(INSERT-NEW-AD-INSERT-2ND-NEW-AD
 (66 6 (:REWRITE SET::INSERT-IDENTITY))
 (46 2 (:REWRITE SET::IN-INSERT))
 (12 6 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (12 6 (:REWRITE INSERT-WHEN-EMPTY))
 (11 11 (:TYPE-PRESCRIPTION SET::IN-TYPE))
 (10 10 (:TYPE-PRESCRIPTION NTH-NEW-AD))
 (10 10 (:TYPE-PRESCRIPTION NEW-AD-NON-NEGATIVE))
 (10 10 (:TYPE-PRESCRIPTION INTEGERP-OF-NEW-AD))
 (10 10 (:REWRITE SET::SUBSET-IN))
 (9 3 (:REWRITE SET::IN-TAIL))
 (6 6 (:REWRITE SET::INSERT-NEVER-EMPTY))
 (6 2 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (5 3 (:REWRITE SET::UNION-EMPTYP-Y))
 (3 1 (:REWRITE SET::SFIX-WHEN-EMPTYP))
 (3 1 (:REWRITE SET::NONEMPTY-MEANS-SET))
 (1 1 (:REWRITE NTH-NEW-AD-NOT-IN-ADS))
 (1 1 (:REWRITE NEW-AD-NOT-MEMBERP-ADS))
 (1 1 (:REWRITE SET::IN-SET))
 )
(NEW-AD-OF-UNION-N-NEW-ADS
 (102 13 (:REWRITE SET::INSERT-IDENTITY))
 (63 3 (:REWRITE SET::IN-INSERT))
 (24 13 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (24 13 (:REWRITE INSERT-WHEN-EMPTY))
 (15 15 (:TYPE-PRESCRIPTION SET::IN-TYPE))
 (14 14 (:REWRITE SET::SUBSET-IN))
 (11 4 (:REWRITE SET::IN-TAIL))
 (8 8 (:REWRITE SET::INSERT-NEVER-EMPTY))
 (8 3 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (7 3 (:REWRITE INSERT-NEW-AD-INSERT-2ND-NEW-AD))
 (7 1 (:REWRITE SET::SFIX-SET-IDENTITY))
 (4 4 (:TYPE-PRESCRIPTION SET::SETP-TYPE))
 (4 2 (:REWRITE SET::UNION-EMPTYP-X))
 (4 2 (:REWRITE SET::NONEMPTY-MEANS-SET))
 (4 2 (:REWRITE SET::EMPTYP-SFIX-CANCEL))
 (3 3 (:REWRITE NTH-NEW-AD-NOT-IN-ADS))
 (3 1 (:REWRITE SET::SFIX-WHEN-EMPTYP))
 (2 2 (:REWRITE NEW-AD-NOT-MEMBERP-ADS))
 (2 2 (:REWRITE SET::IN-SET))
 (2 1 (:REWRITE SET::IN-SFIX-CANCEL))
 )
(NEW-AD-NOT-EQUAL-NTH-NEW-AD-HELPER
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 )
(UNION-OF-2SET-AND-2SET
 (282 16 (:REWRITE SET::INSERT-IDENTITY))
 (252 14 (:REWRITE IN-OF-2SET))
 (238 14 (:REWRITE MEMBER-EQUAL-BECOMES-MEMBERP))
 (48 48 (:TYPE-PRESCRIPTION MEMBERP))
 (44 16 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (44 16 (:REWRITE INSERT-WHEN-EMPTY))
 (32 16 (:REWRITE MEMBERP-WHEN-SINGLETON-CHEAP))
 (32 16 (:REWRITE MEMBERP-WHEN-NOT-MEMBERP-OF-CDR-CHEAP))
 (32 16 (:REWRITE MEMBERP-WHEN-MEMBERP-OF-CDR-CHEAP))
 (31 16 (:REWRITE MEMBERP-WHEN-NOT-CONS-OF-CDR-CHEAP))
 (28 1 (:REWRITE MEMBERP-OF-APPEND))
 (22 8 (:REWRITE SET::UNION-EMPTYP-Y))
 (20 10 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (19 19 (:REWRITE DEFAULT-CDR))
 (19 19 (:REWRITE DEFAULT-CAR))
 (16 16 (:TYPE-PRESCRIPTION LEN))
 (16 16 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-OF-TAKE))
 (16 16 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-2))
 (16 16 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-1))
 (16 16 (:REWRITE MEMBERP-WHEN-NOT-EQUAL-OF-CAR-CHEAP))
 (16 16 (:REWRITE MEMBERP-OF-CONSTANT-WHEN-NOT-MEMBER-OF-CONSTANT))
 (14 14 (:TYPE-PRESCRIPTION SET::IN-TYPE))
 (10 10 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (10 10 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (6 3 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (3 3 (:TYPE-PRESCRIPTION BOOLEANP))
 (3 1 (:REWRITE SET::SFIX-WHEN-EMPTYP))
 (1 1 (:REWRITE SET::INSERT-NEVER-EMPTY))
 )
(UNION-OF-2SET-AND-2SET-ALT
 (128 4 (:DEFINITION LIST::2SET))
 (74 4 (:REWRITE SET::INSERT-IDENTITY))
 (66 4 (:REWRITE IN-OF-2SET))
 (62 4 (:REWRITE MEMBER-EQUAL-BECOMES-MEMBERP))
 (34 34 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (17 6 (:REWRITE SET::UNION-EMPTYP-Y))
 (14 6 (:REWRITE SET::UNION-EMPTYP-X))
 (12 12 (:TYPE-PRESCRIPTION MEMBERP))
 (12 4 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (12 4 (:REWRITE INSERT-WHEN-EMPTY))
 (10 4 (:REWRITE MEMBERP-WHEN-NOT-CONS-OF-CDR-CHEAP))
 (8 4 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (8 4 (:REWRITE MEMBERP-WHEN-SINGLETON-CHEAP))
 (8 4 (:REWRITE MEMBERP-WHEN-NOT-MEMBERP-OF-CDR-CHEAP))
 (8 4 (:REWRITE MEMBERP-WHEN-MEMBERP-OF-CDR-CHEAP))
 (8 2 (:REWRITE CDR-OF-APPEND))
 (6 6 (:REWRITE DEFAULT-CDR))
 (6 6 (:REWRITE DEFAULT-CAR))
 (6 2 (:REWRITE CAR-OF-APPEND))
 (4 4 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (4 4 (:TYPE-PRESCRIPTION LEN))
 (4 4 (:TYPE-PRESCRIPTION SET::IN-TYPE))
 (4 4 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (4 4 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-OF-TAKE))
 (4 4 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-2))
 (4 4 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-1))
 (4 4 (:REWRITE MEMBERP-WHEN-NOT-EQUAL-OF-CAR-CHEAP))
 (4 4 (:REWRITE MEMBERP-OF-CONSTANT-WHEN-NOT-MEMBER-OF-CONSTANT))
 (4 4 (:REWRITE APPEND-WHEN-NOT-CONSP-ARG1-CHEAP))
 (4 1 (:REWRITE SET::UNION-EMPTYP))
 (2 2 (:REWRITE CONSP-OF-APPEND))
 )
(UNION-OF-2SET-AND-2SET-BACK)
(INSERT-OF-NEXT-AD-ONTO-UNION-OF-DOM-AND-N-NEW-ADS
 (140 2 (:DEFINITION LIST::2SET))
 (82 6 (:REWRITE SET::INSERT-IDENTITY))
 (64 4 (:REWRITE IN-OF-2SET))
 (62 2 (:REWRITE CAR-OF-REVERSE-LIST))
 (60 4 (:REWRITE MEMBER-EQUAL-BECOMES-MEMBERP))
 (52 2 (:DEFINITION NTH))
 (24 8 (:REWRITE CONSP-OF-N-NEW-ADS-AUX))
 (23 23 (:TYPE-PRESCRIPTION SET::INSERT))
 (18 1 (:REWRITE SET::UNION-IN))
 (17 6 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (17 6 (:REWRITE INSERT-WHEN-EMPTY))
 (16 2 (:REWRITE CDR-OF-REVERSE-LIST))
 (12 12 (:TYPE-PRESCRIPTION N-NEW-ADS-AUX))
 (12 12 (:TYPE-PRESCRIPTION MEMBERP))
 (12 12 (:REWRITE DEFAULT-<-2))
 (12 12 (:REWRITE DEFAULT-<-1))
 (12 12 (:REWRITE DEFAULT-+-2))
 (12 12 (:REWRITE DEFAULT-+-1))
 (12 2 (:REWRITE DEFAULT-CDR))
 (12 2 (:REWRITE DEFAULT-CAR))
 (10 2 (:REWRITE CONSP-OF-REVERSE-LIST))
 (8 4 (:REWRITE SET::UNION-EMPTYP-X))
 (8 4 (:REWRITE MEMBERP-WHEN-SINGLETON-CHEAP))
 (8 4 (:REWRITE MEMBERP-WHEN-NOT-MEMBERP-OF-CDR-CHEAP))
 (8 4 (:REWRITE MEMBERP-WHEN-NOT-CONS-OF-CDR-CHEAP))
 (8 4 (:REWRITE MEMBERP-WHEN-MEMBERP-OF-CDR-CHEAP))
 (8 2 (:REWRITE ZP-OPEN))
 (8 2 (:REWRITE SET::UNION-EMPTYP))
 (8 2 (:REWRITE TAKE-DOES-NOTHING))
 (7 7 (:TYPE-PRESCRIPTION REVERSE-LIST))
 (7 7 (:TYPE-PRESCRIPTION SET::IN-TYPE))
 (6 6 (:TYPE-PRESCRIPTION LEN))
 (6 6 (:REWRITE LEN-OF-N-NEW-ADS-AUX))
 (4 4 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-OF-TAKE))
 (4 4 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-2))
 (4 4 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-1))
 (4 4 (:REWRITE MEMBERP-WHEN-NOT-EQUAL-OF-CAR-CHEAP))
 (4 4 (:REWRITE MEMBERP-OF-CONSTANT-WHEN-NOT-MEMBER-OF-CONSTANT))
 (3 1 (:REWRITE SET::SFIX-WHEN-EMPTYP))
 (2 2 (:REWRITE SET::SUBSET-IN))
 (2 2 (:REWRITE NTH-WHEN-EQUAL-OF-TAKE-AND-CONSTANT))
 (2 2 (:REWRITE SET::INSERT-NEVER-EMPTY))
 (2 2 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (2 1 (:REWRITE SET::IN-TAIL))
 (2 1 (:REWRITE APPEND-WHEN-NOT-CONSP-ARG1-CHEAP))
 (1 1 (:REWRITE NTH-NEW-AD-NOT-IN-ADS))
 )
(MEMBERP-NEW-AD-N-NEW-ADS-AUX-1
 (2 1 (:REWRITE MEMBERP-WHEN-SINGLETON-CHEAP))
 (2 1 (:REWRITE MEMBERP-WHEN-NOT-MEMBERP-OF-CDR-CHEAP))
 (2 1 (:REWRITE MEMBERP-WHEN-MEMBERP-OF-CDR-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION LEN))
 (1 1 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-OF-TAKE))
 (1 1 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-AND-NOT-INTERSECTION-EQUAL-CHEAP))
 (1 1 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-2))
 (1 1 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-1))
 (1 1 (:REWRITE MEMBERP-WHEN-NOT-EQUAL-OF-CAR-CHEAP))
 (1 1 (:REWRITE MEMBERP-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:REWRITE MEMBERP-WHEN-NOT-CONS-OF-CDR-CHEAP))
 (1 1 (:REWRITE MEMBERP-OF-CONSTANT-WHEN-NOT-MEMBER-OF-CONSTANT))
 )
(INSERT-NTH-NEW-AD-2-UNION-NEW-ADS-SLICE-3
 (229 9 (:REWRITE SET::INSERT-IDENTITY))
 (132 8 (:REWRITE IN-OF-2SET))
 (124 8 (:REWRITE MEMBER-EQUAL-BECOMES-MEMBERP))
 (112 2 (:REWRITE IN-OF-IF))
 (86 2 (:REWRITE SET::IN-INSERT))
 (58 1 (:REWRITE SET::UNION-IN))
 (41 41 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (38 6 (:REWRITE DEFAULT-CDR))
 (34 34 (:TYPE-PRESCRIPTION MEMBERP))
 (28 9 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (28 9 (:REWRITE INSERT-WHEN-EMPTY))
 (26 10 (:REWRITE MEMBERP-WHEN-NOT-CONS-OF-CDR-CHEAP))
 (23 23 (:TYPE-PRESCRIPTION SET::INSERT))
 (20 10 (:REWRITE MEMBERP-WHEN-SINGLETON-CHEAP))
 (20 10 (:REWRITE MEMBERP-WHEN-NOT-MEMBERP-OF-CDR-CHEAP))
 (20 10 (:REWRITE MEMBERP-WHEN-MEMBERP-OF-CDR-CHEAP))
 (16 16 (:TYPE-PRESCRIPTION SET::IN-TYPE))
 (14 14 (:TYPE-PRESCRIPTION NTH-NEW-AD))
 (14 4 (:REWRITE SET::IN-TAIL))
 (12 12 (:REWRITE SET::SUBSET-IN))
 (12 12 (:REWRITE DEFAULT-<-2))
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 (10 10 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-OF-TAKE))
 (10 10 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-2))
 (10 10 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-1))
 (10 10 (:REWRITE MEMBERP-WHEN-NOT-EQUAL-OF-CAR-CHEAP))
 (10 10 (:REWRITE MEMBERP-OF-CONSTANT-WHEN-NOT-MEMBER-OF-CONSTANT))
 (8 2 (:REWRITE SET::UNION-EMPTYP))
 (7 3 (:REWRITE SET::UNION-EMPTYP-Y))
 (5 3 (:REWRITE SET::UNION-EMPTYP-X))
 (4 4 (:REWRITE NTH-WHEN-EQUAL-OF-TAKE-AND-CONSTANT))
 (4 2 (:REWRITE NTHCDR-WHEN-NOT-CONSP-CHEAP))
 (3 1 (:REWRITE NEW-ADS-SLICE-OUT-OF-ORDER-INDICES))
 (2 2 (:REWRITE NTHCDR-WHEN-NOT-POSP))
 (2 2 (:REWRITE NTHCDR-WHEN-EQUAL-OF-LEN))
 (2 2 (:REWRITE EQUAL-NTH-NEW-AD-NTH-NEW-AD))
 (2 2 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE NTH-NEW-AD-NOT-IN-ADS))
 (1 1 (:REWRITE SET::INSERT-NEVER-EMPTY))
 )
(N-NEW-ADS-AUX-OF-0)
(INSERT-CAR-2SET-CDR
 (53 5 (:REWRITE SET::INSERT-IDENTITY))
 (45 3 (:REWRITE IN-OF-2SET))
 (42 3 (:REWRITE MEMBER-EQUAL-BECOMES-MEMBERP))
 (12 12 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
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 (9 9 (:TYPE-PRESCRIPTION MEMBERP))
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 (6 3 (:REWRITE MEMBERP-WHEN-NOT-MEMBERP-OF-CDR-CHEAP))
 (6 3 (:REWRITE MEMBERP-WHEN-MEMBERP-OF-CDR-CHEAP))
 (5 5 (:REWRITE DEFAULT-CDR))
 (5 5 (:REWRITE DEFAULT-CAR))
 (3 3 (:TYPE-PRESCRIPTION LEN))
 (3 3 (:TYPE-PRESCRIPTION SET::IN-TYPE))
 (3 3 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-OF-TAKE))
 (3 3 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-2))
 (3 3 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-1))
 (3 3 (:REWRITE MEMBERP-WHEN-NOT-EQUAL-OF-CAR-CHEAP))
 (3 3 (:REWRITE MEMBERP-WHEN-NOT-CONS-OF-CDR-CHEAP))
 (3 3 (:REWRITE MEMBERP-OF-CONSTANT-WHEN-NOT-MEMBER-OF-CONSTANT))
 )
(INSERT-NEW-AD-UNION-NEW-ADS-SLICE-2-HELPER
 (108 10 (:REWRITE SET::INSERT-IDENTITY))
 (92 6 (:REWRITE IN-OF-2SET))
 (86 6 (:REWRITE MEMBER-EQUAL-BECOMES-MEMBERP))
 (24 24 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (22 10 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (22 10 (:REWRITE INSERT-WHEN-EMPTY))
 (18 18 (:TYPE-PRESCRIPTION MEMBERP))
 (16 10 (:REWRITE DEFAULT-CDR))
 (12 6 (:REWRITE MEMBERP-WHEN-SINGLETON-CHEAP))
 (12 6 (:REWRITE MEMBERP-WHEN-NOT-MEMBERP-OF-CDR-CHEAP))
 (12 6 (:REWRITE MEMBERP-WHEN-MEMBERP-OF-CDR-CHEAP))
 (8 6 (:REWRITE MEMBERP-WHEN-NOT-CONS-OF-CDR-CHEAP))
 (6 6 (:TYPE-PRESCRIPTION LEN))
 (6 6 (:TYPE-PRESCRIPTION SET::IN-TYPE))
 (6 6 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-OF-TAKE))
 (6 6 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-2))
 (6 6 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-1))
 (6 6 (:REWRITE MEMBERP-WHEN-NOT-EQUAL-OF-CAR-CHEAP))
 (6 6 (:REWRITE MEMBERP-OF-CONSTANT-WHEN-NOT-MEMBER-OF-CONSTANT))
 (4 4 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 )
(INSERT-NEW-AD-UNION-NEW-ADS-SLICE-2
 (161 11 (:REWRITE SET::INSERT-IDENTITY))
 (140 8 (:REWRITE IN-OF-2SET))
 (132 8 (:REWRITE MEMBER-EQUAL-BECOMES-MEMBERP))
 (48 4 (:REWRITE CDR-OF-NEW-ADS-SLICE))
 (41 41 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (30 11 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (30 11 (:REWRITE INSERT-WHEN-EMPTY))
 (24 24 (:TYPE-PRESCRIPTION MEMBERP))
 (24 8 (:REWRITE MEMBERP-WHEN-NOT-CONS-OF-CDR-CHEAP))
 (24 8 (:REWRITE COMMUTATIVITY-OF-+))
 (24 4 (:REWRITE CAR-OF-NEW-ADS-SLICE))
 (22 10 (:REWRITE NEW-ADS-SLICE-OUT-OF-ORDER-INDICES))
 (22 10 (:REWRITE NEW-ADS-SLICE-OPENER))
 (19 19 (:REWRITE DEFAULT-<-2))
 (19 19 (:REWRITE DEFAULT-<-1))
 (19 1 (:REWRITE SET::UNION-IN))
 (16 16 (:REWRITE DEFAULT-+-2))
 (16 16 (:REWRITE DEFAULT-+-1))
 (16 8 (:REWRITE MEMBERP-WHEN-SINGLETON-CHEAP))
 (16 8 (:REWRITE MEMBERP-WHEN-NOT-MEMBERP-OF-CDR-CHEAP))
 (16 8 (:REWRITE MEMBERP-WHEN-MEMBERP-OF-CDR-CHEAP))
 (16 4 (:REWRITE CONSP-OF-NEW-ADS-SLICE))
 (12 12 (:TYPE-PRESCRIPTION NEW-ADS-TYPE))
 (12 12 (:TYPE-PRESCRIPTION NEW-ADS-SLICE))
 (8 8 (:TYPE-PRESCRIPTION LEN))
 (8 8 (:TYPE-PRESCRIPTION SET::IN-TYPE))
 (8 8 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-OF-TAKE))
 (8 8 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-2))
 (8 8 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-1))
 (8 8 (:REWRITE MEMBERP-WHEN-NOT-EQUAL-OF-CAR-CHEAP))
 (8 8 (:REWRITE MEMBERP-OF-CONSTANT-WHEN-NOT-MEMBER-OF-CONSTANT))
 (8 2 (:REWRITE SET::UNION-EMPTYP))
 (7 3 (:REWRITE SET::UNION-EMPTYP-Y))
 (5 3 (:REWRITE SET::UNION-EMPTYP-X))
 (4 4 (:REWRITE MEMBERP-OF-NTH-NEW-AD-AND-NEW-ADS-SLICE))
 (1 1 (:REWRITE NEW-AD-NOT-MEMBERP-ADS))
 (1 1 (:REWRITE SET::INSERT-NEVER-EMPTY))
 )
(NEW-AD-OF-UNION-DOM-AND-N-NEW-ADS
 (42 6 (:REWRITE SET::INSERT-IDENTITY))
 (18 1 (:REWRITE IN-OF-2SET))
 (17 1 (:REWRITE MEMBER-EQUAL-BECOMES-MEMBERP))
 (15 6 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (15 6 (:REWRITE INSERT-WHEN-EMPTY))
 (14 2 (:REWRITE SET::SFIX-SET-IDENTITY))
 (13 13 (:REWRITE DEFAULT-+-2))
 (13 13 (:REWRITE DEFAULT-+-1))
 (9 1 (:REWRITE CDR-OF-NEW-ADS-SLICE))
 (8 8 (:TYPE-PRESCRIPTION SET::IN-TYPE))
 (7 3 (:REWRITE SET::UNION-EMPTYP-X))
 (7 3 (:REWRITE NEW-ADS-SLICE-OUT-OF-ORDER-INDICES))
 (6 2 (:REWRITE SET::SFIX-WHEN-EMPTYP))
 (6 2 (:REWRITE SET::NONEMPTY-MEANS-SET))
 (6 2 (:REWRITE COMMUTATIVITY-OF-+))
 (6 1 (:REWRITE CAR-OF-NEW-ADS-SLICE))
 (5 5 (:REWRITE DEFAULT-<-2))
 (5 5 (:REWRITE DEFAULT-<-1))
 (4 4 (:TYPE-PRESCRIPTION SET::SETP-TYPE))
 (4 4 (:REWRITE SET::SUBSET-IN))
 (4 2 (:REWRITE SET::IN-TAIL))
 (4 2 (:REWRITE SET::EMPTYP-SFIX-CANCEL))
 (4 1 (:REWRITE CONSP-OF-NEW-ADS-SLICE))
 (3 3 (:TYPE-PRESCRIPTION MEMBERP))
 (3 3 (:REWRITE NEW-AD-NOT-MEMBERP-ADS))
 (3 1 (:REWRITE MEMBERP-WHEN-NOT-CONS-OF-CDR-CHEAP))
 (2 2 (:TYPE-PRESCRIPTION NEW-ADS-TYPE))
 (2 2 (:TYPE-PRESCRIPTION NEW-ADS-SLICE))
 (2 2 (:REWRITE ZP-OPEN))
 (2 2 (:REWRITE SET::IN-SET))
 (2 2 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (2 1 (:REWRITE MEMBERP-WHEN-SINGLETON-CHEAP))
 (2 1 (:REWRITE MEMBERP-WHEN-NOT-MEMBERP-OF-CDR-CHEAP))
 (2 1 (:REWRITE MEMBERP-WHEN-MEMBERP-OF-CDR-CHEAP))
 (2 1 (:REWRITE SET::IN-SFIX-CANCEL))
 (1 1 (:TYPE-PRESCRIPTION LEN))
 (1 1 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-OF-TAKE))
 (1 1 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-2))
 (1 1 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-1))
 (1 1 (:REWRITE MEMBERP-WHEN-NOT-EQUAL-OF-CAR-CHEAP))
 (1 1 (:REWRITE MEMBERP-OF-NTH-NEW-AD-AND-NEW-ADS-SLICE))
 (1 1 (:REWRITE MEMBERP-OF-CONSTANT-WHEN-NOT-MEMBER-OF-CONSTANT))
 (1 1 (:REWRITE SET::INSERT-NEVER-EMPTY))
 )
(NTH-NEW-AD-OF-SFIX
 (54 54 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (48 3 (:REWRITE NOT-EQUAL-NTH-NEW-AD-WHEN-BOUND))
 (39 8 (:REWRITE SET::INSERT-IDENTITY))
 (35 5 (:REWRITE SET::SFIX-SET-IDENTITY))
 (30 1 (:REWRITE SET::IN-INSERT))
 (29 29 (:TYPE-PRESCRIPTION SET::IN-TYPE))
 (27 8 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (27 8 (:REWRITE INSERT-WHEN-EMPTY))
 (26 10 (:REWRITE SET::IN-TAIL))
 (24 3 (:REWRITE NOT-EQUAL-NTH-NEW-AD-WHEN-BOUND-ALT))
 (22 22 (:REWRITE SET::SUBSET-IN))
 (15 5 (:REWRITE SET::SFIX-WHEN-EMPTYP))
 (15 5 (:REWRITE SET::NONEMPTY-MEANS-SET))
 (14 10 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (12 6 (:REWRITE SET::IN-SFIX-CANCEL))
 (12 6 (:REWRITE SET::EMPTYP-SFIX-CANCEL))
 (10 10 (:TYPE-PRESCRIPTION SET::SETP-TYPE))
 (8 8 (:REWRITE NEW-AD-NOT-MEMBERP-ADS))
 (6 6 (:REWRITE ZP-OPEN))
 (5 5 (:REWRITE SET::IN-SET))
 (5 5 (:REWRITE DEFAULT-+-2))
 (5 5 (:REWRITE DEFAULT-+-1))
 (4 4 (:TYPE-PRESCRIPTION NEW-AD-NON-NEGATIVE))
 (4 4 (:TYPE-PRESCRIPTION INTEGERP-OF-NEW-AD))
 (3 3 (:REWRITE NTH-NEW-AD-NOT-IN-ADS))
 (3 1 (:REWRITE SET::TAIL-WHEN-EMPTYP))
 )
(NTH-NEW-AD-OF-UNION-DOM-N-NEW-ADS
 (42 6 (:REWRITE SET::INSERT-IDENTITY))
 (19 19 (:REWRITE DEFAULT-+-2))
 (19 19 (:REWRITE DEFAULT-+-1))
 (18 1 (:REWRITE IN-OF-2SET))
 (17 1 (:REWRITE MEMBER-EQUAL-BECOMES-MEMBERP))
 (15 6 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (15 6 (:REWRITE INSERT-WHEN-EMPTY))
 (14 2 (:REWRITE SET::SFIX-SET-IDENTITY))
 (9 9 (:REWRITE DEFAULT-<-2))
 (9 9 (:REWRITE DEFAULT-<-1))
 (9 1 (:REWRITE CDR-OF-NEW-ADS-SLICE))
 (8 8 (:TYPE-PRESCRIPTION SET::IN-TYPE))
 (7 3 (:REWRITE SET::UNION-EMPTYP-X))
 (7 3 (:REWRITE NEW-ADS-SLICE-OUT-OF-ORDER-INDICES))
 (6 2 (:REWRITE SET::SFIX-WHEN-EMPTYP))
 (6 2 (:REWRITE SET::NONEMPTY-MEANS-SET))
 (6 1 (:REWRITE CAR-OF-NEW-ADS-SLICE))
 (4 4 (:TYPE-PRESCRIPTION SET::SETP-TYPE))
 (4 4 (:REWRITE SET::SUBSET-IN))
 (4 2 (:REWRITE SET::IN-TAIL))
 (4 2 (:REWRITE SET::EMPTYP-SFIX-CANCEL))
 (4 1 (:REWRITE CONSP-OF-NEW-ADS-SLICE))
 (3 3 (:TYPE-PRESCRIPTION MEMBERP))
 (3 3 (:REWRITE NEW-AD-NOT-MEMBERP-ADS))
 (3 1 (:REWRITE MEMBERP-WHEN-NOT-CONS-OF-CDR-CHEAP))
 (2 2 (:TYPE-PRESCRIPTION NEW-ADS-TYPE))
 (2 2 (:TYPE-PRESCRIPTION NEW-ADS-SLICE))
 (2 2 (:REWRITE ZP-OPEN))
 (2 2 (:REWRITE SET::IN-SET))
 (2 2 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (2 1 (:REWRITE MEMBERP-WHEN-SINGLETON-CHEAP))
 (2 1 (:REWRITE MEMBERP-WHEN-NOT-MEMBERP-OF-CDR-CHEAP))
 (2 1 (:REWRITE MEMBERP-WHEN-MEMBERP-OF-CDR-CHEAP))
 (2 1 (:REWRITE SET::IN-SFIX-CANCEL))
 (1 1 (:TYPE-PRESCRIPTION LEN))
 (1 1 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-OF-TAKE))
 (1 1 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-2))
 (1 1 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-1))
 (1 1 (:REWRITE MEMBERP-WHEN-NOT-EQUAL-OF-CAR-CHEAP))
 (1 1 (:REWRITE MEMBERP-OF-NTH-NEW-AD-AND-NEW-ADS-SLICE))
 (1 1 (:REWRITE MEMBERP-OF-CONSTANT-WHEN-NOT-MEMBER-OF-CONSTANT))
 (1 1 (:REWRITE SET::INSERT-NEVER-EMPTY))
 )
(NTH-NEW-AD-OF-UNION-DOM-N-NEW-ADS-ALT
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 (32 1 (:REWRITE SET::UNION-IN))
 (30 1 (:REWRITE IN-OF-IF))
 (19 1 (:REWRITE IN-OF-2SET))
 (18 1 (:REWRITE MEMBER-EQUAL-BECOMES-MEMBERP))
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 (9 3 (:REWRITE SET::UNION-EMPTYP-X))
 (9 3 (:REWRITE SET::IN-TAIL))
 (8 8 (:TYPE-PRESCRIPTION SET::IN-TYPE))
 (7 1 (:REWRITE SET::SFIX-SET-IDENTITY))
 (7 1 (:REWRITE NOT-EQUAL-NTH-NEW-AD-WHEN-BOUND))
 (6 6 (:REWRITE SET::SUBSET-IN))
 (6 2 (:REWRITE NEW-ADS-SLICE-OUT-OF-ORDER-INDICES))
 (6 2 (:REWRITE NEW-ADS-SLICE-OPENER))
 (5 5 (:REWRITE DEFAULT-+-2))
 (5 5 (:REWRITE DEFAULT-+-1))
 (4 1 (:REWRITE MEMBERP-NTH-NEW-AD-N-NEW-ADS))
 (3 3 (:REWRITE ZP-OPEN))
 (3 1 (:REWRITE SET::SFIX-WHEN-EMPTYP))
 (3 1 (:REWRITE SET::NONEMPTY-MEANS-SET))
 (2 2 (:TYPE-PRESCRIPTION SET::SETP-TYPE))
 (2 2 (:TYPE-PRESCRIPTION MEMBERP))
 (2 1 (:REWRITE MEMBERP-WHEN-SINGLETON-CHEAP))
 (2 1 (:REWRITE MEMBERP-WHEN-NOT-MEMBERP-OF-CDR-CHEAP))
 (2 1 (:REWRITE MEMBERP-WHEN-NOT-CONS-OF-CDR-CHEAP))
 (2 1 (:REWRITE MEMBERP-WHEN-MEMBERP-OF-CDR-CHEAP))
 (2 1 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION LEN))
 (1 1 (:REWRITE NTH-NEW-AD-NOT-IN-ADS))
 (1 1 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-OF-TAKE))
 (1 1 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-2))
 (1 1 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-1))
 (1 1 (:REWRITE MEMBERP-WHEN-NOT-EQUAL-OF-CAR-CHEAP))
 (1 1 (:REWRITE MEMBERP-OF-CONSTANT-WHEN-NOT-MEMBER-OF-CONSTANT))
 (1 1 (:REWRITE SET::IN-SET))
 )
(INSERT-NTH-NEW-AD-INSERT-NTH-NEW-AD-ADJACENT
 (87 7 (:REWRITE SET::INSERT-IDENTITY))
 (46 46 (:TYPE-PRESCRIPTION SET::INSERT))
 (45 2 (:REWRITE SET::IN-INSERT))
 (31 9 (:REWRITE SET::IN-TAIL))
 (24 24 (:TYPE-PRESCRIPTION SET::IN-TYPE))
 (22 22 (:REWRITE SET::SUBSET-IN))
 (16 7 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (16 7 (:REWRITE INSERT-WHEN-EMPTY))
 (14 14 (:TYPE-PRESCRIPTION NTH-NEW-AD))
 (12 1 (:REWRITE SET::IN-SFIX-CANCEL))
 (7 1 (:REWRITE SET::SFIX-SET-IDENTITY))
 (6 6 (:REWRITE SET::INSERT-NEVER-EMPTY))
 (5 5 (:REWRITE DEFAULT-+-2))
 (5 5 (:REWRITE DEFAULT-+-1))
 (5 3 (:REWRITE SET::UNION-EMPTYP-Y))
 (4 2 (:REWRITE SET::TAIL-WHEN-EMPTYP))
 (4 2 (:REWRITE EQUAL-NTH-NEW-AD-NTH-NEW-AD))
 (4 2 (:REWRITE SET::EMPTYP-SFIX-CANCEL))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 (3 1 (:REWRITE SET::SFIX-WHEN-EMPTYP))
 (3 1 (:REWRITE SET::NONEMPTY-MEANS-SET))
 (2 2 (:TYPE-PRESCRIPTION SET::SETP-TYPE))
 (2 2 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (1 1 (:REWRITE SET::IN-SET))
 )
(N-NEW-ADS-OPENER-HIGH
 (8 2 (:REWRITE ZP-OPEN))
 (7 7 (:REWRITE DEFAULT-+-2))
 (7 7 (:REWRITE DEFAULT-+-1))
 (6 2 (:REWRITE FOLD-CONSTS-IN-+))
 (4 2 (:REWRITE APPEND-WHEN-NOT-CONSP-ARG1-CHEAP))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 )
(NEW-ADS-SLICE-OPENER2
 (38 38 (:REWRITE DEFAULT-<-2))
 (38 38 (:REWRITE DEFAULT-<-1))
 (31 31 (:REWRITE DEFAULT-+-2))
 (31 31 (:REWRITE DEFAULT-+-1))
 (29 11 (:REWRITE APPEND-WHEN-NOT-CONSP-ARG1-CHEAP))
 (23 7 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (20 5 (:REWRITE DEFAULT-CDR))
 (16 10 (:REWRITE NTHCDR-WHEN-NOT-CONSP-CHEAP))
 (10 10 (:REWRITE NTHCDR-WHEN-EQUAL-OF-LEN))
 (8 4 (:REWRITE DEFAULT-CAR))
 (6 6 (:TYPE-PRESCRIPTION BOOLEANP))
 (2 2 (:REWRITE DEFAULT-UNARY-MINUS))
 (1 1 (:REWRITE NTH-WHEN-EQUAL-OF-TAKE-AND-CONSTANT))
 )
(INSERT-NTH-NEW-AD-UNION-NEW-ADS-SLICE
 (316 8 (:DEFINITION LIST::2SET))
 (197 197 (:REWRITE DEFAULT-+-2))
 (197 197 (:REWRITE DEFAULT-+-1))
 (177 13 (:REWRITE SET::INSERT-IDENTITY))
 (129 129 (:TYPE-PRESCRIPTION SET::INSERT))
 (112 4 (:REWRITE SET::UNION-IN))
 (96 24 (:REWRITE SET::IN-TAIL))
 (77 31 (:REWRITE NEW-ADS-SLICE-OUT-OF-ORDER-INDICES))
 (64 64 (:TYPE-PRESCRIPTION SET::IN-TYPE))
 (53 53 (:REWRITE DEFAULT-<-2))
 (53 53 (:REWRITE DEFAULT-<-1))
 (52 52 (:REWRITE DEFAULT-UNARY-MINUS))
 (49 13 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (49 13 (:REWRITE INSERT-WHEN-EMPTY))
 (48 48 (:REWRITE SET::SUBSET-IN))
 (32 8 (:REWRITE SET::UNION-EMPTYP))
 (27 9 (:REWRITE APPEND-WHEN-NOT-CONSP-ARG1-CHEAP))
 (24 8 (:REWRITE SET::TAIL-WHEN-EMPTYP))
 (21 6 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (16 8 (:REWRITE SET::UNION-EMPTYP-X))
 (12 6 (:REWRITE DEFAULT-CDR))
 (12 6 (:REWRITE DEFAULT-CAR))
 (6 6 (:TYPE-PRESCRIPTION BOOLEANP))
 (3 1 (:REWRITE SET::SFIX-WHEN-EMPTYP))
 )
(NTH-0-N-NEW-ADS-AUX
 (28 4 (:REWRITE NOT-EQUAL-NTH-NEW-AD-WHEN-BOUND-ALT))
 (28 4 (:REWRITE NOT-EQUAL-NTH-NEW-AD-WHEN-BOUND))
 (27 6 (:REWRITE DEFAULT-CAR))
 (24 24 (:TYPE-PRESCRIPTION SET::IN-TYPE))
 (16 16 (:REWRITE SET::SUBSET-IN))
 (16 8 (:REWRITE SET::IN-TAIL))
 (13 13 (:REWRITE DEFAULT-<-2))
 (13 13 (:REWRITE DEFAULT-<-1))
 (12 4 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (4 4 (:TYPE-PRESCRIPTION BOOLEANP))
 (4 4 (:REWRITE DEFAULT-+-2))
 (4 4 (:REWRITE DEFAULT-+-1))
 (1 1 (:REWRITE NTH-WHEN-EQUAL-OF-TAKE-AND-CONSTANT))
 )
(TAKE-OF-N-NEW-ADS
 (24 7 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (22 22 (:REWRITE DEFAULT-+-2))
 (22 22 (:REWRITE DEFAULT-+-1))
 (21 21 (:REWRITE DEFAULT-<-2))
 (21 21 (:REWRITE DEFAULT-<-1))
 (18 6 (:DEFINITION POSP))
 (14 7 (:REWRITE NTHCDR-WHEN-NOT-CONSP-CHEAP))
 (8 4 (:REWRITE FOLD-CONSTS-IN-+))
 (7 7 (:REWRITE NTHCDR-WHEN-EQUAL-OF-LEN))
 (6 6 (:TYPE-PRESCRIPTION POSP))
 (6 6 (:TYPE-PRESCRIPTION BOOLEANP))
 (5 5 (:REWRITE DEFAULT-UNARY-MINUS))
 (5 2 (:REWRITE TRUE-LIST-FIX-WHEN-NOT-CONSP-CHEAP))
 (5 1 (:REWRITE TAKE-DOES-NOTHING))
 (2 1 (:REWRITE LEN-OF-REVERSE-LIST))
 )
(APPEND-N-NEW-ADS-NEW-ADS-SLICE
 (6 2 (:REWRITE NTHCDR-WHEN-NOT-POSP))
 (5 5 (:REWRITE DEFAULT-<-2))
 (5 5 (:REWRITE DEFAULT-<-1))
 (5 3 (:TYPE-PRESCRIPTION NEW-ADS-TYPE))
 (4 2 (:REWRITE NTHCDR-WHEN-NOT-CONSP-CHEAP))
 (3 3 (:REWRITE DEFAULT-+-2))
 (3 3 (:REWRITE DEFAULT-+-1))
 (3 1 (:DEFINITION POSP))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 (2 2 (:REWRITE NTHCDR-WHEN-EQUAL-OF-LEN))
 (2 1 (:REWRITE TRUE-LIST-FIX-WHEN-NOT-CONSP-CHEAP))
 (2 1 (:REWRITE APPEND-WHEN-NOT-CONSP-ARG1-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION POSP))
 )
(UNION-2SET-N-NEW-ADS-2SET-NEW-ADS-SLICE
 (9 3 (:REWRITE NEW-ADS-SLICE-OUT-OF-ORDER-INDICES))
 (6 6 (:REWRITE DEFAULT-<-2))
 (6 6 (:REWRITE DEFAULT-<-1))
 (4 4 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(UNION-2SET-NEW-ADS-SLICE-2SET-N-NEW-ADS
 (39 39 (:REWRITE DEFAULT-<-2))
 (39 39 (:REWRITE DEFAULT-<-1))
 (36 4 (:REWRITE COMMUTATIVITY-2-OF-+))
 (27 27 (:REWRITE DEFAULT-+-2))
 (27 27 (:REWRITE DEFAULT-+-1))
 (16 4 (:REWRITE DISTRIBUTIVITY-OF-MINUS-OVER-+))
 (12 4 (:REWRITE COMMUTATIVITY-OF-+))
 (9 3 (:REWRITE SET::SFIX-WHEN-EMPTYP))
 (8 8 (:REWRITE FOLD-CONSTS-IN-+))
 (8 8 (:REWRITE DEFAULT-UNARY-MINUS))
 (6 6 (:REWRITE ZP-OPEN))
 (6 2 (:REWRITE NEW-ADS-TYPE))
 (6 2 (:DEFINITION POSP))
 (5 2 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (2 2 (:TYPE-PRESCRIPTION POSP))
 (2 2 (:TYPE-PRESCRIPTION BOOLEANP))
 (2 2 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE DEFAULT-CAR))
 )
