
 (1 1 (:REWRITE ALL-DARGP-WHEN-BOUNDED-DARG-LISTP))
 (1 1 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (1 1 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 )
(DAG-SIZE-UNGUARDED)
(NATP-OF-DAG-SIZE-UNGUARDED
 (2 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE USE-ALL-<=-2))
 (1 1 (:REWRITE USE-ALL-<=))
 (1 1 (:REWRITE USE-ALL-<-2))
 (1 1 (:REWRITE USE-ALL-<))
 (1 1 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (1 1 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (1 1 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 )
(DAG-OR-QUOTEP-SIZE
 (36 2 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (19 1 (:LINEAR LEN-OF-CDR-LINEAR-STRONG))
 (17 1 (:LINEAR LEN-OF-CDR-LINEAR))
 (12 12 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (12 12 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (12 12 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (12 12 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (5 5 (:REWRITE DEFAULT-CDR))
 (5 5 (:REWRITE DEFAULT-+-2))
 (5 5 (:REWRITE DEFAULT-+-1))
 (3 2 (:REWRITE DEFAULT-<-2))
 (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-CAR))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (2 2 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (2 2 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (1 1 (:REWRITE QUOTE-LEMMA-FOR-BOUNDED-DARG-LISTP-GEN-ALT))
 (1 1 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (1 1 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (1 1 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 )
(NATP-OF-DAG-OR-QUOTEP-SIZE
 (68 3 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (14 1 (:REWRITE LEN-OF-CDR))
 (9 3 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (7 4 (:REWRITE DEFAULT-<-2))
 (6 6 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (6 6 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (6 6 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (6 6 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (5 4 (:REWRITE DEFAULT-<-1))
 (4 4 (:REWRITE USE-ALL-<-2))
 (4 4 (:REWRITE USE-ALL-<))
 (4 4 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (3 3 (:REWRITE USE-ALL-CONSP-2))
 (3 3 (:REWRITE USE-ALL-CONSP))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (3 3 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (2 2 (:REWRITE QUOTE-LEMMA-FOR-BOUNDED-DARG-LISTP-GEN-ALT))
 (2 2 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (2 2 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (2 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE USE-ALL-<=-2))
 (1 1 (:REWRITE USE-ALL-<=))
 (1 1 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 (1 1 (:REWRITE EQUAL-OF-LEN-AND-0))
 (1 1 (:REWRITE DEFAULT-+-1))
 (1 1 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (1 1 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 )
