(ALL-<-OF-+-OF-1-AND-MAXELEM-GEN
 (46127 283 (:REWRITE USE-ALL-<-FOR-CAR))
 (45393 107 (:DEFINITION NAT-LISTP))
 (37313 107 (:DEFINITION NATP))
 (34743 472 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (29649 89 (:REWRITE ACL2-NUMBERP-OF-MAXELEM))
 (29432 64 (:REWRITE INTEGER-LISTP-WHEN-ALL-NATP))
 (29306 327 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (22750 497 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (22119 30 (:REWRITE <-OF-+-AND-+-COMBINE-CONSTANTS))
 (21334 256 (:REWRITE ALL-<-OF-CDR))
 (19186 930 (:REWRITE DEFAULT-+-2))
 (16855 40 (:REWRITE ALL-<-OF-+-OF-1-AND-MAXELEM))
 (15122 780 (:REWRITE DEFAULT-<-2))
 (14896 288 (:LINEAR MAXELEM-OF-CDR-LINEAR))
 (8560 576 (:DEFINITION LEN))
 (7352 3676 (:TYPE-PRESCRIPTION NATP-OF-MAXELEM-WHEN-ALL-NATP))
 (6674 3676 (:TYPE-PRESCRIPTION RATIONALP-OF-MAXELEM))
 (4885 180 (:REWRITE NOT-<-OF-MAXELEM-WHEN-ALL-<))
 (4783 4783 (:TYPE-PRESCRIPTION ALL-NATP))
 (3375 780 (:REWRITE DEFAULT-<-1))
 (3222 3222 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (3167 176 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (3117 3117 (:TYPE-PRESCRIPTION LEN))
 (2304 1152 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (2083 284 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (2029 2029 (:REWRITE DEFAULT-CDR))
 (1833 117 (:REWRITE ALL-NATP-OF-CDR))
 (1209 180 (:REWRITE MAXELEM-BOUND-MAXINT))
 (1191 65 (:REWRITE RATIONALP-OF-MAXELEM))
 (1152 1152 (:TYPE-PRESCRIPTION DARGP))
 (1152 1152 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (1152 1152 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (1152 1152 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (1088 1088 (:REWRITE USE-ALL-CONSP-2))
 (1088 1088 (:REWRITE USE-ALL-CONSP))
 (930 930 (:REWRITE DEFAULT-+-1))
 (930 52 (:DEFINITION RATIONAL-LISTP))
 (920 184 (:REWRITE NTH-OF-CDR))
 (903 467 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (865 180 (:REWRITE NOT-<-OF-MAXELEM-WHEN-ALL-<-2))
 (818 780 (:REWRITE USE-ALL-<))
 (780 780 (:REWRITE USE-ALL-<-2))
 (780 780 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (758 5 (:REWRITE <-OF-MAXELEM-WHEN-ALL-<))
 (737 737 (:REWRITE DEFAULT-CAR))
 (725 110 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (723 107 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (654 327 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (620 284 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (565 283 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (527 527 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (474 237 (:REWRITE NTH-WHEN-<=-LEN-CHEAP))
 (472 472 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (449 327 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (402 30 (:REWRITE UNICITY-OF-0))
 (389 32 (:DEFINITION FIX))
 (384 150 (:REWRITE MAXELEM-BOUND-WHEN-ALL-<))
 (358 358 (:REWRITE USE-ALL-<=-2))
 (358 358 (:REWRITE USE-ALL-<=))
 (327 327 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (290 290 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (288 288 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (288 288 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (274 137 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (274 137 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (237 237 (:REWRITE NTH-WHEN-ZP-CHEAP))
 (237 237 (:REWRITE NTH-WHEN-NOT-CONSP-CHEAP))
 (208 104 (:REWRITE RATIONAL-LISTP-WHEN-ALL-NATP-CHEAP))
 (193 193 (:REWRITE USE-ALL-RATIONALP-2))
 (193 193 (:REWRITE USE-ALL-RATIONALP))
 (180 180 (:REWRITE LESS-THAN-MAXELEM-WHEN-LESS-THAN-SOME-ELEM))
 (175 35 (:REWRITE ALL-RATIONALP-OF-CDR))
 (149 149 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (145 145 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (145 145 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (137 137 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (137 137 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (137 137 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (134 134 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (128 128 (:TYPE-PRESCRIPTION INTEGER-LISTP))
 (107 107 (:REWRITE USE-ALL-NATP-2))
 (107 107 (:REWRITE USE-ALL-NATP))
 (107 107 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (75 57 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (47 5 (:REWRITE <=-OF-MAXELEM-WHEN-MEMBER-EQUAL))
 (38 38 (:TYPE-PRESCRIPTION MEMBERP))
 (35 2 (:REWRITE RATIONALP-OF-+-WHEN-RATIONALP-ARG1))
 (32 5 (:DEFINITION MEMBER-EQUAL))
 (30 30 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (28 28 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (28 28 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (25 25 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (25 2 (:REWRITE RATIONALP-OF-+-WHEN-RATIONALP-ARG2))
 (10 5 (:REWRITE <-OF-MAXELEM-WHEN-ALL-<-CHEAP))
 )
(DEPTH-ARRAYP-AUX
 (87 87 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (9 7 (:REWRITE DEFAULT-<-2))
 (7 7 (:REWRITE USE-ALL-<=-2))
 (7 7 (:REWRITE USE-ALL-<=))
 (7 7 (:REWRITE USE-ALL-<-2))
 (7 7 (:REWRITE USE-ALL-<))
 (7 7 (:REWRITE DEFAULT-<-1))
 (7 7 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (5 5 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (5 5 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (4 4 (:REWRITE USE-ALL-NATP-2))
 (4 4 (:REWRITE USE-ALL-NATP))
 (4 4 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (4 3 (:REWRITE DEFAULT-+-2))
 (3 3 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (2 2 (:LINEAR ARRAY2P-LINEAR))
 (1 1 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (1 1 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (1 1 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (1 1 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 )
(DEPTH-ARRAYP-AUX-OF-MINUS1)
(DEPTH-ARRAYP-AUX-OF-0
 (27 27 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (4 2 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (2 2 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (2 2 (:REWRITE USE-ALL-NATP-2))
 (2 2 (:REWRITE USE-ALL-NATP))
 (2 2 (:REWRITE USE-ALL-<=-2))
 (2 2 (:REWRITE USE-ALL-<=))
 (2 2 (:REWRITE USE-ALL-<-2))
 (2 2 (:REWRITE USE-ALL-<))
 (2 2 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (2 2 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 )
(DEPTH-ARRAYP-AUX-MONOTONE
 (111 111 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (30 15 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (29 29 (:REWRITE USE-ALL-<=-2))
 (29 29 (:REWRITE USE-ALL-<=))
 (29 29 (:REWRITE USE-ALL-<-2))
 (29 29 (:REWRITE USE-ALL-<))
 (29 29 (:REWRITE DEFAULT-<-2))
 (29 29 (:REWRITE DEFAULT-<-1))
 (29 29 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (23 23 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (23 23 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (18 18 (:REWRITE USE-ALL-NATP-2))
 (18 18 (:REWRITE USE-ALL-NATP))
 (18 18 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (15 15 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (14 14 (:REWRITE DEFAULT-+-2))
 (14 14 (:REWRITE DEFAULT-+-1))
 )
(TYPE-OF-AREF1-WHEN-DEPTH-ARRAYP-AUX
 (294 294 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (28 14 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (14 14 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (14 14 (:REWRITE USE-ALL-<=-2))
 (14 14 (:REWRITE USE-ALL-<=))
 (14 14 (:REWRITE USE-ALL-<-2))
 (14 14 (:REWRITE USE-ALL-<))
 (14 14 (:REWRITE DEFAULT-<-2))
 (14 14 (:REWRITE DEFAULT-<-1))
 (14 14 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (10 10 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (10 10 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (6 6 (:REWRITE USE-ALL-NATP-2))
 (6 6 (:REWRITE USE-ALL-NATP))
 (6 6 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (6 6 (:REWRITE DEPTH-ARRAYP-AUX-MONOTONE))
 (6 6 (:REWRITE DEFAULT-+-2))
 (6 6 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (2 2 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (2 2 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 )
(DEPTH-ARRAYP-AUX-OF-ASET1-TOO-HIGH
 (161 161 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (36 29 (:REWRITE DEFAULT-<-2))
 (29 29 (:REWRITE USE-ALL-<=-2))
 (29 29 (:REWRITE USE-ALL-<=))
 (29 29 (:REWRITE USE-ALL-<-2))
 (29 29 (:REWRITE USE-ALL-<))
 (29 29 (:REWRITE DEFAULT-<-1))
 (29 29 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (28 14 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (16 16 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (11 11 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (10 10 (:REWRITE DEPTH-ARRAYP-AUX-MONOTONE))
 (9 9 (:REWRITE USE-ALL-NATP-2))
 (9 9 (:REWRITE USE-ALL-NATP))
 (9 9 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (7 7 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (6 6 (:REWRITE DEFAULT-+-2))
 (6 6 (:REWRITE DEFAULT-+-1))
 (6 6 (:LINEAR ARRAY2P-LINEAR))
 (4 4 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (4 4 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (4 4 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 )
(DEPTH-ARRAYP-AUX-OF-ASET1
 (235 235 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (54 46 (:REWRITE DEFAULT-<-2))
 (46 46 (:REWRITE USE-ALL-<-2))
 (46 46 (:REWRITE USE-ALL-<))
 (46 46 (:REWRITE DEFAULT-<-1))
 (46 46 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (40 40 (:REWRITE USE-ALL-<=-2))
 (40 40 (:REWRITE USE-ALL-<=))
 (26 26 (:REWRITE DEFAULT-+-2))
 (26 26 (:REWRITE DEFAULT-+-1))
 (23 23 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (20 20 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (20 2 (:REWRITE NATP-OF-+-WHEN-NEGATIVE-CONSTANT))
 (16 16 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (16 6 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (12 12 (:REWRITE USE-ALL-NATP-2))
 (12 12 (:REWRITE USE-ALL-NATP))
 (12 12 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (12 4 (:REWRITE +-COMBINE-CONSTANTS))
 (10 10 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (10 10 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (8 8 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (8 8 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (6 6 (:LINEAR ARRAY2P-LINEAR))
 (4 4 (:REWRITE EQUAL-OF-+-COMBINE-CONSTANTS))
 (4 4 (:REWRITE <-OF-+-CANCEL-1-2))
 (2 2 (:DEFINITION FIX))
 )
(DEPTH-ARRAYP-AUX-OF-ASET1-AT-END
 (23 11 (:REWRITE DEPTH-ARRAYP-AUX-MONOTONE))
 (17 17 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (13 11 (:REWRITE DEFAULT-<-2))
 (12 2 (:REWRITE DEPTH-ARRAYP-AUX-OF-ASET1-TOO-HIGH))
 (12 2 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (11 11 (:REWRITE USE-ALL-<-2))
 (11 11 (:REWRITE USE-ALL-<))
 (11 11 (:REWRITE DEFAULT-<-1))
 (11 11 (:REWRITE DEFAULT-+-2))
 (11 11 (:REWRITE DEFAULT-+-1))
 (11 11 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (10 1 (:REWRITE NATP-OF-+-WHEN-NEGATIVE-CONSTANT))
 (9 9 (:REWRITE USE-ALL-<=-2))
 (9 9 (:REWRITE USE-ALL-<=))
 (6 6 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (6 6 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (6 5 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (6 2 (:REWRITE +-COMBINE-CONSTANTS))
 (4 4 (:REWRITE USE-ALL-NATP-2))
 (4 4 (:REWRITE USE-ALL-NATP))
 (4 4 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (2 2 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (2 2 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (2 2 (:REWRITE <-OF-+-CANCEL-1-2))
 (2 2 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (2 2 (:LINEAR ARRAY2P-LINEAR))
 (1 1 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 )
(DEPTH-ARRAYP-AUX-OF-COMPRESS1
 (132 132 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (41 25 (:REWRITE DEFAULT-<-2))
 (28 25 (:REWRITE DEFAULT-<-1))
 (25 25 (:REWRITE USE-ALL-<=-2))
 (25 25 (:REWRITE USE-ALL-<=))
 (25 25 (:REWRITE USE-ALL-<-2))
 (25 25 (:REWRITE USE-ALL-<))
 (25 25 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (20 20 (:REWRITE DEPTH-ARRAYP-AUX-MONOTONE))
 (20 2 (:REWRITE NATP-OF-+-WHEN-NEGATIVE-CONSTANT))
 (18 14 (:REWRITE DEFAULT-+-2))
 (16 14 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (14 14 (:REWRITE DEFAULT-+-1))
 (12 4 (:REWRITE +-COMBINE-CONSTANTS))
 (10 10 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (7 7 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (7 7 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (6 6 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (6 6 (:LINEAR ARRAY2P-LINEAR))
 (5 5 (:REWRITE USE-ALL-NATP-2))
 (5 5 (:REWRITE USE-ALL-NATP))
 (5 5 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (4 4 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (4 4 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (3 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (1 1 (:REWRITE USE-ALL-RATIONALP-2))
 (1 1 (:REWRITE USE-ALL-RATIONALP))
 )
(DEPTH-ARRAYP-AUX-OF-CONS-OF-CONS-OF-HEADER
 (36 24 (:REWRITE DEPTH-ARRAYP-AUX-MONOTONE))
 (36 18 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (36 6 (:REWRITE DEFAULT-CDR))
 (36 6 (:REWRITE DEFAULT-CAR))
 (18 18 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (15 15 (:REWRITE USE-ALL-<=-2))
 (15 15 (:REWRITE USE-ALL-<=))
 (15 15 (:REWRITE USE-ALL-<-2))
 (15 15 (:REWRITE USE-ALL-<))
 (15 15 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (15 15 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (15 15 (:REWRITE DEFAULT-<-2))
 (15 15 (:REWRITE DEFAULT-<-1))
 (15 15 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (12 12 (:REWRITE USE-ALL-NATP-2))
 (12 12 (:REWRITE USE-ALL-NATP))
 (12 12 (:REWRITE USE-ALL-CONSP-2))
 (12 12 (:REWRITE USE-ALL-CONSP))
 (12 12 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (12 2 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (10 10 (:REWRITE DEFAULT-+-2))
 (10 10 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (2 2 (:REWRITE <-OF-+-CANCEL-1-2))
 (2 2 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 )
(DEPTH-ARRAYP-AUX-OF-CONS-OF-CONS-OF-HEADER-IRREL
 (126 10 (:REWRITE DEPTH-ARRAYP-AUX-OF-CONS-OF-CONS-OF-HEADER))
 (60 30 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (48 8 (:REWRITE DEFAULT-CDR))
 (48 8 (:REWRITE DEFAULT-CAR))
 (34 34 (:REWRITE DEPTH-ARRAYP-AUX-MONOTONE))
 (30 30 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (16 16 (:REWRITE USE-ALL-CONSP-2))
 (16 16 (:REWRITE USE-ALL-CONSP))
 (13 13 (:REWRITE USE-ALL-<=-2))
 (13 13 (:REWRITE USE-ALL-<=))
 (13 13 (:REWRITE USE-ALL-<-2))
 (13 13 (:REWRITE USE-ALL-<))
 (13 13 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (13 13 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (13 13 (:REWRITE DEFAULT-<-2))
 (13 13 (:REWRITE DEFAULT-<-1))
 (13 13 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (12 12 (:REWRITE DEFAULT-+-2))
 (12 12 (:REWRITE DEFAULT-+-1))
 (9 9 (:REWRITE USE-ALL-NATP-2))
 (9 9 (:REWRITE USE-ALL-NATP))
 (9 9 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 )
(ENSURE-DEFAULT-SATISFIES-PRED)
(DEPTH-ARRAYP-AUX-OF-MAKE-EMPTY-ARRAY-WITH-DEFAULT
 (21 7 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (14 7 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (13 13 (:REWRITE USE-ALL-<=-2))
 (13 13 (:REWRITE USE-ALL-<=))
 (13 13 (:REWRITE USE-ALL-<-2))
 (13 13 (:REWRITE USE-ALL-<))
 (13 13 (:REWRITE DEFAULT-<-2))
 (13 13 (:REWRITE DEFAULT-<-1))
 (13 13 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (11 5 (:REWRITE DEPTH-ARRAYP-AUX-MONOTONE))
 (7 7 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (6 1 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (4 4 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (3 3 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (3 3 (:REWRITE DEFAULT-+-2))
 (3 3 (:REWRITE DEFAULT-+-1))
 (1 1 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (1 1 (:REWRITE <-OF-+-CANCEL-1-2))
 (1 1 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 )
(DEPTH-ARRAYP)
(ARRAY1P-WHEN-DEPTH-ARRAYP)
(DEPTH-ARRAYP-FORWARD-TO-ARRAY1P)
(DEPTH-ARRAYP-FORWARD-TO-LEN-BOUND)
(DEPTH-ARRAYP-FORWARD-TO-LEN-BOUND-2)
(TYPE-OF-AREF1-WHEN-DEPTH-ARRAYP
 (41 41 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (4 4 (:REWRITE DEFAULT-+-2))
 (4 4 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE USE-ALL-<=-2))
 (2 2 (:REWRITE USE-ALL-<=))
 (2 2 (:REWRITE USE-ALL-<-2))
 (2 2 (:REWRITE USE-ALL-<))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (2 2 (:LINEAR ARRAY2P-LINEAR))
 (2 1 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (1 1 (:REWRITE USE-ALL-NATP-2))
 (1 1 (:REWRITE USE-ALL-NATP))
 (1 1 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (1 1 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (1 1 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (1 1 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 )
(TYPE-OF-AREF1-WHEN-DEPTH-ARRAYP-SPECIAL
 (35 35 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (2 2 (:LINEAR ARRAY2P-LINEAR))
 )
(DEPTH-ARRAYP-MONOTONE
 (8 2 (:REWRITE NOT-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP))
 (7 5 (:REWRITE DEFAULT-<-1))
 (5 5 (:REWRITE USE-ALL-<=-2))
 (5 5 (:REWRITE USE-ALL-<=))
 (5 5 (:REWRITE USE-ALL-<-2))
 (5 5 (:REWRITE USE-ALL-<))
 (5 5 (:REWRITE DEFAULT-<-2))
 (5 5 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (4 4 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP))
 (2 2 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (2 2 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (2 2 (:REWRITE ARRAY1P-WHEN-DEPTH-ARRAYP))
 (2 2 (:LINEAR ARRAY2P-LINEAR))
 )
(DEPTH-ARRAYP-OF-ASET1
 (39 1 (:DEFINITION DEPTH-ARRAYP-AUX))
 (14 11 (:REWRITE DEFAULT-<-1))
 (13 11 (:REWRITE DEFAULT-<-2))
 (12 3 (:REWRITE NOT-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP))
 (11 11 (:REWRITE USE-ALL-<=-2))
 (11 11 (:REWRITE USE-ALL-<=))
 (11 11 (:REWRITE USE-ALL-<-2))
 (11 11 (:REWRITE USE-ALL-<))
 (11 11 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (10 1 (:REWRITE NATP-OF-+-WHEN-NEGATIVE-CONSTANT))
 (6 6 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP))
 (6 2 (:REWRITE +-COMBINE-CONSTANTS))
 (5 5 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (5 5 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (5 5 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (5 5 (:REWRITE DEFAULT-+-2))
 (5 5 (:REWRITE DEFAULT-+-1))
 (3 3 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (3 3 (:REWRITE DEPTH-ARRAYP-AUX-MONOTONE))
 (3 3 (:REWRITE ARRAY1P-WHEN-DEPTH-ARRAYP))
 (2 2 (:REWRITE USE-ALL-NATP-2))
 (2 2 (:REWRITE USE-ALL-NATP))
 (2 2 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (2 2 (:REWRITE DEPTH-ARRAYP-MONOTONE))
 (2 2 (:LINEAR ARRAY2P-LINEAR))
 (2 1 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (1 1 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (1 1 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 )
(DEPTH-ARRAYP-OF-ASET1-AT-END
 (104 2 (:REWRITE DEPTH-ARRAYP-OF-ASET1))
 (95 3 (:DEFINITION DEPTH-ARRAYP-AUX))
 (25 25 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (21 9 (:REWRITE DEPTH-ARRAYP-AUX-MONOTONE))
 (15 15 (:REWRITE DEFAULT-+-2))
 (15 15 (:REWRITE DEFAULT-+-1))
 (14 11 (:REWRITE DEFAULT-<-1))
 (13 11 (:REWRITE DEFAULT-<-2))
 (12 3 (:REWRITE NOT-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP))
 (12 2 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (11 11 (:REWRITE USE-ALL-<=-2))
 (11 11 (:REWRITE USE-ALL-<=))
 (11 11 (:REWRITE USE-ALL-<-2))
 (11 11 (:REWRITE USE-ALL-<))
 (11 11 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (10 1 (:REWRITE NATP-OF-+-WHEN-NEGATIVE-CONSTANT))
 (6 6 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP))
 (6 5 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (5 5 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (5 5 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (5 5 (:REWRITE ARRAY1P-WHEN-DEPTH-ARRAYP))
 (4 4 (:REWRITE USE-ALL-NATP-2))
 (4 4 (:REWRITE USE-ALL-NATP))
 (4 4 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (4 4 (:REWRITE DEPTH-ARRAYP-MONOTONE))
 (4 4 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (4 4 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (3 3 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (3 3 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (3 3 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (2 2 (:REWRITE <-OF-+-CANCEL-1-2))
 (2 2 (:LINEAR ARRAY2P-LINEAR))
 )
(DEPTH-ARRAYP-OF-ASET1-AT-END-GEN
 (29 3 (:REWRITE DEPTH-ARRAYP-OF-ASET1))
 (12 12 (:REWRITE USE-ALL-<=-2))
 (12 12 (:REWRITE USE-ALL-<=))
 (12 12 (:REWRITE USE-ALL-<-2))
 (12 12 (:REWRITE USE-ALL-<))
 (12 12 (:REWRITE DEFAULT-<-2))
 (12 12 (:REWRITE DEFAULT-<-1))
 (12 12 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (6 6 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (6 6 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE USE-ALL-NATP-2))
 (2 2 (:REWRITE USE-ALL-NATP))
 (2 2 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:LINEAR ARRAY2P-LINEAR))
 (1 1 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (1 1 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (1 1 (:REWRITE <-OF-+-CANCEL-1-2))
 (1 1 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (1 1 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 )
(DEPTH-ARRAYP-OF-MAKE-EMPTY-ARRAY-WITH-DEFAULT
 (5 5 (:REWRITE USE-ALL-<=-2))
 (5 5 (:REWRITE USE-ALL-<=))
 (5 5 (:REWRITE USE-ALL-<-2))
 (5 5 (:REWRITE USE-ALL-<))
 (5 5 (:REWRITE DEFAULT-<-2))
 (5 5 (:REWRITE DEFAULT-<-1))
 (5 5 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (2 2 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (1 1 (:REWRITE DEPTH-ARRAYP-MONOTONE))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 (1 1 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (1 1 (:REWRITE ARRAY1P-WHEN-DEPTH-ARRAYP))
 )
(DEPTH-ARRAYP-OF-MAKE-EMPTY-ARRAY
 (4 4 (:REWRITE USE-ALL-<=-2))
 (4 4 (:REWRITE USE-ALL-<=))
 (4 4 (:REWRITE USE-ALL-<-2))
 (4 4 (:REWRITE USE-ALL-<))
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (4 4 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (2 2 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 )
(DEPTH-ARRAYP-OF-MAKE-EMPTY-ARRAY-WITH-DEFAULT-AND-0
 (4 4 (:REWRITE USE-ALL-<=-2))
 (4 4 (:REWRITE USE-ALL-<=))
 (4 4 (:REWRITE USE-ALL-<-2))
 (4 4 (:REWRITE USE-ALL-<))
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (4 4 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (1 1 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (1 1 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE DEPTH-ARRAYP-MONOTONE))
 (1 1 (:REWRITE DEPTH-ARRAYP-AUX-OF-MAKE-EMPTY-ARRAY-WITH-DEFAULT))
 (1 1 (:REWRITE DEPTH-ARRAYP-AUX-MONOTONE))
 (1 1 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (1 1 (:REWRITE ARRAY1P-WHEN-DEPTH-ARRAYP))
 )
(DEPTH-ARRAYP-OF-MAKE-EMPTY-ARRAY-AND-0
 (8 1 (:REWRITE DEPTH-ARRAYP-OF-MAKE-EMPTY-ARRAY-WITH-DEFAULT-AND-0))
 (5 5 (:REWRITE USE-ALL-<=-2))
 (5 5 (:REWRITE USE-ALL-<=))
 (5 5 (:REWRITE USE-ALL-<-2))
 (5 5 (:REWRITE USE-ALL-<))
 (5 5 (:REWRITE DEFAULT-<-2))
 (5 5 (:REWRITE DEFAULT-<-1))
 (5 5 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (1 1 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (1 1 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE DEPTH-ARRAYP-MONOTONE))
 (1 1 (:REWRITE DEPTH-ARRAYP-AUX-OF-MAKE-EMPTY-ARRAY-WITH-DEFAULT))
 (1 1 (:REWRITE DEPTH-ARRAYP-AUX-MONOTONE))
 (1 1 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (1 1 (:REWRITE ARRAY1P-WHEN-DEPTH-ARRAYP))
 )
(DEPTH-ARRAYP-OF-MAKE-EMPTY-ARRAY-GEN
 (5 5 (:REWRITE USE-ALL-<=-2))
 (5 5 (:REWRITE USE-ALL-<=))
 (5 5 (:REWRITE USE-ALL-<-2))
 (5 5 (:REWRITE USE-ALL-<))
 (5 5 (:REWRITE DEFAULT-<-2))
 (5 5 (:REWRITE DEFAULT-<-1))
 (5 5 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (2 2 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (1 1 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 )
(DEPTH-ARRAYP-OF-ASET1-LIST
 (1076 43 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (1044 14 (:DEFINITION NAT-LISTP))
 (197 29 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (154 16 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (145 145 (:TYPE-PRESCRIPTION NAT-LISTP))
 (105 21 (:REWRITE DEPTH-ARRAYP-MONOTONE))
 (100 52 (:REWRITE DEFAULT-<-2))
 (86 43 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (81 53 (:REWRITE USE-ALL-<))
 (56 29 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (55 52 (:REWRITE DEFAULT-<-1))
 (53 53 (:REWRITE USE-ALL-<-2))
 (53 53 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (53 39 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (52 52 (:REWRITE USE-ALL-<=-2))
 (52 52 (:REWRITE USE-ALL-<=))
 (51 16 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (44 44 (:TYPE-PRESCRIPTION MEMBERP))
 (39 25 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (37 21 (:REWRITE USE-ALL-NATP))
 (34 34 (:REWRITE USE-ALL-CONSP-2))
 (34 34 (:REWRITE USE-ALL-CONSP))
 (30 15 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (28 14 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (28 1 (:REWRITE DEPTH-ARRAYP-OF-ASET1-AT-END-GEN))
 (27 27 (:REWRITE DEFAULT-CAR))
 (26 26 (:REWRITE DEFAULT-CDR))
 (26 13 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (26 13 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (23 23 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (23 23 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (21 21 (:REWRITE USE-ALL-NATP-2))
 (21 21 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (17 17 (:REWRITE USE-ALL-RATIONALP-2))
 (17 17 (:REWRITE USE-ALL-RATIONALP))
 (16 16 (:LINEAR ARRAY2P-LINEAR))
 (13 13 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (13 13 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (13 13 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (12 12 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (12 12 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (6 6 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (6 1 (:REWRITE USE-ALL-<=-FOR-CAR))
 (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 1 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (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))
 (2 2 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (2 2 (:TYPE-PRESCRIPTION ALL-<=))
 (1 1 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (1 1 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (1 1 (:REWRITE ALL-<=-MONOTONE))
 )
(TYPE-OF-AREF1-WHEN-DEPTH-ARRAYP-AUX-ALT
 (329 329 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (36 18 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (18 18 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (12 12 (:REWRITE USE-ALL-<=-2))
 (12 12 (:REWRITE USE-ALL-<=))
 (12 12 (:REWRITE USE-ALL-<-2))
 (12 12 (:REWRITE USE-ALL-<))
 (12 12 (:REWRITE DEFAULT-<-2))
 (12 12 (:REWRITE DEFAULT-<-1))
 (12 12 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (8 8 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (8 8 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (6 6 (:REWRITE DEPTH-ARRAYP-AUX-MONOTONE))
 (6 6 (:REWRITE DEFAULT-+-2))
 (6 6 (:REWRITE DEFAULT-+-1))
 (4 4 (:REWRITE USE-ALL-NATP-2))
 (4 4 (:REWRITE USE-ALL-NATP))
 (4 4 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (2 2 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (2 2 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (2 2 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 )
(TYPE-OF-AREF1-WHEN-DEPTH-ARRAYP-ALT
 (54 54 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (4 4 (:REWRITE DEFAULT-+-2))
 (4 4 (:REWRITE DEFAULT-+-1))
 (2 2 (:LINEAR ARRAY2P-LINEAR))
 (2 1 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (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 DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (1 1 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (1 1 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (1 1 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 )
(SET-DEPTHS-OF-NODENUMS-IF-LOWER
 (3769 159 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (2960 40 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-<))
 (2419 130 (:DEFINITION NAT-LISTP))
 (2077 2077 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (1809 71 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (1762 74 (:REWRITE USE-ALL-<-FOR-CAR))
 (1487 71 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (1347 95 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (662 662 (:TYPE-PRESCRIPTION NAT-LISTP))
 (429 429 (:TYPE-PRESCRIPTION ALL-<))
 (385 385 (:REWRITE DEFAULT-CAR))
 (359 274 (:REWRITE DEFAULT-<-2))
 (289 69 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (280 280 (:REWRITE USE-ALL-<-2))
 (280 280 (:REWRITE USE-ALL-<))
 (265 44 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (264 264 (:TYPE-PRESCRIPTION ALL-NATP))
 (262 44 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (246 246 (:REWRITE USE-ALL-<=-2))
 (246 246 (:REWRITE USE-ALL-<=))
 (239 29 (:REWRITE <-OF-CAR-AND-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (238 8 (:REWRITE ALL-<-OF-CDR))
 (218 2 (:REWRITE DEPTH-ARRAYP-OF-ASET1))
 (204 51 (:REWRITE NOT-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP))
 (197 197 (:REWRITE DEFAULT-CDR))
 (190 95 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (187 159 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (179 69 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (175 8 (:REWRITE ALL-NATP-OF-CDR))
 (172 8 (:REWRITE ARRAY1P-OF-ASET1-SIMPLE))
 (168 63 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL))
 (159 159 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (159 159 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (159 159 (:REWRITE ALL-<-TRANSITIVE))
 (158 2 (:REWRITE DEPTH-ARRAYP-OF-ASET1-AT-END-GEN))
 (149 149 (:REWRITE USE-ALL-CONSP-2))
 (149 149 (:REWRITE USE-ALL-CONSP))
 (148 74 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (147 147 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (144 144 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP))
 (135 27 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (134 29 (:REWRITE <-OF-CAR-AND-ALEN1))
 (133 133 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (126 126 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (126 21 (:REWRITE ALL-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (116 93 (:REWRITE DEFAULT-+-2))
 (110 110 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (110 110 (:TYPE-PRESCRIPTION ALL-CONSP))
 (109 9 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (107 95 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (104 52 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (104 52 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (104 10 (:REWRITE DEPTH-ARRAYP-AUX-OF-ASET1-TOO-HIGH))
 (95 95 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (93 93 (:REWRITE DEFAULT-+-1))
 (80 40 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (78 39 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (76 76 (:LINEAR ARRAY2P-LINEAR))
 (72 72 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (69 69 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (69 69 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (69 69 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (69 69 (:REWRITE ARRAY1P-WHEN-DEPTH-ARRAYP))
 (67 67 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (64 64 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DIMENSIONS-WHEN-ARRAY1P))
 (64 64 (:TYPE-PRESCRIPTION POSP-OF-CAR-OF-DIMENSIONS-WHEN-ARRAY1P))
 (63 63 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (63 63 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP))
 (55 55 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (55 55 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (54 54 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (52 52 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (51 35 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (49 49 (:REWRITE USE-ALL-NATP-2))
 (49 49 (:REWRITE USE-ALL-NATP))
 (49 11 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (39 39 (:REWRITE BOUNDED-DARG-LISTP-MONOTONE))
 (36 36 (:REWRITE USE-ALL-RATIONALP-2))
 (36 36 (:REWRITE USE-ALL-RATIONALP))
 (27 27 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (27 27 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (24 4 (:REWRITE USE-ALL-<=-FOR-CAR))
 (19 19 (:REWRITE DEPTH-ARRAYP-MONOTONE))
 (16 1 (:REWRITE TYPE-OF-AREF1-WHEN-DEPTH-ARRAYP-AUX-ALT))
 (10 2 (:REWRITE +-COMBINE-CONSTANTS))
 (9 9 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (9 9 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (8 8 (:TYPE-PRESCRIPTION ALL-<=))
 (8 8 (:REWRITE DIMENSIONS-WHEN-NOT-CONSP-OF-HEADER-CHEAP))
 (8 4 (:REWRITE DARGP-LESS-THAN-WHEN-NATP-CHEAP))
 (8 4 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (4 4 (:TYPE-PRESCRIPTION MYQUOTEP))
 (4 4 (:REWRITE DARGP-LESS-THAN-WHEN-QUOTEP-CHEAP))
 (4 4 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (4 4 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-CAR-AND-QUOTE))
 (4 4 (:REWRITE DARGP-LESS-THAN-MONO))
 (4 4 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (4 4 (:REWRITE ALL-<=-MONOTONE))
 (4 2 (:REWRITE UNICITY-OF-0))
 (2 2 (:DEFINITION FIX))
 (1 1 (:REWRITE TYPE-OF-AREF1-WHEN-DEPTH-ARRAYP-ALT))
 (1 1 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (1 1 (:REWRITE NOT-<-OF-+-1-AND-CAR-WHEN-ALL-<))
 (1 1 (:REWRITE ALL-MYQUOTEP-WHEN-NOT-CONSP))
 )
(DEPTH-ARRAYP-OF-SET-DEPTHS-OF-NODENUMS-IF-LOWER
 (2848 74 (:DEFINITION NAT-LISTP))
 (1938 68 (:REWRITE USE-ALL-<-FOR-CAR))
 (1712 49 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (1371 80 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (1228 6 (:REWRITE AREF1-OF-ASET1-BOTH))
 (547 515 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (412 412 (:TYPE-PRESCRIPTION NAT-LISTP))
 (390 48 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (362 76 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (301 24 (:REWRITE ALL-NATP-OF-CDR))
 (297 125 (:REWRITE DEFAULT-<-2))
 (196 50 (:DEFINITION MEMBER-EQUAL))
 (181 32 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (180 180 (:REWRITE DEFAULT-CAR))
 (177 125 (:REWRITE DEFAULT-<-1))
 (170 18 (:REWRITE ALL-<-OF-CDR))
 (160 80 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (152 6 (:REWRITE DEPTH-ARRAYP-OF-ASET1-AT-END-GEN))
 (149 125 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (145 145 (:REWRITE DEFAULT-CDR))
 (138 138 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (137 21 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (136 68 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (125 125 (:REWRITE USE-ALL-<-2))
 (125 125 (:REWRITE USE-ALL-<))
 (116 58 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (116 58 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (115 115 (:REWRITE USE-ALL-<=-2))
 (115 115 (:REWRITE USE-ALL-<=))
 (110 10 (:REWRITE <-OF-CAR-AND-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (98 91 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (91 91 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (91 91 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (91 91 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (91 91 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (91 91 (:REWRITE ALL-<-TRANSITIVE))
 (85 78 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (83 21 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (80 30 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL))
 (77 77 (:REWRITE USE-ALL-CONSP-2))
 (77 77 (:REWRITE USE-ALL-CONSP))
 (60 60 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (60 10 (:REWRITE ALL-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (60 10 (:REWRITE <-OF-CAR-AND-ALEN1))
 (58 58 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (58 58 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (58 58 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (54 54 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (54 54 (:TYPE-PRESCRIPTION ALL-CONSP))
 (50 10 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (48 48 (:REWRITE USE-ALL-NATP-2))
 (48 48 (:REWRITE USE-ALL-NATP))
 (40 8 (:REWRITE ALL-CONSP-OF-CDR))
 (39 23 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (30 30 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (30 30 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP))
 (28 28 (:REWRITE USE-ALL-RATIONALP-2))
 (28 28 (:REWRITE USE-ALL-RATIONALP))
 (27 27 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (27 27 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (26 26 (:LINEAR ARRAY2P-LINEAR))
 (24 8 (:REWRITE PSEUDO-DAGP-OF-CDR-WHEN-PSEUDO-DAGP))
 (24 4 (:REWRITE USE-ALL-<=-FOR-CAR))
 (22 11 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (22 11 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (21 21 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (21 21 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (21 21 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (20 20 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP))
 (20 20 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (14 10 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (12 12 (:REWRITE DEFAULT-+-2))
 (12 12 (:REWRITE DEFAULT-+-1))
 (11 11 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (11 11 (:REWRITE BOUNDED-DARG-LISTP-MONOTONE))
 (10 10 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (10 10 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (10 10 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (8 8 (:TYPE-PRESCRIPTION ALL-<=))
 (6 6 (:TYPE-PRESCRIPTION NATP))
 (6 6 (:REWRITE AREF1-OF-ASET1-DIFF))
 (4 4 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (4 4 (:REWRITE ALL-<=-MONOTONE))
 (2 2 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (2 2 (:REWRITE EQUAL-OF-+-COMBINE-CONSTANTS))
 (2 2 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (2 2 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (1 1 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 )
(ARRAY1P-OF-SET-DEPTHS-OF-NODENUMS-IF-LOWER
 (2471 43 (:REWRITE DARGP-LESS-THAN-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (1754 64 (:REWRITE USE-ALL-<-FOR-CAR))
 (1734 56 (:REWRITE BOUNDED-DARG-LISTP-OF-CDR))
 (1503 51 (:DEFINITION NAT-LISTP))
 (1008 151 (:REWRITE ALL-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (1003 53 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (884 70 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (695 54 (:REWRITE ALL-<-OF-CDR))
 (666 28 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (560 28 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (444 38 (:REWRITE DARGP-LESS-THAN-WHEN-NATP-CHEAP))
 (432 432 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (304 59 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-OF-CDR))
 (288 288 (:TYPE-PRESCRIPTION NAT-LISTP))
 (286 178 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (240 216 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL))
 (235 223 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (216 216 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP-SPECIAL-ALT))
 (216 216 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-BOUNDED-DARG-LISTP))
 (214 82 (:REWRITE DEFAULT-<-2))
 (203 203 (:REWRITE DEFAULT-CDR))
 (198 99 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (195 99 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (192 28 (:REWRITE <-OF-CAR-AND-ALEN1-WHEN-PSEUDO-DAG-ARRAYP-LIST))
 (179 179 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (179 179 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (179 179 (:REWRITE ALL-<-TRANSITIVE))
 (170 28 (:REWRITE <-OF-CAR-AND-ALEN1))
 (165 165 (:REWRITE DEFAULT-CAR))
 (163 97 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (133 82 (:REWRITE DEFAULT-<-1))
 (129 34 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (128 64 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (121 121 (:REWRITE USE-ALL-CONSP-2))
 (121 121 (:REWRITE USE-ALL-CONSP))
 (106 53 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (104 104 (:TYPE-PRESCRIPTION NATP))
 (99 99 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (90 84 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (88 43 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-CAR-AND-QUOTE))
 (86 43 (:REWRITE DARGP-LESS-THAN-WHEN-MYQUOTEP-CHEAP))
 (82 82 (:REWRITE USE-ALL-<-2))
 (82 82 (:REWRITE USE-ALL-<))
 (80 2 (:REWRITE AREF1-OF-ASET1-BOTH))
 (78 72 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (75 9 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (70 70 (:REWRITE USE-ALL-NATP-2))
 (70 70 (:REWRITE USE-ALL-NATP))
 (64 64 (:REWRITE USE-ALL-<=-2))
 (64 64 (:REWRITE USE-ALL-<=))
 (60 30 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (60 30 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (54 6 (:REWRITE ALL-NATP-OF-CDR))
 (52 52 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (46 46 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (45 9 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (43 43 (:TYPE-PRESCRIPTION MYQUOTEP))
 (43 43 (:REWRITE DARGP-LESS-THAN-WHEN-EQUAL-OF-NTH-0-AND-QUOTE))
 (38 38 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (38 38 (:REWRITE DARGP-LESS-THAN-WHEN-QUOTEP-CHEAP))
 (38 38 (:REWRITE DARGP-LESS-THAN-MONO))
 (36 21 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (34 34 (:REWRITE USE-ALL-RATIONALP-2))
 (34 34 (:REWRITE USE-ALL-RATIONALP))
 (30 30 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (30 30 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (30 30 (:TYPE-PRESCRIPTION ALL-CONSP))
 (30 30 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (30 30 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (30 6 (:REWRITE ALL-CONSP-OF-CDR))
 (22 22 (:REWRITE ARRAY1P-WHEN-DEPTH-ARRAYP))
 (22 22 (:LINEAR ARRAY2P-LINEAR))
 (20 20 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (20 2 (:DEFINITION LEN))
 (18 6 (:REWRITE PSEUDO-DAGP-OF-CDR-WHEN-PSEUDO-DAGP))
 (15 15 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (15 15 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (13 13 (:TYPE-PRESCRIPTION DARGP-LESS-THAN))
 (12 6 (:REWRITE DEFAULT-+-2))
 (10 10 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (9 9 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (9 9 (:REWRITE MYQUOTEP-WHEN-DARGP-LESS-THAN))
 (9 9 (:REWRITE MYQUOTEP-WHEN-BOUNDED-DAG-EXPRP))
 (9 9 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (9 9 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (8 4 (:REWRITE LEN-WHEN-DARGP-CHEAP))
 (8 4 (:DEFINITION MEMBER-EQUAL))
 (6 6 (:REWRITE DEFAULT-+-1))
 (5 5 (:REWRITE QUOTE-LEMMA-FOR-BOUNDED-DARG-LISTP-GEN-ALT))
 (4 4 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (4 4 (:TYPE-PRESCRIPTION DARGP))
 (4 4 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (4 4 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (4 4 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (4 4 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (3 3 (:REWRITE EQUAL-OF-NON-NATP-AND-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (2 2 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (1 1 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (1 1 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 )
(ALEN1-OF-SET-DEPTHS-OF-NODENUMS-IF-LOWER
 (1052 40 (:DEFINITION NAT-LISTP))
 (707 147 (:REWRITE DEFAULT-CAR))
 (616 16 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (567 34 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (537 33 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (505 467 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (325 55 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (260 150 (:REWRITE DEFAULT-CDR))
 (255 23 (:REWRITE ALL-CONSP-OF-CDR))
 (240 30 (:DEFINITION ASSOC-KEYWORD))
 (230 63 (:REWRITE DEFAULT-<-2))
 (187 46 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (180 180 (:REWRITE USE-ALL-CONSP-2))
 (180 180 (:REWRITE USE-ALL-CONSP))
 (167 34 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (154 20 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (151 151 (:TYPE-PRESCRIPTION NAT-LISTP))
 (143 6 (:REWRITE ALL-NATP-OF-CDR))
 (138 2 (:REWRITE ALL-<-OF-CDR))
 (132 63 (:REWRITE DEFAULT-<-1))
 (110 110 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (110 110 (:TYPE-PRESCRIPTION ALL-CONSP))
 (102 22 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (75 55 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (69 23 (:REWRITE PSEUDO-DAGP-OF-CDR-WHEN-PSEUDO-DAGP))
 (68 29 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (66 33 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (63 63 (:REWRITE USE-ALL-<=-2))
 (63 63 (:REWRITE USE-ALL-<=))
 (63 63 (:REWRITE USE-ALL-<-2))
 (63 63 (:REWRITE USE-ALL-<))
 (63 63 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (52 26 (:REWRITE USE-ALL-<-FOR-CAR))
 (52 26 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (52 26 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (52 26 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (50 10 (:REWRITE AREF1-OF-ASET1-BOTH))
 (46 46 (:REWRITE USE-ALL-RATIONALP-2))
 (46 46 (:REWRITE USE-ALL-RATIONALP))
 (40 40 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (40 40 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (38 31 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (38 31 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (34 34 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (34 34 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (34 34 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (31 31 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (31 31 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (31 31 (:REWRITE ALL-<-TRANSITIVE))
 (28 14 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (28 14 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (28 6 (:DEFINITION MEMBER-EQUAL))
 (26 26 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (26 26 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (26 26 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (22 22 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (20 20 (:REWRITE USE-ALL-NATP-2))
 (20 20 (:REWRITE USE-ALL-NATP))
 (17 13 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (14 14 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (14 14 (:REWRITE BOUNDED-DARG-LISTP-MONOTONE))
 (10 10 (:REWRITE EQUAL-OF-NON-NATP-AND-CAAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (10 10 (:REWRITE CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (10 10 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (10 10 (:REWRITE ARRAY1P-WHEN-DEPTH-ARRAYP))
 (10 10 (:REWRITE AREF1-OF-ASET1-DIFF))
 (1 1 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 )
(DEFAULT-OF-SET-DEPTHS-OF-NODENUMS-IF-LOWER
 (1028 28 (:DEFINITION NAT-LISTP))
 (592 10 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (513 27 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (156 144 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (154 20 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (143 6 (:REWRITE ALL-NATP-OF-CDR))
 (140 49 (:REWRITE DEFAULT-<-2))
 (138 2 (:REWRITE ALL-<-OF-CDR))
 (133 133 (:TYPE-PRESCRIPTION NAT-LISTP))
 (117 18 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (113 30 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (102 22 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (94 49 (:REWRITE DEFAULT-<-1))
 (77 77 (:REWRITE DEFAULT-CAR))
 (71 18 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (58 58 (:REWRITE DEFAULT-CDR))
 (54 54 (:REWRITE USE-ALL-CONSP-2))
 (54 54 (:REWRITE USE-ALL-CONSP))
 (54 27 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (52 26 (:REWRITE USE-ALL-<-FOR-CAR))
 (52 26 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (52 26 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (52 26 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (49 49 (:REWRITE USE-ALL-<=-2))
 (49 49 (:REWRITE USE-ALL-<=))
 (49 49 (:REWRITE USE-ALL-<-2))
 (49 49 (:REWRITE USE-ALL-<))
 (49 49 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (46 46 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (46 46 (:TYPE-PRESCRIPTION ALL-CONSP))
 (42 19 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (35 7 (:REWRITE ALL-CONSP-OF-CDR))
 (34 34 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (34 34 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (32 25 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (30 30 (:REWRITE USE-ALL-RATIONALP-2))
 (30 30 (:REWRITE USE-ALL-RATIONALP))
 (28 6 (:DEFINITION MEMBER-EQUAL))
 (26 26 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (26 26 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (26 19 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (23 23 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (23 23 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (23 19 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (22 22 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (21 7 (:REWRITE PSEUDO-DAGP-OF-CDR-WHEN-PSEUDO-DAGP))
 (20 20 (:REWRITE USE-ALL-NATP-2))
 (20 20 (:REWRITE USE-ALL-NATP))
 (20 4 (:REWRITE AREF1-OF-ASET1-BOTH))
 (19 19 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (19 19 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (19 19 (:REWRITE ALL-<-TRANSITIVE))
 (18 18 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (18 18 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (18 18 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (16 16 (:TYPE-PRESCRIPTION ASET1))
 (16 8 (:REWRITE BOUNDED-DARG-LISTP-WHEN-BOUNDED-DARG-LISTP-OF-CDR-CHEAP))
 (16 8 (:REWRITE BOUNDED-DARG-LISTP-WHEN-ALL-MYQUOTEP-CHEAP))
 (11 7 (:REWRITE BOUNDED-DARG-LISTP-WHEN-NOT-CONSP))
 (8 8 (:TYPE-PRESCRIPTION ARRAY1P))
 (8 8 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (8 8 (:REWRITE BOUNDED-DARG-LISTP-MONOTONE))
 (4 4 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (4 4 (:REWRITE ARRAY1P-WHEN-DEPTH-ARRAYP))
 (4 4 (:REWRITE AREF1-OF-ASET1-DIFF))
 (1 1 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 )
(MAKE-DEPTH-ARRAY-AUX
 (301 301 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (250 54 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (217 69 (:REWRITE DEFAULT-<-2))
 (208 26 (:REWRITE NOT-EQUAL-OF-CAR-AND-QUOTE-WHEN-LEN-WRONG-AND-PSEUDO-DAG-ARRAYP-AUX))
 (122 46 (:REWRITE DEFAULT-+-2))
 (104 26 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (80 11 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (69 69 (:REWRITE USE-ALL-<=-2))
 (69 69 (:REWRITE USE-ALL-<=))
 (69 69 (:REWRITE USE-ALL-<-2))
 (69 69 (:REWRITE USE-ALL-<))
 (69 69 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (56 14 (:REWRITE RATIONALP-OF-ALEN1-WHEN-ARRAY1P))
 (53 53 (:REWRITE USE-ALL-RATIONALP-2))
 (53 53 (:REWRITE USE-ALL-RATIONALP))
 (52 52 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (48 36 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DIMENSIONS-WHEN-ARRAY1P))
 (48 36 (:TYPE-PRESCRIPTION POSP-OF-CAR-OF-DIMENSIONS-WHEN-ARRAY1P))
 (46 46 (:REWRITE DEFAULT-+-1))
 (33 33 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (28 28 (:REWRITE USE-ALL-CONSP-2))
 (28 28 (:REWRITE USE-ALL-CONSP))
 (28 28 (:REWRITE DEFAULT-CAR))
 (26 26 (:REWRITE QUOTE-LEMMA-FOR-BOUNDED-DARG-LISTP-GEN-ALT))
 (26 26 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (26 26 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (21 21 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (19 19 (:REWRITE USE-ALL-NATP-2))
 (19 19 (:REWRITE USE-ALL-NATP))
 (19 19 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (19 1 (:REWRITE DARG-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (11 11 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (11 11 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (10 10 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (8 5 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (8 4 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (1 1 (:REWRITE TYPE-OF-AREF1-WHEN-DEPTH-ARRAYP-AUX-ALT))
 (1 1 (:REWRITE TYPE-OF-AREF1-WHEN-DEPTH-ARRAYP-ALT))
 )
(ALEN1-OF-MV-NTH-0-OF-MAKE-DEPTH-ARRAY-AUX
 (597 597 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (216 108 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (72 9 (:REWRITE NOT-EQUAL-OF-CAR-AND-QUOTE-WHEN-LEN-WRONG-AND-PSEUDO-DAG-ARRAYP-AUX))
 (71 37 (:REWRITE DEFAULT-+-2))
 (42 42 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (37 37 (:REWRITE DEFAULT-+-1))
 (36 9 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (32 8 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (28 2 (:DEFINITION MAX))
 (25 19 (:REWRITE DEFAULT-<-2))
 (22 22 (:LINEAR ARRAY2P-LINEAR))
 (21 19 (:REWRITE DEFAULT-<-1))
 (19 19 (:REWRITE USE-ALL-<=-2))
 (19 19 (:REWRITE USE-ALL-<=))
 (19 19 (:REWRITE USE-ALL-<-2))
 (19 19 (:REWRITE USE-ALL-<))
 (19 19 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (18 18 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (12 12 (:REWRITE DEFAULT-CAR))
 (11 11 (:REWRITE USE-ALL-NATP-2))
 (11 11 (:REWRITE USE-ALL-NATP))
 (11 11 (:REWRITE NATP-WHEN-BOUNDED-DARG-LISTP-GEN))
 (10 10 (:REWRITE USE-ALL-CONSP-2))
 (10 10 (:REWRITE USE-ALL-CONSP))
 (9 9 (:REWRITE QUOTE-LEMMA-FOR-BOUNDED-DARG-LISTP-GEN-ALT))
 (9 9 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (9 9 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (8 8 (:REWRITE USE-ALL-RATIONALP-2))
 (8 8 (:REWRITE USE-ALL-RATIONALP))
 (8 8 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (4 4 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (1 1 (:REWRITE NATP-OF-+-WHEN-NEGATIVE-CONSTANT))
 (1 1 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (1 1 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (1 1 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 )
(ARRAY1P-OF-MV-NTH-0-OF-MAKE-DEPTH-ARRAY-AUX
 (595 595 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (216 108 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (72 9 (:REWRITE NOT-EQUAL-OF-CAR-AND-QUOTE-WHEN-LEN-WRONG-AND-PSEUDO-DAG-ARRAYP-AUX))
 (64 35 (:REWRITE DEFAULT-+-2))
 (40 40 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (36 9 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (35 35 (:REWRITE DEFAULT-+-1))
 (28 28 (:LINEAR ARRAY2P-LINEAR))
 (28 7 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (28 2 (:DEFINITION MAX))
 (25 19 (:REWRITE DEFAULT-<-2))
 (21 19 (:REWRITE DEFAULT-<-1))
 (19 19 (:REWRITE USE-ALL-<=-2))
 (19 19 (:REWRITE USE-ALL-<=))
 (19 19 (:REWRITE USE-ALL-<-2))
 (19 19 (:REWRITE USE-ALL-<))
 (19 19 (:REWRITE <-WHEN-BOUNDED-DARG-LISTP-GEN))
 (18 18 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
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(DEPTH-ARRAYP-OF-MV-NTH-0-OF-MAKE-DEPTH-ARRAY-AUX
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(INTEGERP-OF-MV-NTH-1-OF-MAKE-DEPTH-ARRAY-AUX
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(MAKE-DEPTH-ARRAY-FOR-NODES
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(ALEN1-OF-MV-NTH-0-OF-MAKE-DEPTH-ARRAY-FOR-NODES
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(ARRAY1P-OF-MV-NTH-0-OF-MAKE-DEPTH-ARRAY-FOR-NODES
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(DEPTH-ARRAYP-OF-MV-NTH-0-OF-MAKE-DEPTH-ARRAY-FOR-NODES
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(DEPTH-ARRAYP-OF-MV-NTH-0-OF-MAKE-DEPTH-ARRAY-FOR-NODES-GEN
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(INTEGERP-OF-MV-NTH-1-OF-MAKE-DEPTH-ARRAY-FOR-NODES-GEN
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 (1 1 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (1 1 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (1 1 (:REWRITE NOT-<-OF-CAR-WHEN-BOUNDED-DARG-LISTP-2))
 (1 1 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE INTEGERP-OF-CAR-WHEN-BOUNDED-DARG-LISTP))
 (1 1 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 )
