(<-OF-0-AND-LEN
 (102 6 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (92 4 (:DEFINITION LEN))
 (12 6 (:REWRITE DEFAULT-<-2))
 (10 10 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (10 10 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (10 10 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (10 10 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (8 4 (:REWRITE DEFAULT-+-2))
 (6 6 (:REWRITE USE-ALL-CONSP-2))
 (6 6 (:REWRITE USE-ALL-CONSP))
 (6 6 (:REWRITE USE-ALL-<-2))
 (6 6 (:REWRITE USE-ALL-<))
 (6 6 (:REWRITE DEFAULT-<-1))
 (6 6 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (6 6 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (6 6 (:REWRITE <-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (6 6 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (6 6 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (4 4 (:REWRITE DEFAULT-CDR))
 (4 4 (:REWRITE DEFAULT-+-1))
 (4 4 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (2 2 (:REWRITE USE-ALL-<=-2))
 (2 2 (:REWRITE USE-ALL-<=))
 )
(SIZE-ARRAYP-AUX
 (141 141 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (102 102 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (15 13 (:REWRITE DEFAULT-<-2))
 (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-<-1))
 (13 13 (:REWRITE <-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (10 10 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (10 7 (:REWRITE DEFAULT-+-2))
 (9 3 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (8 8 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (7 7 (:REWRITE DEFAULT-+-1))
 (4 4 (:REWRITE USE-ALL-NATP-2))
 (4 4 (:REWRITE USE-ALL-NATP))
 (4 4 (:REWRITE NATP-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (3 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2 2 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (2 2 (:LINEAR ARRAY2P-LINEAR))
 (1 1 (:REWRITE USE-ALL-RATIONALP-2))
 (1 1 (:REWRITE USE-ALL-RATIONALP))
 (1 1 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 )
(SIZE-ARRAYP-AUX-OF-MINUS1)
(SIZE-ARRAYP-AUX-OF-0
 (25 25 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (8 2 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (4 2 (:TYPE-PRESCRIPTION ALEN1-TYPE))
 (2 2 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (2 2 (:TYPE-PRESCRIPTION ARRAY1P))
 (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-ALL-DARGP-LESS-THAN-GEN))
 (2 2 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE <-WHEN-ALL-DARGP-LESS-THAN-GEN))
 )
(SIZE-ARRAYP-AUX-MONOTONE
 (116 116 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (52 13 (: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-ALL-DARGP-LESS-THAN-GEN))
 (26 13 (:TYPE-PRESCRIPTION ALEN1-TYPE))
 (23 23 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (23 23 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (17 17 (:REWRITE USE-ALL-NATP-2))
 (17 17 (:REWRITE USE-ALL-NATP))
 (17 17 (:REWRITE NATP-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (13 13 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (13 13 (:TYPE-PRESCRIPTION ARRAY1P))
 (7 7 (:REWRITE DEFAULT-+-2))
 (7 7 (:REWRITE DEFAULT-+-1))
 )
(TYPE-OF-AREF1-WHEN-SIZE-ARRAYP-AUX
 (180 180 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (36 9 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (18 9 (:TYPE-PRESCRIPTION ALEN1-TYPE))
 (9 9 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (9 9 (:TYPE-PRESCRIPTION ARRAY1P))
 (8 8 (:REWRITE USE-ALL-<=-2))
 (8 8 (:REWRITE USE-ALL-<=))
 (8 8 (:REWRITE USE-ALL-<-2))
 (8 8 (:REWRITE USE-ALL-<))
 (8 8 (:REWRITE DEFAULT-<-2))
 (8 8 (:REWRITE DEFAULT-<-1))
 (8 8 (:REWRITE <-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (6 6 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (6 6 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (4 4 (:REWRITE SIZE-ARRAYP-AUX-MONOTONE))
 (2 2 (:REWRITE USE-ALL-NATP-2))
 (2 2 (:REWRITE USE-ALL-NATP))
 (2 2 (:REWRITE NATP-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(SIZE-ARRAYP-AUX-OF-ASET1-TOO-HIGH
 (205 205 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (157 157 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (65 22 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (36 30 (:REWRITE DEFAULT-<-2))
 (30 30 (:REWRITE USE-ALL-<=-2))
 (30 30 (:REWRITE USE-ALL-<=))
 (30 30 (:REWRITE USE-ALL-<-2))
 (30 30 (:REWRITE USE-ALL-<))
 (30 30 (:REWRITE DEFAULT-<-1))
 (30 30 (:REWRITE <-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (22 22 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (18 18 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (17 17 (:REWRITE USE-ALL-NATP-2))
 (17 17 (:REWRITE USE-ALL-NATP))
 (17 17 (:REWRITE NATP-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (16 16 (:REWRITE SIZE-ARRAYP-AUX-MONOTONE))
 (10 10 (:LINEAR ARRAY2P-LINEAR))
 (7 7 (:TYPE-PRESCRIPTION ASET1))
 (6 6 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (4 4 (:REWRITE DEFAULT-+-2))
 (4 4 (:REWRITE DEFAULT-+-1))
 (3 3 (:REWRITE TYPE-OF-AREF1-WHEN-SIZE-ARRAYP-AUX))
 )
(SIZE-ARRAYP-AUX-OF-ASET1
 (251 251 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (133 133 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (23 20 (:REWRITE DEFAULT-<-2))
 (20 20 (:REWRITE USE-ALL-<-2))
 (20 20 (:REWRITE USE-ALL-<))
 (20 20 (:REWRITE DEFAULT-<-1))
 (20 20 (:REWRITE <-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (18 18 (:REWRITE USE-ALL-<=-2))
 (18 18 (:REWRITE USE-ALL-<=))
 (17 9 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (10 10 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (9 9 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (6 6 (:REWRITE DEFAULT-+-2))
 (6 6 (:REWRITE DEFAULT-+-1))
 (6 6 (:LINEAR ARRAY2P-LINEAR))
 (3 3 (:REWRITE USE-ALL-NATP-2))
 (3 3 (:REWRITE USE-ALL-NATP))
 (3 3 (:REWRITE NATP-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (3 3 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (3 1 (:REWRITE FOLD-CONSTS-IN-+))
 (2 2 (:TYPE-PRESCRIPTION ASET1))
 )
(SIZE-ARRAYP-AUX-OF-ASET1-AT-END
 (38 38 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (12 5 (:REWRITE SIZE-ARRAYP-AUX-MONOTONE))
 (11 11 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (10 9 (:REWRITE DEFAULT-<-2))
 (9 9 (:REWRITE USE-ALL-<-2))
 (9 9 (:REWRITE USE-ALL-<))
 (9 9 (:REWRITE DEFAULT-<-1))
 (9 9 (:REWRITE <-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (9 2 (:REWRITE TYPE-OF-AREF1-WHEN-SIZE-ARRAYP-AUX))
 (8 8 (:REWRITE USE-ALL-<=-2))
 (8 8 (:REWRITE USE-ALL-<=))
 (8 3 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (6 1 (:REWRITE SIZE-ARRAYP-AUX-OF-ASET1-TOO-HIGH))
 (5 5 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (5 5 (:REWRITE DEFAULT-+-2))
 (5 5 (:REWRITE DEFAULT-+-1))
 (4 4 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (3 3 (:REWRITE USE-ALL-NATP-2))
 (3 3 (:REWRITE USE-ALL-NATP))
 (3 3 (:REWRITE NATP-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (3 1 (:REWRITE FOLD-CONSTS-IN-+))
 (2 2 (:LINEAR ARRAY2P-LINEAR))
 (1 1 (:TYPE-PRESCRIPTION ASET1))
 (1 1 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 )
(SIZE-ARRAYP-AUX-OF-COMPRESS1
 (129 129 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (37 25 (:REWRITE DEFAULT-<-2))
 (34 34 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (34 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-ALL-DARGP-LESS-THAN-GEN))
 (18 18 (:REWRITE SIZE-ARRAYP-AUX-MONOTONE))
 (13 13 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (13 13 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (13 13 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (10 10 (:REWRITE USE-ALL-NATP-2))
 (10 10 (:REWRITE USE-ALL-NATP))
 (10 10 (:REWRITE NATP-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (10 10 (:LINEAR ARRAY2P-LINEAR))
 (9 3 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (7 7 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (5 5 (:REWRITE TYPE-OF-AREF1-WHEN-SIZE-ARRAYP-AUX))
 (4 4 (:REWRITE DEFAULT-+-2))
 (4 4 (:REWRITE DEFAULT-+-1))
 (3 3 (:REWRITE USE-ALL-RATIONALP-2))
 (3 3 (:REWRITE USE-ALL-RATIONALP))
 )
(SIZE-ARRAYP-AUX-OF-CONS-OF-CONS-OF-HEADER
 (285 15 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (245 5 (:REWRITE DEFAULT-CAR))
 (125 5 (:REWRITE LEN-OF-CDR))
 (105 5 (:REWRITE DEFAULT-CDR))
 (60 60 (:TYPE-PRESCRIPTION LEN))
 (50 5 (:REWRITE EQUAL-OF-LEN-AND-0))
 (48 12 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (40 5 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (35 20 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (28 18 (:REWRITE DEFAULT-<-2))
 (24 12 (:TYPE-PRESCRIPTION ALEN1-TYPE))
 (22 15 (:REWRITE SIZE-ARRAYP-AUX-MONOTONE))
 (20 20 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (20 20 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (20 20 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (18 18 (:REWRITE USE-ALL-<-2))
 (18 18 (:REWRITE USE-ALL-<))
 (18 18 (:REWRITE DEFAULT-<-1))
 (18 18 (:REWRITE <-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (15 15 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (14 9 (:REWRITE DEFAULT-+-2))
 (13 13 (:REWRITE USE-ALL-<=-2))
 (13 13 (:REWRITE USE-ALL-<=))
 (12 12 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (12 12 (:TYPE-PRESCRIPTION ARRAY1P))
 (12 12 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (12 12 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (10 10 (:REWRITE USE-ALL-CONSP-2))
 (10 10 (:REWRITE USE-ALL-CONSP))
 (10 10 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (9 9 (:REWRITE DEFAULT-+-1))
 (7 7 (:REWRITE USE-ALL-NATP-2))
 (7 7 (:REWRITE USE-ALL-NATP))
 (7 7 (:REWRITE NATP-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (5 5 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 )
(SIZE-ARRAYP-AUX-OF-CONS-OF-CONS-OF-HEADER-IRREL
 (342 18 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (294 6 (:REWRITE DEFAULT-CAR))
 (150 6 (:REWRITE LEN-OF-CDR))
 (126 6 (:REWRITE DEFAULT-CDR))
 (105 7 (:REWRITE SIZE-ARRAYP-AUX-OF-CONS-OF-CONS-OF-HEADER))
 (88 22 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (72 72 (:TYPE-PRESCRIPTION LEN))
 (60 6 (:REWRITE EQUAL-OF-LEN-AND-0))
 (48 6 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (44 22 (:TYPE-PRESCRIPTION ALEN1-TYPE))
 (42 24 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (31 19 (:REWRITE DEFAULT-<-2))
 (24 24 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (24 24 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (24 24 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (23 23 (:REWRITE SIZE-ARRAYP-AUX-MONOTONE))
 (22 22 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (22 22 (:TYPE-PRESCRIPTION ARRAY1P))
 (19 19 (:REWRITE USE-ALL-<-2))
 (19 19 (:REWRITE USE-ALL-<))
 (19 19 (:REWRITE DEFAULT-<-1))
 (19 19 (:REWRITE <-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (18 18 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (18 12 (:REWRITE DEFAULT-+-2))
 (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))
 (12 12 (:REWRITE USE-ALL-CONSP-2))
 (12 12 (:REWRITE USE-ALL-CONSP))
 (12 12 (:REWRITE DEFAULT-+-1))
 (12 12 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (7 7 (:REWRITE USE-ALL-NATP-2))
 (7 7 (:REWRITE USE-ALL-NATP))
 (7 7 (:REWRITE TYPE-OF-AREF1-WHEN-SIZE-ARRAYP-AUX))
 (7 7 (:REWRITE NATP-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (6 6 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 )
(SIZE-ARRAYP)
(ARRAY1P-WHEN-SIZE-ARRAYP)
(SIZE-ARRAYP-FORWARD-TO-ARRAY1P)
(SIZE-ARRAYP-FORWARD-TO-LEN-BOUNDSIZE-ARRAYP
 (10 10 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 )
(SIZE-ARRAYP-FORWARD-TO-LEN-BOUND-2SIZE-ARRAYP
 (3 3 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 )
(TYPE-OF-AREF1-WHEN-SIZE-ARRAYP
 (34 34 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (12 12 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (3 3 (:REWRITE DEFAULT-+-2))
 (3 3 (: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-ALL-DARGP-LESS-THAN-GEN))
 )
(SIZE-ARRAYP-MONOTONE
 (12 12 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (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-ALL-DARGP-LESS-THAN-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-SIZE-ARRAYP))
 (2 2 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (2 2 (:LINEAR ARRAY2P-LINEAR))
 )
(SIZE-ARRAYP-OF-ASET1
 (40 1 (:DEFINITION SIZE-ARRAYP-AUX))
 (16 16 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (10 8 (:REWRITE DEFAULT-<-1))
 (9 8 (:REWRITE DEFAULT-<-2))
 (8 8 (:REWRITE USE-ALL-<=-2))
 (8 8 (:REWRITE USE-ALL-<=))
 (8 8 (:REWRITE USE-ALL-<-2))
 (8 8 (:REWRITE USE-ALL-<))
 (8 8 (:REWRITE <-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (8 2 (:REWRITE NOT-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP))
 (5 5 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (4 4 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (4 4 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP))
 (4 4 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (4 4 (:REWRITE DEFAULT-+-2))
 (4 4 (:REWRITE DEFAULT-+-1))
 (3 1 (:REWRITE FOLD-CONSTS-IN-+))
 (2 2 (:REWRITE USE-ALL-NATP-2))
 (2 2 (:REWRITE USE-ALL-NATP))
 (2 2 (:REWRITE SIZE-ARRAYP-AUX-MONOTONE))
 (2 2 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (2 2 (:REWRITE NATP-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (2 2 (:REWRITE ARRAY1P-WHEN-SIZE-ARRAYP))
 (2 2 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (2 2 (:LINEAR ARRAY2P-LINEAR))
 (2 1 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (1 1 (:REWRITE TYPE-OF-AREF1-WHEN-SIZE-ARRAYP-AUX))
 (1 1 (:REWRITE TYPE-OF-AREF1-WHEN-SIZE-ARRAYP))
 (1 1 (:REWRITE SIZE-ARRAYP-MONOTONE))
 )
(SIZE-ARRAYP-OF-ASET1-AT-END
 (74 2 (:DEFINITION SIZE-ARRAYP-AUX))
 (59 1 (:REWRITE SIZE-ARRAYP-OF-ASET1))
 (17 17 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (13 13 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (12 10 (:REWRITE DEFAULT-<-1))
 (11 10 (:REWRITE DEFAULT-<-2))
 (11 4 (:REWRITE SIZE-ARRAYP-AUX-MONOTONE))
 (10 10 (:REWRITE USE-ALL-<=-2))
 (10 10 (:REWRITE USE-ALL-<=))
 (10 10 (:REWRITE USE-ALL-<-2))
 (10 10 (:REWRITE USE-ALL-<))
 (10 10 (:REWRITE <-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (9 9 (:REWRITE DEFAULT-+-2))
 (9 9 (:REWRITE DEFAULT-+-1))
 (9 2 (:REWRITE TYPE-OF-AREF1-WHEN-SIZE-ARRAYP-AUX))
 (8 2 (:REWRITE NOT-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP))
 (5 5 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (4 4 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP))
 (4 4 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (3 3 (:REWRITE USE-ALL-NATP-2))
 (3 3 (:REWRITE USE-ALL-NATP))
 (3 3 (:REWRITE NATP-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (3 3 (:REWRITE ARRAY1P-WHEN-SIZE-ARRAYP))
 (3 3 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 (3 2 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (2 2 (:REWRITE TYPE-OF-AREF1-WHEN-SIZE-ARRAYP))
 (2 2 (:REWRITE SIZE-ARRAYP-MONOTONE))
 (2 2 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 (2 2 (:LINEAR ARRAY2P-LINEAR))
 (1 1 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 )
(SIZE-ARRAYP-OF-MAKE-EMPTY-ARRAY-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-ALL-DARGP-LESS-THAN-GEN))
 (1 1 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (1 1 (:REWRITE SIZE-ARRAYP-MONOTONE))
 (1 1 (:REWRITE SIZE-ARRAYP-AUX-MONOTONE))
 (1 1 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE ARRAY1P-WHEN-SIZE-ARRAYP))
 (1 1 (:REWRITE ARRAY1P-WHEN-PSEUDO-DAG-ARRAYP))
 )
(TYPE-OF-AREF1-WHEN-SIZE-ARRAYP-2
 (35 35 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (12 12 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (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-ALL-DARGP-LESS-THAN-GEN))
 )
(INTEGER-WHEN-NATP)
(ACL2-NUMBERP-WHEN-NATP)
(<=-OF-+-WHEN-NATP-AND-NATP)
(NATP-OF-+-WHEN-NATP-AND-NATP)
(NATP-OF-IF)
(ADD-ARG-SIZES-WITH-NAME
 (468 234 (:TYPE-PRESCRIPTION NATP-OF-LARGEST-NON-QUOTEP))
 (280 26 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (234 234 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (205 3 (:REWRITE NATP-OF-IF))
 (195 17 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (193 193 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (150 11 (:DEFINITION NAT-LISTP))
 (145 4 (:REWRITE USE-ALL-<-FOR-CAR))
 (144 12 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (133 10 (:REWRITE <-OF-0-AND-LEN))
 (127 127 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (70 2 (:REWRITE TYPE-OF-AREF1-WHEN-SIZE-ARRAYP))
 (68 7 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (67 67 (:TYPE-PRESCRIPTION NAT-LISTP))
 (54 15 (:REWRITE DEFAULT-+-2))
 (54 1 (:REWRITE NATP-OF-LARGEST-NON-QUOTEP-2))
 (52 28 (:REWRITE DEFAULT-CAR))
 (50 15 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (44 2 (:REWRITE ALL-NATP-OF-CDR))
 (44 2 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (42 42 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DIMENSIONS))
 (42 2 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (39 9 (:REWRITE DEFAULT-<-1))
 (37 37 (:TYPE-PRESCRIPTION ALL-CONSP))
 (36 15 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (34 34 (:TYPE-PRESCRIPTION ALL-NATP))
 (33 3 (:REWRITE LEN-OF-CDR))
 (33 1 (:REWRITE EQUAL-OF--1-AND-LARGEST-NON-QUOTEP))
 (32 16 (:REWRITE LARGEST-NON-QUOTEP-WHEN-ALL-MYQUOTEP-CHEAP))
 (32 16 (:REWRITE LARGEST-NON-QUOTEP-WHEN-ALL-CONSP-CHEAP))
 (30 15 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (28 1 (:REWRITE INTEGER-WHEN-NATP))
 (26 26 (:REWRITE USE-ALL-CONSP-2))
 (26 26 (:REWRITE USE-ALL-CONSP))
 (26 26 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (26 26 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (26 2 (:REWRITE ALL-MYQUOTEP-WHEN-NOT-CONSP))
 (25 25 (:REWRITE NATP-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (24 12 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (23 23 (:REWRITE USE-ALL-NATP-2))
 (23 23 (:REWRITE USE-ALL-NATP))
 (21 21 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (19 19 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (19 19 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (19 19 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (19 19 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (19 12 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (17 9 (:REWRITE DEFAULT-<-2))
 (16 16 (:REWRITE DEFAULT-CDR))
 (15 15 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (15 15 (:REWRITE DEFAULT-+-1))
 (15 15 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (15 15 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (14 14 (:TYPE-PRESCRIPTION ALL-<))
 (14 7 (:REWRITE ALL-DARGP-WHEN-ALL-MYQUOTEP-CHEAP))
 (14 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (12 12 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (9 9 (:REWRITE USE-ALL-<-2))
 (9 9 (:REWRITE USE-ALL-<))
 (9 9 (:REWRITE <-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (7 7 (:REWRITE ALL-DARGP-WHEN-ALL-DARGP-LESS-THAN))
 (7 7 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (7 7 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (7 7 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (7 7 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (7 7 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (7 7 (:REWRITE ALL-<-TRANSITIVE))
 (6 6 (:TYPE-PRESCRIPTION PSEUDO-DAG-ARRAYP-LIST))
 (6 6 (:LINEAR ARRAY2P-LINEAR))
 (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 CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (5 5 (:LINEAR <-OF-LARGEST-NON-QUOTEP))
 (5 1 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (4 4 (:REWRITE USE-ALL-<=-2))
 (4 4 (:REWRITE USE-ALL-<=))
 (4 4 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (4 4 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (4 2 (:REWRITE ALL-MYQUOTEP-OF-CDR-CHEAP))
 (3 3 (:REWRITE TRUE-LISTP-WHEN-PSEUDO-DAGP-AUX))
 (3 3 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-ALL-DARGP-LESS-THAN-SPECIAL-ALT))
 (3 3 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-ALL-DARGP-LESS-THAN-SPECIAL))
 (3 3 (:REWRITE PSEUDO-DAG-ARRAYP-LIST-WHEN-ALL-DARGP-LESS-THAN))
 (3 3 (:REWRITE ALL-DARGP-WHEN-NOT-CONSP-CHEAP))
 (3 3 (:REWRITE ALL-DARGP-WHEN-NOT-CONSP))
 (2 2 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (2 2 (:REWRITE USE-ALL-RATIONALP-2))
 (2 2 (:REWRITE USE-ALL-RATIONALP))
 (2 2 (:REWRITE TYPE-OF-AREF1-WHEN-SIZE-ARRAYP-AUX))
 (2 2 (:REWRITE NOT-<-OF-CAR-WHEN-ALL-DARGP-LESS-THAN-2))
 (2 2 (:REWRITE NOT-<-OF-+-1-AND-CAR-WHEN-ALL-<))
 (2 1 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-NATP-CHEAP))
 (2 1 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-INTEGERP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION ALL-INTEGERP))
 (1 1 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE INTEGERP-OF-CAR-WHEN-ALL-DARGP-LESS-THAN))
 (1 1 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 )
(NATP-OF-ADD-ARG-SIZES-WITH-NAME
 (1821 57 (:REWRITE ACL2-NUMBERP-WHEN-NATP))
 (1709 83 (:REWRITE DEFAULT-+-1))
 (1238 619 (:TYPE-PRESCRIPTION NATP-OF-LARGEST-NON-QUOTEP))
 (1233 81 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (1085 83 (:REWRITE DEFAULT-+-2))
 (948 34 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (863 44 (:DEFINITION NAT-LISTP))
 (825 72 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (600 600 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (534 14 (:REWRITE TYPE-OF-AREF1-WHEN-SIZE-ARRAYP))
 (354 5 (:REWRITE NATP-OF-IF))
 (323 323 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (299 4 (:REWRITE COMMUTATIVITY-2-OF-+))
 (263 26 (:REWRITE <-OF-0-AND-LEN))
 (244 244 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (237 54 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (214 214 (:TYPE-PRESCRIPTION NAT-LISTP))
 (208 6 (:REWRITE ALL-NATP-OF-CDR))
 (176 16 (:REWRITE LEN-OF-CDR))
 (147 93 (:REWRITE DEFAULT-CAR))
 (144 14 (:REWRITE USE-ALL-<-FOR-CAR))
 (128 44 (:REWRITE DEFAULT-<-1))
 (121 121 (:TYPE-PRESCRIPTION ALL-NATP))
 (109 109 (:REWRITE NATP-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (107 107 (:REWRITE USE-ALL-NATP-2))
 (107 107 (:REWRITE USE-ALL-NATP))
 (100 44 (:REWRITE DEFAULT-<-2))
 (90 14 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (83 18 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (81 34 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (78 78 (:REWRITE DEFAULT-CDR))
 (72 72 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (70 70 (:REWRITE USE-ALL-CONSP-2))
 (70 70 (:REWRITE USE-ALL-CONSP))
 (70 70 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (68 68 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (68 68 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (68 68 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (68 68 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (68 34 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (59 59 (:TYPE-PRESCRIPTION ALL-CONSP))
 (54 1 (:REWRITE NATP-OF-LARGEST-NON-QUOTEP-2))
 (48 24 (:REWRITE LARGEST-NON-QUOTEP-WHEN-ALL-MYQUOTEP-CHEAP))
 (48 24 (:REWRITE LARGEST-NON-QUOTEP-WHEN-ALL-CONSP-CHEAP))
 (45 18 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (45 5 (:REWRITE ALL-DARGP-WHEN-NOT-CONSP))
 (44 44 (:REWRITE USE-ALL-<-2))
 (44 44 (:REWRITE USE-ALL-<))
 (44 44 (:REWRITE <-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (36 36 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (36 36 (:TYPE-PRESCRIPTION ALL-<))
 (36 18 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (34 34 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (33 1 (:REWRITE EQUAL-OF--1-AND-LARGEST-NON-QUOTEP))
 (32 4 (:REWRITE ALL-<-OF-CDR))
 (28 28 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (27 27 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (27 27 (:REWRITE USE-ALL-RATIONALP-2))
 (27 27 (:REWRITE USE-ALL-RATIONALP))
 (26 2 (:REWRITE ALL-MYQUOTEP-WHEN-NOT-CONSP))
 (20 10 (:REWRITE ALL-DARGP-WHEN-ALL-MYQUOTEP-CHEAP))
 (20 4 (:REWRITE ALL-RATIONALP-OF-CDR))
 (20 4 (:REWRITE ALL-CONSP-OF-CDR))
 (18 18 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (18 18 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (18 18 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (18 18 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (18 18 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (18 18 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (18 18 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (18 18 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (18 18 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (18 18 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (18 18 (:REWRITE ALL-<-TRANSITIVE))
 (18 18 (:LINEAR ARRAY2P-LINEAR))
 (14 14 (:REWRITE USE-ALL-<=-2))
 (14 14 (:REWRITE USE-ALL-<=))
 (14 14 (:REWRITE TYPE-OF-AREF1-WHEN-SIZE-ARRAYP-AUX))
 (14 14 (:REWRITE NOT-<-OF-+-1-AND-CAR-WHEN-ALL-<))
 (14 12 (:REWRITE FOLD-CONSTS-IN-+))
 (13 13 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (13 13 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (13 13 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (10 10 (:REWRITE ALL-DARGP-WHEN-ALL-DARGP-LESS-THAN))
 (10 10 (:LINEAR <-OF-LARGEST-NON-QUOTEP))
 (4 2 (:REWRITE ALL-MYQUOTEP-OF-CDR-CHEAP))
 )
(MAKE-SIZE-ARRAY-FOR-DAG-ARRAY-AUX
 (3308 260 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (2472 14 (:LINEAR <-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-LINEAR))
 (2056 4 (:REWRITE USE-ALL-<-FOR-CAR))
 (2014 6 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (1462 46 (:DEFINITION NTH))
 (1419 1419 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (1091 95 (:REWRITE <-OF-0-AND-LEN))
 (1050 10 (:DEFINITION ASSOC-KEYWORD))
 (940 3 (:LINEAR LARGEST-NON-QUOTEP-BOUND))
 (928 3 (:LINEAR LARGEST-NON-QUOTEP-BOUND-ALT))
 (900 6 (:REWRITE NATP-OF-NTH-FROM-ALL-NATP))
 (882 441 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (832 80 (:REWRITE DEFAULT-CDR))
 (824 1 (:REWRITE NATP-OF-IF))
 (766 44 (:REWRITE LEN-OF-CDR))
 (696 4 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (676 4 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (640 640 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (588 6 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (570 6 (:DEFINITION NAT-LISTP))
 (507 230 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (468 12 (:REWRITE NATP-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (460 10 (:DEFINITION ASSOC-EQUAL))
 (398 2 (:REWRITE ALL-<-OF-CDR))
 (362 2 (:REWRITE ALL-CONSP-OF-CDR))
 (306 52 (:REWRITE DEFAULT-CAR))
 (288 6 (:REWRITE NATP-OF-NTH-OF-DARGS))
 (270 34 (:REWRITE EQUAL-OF-LEN-AND-0))
 (260 260 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (258 6 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (247 4 (:REWRITE NATP-OF-+-WHEN-NATP-AND-NATP))
 (240 240 (:REWRITE USE-ALL-CONSP-2))
 (240 240 (:REWRITE USE-ALL-CONSP))
 (240 240 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (230 230 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (230 230 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (230 230 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (212 6 (:REWRITE NATP-OF-NTH-WHEN-ALL-DARGP))
 (186 128 (:REWRITE DEFAULT-+-2))
 (184 3 (:REWRITE NATP-OF-LARGEST-NON-QUOTEP-2))
 (172 82 (:REWRITE DEFAULT-<-1))
 (164 41 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (158 35 (:REWRITE CAR-OF-DARGS-BECOMES-NTH-0-OF-DARGS))
 (138 82 (:REWRITE DEFAULT-<-2))
 (137 128 (:REWRITE DEFAULT-+-1))
 (112 14 (:LINEAR NONNEG-OF-NTH-OF-DARGS-OF-AREF1))
 (112 14 (:LINEAR <-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (108 3 (:REWRITE EQUAL-OF--1-AND-LARGEST-NON-QUOTEP))
 (96 6 (:REWRITE ALL-MYQUOTEP-WHEN-NOT-CONSP))
 (85 85 (:REWRITE <-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (84 14 (:REWRITE ACL2-NUMBERP-WHEN-NATP))
 (82 82 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (82 82 (:REWRITE USE-ALL-<-2))
 (82 82 (:REWRITE USE-ALL-<))
 (78 78 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (66 33 (:TYPE-PRESCRIPTION NATP-OF-LARGEST-NON-QUOTEP))
 (66 6 (:REWRITE DAG-EXPRP0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (64 8 (:REWRITE NOT-EQUAL-OF-CAR-AND-QUOTE-WHEN-LEN-WRONG-AND-PSEUDO-DAG-ARRAYP-AUX))
 (46 46 (:REWRITE USE-ALL-<=-2))
 (46 46 (:REWRITE USE-ALL-<=))
 (42 14 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (41 41 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (41 41 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (39 39 (:REWRITE NATP-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (36 36 (:TYPE-PRESCRIPTION NAT-LISTP))
 (36 18 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (33 33 (:REWRITE USE-ALL-NATP-2))
 (33 33 (:REWRITE USE-ALL-NATP))
 (32 8 (:REWRITE NOT-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP))
 (32 4 (:REWRITE DAG-EXPRP0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (30 12 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (30 10 (:REWRITE ZP-OPEN))
 (26 26 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (24 6 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (20 20 (:LINEAR ARRAY2P-LINEAR))
 (19 19 (:TYPE-PRESCRIPTION ALL-CONSP))
 (18 9 (:REWRITE LARGEST-NON-QUOTEP-WHEN-ALL-MYQUOTEP-CHEAP))
 (18 9 (:REWRITE LARGEST-NON-QUOTEP-WHEN-ALL-CONSP-CHEAP))
 (16 4 (:REWRITE DAG-EXPRP0-OF-AREF1-WHEN-BOUNDED-DAG-EXPRP-OF-AREF1))
 (16 3 (:REWRITE INTEGER-WHEN-NATP))
 (15 15 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (14 14 (:REWRITE USE-ALL-RATIONALP-2))
 (14 14 (:REWRITE USE-ALL-RATIONALP))
 (14 14 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (14 14 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (13 13 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (13 3 (:REWRITE <=-OF-+-WHEN-NATP-AND-NATP))
 (12 12 (:TYPE-PRESCRIPTION DAG-EXPRP0))
 (12 12 (:TYPE-PRESCRIPTION ALL-NATP))
 (12 12 (:TYPE-PRESCRIPTION ALL-<))
 (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 3 (:REWRITE DEFAULT-UNARY-MINUS))
 (12 1 (:REWRITE SIZE-ARRAYP-OF-ASET1))
 (10 10 (:REWRITE LEN-OF-CDDR-WHEN-EQUAL-OF-LEN))
 (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 4 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (8 8 (:REWRITE QUOTE-LEMMA-FOR-ALL-DARGP-LESS-THAN-GEN-ALT))
 (8 4 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (6 6 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (6 6 (:REWRITE NATP-OF-NTH-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (6 6 (:REWRITE LEN-OF-NTH-WHEN-ALL-DARGP-LESS-THAN))
 (6 6 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (6 6 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (6 6 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (6 6 (:REWRITE ALL-<-TRANSITIVE))
 (4 4 (:TYPE-PRESCRIPTION BOUNDED-DAG-EXPRP))
 (4 4 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (4 4 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (4 4 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (4 4 (:REWRITE BOUNDED-DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-BETTER))
 (4 4 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (3 3 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (3 3 (:LINEAR <-OF-LARGEST-NON-QUOTEP))
 (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-AUX
 (327 29 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (176 176 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (152 76 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (143 143 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (126 14 (:REWRITE <-OF-0-AND-LEN))
 (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))
 (52 13 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (42 21 (:REWRITE DEFAULT-<-2))
 (40 17 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (40 16 (:REWRITE DEFAULT-CAR))
 (33 17 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (29 29 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (28 28 (:REWRITE USE-ALL-CONSP-2))
 (28 28 (:REWRITE USE-ALL-CONSP))
 (28 28 (:REWRITE DEFAULT-+-2))
 (28 28 (:REWRITE DEFAULT-+-1))
 (28 28 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (26 26 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (21 21 (:REWRITE USE-ALL-<=-2))
 (21 21 (:REWRITE USE-ALL-<=))
 (21 21 (:REWRITE USE-ALL-<-2))
 (21 21 (:REWRITE USE-ALL-<))
 (21 21 (:REWRITE DEFAULT-<-1))
 (21 21 (:REWRITE <-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (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))
 (13 13 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (13 13 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (12 12 (:REWRITE QUOTE-LEMMA-FOR-ALL-DARGP-LESS-THAN-GEN-ALT))
 (7 7 (:REWRITE USE-ALL-NATP-2))
 (7 7 (:REWRITE USE-ALL-NATP))
 (7 7 (:REWRITE NATP-WHEN-ALL-DARGP-LESS-THAN-GEN))
 )
(ALEN1-OF-MAKE-SIZE-ARRAY-FOR-DAG-ARRAY-AUX
 (488 488 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (349 31 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (185 185 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (156 78 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (135 15 (:REWRITE <-OF-0-AND-LEN))
 (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))
 (56 14 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (42 21 (:REWRITE DEFAULT-<-2))
 (42 18 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (41 17 (:REWRITE DEFAULT-CAR))
 (35 18 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (31 31 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (30 30 (:REWRITE USE-ALL-CONSP-2))
 (30 30 (:REWRITE USE-ALL-CONSP))
 (30 30 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (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 21 (:REWRITE USE-ALL-<-2))
 (21 21 (:REWRITE USE-ALL-<))
 (21 21 (:REWRITE DEFAULT-<-1))
 (21 21 (:REWRITE <-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (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))
 (14 14 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (14 14 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (13 13 (:REWRITE QUOTE-LEMMA-FOR-ALL-DARGP-LESS-THAN-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-ALL-DARGP-LESS-THAN-GEN))
 )
(SIZE-ARRAYP-OF-MAKE-SIZE-ARRAY-FOR-DAG-ARRAY-AUX
 (3427 265 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (2560 17 (:LINEAR <-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-LINEAR))
 (2056 4 (:REWRITE USE-ALL-<-FOR-CAR))
 (2014 6 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (1808 1808 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (1656 46 (:DEFINITION NTH))
 (1080 96 (:REWRITE <-OF-0-AND-LEN))
 (1050 10 (:DEFINITION ASSOC-KEYWORD))
 (836 84 (:REWRITE DEFAULT-CDR))
 (824 1 (:REWRITE NATP-OF-IF))
 (800 400 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-SIMPLE))
 (766 44 (:REWRITE LEN-OF-CDR))
 (696 4 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (676 4 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (663 663 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (619 2 (:LINEAR LARGEST-NON-QUOTEP-BOUND))
 (611 2 (:LINEAR LARGEST-NON-QUOTEP-BOUND-ALT))
 (600 4 (:REWRITE NATP-OF-NTH-FROM-ALL-NATP))
 (499 228 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (460 10 (:DEFINITION ASSOC-EQUAL))
 (398 2 (:REWRITE ALL-<-OF-CDR))
 (392 4 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (380 4 (:DEFINITION NAT-LISTP))
 (362 2 (:REWRITE ALL-CONSP-OF-CDR))
 (318 64 (:REWRITE DEFAULT-CAR))
 (312 8 (:REWRITE NATP-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (270 34 (:REWRITE EQUAL-OF-LEN-AND-0))
 (265 265 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (246 246 (:REWRITE USE-ALL-CONSP-2))
 (246 246 (:REWRITE USE-ALL-CONSP))
 (246 246 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (228 228 (:REWRITE LEN-WHEN-PSEUDO-DAGP-AUX))
 (228 228 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (228 228 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (204 51 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-WHEN-PSEUDO-DAGP-AUX))
 (202 152 (:REWRITE DEFAULT-+-2))
 (178 4 (:REWRITE NATP-OF-NTH-OF-DARGS))
 (172 4 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (156 115 (:REWRITE DEFAULT-<-2))
 (154 2 (:REWRITE NATP-OF-+-WHEN-NATP-AND-NATP))
 (152 152 (:REWRITE DEFAULT-+-1))
 (140 4 (:REWRITE NATP-OF-NTH-WHEN-ALL-DARGP))
 (136 17 (:LINEAR NONNEG-OF-NTH-OF-DARGS-OF-AREF1))
 (136 17 (:LINEAR <-OF-NTH-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (122 61 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-AREF1))
 (117 117 (:REWRITE <-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (116 2 (:REWRITE NATP-OF-LARGEST-NON-QUOTEP-2))
 (115 115 (:REWRITE USE-ALL-<-2))
 (115 115 (:REWRITE USE-ALL-<))
 (115 115 (:REWRITE DEFAULT-<-1))
 (112 30 (:REWRITE CAR-OF-DARGS-BECOMES-NTH-0-OF-DARGS))
 (112 14 (:REWRITE NOT-EQUAL-OF-CAR-AND-QUOTE-WHEN-LEN-WRONG-AND-PSEUDO-DAG-ARRAYP-AUX))
 (102 102 (:TYPE-PRESCRIPTION PSEUDO-DAGP-AUX))
 (98 98 (:REWRITE AREF1-WHEN-TOO-LARGE-CHEAP))
 (75 75 (:REWRITE USE-ALL-<=-2))
 (75 75 (:REWRITE USE-ALL-<=))
 (73 2 (:REWRITE EQUAL-OF--1-AND-LARGEST-NON-QUOTEP))
 (64 4 (:REWRITE ALL-MYQUOTEP-WHEN-NOT-CONSP))
 (56 16 (:REWRITE ZP-OPEN))
 (51 51 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (51 51 (:REWRITE PSEUDO-DAG-ARRAYP-AUX-MONOTONE))
 (48 21 (:REWRITE LEN-OF-AREF1-WHEN-QUOTEP-AND-PSEUDO-DAG-ARRAYP-AUX))
 (44 22 (:TYPE-PRESCRIPTION NATP-OF-LARGEST-NON-QUOTEP))
 (44 11 (:REWRITE NOT-<-OF-ALEN1-WHEN-PSEUDO-DAG-ARRAYP))
 (38 4 (:REWRITE DAG-EXPRP0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (27 27 (:REWRITE NATP-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (26 26 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (26 26 (:LINEAR ARRAY2P-LINEAR))
 (24 24 (:TYPE-PRESCRIPTION NAT-LISTP))
 (23 23 (:REWRITE USE-ALL-NATP-2))
 (23 23 (:REWRITE USE-ALL-NATP))
 (21 7 (:REWRITE FOLD-CONSTS-IN-+))
 (17 17 (:REWRITE <-OF-LEN-WHEN-NTH-NON-NIL))
 (17 17 (:REWRITE <-OF-LEN-WHEN-INTEGERP-OF-NTH))
 (16 16 (:TYPE-PRESCRIPTION ALL-CONSP))
 (16 4 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (16 2 (:REWRITE DAG-EXPRP0-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (14 14 (:REWRITE QUOTE-LEMMA-FOR-ALL-DARGP-LESS-THAN-GEN-ALT))
 (12 12 (:TYPE-PRESCRIPTION ALL-<))
 (12 6 (:REWRITE LARGEST-NON-QUOTEP-WHEN-ALL-MYQUOTEP-CHEAP))
 (12 6 (:REWRITE LARGEST-NON-QUOTEP-WHEN-ALL-CONSP-CHEAP))
 (12 1 (:REWRITE SIZE-ARRAYP-OF-ASET1))
 (10 10 (:TYPE-PRESCRIPTION ALL-MYQUOTEP))
 (10 10 (:REWRITE LEN-OF-CDDR-WHEN-EQUAL-OF-LEN))
 (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 4 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (8 8 (:TYPE-PRESCRIPTION DAG-EXPRP0))
 (8 8 (:TYPE-PRESCRIPTION ALL-NATP))
 (8 4 (:REWRITE LEN-OF-NTH-WHEN-ALL-DARGP))
 (8 4 (:REWRITE LEN-OF-NTH-OF-DARGS))
 (8 4 (:REWRITE INTEGER-WHEN-NATP))
 (8 4 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (8 4 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (8 2 (:REWRITE DAG-EXPRP0-OF-AREF1-WHEN-BOUNDED-DAG-EXPRP-OF-AREF1))
 (6 6 (:TYPE-PRESCRIPTION PSEUDO-DAGP))
 (6 6 (:REWRITE ALL-DARGP-OF-DARGS-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP))
 (6 6 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (6 6 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (6 6 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (6 6 (:REWRITE ALL-<-TRANSITIVE))
 (6 6 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (4 4 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (4 4 (:REWRITE NATP-OF-NTH-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (4 4 (:REWRITE LEN-OF-NTH-WHEN-ALL-DARGP-LESS-THAN))
 (4 4 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (4 4 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX))
 (4 4 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:TYPE-PRESCRIPTION BOUNDED-DAG-EXPRP))
 (2 2 (:REWRITE BOUNDED-DAG-EXPRP-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-BETTER))
 (2 2 (:LINEAR <-OF-LARGEST-NON-QUOTEP))
 )
(MAKE-SIZE-ARRAY-FOR-DAG-ARRAY
 (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-ALL-DARGP-LESS-THAN-GEN))
 (2 2 (:REWRITE SYMBOLP-WHEN-BOUNDED-DAG-EXPRP))
 (2 2 (:REWRITE PSEUDO-DAG-ARRAYP-MONOTONE))
 )
(ARRAY1P-OF-MAKE-SIZE-ARRAY-FOR-DAG-ARRAY
 (6 1 (:REWRITE INTEGER-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-ALL-DARGP-LESS-THAN-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-ALL-DARGP-LESS-THAN-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
 (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-ALL-DARGP-LESS-THAN-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-ALL-DARGP-LESS-THAN-GEN))
 )
(ALEN1-OF-MAKE-SIZE-ARRAY-FOR-DAG-ARRAY
 (32 32 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (6 1 (:REWRITE INTEGER-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-ALL-DARGP-LESS-THAN-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-ALL-DARGP-LESS-THAN-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
 (1700 45 (:REWRITE USE-ALL-NATP-FOR-CAR))
 (1053 59 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP))
 (964 7 (:DEFINITION NAT-LISTP))
 (940 6 (:REWRITE ALL-NATP-WHEN-NAT-LISTP))
 (866 106 (:REWRITE DEFAULT-CAR))
 (786 393 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-TYPE))
 (780 6 (:REWRITE ALL-NATP-WHEN-NOT-CONSP))
 (422 422 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (225 45 (:REWRITE NATP-OF-CAR-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (182 182 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (179 3 (:REWRITE USE-ALL-<-FOR-CAR))
 (144 29 (:REWRITE USE-ALL-CONSP-FOR-CAR))
 (136 136 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (127 127 (:REWRITE LEN-WHEN-BOUNDED-DAG-EXPRP-AND-QUOTEP))
 (125 59 (:REWRITE CONSP-OF-CAR-WHEN-PSEUDO-DAGP-AUX-2))
 (110 110 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (93 93 (:REWRITE LEN-WHEN-DARGP-LESS-THAN))
 (80 80 (:REWRITE USE-ALL-CONSP-2))
 (80 80 (:REWRITE USE-ALL-CONSP))
 (71 1 (:REWRITE ALL-<-OF-0-WHEN-ALL-NATP))
 (67 12 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP))
 (58 29 (:REWRITE CONSP-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-CHEAP))
 (46 46 (:REWRITE USE-ALL-NATP-2))
 (46 46 (:REWRITE USE-ALL-NATP))
 (46 46 (:REWRITE NATP-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (46 46 (:REWRITE DEFAULT-+-2))
 (46 46 (:REWRITE DEFAULT-+-1))
 (45 1 (:REWRITE INTEGER-WHEN-NATP))
 (45 1 (:REWRITE ALL-<-OF-0-WHEN-NAT-LISTP))
 (43 7 (:REWRITE DEFAULT-CDR))
 (42 3 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (41 41 (:TYPE-PRESCRIPTION NAT-LISTP))
 (37 37 (:TYPE-PRESCRIPTION ALL-NATP))
 (36 36 (:TYPE-PRESCRIPTION ALL-CONSP))
 (36 1 (:REWRITE BOUNDED-NATP-ALISTP-WHEN-PSEUDO-DAGP-AUX))
 (33 1 (:REWRITE NATP-OF-TOP-NODENUM-OF-DAG))
 (29 29 (:REWRITE TRUE-LISTP-OF-CAR-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (27 27 (:TYPE-PRESCRIPTION POSP-OF-ALEN1))
 (15 13 (:REWRITE DEFAULT-<-2))
 (15 5 (:TYPE-PRESCRIPTION TYPE-OF-AREF1-WHEN-PSEUDO-DAG-ARRAYP-AUX))
 (13 13 (:REWRITE USE-ALL-<-2))
 (13 13 (:REWRITE USE-ALL-<))
 (13 13 (:REWRITE DEFAULT-<-1))
 (13 13 (:REWRITE <-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (12 12 (:REWRITE ALL-CONSP-WHEN-NOT-CONSP-CHEAP))
 (12 6 (:REWRITE ALL-NATP-WHEN-NAT-LISTP-CHEAP))
 (11 11 (:REWRITE USE-ALL-<=-2))
 (11 11 (:REWRITE USE-ALL-<=))
 (11 11 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 (8 1 (:REWRITE <-OF-0-WHEN-WHEN-BOUNDED-NATP-ALISTP))
 (6 6 (:TYPE-PRESCRIPTION ALL-<))
 (6 6 (:REWRITE PSEUDO-DAGP-AUX-WHEN-NOT-CONSP-CHEAP))
 (6 6 (:REWRITE ALL-NATP-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:REWRITE NOT-<-OF-+-1-AND-CAR-WHEN-ALL-<))
 (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-ALL-DARGP-LESS-THAN-2))
 (1 1 (:REWRITE NONNEG-WHEN-DARGP-LESS-THAN))
 (1 1 (:REWRITE INTEGERP-WHEN-DARGP-LESS-THAN))
 (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
 (38 19 (:TYPE-PRESCRIPTION SYMBOLP-OF-CAR-OF-CAR-WHEN-SYMBOL-TERM-ALISTP-TYPE))
 (19 19 (:TYPE-PRESCRIPTION SYMBOL-TERM-ALISTP))
 (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-ALL-DARGP-LESS-THAN))
 (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-ALL-DARGP-LESS-THAN))
 (1 1 (:REWRITE <-WHEN-ALL-DARGP-LESS-THAN-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-ALL-DARGP-LESS-THAN-GEN))
 (1 1 (:REWRITE <-OF-+-OF-1-STRENGTHEN))
 )
(DAG-OR-QUOTEP-SIZE
 (34 3 (: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))
 (7 1 (:REWRITE <-OF-0-AND-LEN))
 (5 5 (:REWRITE DEFAULT-CDR))
 (5 5 (:REWRITE DEFAULT-+-2))
 (5 5 (:REWRITE DEFAULT-+-1))
 (3 3 (:REWRITE USE-ALL-CONSP-2))
 (3 3 (:REWRITE USE-ALL-CONSP))
 (3 3 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (3 3 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (2 2 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE USE-ALL-<-2))
 (1 1 (:REWRITE USE-ALL-<))
 (1 1 (:REWRITE QUOTE-LEMMA-FOR-ALL-DARGP-LESS-THAN-GEN-ALT))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (1 1 (:REWRITE <-WHEN-ALL-DARGP-LESS-THAN-GEN))
 )
(NATP-OF-DAG-OR-QUOTEP-SIZE
 (64 5 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (14 2 (:REWRITE <-OF-0-AND-LEN))
 (14 1 (:REWRITE LEN-OF-CDR))
 (9 3 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (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 5 (:REWRITE USE-ALL-CONSP-2))
 (5 5 (:REWRITE USE-ALL-CONSP))
 (5 5 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (5 5 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
 (3 2 (:REWRITE DEFAULT-<-2))
 (3 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE USE-ALL-<-2))
 (2 2 (:REWRITE USE-ALL-<))
 (2 2 (:REWRITE QUOTE-LEMMA-FOR-ALL-DARGP-LESS-THAN-GEN-ALT))
 (2 2 (:REWRITE <-WHEN-ALL-DARGP-LESS-THAN-GEN))
 (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))
 )
