18.16/5.58 MAYBE 18.16/5.60 proof of /export/starexec/sandbox/benchmark/theBenchmark.pl 18.16/5.60 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 18.16/5.60 18.16/5.60 18.16/5.60 Left Termination of the query pattern 18.16/5.60 18.16/5.60 times(a,a,g) 18.16/5.60 18.16/5.60 w.r.t. the given Prolog program could not be shown: 18.16/5.60 18.16/5.60 (0) Prolog 18.16/5.60 (1) PrologToPiTRSProof [SOUND, 22 ms] 18.16/5.60 (2) PiTRS 18.16/5.60 (3) DependencyPairsProof [EQUIVALENT, 266 ms] 18.16/5.60 (4) PiDP 18.16/5.60 (5) DependencyGraphProof [EQUIVALENT, 0 ms] 18.16/5.60 (6) AND 18.16/5.60 (7) PiDP 18.16/5.60 (8) UsableRulesProof [EQUIVALENT, 0 ms] 18.16/5.60 (9) PiDP 18.16/5.60 (10) PiDPToQDPProof [EQUIVALENT, 1 ms] 18.16/5.60 (11) QDP 18.16/5.60 (12) QDPSizeChangeProof [EQUIVALENT, 0 ms] 18.16/5.60 (13) YES 18.16/5.60 (14) PiDP 18.16/5.60 (15) UsableRulesProof [EQUIVALENT, 0 ms] 18.16/5.60 (16) PiDP 18.16/5.60 (17) PiDPToQDPProof [SOUND, 0 ms] 18.16/5.60 (18) QDP 18.16/5.60 (19) QDPSizeChangeProof [EQUIVALENT, 0 ms] 18.16/5.60 (20) YES 18.16/5.60 (21) PiDP 18.16/5.60 (22) UsableRulesProof [EQUIVALENT, 0 ms] 18.16/5.60 (23) PiDP 18.16/5.60 (24) PiDPToQDPProof [SOUND, 0 ms] 18.16/5.60 (25) QDP 18.16/5.60 (26) QDPSizeChangeProof [EQUIVALENT, 0 ms] 18.16/5.60 (27) YES 18.16/5.60 (28) PiDP 18.16/5.60 (29) UsableRulesProof [EQUIVALENT, 0 ms] 18.16/5.60 (30) PiDP 18.16/5.60 (31) PiDPToQDPProof [SOUND, 0 ms] 18.16/5.60 (32) QDP 18.16/5.60 (33) NonTerminationLoopProof [COMPLETE, 0 ms] 18.16/5.60 (34) NO 18.16/5.60 (35) PiDP 18.16/5.60 (36) UsableRulesProof [EQUIVALENT, 0 ms] 18.16/5.60 (37) PiDP 18.16/5.60 (38) PiDPToQDPProof [SOUND, 0 ms] 18.16/5.60 (39) QDP 18.16/5.60 (40) PiDP 18.16/5.60 (41) UsableRulesProof [EQUIVALENT, 0 ms] 18.16/5.60 (42) PiDP 18.16/5.60 (43) PiDP 18.16/5.60 (44) UsableRulesProof [EQUIVALENT, 0 ms] 18.16/5.60 (45) PiDP 18.16/5.60 (46) PiDP 18.16/5.60 (47) UsableRulesProof [EQUIVALENT, 0 ms] 18.16/5.60 (48) PiDP 18.16/5.60 (49) PrologToPiTRSProof [SOUND, 37 ms] 18.16/5.60 (50) PiTRS 18.16/5.60 (51) DependencyPairsProof [EQUIVALENT, 219 ms] 18.16/5.60 (52) PiDP 18.16/5.60 (53) DependencyGraphProof [EQUIVALENT, 3 ms] 18.16/5.60 (54) AND 18.16/5.60 (55) PiDP 18.16/5.60 (56) UsableRulesProof [EQUIVALENT, 0 ms] 18.16/5.60 (57) PiDP 18.16/5.60 (58) PiDPToQDPProof [EQUIVALENT, 9 ms] 18.16/5.60 (59) QDP 18.16/5.60 (60) QDPSizeChangeProof [EQUIVALENT, 0 ms] 18.16/5.60 (61) YES 18.16/5.60 (62) PiDP 18.16/5.60 (63) UsableRulesProof [EQUIVALENT, 0 ms] 18.16/5.60 (64) PiDP 18.16/5.60 (65) PiDPToQDPProof [SOUND, 0 ms] 18.16/5.60 (66) QDP 18.16/5.60 (67) QDPSizeChangeProof [EQUIVALENT, 0 ms] 18.16/5.60 (68) YES 18.16/5.60 (69) PiDP 18.16/5.60 (70) UsableRulesProof [EQUIVALENT, 0 ms] 18.16/5.60 (71) PiDP 18.16/5.60 (72) PiDPToQDPProof [SOUND, 0 ms] 18.16/5.60 (73) QDP 18.16/5.60 (74) QDPSizeChangeProof [EQUIVALENT, 0 ms] 18.16/5.60 (75) YES 18.16/5.60 (76) PiDP 18.16/5.60 (77) UsableRulesProof [EQUIVALENT, 0 ms] 18.16/5.60 (78) PiDP 18.16/5.60 (79) PiDPToQDPProof [SOUND, 0 ms] 18.16/5.60 (80) QDP 18.16/5.60 (81) NonTerminationLoopProof [COMPLETE, 0 ms] 18.16/5.60 (82) NO 18.16/5.60 (83) PiDP 18.16/5.60 (84) UsableRulesProof [EQUIVALENT, 0 ms] 18.16/5.60 (85) PiDP 18.16/5.60 (86) PiDPToQDPProof [SOUND, 0 ms] 18.16/5.60 (87) QDP 18.16/5.60 (88) PiDP 18.16/5.60 (89) UsableRulesProof [EQUIVALENT, 0 ms] 18.16/5.60 (90) PiDP 18.16/5.60 (91) PiDP 18.16/5.60 (92) UsableRulesProof [EQUIVALENT, 0 ms] 18.16/5.60 (93) PiDP 18.16/5.60 (94) PiDP 18.16/5.60 (95) UsableRulesProof [EQUIVALENT, 0 ms] 18.16/5.60 (96) PiDP 18.16/5.60 (97) PrologToTRSTransformerProof [SOUND, 302 ms] 18.16/5.60 (98) QTRS 18.16/5.60 (99) DependencyPairsProof [EQUIVALENT, 6 ms] 18.16/5.60 (100) QDP 18.16/5.60 (101) DependencyGraphProof [EQUIVALENT, 0 ms] 18.16/5.60 (102) AND 18.16/5.60 (103) QDP 18.16/5.60 (104) UsableRulesProof [EQUIVALENT, 0 ms] 18.16/5.60 (105) QDP 18.16/5.60 (106) QDPSizeChangeProof [EQUIVALENT, 0 ms] 18.16/5.60 (107) YES 18.16/5.60 (108) QDP 18.16/5.60 (109) UsableRulesProof [EQUIVALENT, 0 ms] 18.16/5.60 (110) QDP 18.16/5.60 (111) QDPSizeChangeProof [EQUIVALENT, 0 ms] 18.16/5.60 (112) YES 18.16/5.60 (113) QDP 18.16/5.60 (114) UsableRulesProof [EQUIVALENT, 0 ms] 18.16/5.60 (115) QDP 18.16/5.60 (116) QDPSizeChangeProof [EQUIVALENT, 0 ms] 18.16/5.60 (117) YES 18.16/5.60 (118) QDP 18.16/5.60 (119) UsableRulesProof [EQUIVALENT, 0 ms] 18.16/5.60 (120) QDP 18.16/5.60 (121) QDP 18.16/5.60 (122) UsableRulesProof [EQUIVALENT, 0 ms] 18.16/5.60 (123) QDP 18.16/5.60 (124) QDP 18.16/5.60 (125) UsableRulesProof [EQUIVALENT, 0 ms] 18.16/5.60 (126) QDP 18.16/5.60 (127) QDP 18.16/5.60 (128) UsableRulesProof [EQUIVALENT, 0 ms] 18.16/5.60 (129) QDP 18.16/5.60 (130) QDP 18.16/5.60 (131) UsableRulesProof [EQUIVALENT, 0 ms] 18.16/5.60 (132) QDP 18.16/5.60 (133) QDPSizeChangeProof [EQUIVALENT, 0 ms] 18.16/5.60 (134) YES 18.16/5.60 (135) PrologToDTProblemTransformerProof [SOUND, 332 ms] 18.16/5.60 (136) TRIPLES 18.16/5.60 (137) TriplesToPiDPProof [SOUND, 213 ms] 18.16/5.60 (138) PiDP 18.16/5.60 (139) DependencyGraphProof [EQUIVALENT, 0 ms] 18.16/5.60 (140) AND 18.16/5.60 (141) PiDP 18.16/5.60 (142) UsableRulesProof [EQUIVALENT, 0 ms] 18.16/5.60 (143) PiDP 18.16/5.60 (144) PiDPToQDPProof [EQUIVALENT, 0 ms] 18.16/5.60 (145) QDP 18.16/5.60 (146) QDPSizeChangeProof [EQUIVALENT, 0 ms] 18.16/5.60 (147) YES 18.16/5.60 (148) PiDP 18.16/5.60 (149) UsableRulesProof [EQUIVALENT, 0 ms] 18.16/5.60 (150) PiDP 18.16/5.60 (151) PiDPToQDPProof [EQUIVALENT, 0 ms] 18.16/5.60 (152) QDP 18.16/5.60 (153) QDPSizeChangeProof [EQUIVALENT, 0 ms] 18.16/5.60 (154) YES 18.16/5.60 (155) PiDP 18.16/5.60 (156) UsableRulesProof [EQUIVALENT, 0 ms] 18.16/5.60 (157) PiDP 18.16/5.60 (158) PiDPToQDPProof [EQUIVALENT, 0 ms] 18.16/5.60 (159) QDP 18.16/5.60 (160) QDPSizeChangeProof [EQUIVALENT, 0 ms] 18.16/5.60 (161) YES 18.16/5.60 (162) PiDP 18.16/5.60 (163) UsableRulesProof [EQUIVALENT, 0 ms] 18.16/5.60 (164) PiDP 18.16/5.60 (165) PiDPToQDPProof [SOUND, 0 ms] 18.16/5.60 (166) QDP 18.16/5.60 (167) QDPSizeChangeProof [EQUIVALENT, 0 ms] 18.16/5.60 (168) YES 18.16/5.60 (169) PiDP 18.16/5.60 (170) UsableRulesProof [EQUIVALENT, 0 ms] 18.16/5.60 (171) PiDP 18.16/5.60 (172) PiDPToQDPProof [SOUND, 0 ms] 18.16/5.60 (173) QDP 18.16/5.60 (174) QDPSizeChangeProof [EQUIVALENT, 0 ms] 18.16/5.60 (175) YES 18.16/5.60 (176) PiDP 18.16/5.60 (177) UsableRulesProof [EQUIVALENT, 0 ms] 18.16/5.60 (178) PiDP 18.16/5.60 (179) PiDPToQDPProof [SOUND, 0 ms] 18.16/5.60 (180) QDP 18.16/5.60 (181) NonTerminationLoopProof [COMPLETE, 0 ms] 18.16/5.60 (182) NO 18.16/5.60 (183) PiDP 18.16/5.60 (184) UsableRulesProof [EQUIVALENT, 0 ms] 18.16/5.60 (185) PiDP 18.16/5.60 (186) PiDP 18.16/5.60 (187) UsableRulesProof [EQUIVALENT, 0 ms] 18.16/5.60 (188) PiDP 18.16/5.60 (189) PiDP 18.16/5.60 (190) UsableRulesProof [EQUIVALENT, 0 ms] 18.16/5.60 (191) PiDP 18.16/5.60 (192) PiDP 18.16/5.60 (193) UsableRulesProof [EQUIVALENT, 0 ms] 18.16/5.60 (194) PiDP 18.16/5.60 (195) PrologToIRSwTTransformerProof [SOUND, 470 ms] 18.16/5.60 (196) AND 18.16/5.60 (197) IRSwT 18.16/5.60 (198) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms] 18.16/5.60 (199) TRUE 18.16/5.60 (200) IRSwT 18.16/5.60 (201) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms] 18.16/5.60 (202) TRUE 18.16/5.60 (203) IRSwT 18.16/5.60 (204) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms] 18.16/5.60 (205) TRUE 18.16/5.60 (206) IRSwT 18.16/5.60 (207) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms] 18.16/5.60 (208) TRUE 18.16/5.60 (209) IRSwT 18.16/5.60 (210) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms] 18.16/5.60 (211) TRUE 18.16/5.60 (212) IRSwT 18.16/5.60 (213) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms] 18.16/5.60 (214) TRUE 18.16/5.60 (215) IRSwT 18.16/5.60 (216) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms] 18.16/5.60 (217) IRSwT 18.16/5.60 (218) IntTRSCompressionProof [EQUIVALENT, 21 ms] 18.16/5.60 (219) IRSwT 18.16/5.60 (220) IRSFormatTransformerProof [EQUIVALENT, 0 ms] 18.16/5.60 (221) IRSwT 18.16/5.60 (222) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms] 18.16/5.60 (223) IRSwT 18.16/5.60 (224) FilterProof [EQUIVALENT, 0 ms] 18.16/5.60 (225) IntTRS 18.16/5.60 (226) IntTRSPeriodicNontermProof [COMPLETE, 5 ms] 18.16/5.60 (227) NO 18.16/5.60 (228) IRSwT 18.16/5.60 (229) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms] 18.16/5.60 (230) IRSwT 18.16/5.60 (231) IntTRSCompressionProof [EQUIVALENT, 0 ms] 18.16/5.60 (232) IRSwT 18.16/5.60 (233) IRSFormatTransformerProof [EQUIVALENT, 0 ms] 18.16/5.60 (234) IRSwT 18.16/5.60 (235) IRSwTTerminationDigraphProof [EQUIVALENT, 2 ms] 18.16/5.60 (236) IRSwT 18.16/5.60 (237) TempFilterProof [SOUND, 3 ms] 18.16/5.60 (238) IRSwT 18.16/5.60 (239) IRSwTToQDPProof [SOUND, 0 ms] 18.16/5.60 (240) QDP 18.16/5.60 (241) QDPSizeChangeProof [EQUIVALENT, 0 ms] 18.16/5.60 (242) YES 18.16/5.60 18.16/5.60 18.16/5.60 ---------------------------------------- 18.16/5.60 18.16/5.60 (0) 18.16/5.60 Obligation: 18.16/5.60 Clauses: 18.16/5.60 18.16/5.60 add(b, b, b). 18.16/5.60 add(X, b, X) :- binaryZ(X). 18.16/5.60 add(b, Y, Y) :- binaryZ(Y). 18.16/5.60 add(X, Y, Z) :- addz(X, Y, Z). 18.16/5.60 addx(one(X), b, one(X)) :- binary(X). 18.16/5.60 addx(zero(X), b, zero(X)) :- binaryZ(X). 18.16/5.60 addx(X, Y, Z) :- addz(X, Y, Z). 18.16/5.60 addy(b, one(Y), one(Y)) :- binary(Y). 18.16/5.60 addy(b, zero(Y), zero(Y)) :- binaryZ(Y). 18.16/5.60 addy(X, Y, Z) :- addz(X, Y, Z). 18.16/5.60 addz(zero(X), zero(Y), zero(Z)) :- addz(X, Y, Z). 18.16/5.60 addz(zero(X), one(Y), one(Z)) :- addx(X, Y, Z). 18.16/5.60 addz(one(X), zero(Y), one(Z)) :- addy(X, Y, Z). 18.16/5.60 addz(one(X), one(Y), zero(Z)) :- addc(X, Y, Z). 18.16/5.60 addc(b, b, one(b)). 18.16/5.60 addc(X, b, Z) :- succZ(X, Z). 18.16/5.60 addc(b, Y, Z) :- succZ(Y, Z). 18.16/5.60 addc(X, Y, Z) :- addC(X, Y, Z). 18.16/5.60 addX(zero(X), b, one(X)) :- binaryZ(X). 18.16/5.60 addX(one(X), b, zero(Z)) :- succ(X, Z). 18.16/5.60 addX(X, Y, Z) :- addC(X, Y, Z). 18.16/5.60 addY(b, zero(Y), one(Y)) :- binaryZ(Y). 18.16/5.60 addY(b, one(Y), zero(Z)) :- succ(Y, Z). 18.16/5.60 addY(X, Y, Z) :- addC(X, Y, Z). 18.16/5.60 addC(zero(X), zero(Y), one(Z)) :- addz(X, Y, Z). 18.16/5.60 addC(zero(X), one(Y), zero(Z)) :- addX(X, Y, Z). 18.16/5.60 addC(one(X), zero(Y), zero(Z)) :- addY(X, Y, Z). 18.16/5.60 addC(one(X), one(Y), one(Z)) :- addc(X, Y, Z). 18.16/5.60 binary(b). 18.16/5.60 binary(zero(X)) :- binaryZ(X). 18.16/5.60 binary(one(X)) :- binary(X). 18.16/5.60 binaryZ(zero(X)) :- binaryZ(X). 18.16/5.60 binaryZ(one(X)) :- binary(X). 18.16/5.60 succ(b, one(b)). 18.16/5.60 succ(zero(X), one(X)) :- binaryZ(X). 18.16/5.60 succ(one(X), zero(Z)) :- succ(X, Z). 18.16/5.60 succZ(zero(X), one(X)) :- binaryZ(X). 18.16/5.60 succZ(one(X), zero(Z)) :- succ(X, Z). 18.16/5.60 times(one(b), X, X). 18.16/5.60 times(zero(R), S, zero(RS)) :- times(R, S, RS). 18.16/5.60 times(one(R), S, RSS) :- ','(times(R, S, RS), add(S, zero(RS), RSS)). 18.16/5.60 18.16/5.60 18.16/5.60 Query: times(a,a,g) 18.16/5.60 ---------------------------------------- 18.16/5.60 18.16/5.60 (1) PrologToPiTRSProof (SOUND) 18.16/5.60 We use the technique of [TOCL09]. With regard to the inferred argument filtering the predicates were used in the following modes: 18.16/5.60 18.16/5.60 times_in_3: (f,f,b) (f,f,f) 18.16/5.60 18.16/5.60 add_in_3: (f,f,f) (f,f,b) 18.16/5.60 18.16/5.60 binaryZ_in_1: (f) (b) 18.16/5.60 18.16/5.60 binary_in_1: (f) (b) 18.16/5.60 18.16/5.60 addz_in_3: (f,f,f) (f,f,b) 18.16/5.60 18.16/5.60 addx_in_3: (f,f,f) (f,f,b) 18.16/5.60 18.16/5.60 addy_in_3: (f,f,f) (f,f,b) 18.16/5.60 18.16/5.60 addc_in_3: (f,f,f) (f,f,b) 18.16/5.60 18.16/5.60 succZ_in_2: (f,f) (f,b) 18.16/5.60 18.16/5.60 succ_in_2: (f,f) (f,b) 18.16/5.60 18.16/5.60 addC_in_3: (f,f,f) (f,f,b) 18.16/5.60 18.16/5.60 addX_in_3: (f,f,f) (f,f,b) 18.16/5.60 18.16/5.60 addY_in_3: (f,f,f) (f,f,b) 18.16/5.60 18.16/5.60 Transforming Prolog into the following Term Rewriting System: 18.16/5.60 18.16/5.60 Pi-finite rewrite system: 18.16/5.60 The TRS R consists of the following rules: 18.16/5.60 18.16/5.60 times_in_aag(one(b), X, X) -> times_out_aag(one(b), X, X) 18.16/5.60 times_in_aag(zero(R), S, zero(RS)) -> U35_aag(R, S, RS, times_in_aag(R, S, RS)) 18.16/5.60 times_in_aag(one(R), S, RSS) -> U36_aag(R, S, RSS, times_in_aaa(R, S, RS)) 18.16/5.60 times_in_aaa(one(b), X, X) -> times_out_aaa(one(b), X, X) 18.16/5.60 times_in_aaa(zero(R), S, zero(RS)) -> U35_aaa(R, S, RS, times_in_aaa(R, S, RS)) 18.16/5.60 times_in_aaa(one(R), S, RSS) -> U36_aaa(R, S, RSS, times_in_aaa(R, S, RS)) 18.16/5.60 U36_aaa(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aaa(R, S, RSS, add_in_aaa(S, zero(RS), RSS)) 18.16/5.60 add_in_aaa(b, b, b) -> add_out_aaa(b, b, b) 18.16/5.60 add_in_aaa(X, b, X) -> U1_aaa(X, binaryZ_in_a(X)) 18.16/5.60 binaryZ_in_a(zero(X)) -> U29_a(X, binaryZ_in_a(X)) 18.16/5.60 binaryZ_in_a(one(X)) -> U30_a(X, binary_in_a(X)) 18.16/5.60 binary_in_a(b) -> binary_out_a(b) 18.16/5.60 binary_in_a(zero(X)) -> U27_a(X, binaryZ_in_a(X)) 18.16/5.60 U27_a(X, binaryZ_out_a(X)) -> binary_out_a(zero(X)) 18.16/5.60 binary_in_a(one(X)) -> U28_a(X, binary_in_a(X)) 18.16/5.60 U28_a(X, binary_out_a(X)) -> binary_out_a(one(X)) 18.16/5.60 U30_a(X, binary_out_a(X)) -> binaryZ_out_a(one(X)) 18.16/5.60 U29_a(X, binaryZ_out_a(X)) -> binaryZ_out_a(zero(X)) 18.16/5.60 U1_aaa(X, binaryZ_out_a(X)) -> add_out_aaa(X, b, X) 18.16/5.60 add_in_aaa(b, Y, Y) -> U2_aaa(Y, binaryZ_in_a(Y)) 18.16/5.60 U2_aaa(Y, binaryZ_out_a(Y)) -> add_out_aaa(b, Y, Y) 18.16/5.60 add_in_aaa(X, Y, Z) -> U3_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.60 addz_in_aaa(zero(X), zero(Y), zero(Z)) -> U10_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.60 addz_in_aaa(zero(X), one(Y), one(Z)) -> U11_aaa(X, Y, Z, addx_in_aaa(X, Y, Z)) 18.16/5.60 addx_in_aaa(one(X), b, one(X)) -> U4_aaa(X, binary_in_a(X)) 18.16/5.60 U4_aaa(X, binary_out_a(X)) -> addx_out_aaa(one(X), b, one(X)) 18.16/5.60 addx_in_aaa(zero(X), b, zero(X)) -> U5_aaa(X, binaryZ_in_a(X)) 18.16/5.60 U5_aaa(X, binaryZ_out_a(X)) -> addx_out_aaa(zero(X), b, zero(X)) 18.16/5.60 addx_in_aaa(X, Y, Z) -> U6_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.60 addz_in_aaa(one(X), zero(Y), one(Z)) -> U12_aaa(X, Y, Z, addy_in_aaa(X, Y, Z)) 18.16/5.60 addy_in_aaa(b, one(Y), one(Y)) -> U7_aaa(Y, binary_in_a(Y)) 18.16/5.60 U7_aaa(Y, binary_out_a(Y)) -> addy_out_aaa(b, one(Y), one(Y)) 18.16/5.60 addy_in_aaa(b, zero(Y), zero(Y)) -> U8_aaa(Y, binaryZ_in_a(Y)) 18.16/5.60 U8_aaa(Y, binaryZ_out_a(Y)) -> addy_out_aaa(b, zero(Y), zero(Y)) 18.16/5.60 addy_in_aaa(X, Y, Z) -> U9_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.60 addz_in_aaa(one(X), one(Y), zero(Z)) -> U13_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.16/5.60 addc_in_aaa(b, b, one(b)) -> addc_out_aaa(b, b, one(b)) 18.16/5.60 addc_in_aaa(X, b, Z) -> U14_aaa(X, Z, succZ_in_aa(X, Z)) 18.16/5.60 succZ_in_aa(zero(X), one(X)) -> U33_aa(X, binaryZ_in_a(X)) 18.16/5.60 U33_aa(X, binaryZ_out_a(X)) -> succZ_out_aa(zero(X), one(X)) 18.16/5.60 succZ_in_aa(one(X), zero(Z)) -> U34_aa(X, Z, succ_in_aa(X, Z)) 18.16/5.60 succ_in_aa(b, one(b)) -> succ_out_aa(b, one(b)) 18.16/5.60 succ_in_aa(zero(X), one(X)) -> U31_aa(X, binaryZ_in_a(X)) 18.16/5.60 U31_aa(X, binaryZ_out_a(X)) -> succ_out_aa(zero(X), one(X)) 18.16/5.60 succ_in_aa(one(X), zero(Z)) -> U32_aa(X, Z, succ_in_aa(X, Z)) 18.16/5.60 U32_aa(X, Z, succ_out_aa(X, Z)) -> succ_out_aa(one(X), zero(Z)) 18.16/5.60 U34_aa(X, Z, succ_out_aa(X, Z)) -> succZ_out_aa(one(X), zero(Z)) 18.16/5.60 U14_aaa(X, Z, succZ_out_aa(X, Z)) -> addc_out_aaa(X, b, Z) 18.16/5.60 addc_in_aaa(b, Y, Z) -> U15_aaa(Y, Z, succZ_in_aa(Y, Z)) 18.16/5.60 U15_aaa(Y, Z, succZ_out_aa(Y, Z)) -> addc_out_aaa(b, Y, Z) 18.16/5.60 addc_in_aaa(X, Y, Z) -> U16_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.16/5.60 addC_in_aaa(zero(X), zero(Y), one(Z)) -> U23_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.60 U23_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), zero(Y), one(Z)) 18.16/5.60 addC_in_aaa(zero(X), one(Y), zero(Z)) -> U24_aaa(X, Y, Z, addX_in_aaa(X, Y, Z)) 18.16/5.60 addX_in_aaa(zero(X), b, one(X)) -> U17_aaa(X, binaryZ_in_a(X)) 18.16/5.60 U17_aaa(X, binaryZ_out_a(X)) -> addX_out_aaa(zero(X), b, one(X)) 18.16/5.60 addX_in_aaa(one(X), b, zero(Z)) -> U18_aaa(X, Z, succ_in_aa(X, Z)) 18.16/5.60 U18_aaa(X, Z, succ_out_aa(X, Z)) -> addX_out_aaa(one(X), b, zero(Z)) 18.16/5.60 addX_in_aaa(X, Y, Z) -> U19_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.16/5.60 addC_in_aaa(one(X), zero(Y), zero(Z)) -> U25_aaa(X, Y, Z, addY_in_aaa(X, Y, Z)) 18.16/5.60 addY_in_aaa(b, zero(Y), one(Y)) -> U20_aaa(Y, binaryZ_in_a(Y)) 18.16/5.60 U20_aaa(Y, binaryZ_out_a(Y)) -> addY_out_aaa(b, zero(Y), one(Y)) 18.16/5.60 addY_in_aaa(b, one(Y), zero(Z)) -> U21_aaa(Y, Z, succ_in_aa(Y, Z)) 18.16/5.60 U21_aaa(Y, Z, succ_out_aa(Y, Z)) -> addY_out_aaa(b, one(Y), zero(Z)) 18.16/5.60 addY_in_aaa(X, Y, Z) -> U22_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.16/5.60 addC_in_aaa(one(X), one(Y), one(Z)) -> U26_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.16/5.60 U26_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), one(Y), one(Z)) 18.16/5.60 U22_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addY_out_aaa(X, Y, Z) 18.16/5.60 U25_aaa(X, Y, Z, addY_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), zero(Y), zero(Z)) 18.16/5.60 U19_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addX_out_aaa(X, Y, Z) 18.16/5.60 U24_aaa(X, Y, Z, addX_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), one(Y), zero(Z)) 18.16/5.60 U16_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addc_out_aaa(X, Y, Z) 18.16/5.60 U13_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), one(Y), zero(Z)) 18.16/5.60 U9_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addy_out_aaa(X, Y, Z) 18.16/5.60 U12_aaa(X, Y, Z, addy_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), zero(Y), one(Z)) 18.16/5.60 U6_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addx_out_aaa(X, Y, Z) 18.16/5.60 U11_aaa(X, Y, Z, addx_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), one(Y), one(Z)) 18.16/5.60 U10_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), zero(Y), zero(Z)) 18.16/5.60 U3_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> add_out_aaa(X, Y, Z) 18.16/5.60 U37_aaa(R, S, RSS, add_out_aaa(S, zero(RS), RSS)) -> times_out_aaa(one(R), S, RSS) 18.16/5.60 U35_aaa(R, S, RS, times_out_aaa(R, S, RS)) -> times_out_aaa(zero(R), S, zero(RS)) 18.16/5.60 U36_aag(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aag(R, S, RSS, add_in_aag(S, zero(RS), RSS)) 18.16/5.60 add_in_aag(b, b, b) -> add_out_aag(b, b, b) 18.16/5.60 add_in_aag(X, b, X) -> U1_aag(X, binaryZ_in_g(X)) 18.16/5.60 binaryZ_in_g(zero(X)) -> U29_g(X, binaryZ_in_g(X)) 18.16/5.61 binaryZ_in_g(one(X)) -> U30_g(X, binary_in_g(X)) 18.16/5.61 binary_in_g(b) -> binary_out_g(b) 18.16/5.61 binary_in_g(zero(X)) -> U27_g(X, binaryZ_in_g(X)) 18.16/5.61 U27_g(X, binaryZ_out_g(X)) -> binary_out_g(zero(X)) 18.16/5.61 binary_in_g(one(X)) -> U28_g(X, binary_in_g(X)) 18.16/5.61 U28_g(X, binary_out_g(X)) -> binary_out_g(one(X)) 18.16/5.61 U30_g(X, binary_out_g(X)) -> binaryZ_out_g(one(X)) 18.16/5.61 U29_g(X, binaryZ_out_g(X)) -> binaryZ_out_g(zero(X)) 18.16/5.61 U1_aag(X, binaryZ_out_g(X)) -> add_out_aag(X, b, X) 18.16/5.61 add_in_aag(b, Y, Y) -> U2_aag(Y, binaryZ_in_g(Y)) 18.16/5.61 U2_aag(Y, binaryZ_out_g(Y)) -> add_out_aag(b, Y, Y) 18.16/5.61 add_in_aag(X, Y, Z) -> U3_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.61 addz_in_aag(zero(X), zero(Y), zero(Z)) -> U10_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.61 addz_in_aag(zero(X), one(Y), one(Z)) -> U11_aag(X, Y, Z, addx_in_aag(X, Y, Z)) 18.16/5.61 addx_in_aag(one(X), b, one(X)) -> U4_aag(X, binary_in_g(X)) 18.16/5.61 U4_aag(X, binary_out_g(X)) -> addx_out_aag(one(X), b, one(X)) 18.16/5.61 addx_in_aag(zero(X), b, zero(X)) -> U5_aag(X, binaryZ_in_g(X)) 18.16/5.61 U5_aag(X, binaryZ_out_g(X)) -> addx_out_aag(zero(X), b, zero(X)) 18.16/5.61 addx_in_aag(X, Y, Z) -> U6_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.61 addz_in_aag(one(X), zero(Y), one(Z)) -> U12_aag(X, Y, Z, addy_in_aag(X, Y, Z)) 18.16/5.61 addy_in_aag(b, one(Y), one(Y)) -> U7_aag(Y, binary_in_g(Y)) 18.16/5.61 U7_aag(Y, binary_out_g(Y)) -> addy_out_aag(b, one(Y), one(Y)) 18.16/5.61 addy_in_aag(b, zero(Y), zero(Y)) -> U8_aag(Y, binaryZ_in_g(Y)) 18.16/5.61 U8_aag(Y, binaryZ_out_g(Y)) -> addy_out_aag(b, zero(Y), zero(Y)) 18.16/5.61 addy_in_aag(X, Y, Z) -> U9_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.61 addz_in_aag(one(X), one(Y), zero(Z)) -> U13_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.16/5.61 addc_in_aag(b, b, one(b)) -> addc_out_aag(b, b, one(b)) 18.16/5.61 addc_in_aag(X, b, Z) -> U14_aag(X, Z, succZ_in_ag(X, Z)) 18.16/5.61 succZ_in_ag(zero(X), one(X)) -> U33_ag(X, binaryZ_in_g(X)) 18.16/5.61 U33_ag(X, binaryZ_out_g(X)) -> succZ_out_ag(zero(X), one(X)) 18.16/5.61 succZ_in_ag(one(X), zero(Z)) -> U34_ag(X, Z, succ_in_ag(X, Z)) 18.16/5.61 succ_in_ag(b, one(b)) -> succ_out_ag(b, one(b)) 18.16/5.61 succ_in_ag(zero(X), one(X)) -> U31_ag(X, binaryZ_in_g(X)) 18.16/5.61 U31_ag(X, binaryZ_out_g(X)) -> succ_out_ag(zero(X), one(X)) 18.16/5.61 succ_in_ag(one(X), zero(Z)) -> U32_ag(X, Z, succ_in_ag(X, Z)) 18.16/5.61 U32_ag(X, Z, succ_out_ag(X, Z)) -> succ_out_ag(one(X), zero(Z)) 18.16/5.61 U34_ag(X, Z, succ_out_ag(X, Z)) -> succZ_out_ag(one(X), zero(Z)) 18.16/5.61 U14_aag(X, Z, succZ_out_ag(X, Z)) -> addc_out_aag(X, b, Z) 18.16/5.61 addc_in_aag(b, Y, Z) -> U15_aag(Y, Z, succZ_in_ag(Y, Z)) 18.16/5.61 U15_aag(Y, Z, succZ_out_ag(Y, Z)) -> addc_out_aag(b, Y, Z) 18.16/5.61 addc_in_aag(X, Y, Z) -> U16_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.16/5.61 addC_in_aag(zero(X), zero(Y), one(Z)) -> U23_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.61 U23_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), zero(Y), one(Z)) 18.16/5.61 addC_in_aag(zero(X), one(Y), zero(Z)) -> U24_aag(X, Y, Z, addX_in_aag(X, Y, Z)) 18.16/5.61 addX_in_aag(zero(X), b, one(X)) -> U17_aag(X, binaryZ_in_g(X)) 18.16/5.61 U17_aag(X, binaryZ_out_g(X)) -> addX_out_aag(zero(X), b, one(X)) 18.16/5.61 addX_in_aag(one(X), b, zero(Z)) -> U18_aag(X, Z, succ_in_ag(X, Z)) 18.16/5.61 U18_aag(X, Z, succ_out_ag(X, Z)) -> addX_out_aag(one(X), b, zero(Z)) 18.16/5.61 addX_in_aag(X, Y, Z) -> U19_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.16/5.61 addC_in_aag(one(X), zero(Y), zero(Z)) -> U25_aag(X, Y, Z, addY_in_aag(X, Y, Z)) 18.16/5.61 addY_in_aag(b, zero(Y), one(Y)) -> U20_aag(Y, binaryZ_in_g(Y)) 18.16/5.61 U20_aag(Y, binaryZ_out_g(Y)) -> addY_out_aag(b, zero(Y), one(Y)) 18.16/5.61 addY_in_aag(b, one(Y), zero(Z)) -> U21_aag(Y, Z, succ_in_ag(Y, Z)) 18.16/5.61 U21_aag(Y, Z, succ_out_ag(Y, Z)) -> addY_out_aag(b, one(Y), zero(Z)) 18.16/5.61 addY_in_aag(X, Y, Z) -> U22_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.16/5.61 addC_in_aag(one(X), one(Y), one(Z)) -> U26_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.16/5.61 U26_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addC_out_aag(one(X), one(Y), one(Z)) 18.16/5.61 U22_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addY_out_aag(X, Y, Z) 18.16/5.61 U25_aag(X, Y, Z, addY_out_aag(X, Y, Z)) -> addC_out_aag(one(X), zero(Y), zero(Z)) 18.16/5.61 U19_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addX_out_aag(X, Y, Z) 18.16/5.61 U24_aag(X, Y, Z, addX_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), one(Y), zero(Z)) 18.16/5.61 U16_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addc_out_aag(X, Y, Z) 18.16/5.61 U13_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addz_out_aag(one(X), one(Y), zero(Z)) 18.16/5.61 U9_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addy_out_aag(X, Y, Z) 18.16/5.61 U12_aag(X, Y, Z, addy_out_aag(X, Y, Z)) -> addz_out_aag(one(X), zero(Y), one(Z)) 18.16/5.61 U6_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addx_out_aag(X, Y, Z) 18.16/5.61 U11_aag(X, Y, Z, addx_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), one(Y), one(Z)) 18.16/5.61 U10_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), zero(Y), zero(Z)) 18.16/5.61 U3_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> add_out_aag(X, Y, Z) 18.16/5.61 U37_aag(R, S, RSS, add_out_aag(S, zero(RS), RSS)) -> times_out_aag(one(R), S, RSS) 18.16/5.61 U35_aag(R, S, RS, times_out_aag(R, S, RS)) -> times_out_aag(zero(R), S, zero(RS)) 18.16/5.61 18.16/5.61 The argument filtering Pi contains the following mapping: 18.16/5.61 times_in_aag(x1, x2, x3) = times_in_aag(x3) 18.16/5.61 18.16/5.61 times_out_aag(x1, x2, x3) = times_out_aag(x1, x2, x3) 18.16/5.61 18.16/5.61 zero(x1) = zero(x1) 18.16/5.61 18.16/5.61 U35_aag(x1, x2, x3, x4) = U35_aag(x3, x4) 18.16/5.61 18.16/5.61 U36_aag(x1, x2, x3, x4) = U36_aag(x3, x4) 18.16/5.61 18.16/5.61 times_in_aaa(x1, x2, x3) = times_in_aaa 18.16/5.61 18.16/5.61 times_out_aaa(x1, x2, x3) = times_out_aaa(x1) 18.16/5.61 18.16/5.61 U35_aaa(x1, x2, x3, x4) = U35_aaa(x4) 18.16/5.61 18.16/5.61 U36_aaa(x1, x2, x3, x4) = U36_aaa(x4) 18.16/5.61 18.16/5.61 U37_aaa(x1, x2, x3, x4) = U37_aaa(x1, x4) 18.16/5.61 18.16/5.61 add_in_aaa(x1, x2, x3) = add_in_aaa 18.16/5.61 18.16/5.61 add_out_aaa(x1, x2, x3) = add_out_aaa(x1, x2, x3) 18.16/5.61 18.16/5.61 U1_aaa(x1, x2) = U1_aaa(x2) 18.16/5.61 18.16/5.61 binaryZ_in_a(x1) = binaryZ_in_a 18.16/5.61 18.16/5.61 U29_a(x1, x2) = U29_a(x2) 18.16/5.61 18.16/5.61 U30_a(x1, x2) = U30_a(x2) 18.16/5.61 18.16/5.61 binary_in_a(x1) = binary_in_a 18.16/5.61 18.16/5.61 binary_out_a(x1) = binary_out_a(x1) 18.16/5.61 18.16/5.61 U27_a(x1, x2) = U27_a(x2) 18.16/5.61 18.16/5.61 binaryZ_out_a(x1) = binaryZ_out_a(x1) 18.16/5.61 18.16/5.61 U28_a(x1, x2) = U28_a(x2) 18.16/5.61 18.16/5.61 U2_aaa(x1, x2) = U2_aaa(x2) 18.16/5.61 18.16/5.61 U3_aaa(x1, x2, x3, x4) = U3_aaa(x4) 18.16/5.61 18.16/5.61 addz_in_aaa(x1, x2, x3) = addz_in_aaa 18.16/5.61 18.16/5.61 U10_aaa(x1, x2, x3, x4) = U10_aaa(x4) 18.16/5.61 18.16/5.61 U11_aaa(x1, x2, x3, x4) = U11_aaa(x4) 18.16/5.61 18.16/5.61 addx_in_aaa(x1, x2, x3) = addx_in_aaa 18.16/5.61 18.16/5.61 U4_aaa(x1, x2) = U4_aaa(x2) 18.16/5.61 18.16/5.61 addx_out_aaa(x1, x2, x3) = addx_out_aaa(x1, x2, x3) 18.16/5.61 18.16/5.61 U5_aaa(x1, x2) = U5_aaa(x2) 18.16/5.61 18.16/5.61 U6_aaa(x1, x2, x3, x4) = U6_aaa(x4) 18.16/5.61 18.16/5.61 U12_aaa(x1, x2, x3, x4) = U12_aaa(x4) 18.16/5.61 18.16/5.61 addy_in_aaa(x1, x2, x3) = addy_in_aaa 18.16/5.61 18.16/5.61 U7_aaa(x1, x2) = U7_aaa(x2) 18.16/5.61 18.16/5.61 addy_out_aaa(x1, x2, x3) = addy_out_aaa(x1, x2, x3) 18.16/5.61 18.16/5.61 U8_aaa(x1, x2) = U8_aaa(x2) 18.16/5.61 18.16/5.61 U9_aaa(x1, x2, x3, x4) = U9_aaa(x4) 18.16/5.61 18.16/5.61 U13_aaa(x1, x2, x3, x4) = U13_aaa(x4) 18.16/5.61 18.16/5.61 addc_in_aaa(x1, x2, x3) = addc_in_aaa 18.16/5.61 18.16/5.61 addc_out_aaa(x1, x2, x3) = addc_out_aaa(x1, x2, x3) 18.16/5.61 18.16/5.61 U14_aaa(x1, x2, x3) = U14_aaa(x3) 18.16/5.61 18.16/5.61 succZ_in_aa(x1, x2) = succZ_in_aa 18.16/5.61 18.16/5.61 U33_aa(x1, x2) = U33_aa(x2) 18.16/5.61 18.16/5.61 succZ_out_aa(x1, x2) = succZ_out_aa(x1, x2) 18.16/5.61 18.16/5.61 U34_aa(x1, x2, x3) = U34_aa(x3) 18.16/5.61 18.16/5.61 succ_in_aa(x1, x2) = succ_in_aa 18.16/5.61 18.16/5.61 succ_out_aa(x1, x2) = succ_out_aa(x1, x2) 18.16/5.61 18.16/5.61 U31_aa(x1, x2) = U31_aa(x2) 18.16/5.61 18.16/5.61 U32_aa(x1, x2, x3) = U32_aa(x3) 18.16/5.61 18.16/5.61 U15_aaa(x1, x2, x3) = U15_aaa(x3) 18.16/5.61 18.16/5.61 U16_aaa(x1, x2, x3, x4) = U16_aaa(x4) 18.16/5.61 18.16/5.61 addC_in_aaa(x1, x2, x3) = addC_in_aaa 18.16/5.61 18.16/5.61 U23_aaa(x1, x2, x3, x4) = U23_aaa(x4) 18.16/5.61 18.16/5.61 addz_out_aaa(x1, x2, x3) = addz_out_aaa(x1, x2, x3) 18.16/5.61 18.16/5.61 addC_out_aaa(x1, x2, x3) = addC_out_aaa(x1, x2, x3) 18.16/5.61 18.16/5.61 U24_aaa(x1, x2, x3, x4) = U24_aaa(x4) 18.16/5.61 18.16/5.61 addX_in_aaa(x1, x2, x3) = addX_in_aaa 18.16/5.61 18.16/5.61 U17_aaa(x1, x2) = U17_aaa(x2) 18.16/5.61 18.16/5.61 addX_out_aaa(x1, x2, x3) = addX_out_aaa(x1, x2, x3) 18.16/5.61 18.16/5.61 U18_aaa(x1, x2, x3) = U18_aaa(x3) 18.16/5.61 18.16/5.61 U19_aaa(x1, x2, x3, x4) = U19_aaa(x4) 18.16/5.61 18.16/5.61 U25_aaa(x1, x2, x3, x4) = U25_aaa(x4) 18.16/5.61 18.16/5.61 addY_in_aaa(x1, x2, x3) = addY_in_aaa 18.16/5.61 18.16/5.61 U20_aaa(x1, x2) = U20_aaa(x2) 18.16/5.61 18.16/5.61 addY_out_aaa(x1, x2, x3) = addY_out_aaa(x1, x2, x3) 18.16/5.61 18.16/5.61 U21_aaa(x1, x2, x3) = U21_aaa(x3) 18.16/5.61 18.16/5.61 U22_aaa(x1, x2, x3, x4) = U22_aaa(x4) 18.16/5.61 18.16/5.61 U26_aaa(x1, x2, x3, x4) = U26_aaa(x4) 18.16/5.61 18.16/5.61 U37_aag(x1, x2, x3, x4) = U37_aag(x1, x3, x4) 18.16/5.61 18.16/5.61 add_in_aag(x1, x2, x3) = add_in_aag(x3) 18.16/5.61 18.16/5.61 b = b 18.16/5.61 18.16/5.61 add_out_aag(x1, x2, x3) = add_out_aag(x1, x2, x3) 18.16/5.61 18.16/5.61 U1_aag(x1, x2) = U1_aag(x1, x2) 18.16/5.61 18.16/5.61 binaryZ_in_g(x1) = binaryZ_in_g(x1) 18.16/5.61 18.16/5.61 U29_g(x1, x2) = U29_g(x1, x2) 18.16/5.61 18.16/5.61 one(x1) = one(x1) 18.16/5.61 18.16/5.61 U30_g(x1, x2) = U30_g(x1, x2) 18.16/5.61 18.16/5.61 binary_in_g(x1) = binary_in_g(x1) 18.16/5.61 18.16/5.61 binary_out_g(x1) = binary_out_g(x1) 18.16/5.61 18.16/5.61 U27_g(x1, x2) = U27_g(x1, x2) 18.16/5.61 18.16/5.61 binaryZ_out_g(x1) = binaryZ_out_g(x1) 18.16/5.61 18.16/5.61 U28_g(x1, x2) = U28_g(x1, x2) 18.16/5.61 18.16/5.61 U2_aag(x1, x2) = U2_aag(x1, x2) 18.16/5.61 18.16/5.61 U3_aag(x1, x2, x3, x4) = U3_aag(x3, x4) 18.16/5.61 18.16/5.61 addz_in_aag(x1, x2, x3) = addz_in_aag(x3) 18.16/5.61 18.16/5.61 U10_aag(x1, x2, x3, x4) = U10_aag(x3, x4) 18.16/5.61 18.16/5.61 U11_aag(x1, x2, x3, x4) = U11_aag(x3, x4) 18.16/5.61 18.16/5.61 addx_in_aag(x1, x2, x3) = addx_in_aag(x3) 18.16/5.61 18.16/5.61 U4_aag(x1, x2) = U4_aag(x1, x2) 18.16/5.61 18.16/5.61 addx_out_aag(x1, x2, x3) = addx_out_aag(x1, x2, x3) 18.16/5.61 18.16/5.61 U5_aag(x1, x2) = U5_aag(x1, x2) 18.16/5.61 18.16/5.61 U6_aag(x1, x2, x3, x4) = U6_aag(x3, x4) 18.16/5.61 18.16/5.61 U12_aag(x1, x2, x3, x4) = U12_aag(x3, x4) 18.16/5.61 18.16/5.61 addy_in_aag(x1, x2, x3) = addy_in_aag(x3) 18.16/5.61 18.16/5.61 U7_aag(x1, x2) = U7_aag(x1, x2) 18.16/5.61 18.16/5.61 addy_out_aag(x1, x2, x3) = addy_out_aag(x1, x2, x3) 18.16/5.61 18.16/5.61 U8_aag(x1, x2) = U8_aag(x1, x2) 18.16/5.61 18.16/5.61 U9_aag(x1, x2, x3, x4) = U9_aag(x3, x4) 18.16/5.61 18.16/5.61 U13_aag(x1, x2, x3, x4) = U13_aag(x3, x4) 18.16/5.61 18.16/5.61 addc_in_aag(x1, x2, x3) = addc_in_aag(x3) 18.16/5.61 18.16/5.61 addc_out_aag(x1, x2, x3) = addc_out_aag(x1, x2, x3) 18.16/5.61 18.16/5.61 U14_aag(x1, x2, x3) = U14_aag(x2, x3) 18.16/5.61 18.16/5.61 succZ_in_ag(x1, x2) = succZ_in_ag(x2) 18.16/5.61 18.16/5.61 U33_ag(x1, x2) = U33_ag(x1, x2) 18.16/5.61 18.16/5.61 succZ_out_ag(x1, x2) = succZ_out_ag(x1, x2) 18.16/5.61 18.16/5.61 U34_ag(x1, x2, x3) = U34_ag(x2, x3) 18.16/5.61 18.16/5.61 succ_in_ag(x1, x2) = succ_in_ag(x2) 18.16/5.61 18.16/5.61 succ_out_ag(x1, x2) = succ_out_ag(x1, x2) 18.16/5.61 18.16/5.61 U31_ag(x1, x2) = U31_ag(x1, x2) 18.16/5.61 18.16/5.61 U32_ag(x1, x2, x3) = U32_ag(x2, x3) 18.16/5.61 18.16/5.61 U15_aag(x1, x2, x3) = U15_aag(x2, x3) 18.16/5.61 18.16/5.61 U16_aag(x1, x2, x3, x4) = U16_aag(x3, x4) 18.16/5.61 18.16/5.61 addC_in_aag(x1, x2, x3) = addC_in_aag(x3) 18.16/5.61 18.16/5.61 U23_aag(x1, x2, x3, x4) = U23_aag(x3, x4) 18.16/5.61 18.16/5.61 addz_out_aag(x1, x2, x3) = addz_out_aag(x1, x2, x3) 18.16/5.61 18.16/5.61 addC_out_aag(x1, x2, x3) = addC_out_aag(x1, x2, x3) 18.16/5.61 18.16/5.61 U24_aag(x1, x2, x3, x4) = U24_aag(x3, x4) 18.16/5.61 18.16/5.61 addX_in_aag(x1, x2, x3) = addX_in_aag(x3) 18.16/5.61 18.16/5.61 U17_aag(x1, x2) = U17_aag(x1, x2) 18.16/5.61 18.16/5.61 addX_out_aag(x1, x2, x3) = addX_out_aag(x1, x2, x3) 18.16/5.61 18.16/5.61 U18_aag(x1, x2, x3) = U18_aag(x2, x3) 18.16/5.61 18.16/5.61 U19_aag(x1, x2, x3, x4) = U19_aag(x3, x4) 18.16/5.61 18.16/5.61 U25_aag(x1, x2, x3, x4) = U25_aag(x3, x4) 18.16/5.61 18.16/5.61 addY_in_aag(x1, x2, x3) = addY_in_aag(x3) 18.16/5.61 18.16/5.61 U20_aag(x1, x2) = U20_aag(x1, x2) 18.16/5.61 18.16/5.61 addY_out_aag(x1, x2, x3) = addY_out_aag(x1, x2, x3) 18.16/5.61 18.16/5.61 U21_aag(x1, x2, x3) = U21_aag(x2, x3) 18.16/5.61 18.16/5.61 U22_aag(x1, x2, x3, x4) = U22_aag(x3, x4) 18.16/5.61 18.16/5.61 U26_aag(x1, x2, x3, x4) = U26_aag(x3, x4) 18.16/5.61 18.16/5.61 18.16/5.61 18.16/5.61 18.16/5.61 18.16/5.61 Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog 18.16/5.61 18.16/5.61 18.16/5.61 18.16/5.61 ---------------------------------------- 18.16/5.61 18.16/5.61 (2) 18.16/5.61 Obligation: 18.16/5.61 Pi-finite rewrite system: 18.16/5.61 The TRS R consists of the following rules: 18.16/5.61 18.16/5.61 times_in_aag(one(b), X, X) -> times_out_aag(one(b), X, X) 18.16/5.61 times_in_aag(zero(R), S, zero(RS)) -> U35_aag(R, S, RS, times_in_aag(R, S, RS)) 18.16/5.61 times_in_aag(one(R), S, RSS) -> U36_aag(R, S, RSS, times_in_aaa(R, S, RS)) 18.16/5.61 times_in_aaa(one(b), X, X) -> times_out_aaa(one(b), X, X) 18.16/5.61 times_in_aaa(zero(R), S, zero(RS)) -> U35_aaa(R, S, RS, times_in_aaa(R, S, RS)) 18.16/5.61 times_in_aaa(one(R), S, RSS) -> U36_aaa(R, S, RSS, times_in_aaa(R, S, RS)) 18.16/5.61 U36_aaa(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aaa(R, S, RSS, add_in_aaa(S, zero(RS), RSS)) 18.16/5.61 add_in_aaa(b, b, b) -> add_out_aaa(b, b, b) 18.16/5.61 add_in_aaa(X, b, X) -> U1_aaa(X, binaryZ_in_a(X)) 18.16/5.61 binaryZ_in_a(zero(X)) -> U29_a(X, binaryZ_in_a(X)) 18.16/5.61 binaryZ_in_a(one(X)) -> U30_a(X, binary_in_a(X)) 18.16/5.61 binary_in_a(b) -> binary_out_a(b) 18.16/5.61 binary_in_a(zero(X)) -> U27_a(X, binaryZ_in_a(X)) 18.16/5.61 U27_a(X, binaryZ_out_a(X)) -> binary_out_a(zero(X)) 18.16/5.61 binary_in_a(one(X)) -> U28_a(X, binary_in_a(X)) 18.16/5.61 U28_a(X, binary_out_a(X)) -> binary_out_a(one(X)) 18.16/5.61 U30_a(X, binary_out_a(X)) -> binaryZ_out_a(one(X)) 18.16/5.61 U29_a(X, binaryZ_out_a(X)) -> binaryZ_out_a(zero(X)) 18.16/5.61 U1_aaa(X, binaryZ_out_a(X)) -> add_out_aaa(X, b, X) 18.16/5.61 add_in_aaa(b, Y, Y) -> U2_aaa(Y, binaryZ_in_a(Y)) 18.16/5.61 U2_aaa(Y, binaryZ_out_a(Y)) -> add_out_aaa(b, Y, Y) 18.16/5.61 add_in_aaa(X, Y, Z) -> U3_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.61 addz_in_aaa(zero(X), zero(Y), zero(Z)) -> U10_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.61 addz_in_aaa(zero(X), one(Y), one(Z)) -> U11_aaa(X, Y, Z, addx_in_aaa(X, Y, Z)) 18.16/5.61 addx_in_aaa(one(X), b, one(X)) -> U4_aaa(X, binary_in_a(X)) 18.16/5.61 U4_aaa(X, binary_out_a(X)) -> addx_out_aaa(one(X), b, one(X)) 18.16/5.61 addx_in_aaa(zero(X), b, zero(X)) -> U5_aaa(X, binaryZ_in_a(X)) 18.16/5.61 U5_aaa(X, binaryZ_out_a(X)) -> addx_out_aaa(zero(X), b, zero(X)) 18.16/5.61 addx_in_aaa(X, Y, Z) -> U6_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.61 addz_in_aaa(one(X), zero(Y), one(Z)) -> U12_aaa(X, Y, Z, addy_in_aaa(X, Y, Z)) 18.16/5.61 addy_in_aaa(b, one(Y), one(Y)) -> U7_aaa(Y, binary_in_a(Y)) 18.16/5.61 U7_aaa(Y, binary_out_a(Y)) -> addy_out_aaa(b, one(Y), one(Y)) 18.16/5.61 addy_in_aaa(b, zero(Y), zero(Y)) -> U8_aaa(Y, binaryZ_in_a(Y)) 18.16/5.61 U8_aaa(Y, binaryZ_out_a(Y)) -> addy_out_aaa(b, zero(Y), zero(Y)) 18.16/5.61 addy_in_aaa(X, Y, Z) -> U9_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.61 addz_in_aaa(one(X), one(Y), zero(Z)) -> U13_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.16/5.61 addc_in_aaa(b, b, one(b)) -> addc_out_aaa(b, b, one(b)) 18.16/5.61 addc_in_aaa(X, b, Z) -> U14_aaa(X, Z, succZ_in_aa(X, Z)) 18.16/5.61 succZ_in_aa(zero(X), one(X)) -> U33_aa(X, binaryZ_in_a(X)) 18.16/5.61 U33_aa(X, binaryZ_out_a(X)) -> succZ_out_aa(zero(X), one(X)) 18.16/5.61 succZ_in_aa(one(X), zero(Z)) -> U34_aa(X, Z, succ_in_aa(X, Z)) 18.16/5.61 succ_in_aa(b, one(b)) -> succ_out_aa(b, one(b)) 18.16/5.61 succ_in_aa(zero(X), one(X)) -> U31_aa(X, binaryZ_in_a(X)) 18.16/5.61 U31_aa(X, binaryZ_out_a(X)) -> succ_out_aa(zero(X), one(X)) 18.16/5.61 succ_in_aa(one(X), zero(Z)) -> U32_aa(X, Z, succ_in_aa(X, Z)) 18.16/5.61 U32_aa(X, Z, succ_out_aa(X, Z)) -> succ_out_aa(one(X), zero(Z)) 18.16/5.61 U34_aa(X, Z, succ_out_aa(X, Z)) -> succZ_out_aa(one(X), zero(Z)) 18.16/5.61 U14_aaa(X, Z, succZ_out_aa(X, Z)) -> addc_out_aaa(X, b, Z) 18.16/5.61 addc_in_aaa(b, Y, Z) -> U15_aaa(Y, Z, succZ_in_aa(Y, Z)) 18.16/5.61 U15_aaa(Y, Z, succZ_out_aa(Y, Z)) -> addc_out_aaa(b, Y, Z) 18.16/5.61 addc_in_aaa(X, Y, Z) -> U16_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.16/5.61 addC_in_aaa(zero(X), zero(Y), one(Z)) -> U23_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.61 U23_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), zero(Y), one(Z)) 18.16/5.61 addC_in_aaa(zero(X), one(Y), zero(Z)) -> U24_aaa(X, Y, Z, addX_in_aaa(X, Y, Z)) 18.16/5.61 addX_in_aaa(zero(X), b, one(X)) -> U17_aaa(X, binaryZ_in_a(X)) 18.16/5.61 U17_aaa(X, binaryZ_out_a(X)) -> addX_out_aaa(zero(X), b, one(X)) 18.16/5.61 addX_in_aaa(one(X), b, zero(Z)) -> U18_aaa(X, Z, succ_in_aa(X, Z)) 18.16/5.61 U18_aaa(X, Z, succ_out_aa(X, Z)) -> addX_out_aaa(one(X), b, zero(Z)) 18.16/5.61 addX_in_aaa(X, Y, Z) -> U19_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.16/5.61 addC_in_aaa(one(X), zero(Y), zero(Z)) -> U25_aaa(X, Y, Z, addY_in_aaa(X, Y, Z)) 18.16/5.61 addY_in_aaa(b, zero(Y), one(Y)) -> U20_aaa(Y, binaryZ_in_a(Y)) 18.16/5.61 U20_aaa(Y, binaryZ_out_a(Y)) -> addY_out_aaa(b, zero(Y), one(Y)) 18.16/5.61 addY_in_aaa(b, one(Y), zero(Z)) -> U21_aaa(Y, Z, succ_in_aa(Y, Z)) 18.16/5.61 U21_aaa(Y, Z, succ_out_aa(Y, Z)) -> addY_out_aaa(b, one(Y), zero(Z)) 18.16/5.61 addY_in_aaa(X, Y, Z) -> U22_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.16/5.61 addC_in_aaa(one(X), one(Y), one(Z)) -> U26_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.16/5.61 U26_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), one(Y), one(Z)) 18.16/5.61 U22_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addY_out_aaa(X, Y, Z) 18.16/5.61 U25_aaa(X, Y, Z, addY_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), zero(Y), zero(Z)) 18.16/5.61 U19_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addX_out_aaa(X, Y, Z) 18.16/5.61 U24_aaa(X, Y, Z, addX_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), one(Y), zero(Z)) 18.16/5.61 U16_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addc_out_aaa(X, Y, Z) 18.16/5.61 U13_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), one(Y), zero(Z)) 18.16/5.61 U9_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addy_out_aaa(X, Y, Z) 18.16/5.61 U12_aaa(X, Y, Z, addy_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), zero(Y), one(Z)) 18.16/5.61 U6_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addx_out_aaa(X, Y, Z) 18.16/5.61 U11_aaa(X, Y, Z, addx_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), one(Y), one(Z)) 18.16/5.61 U10_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), zero(Y), zero(Z)) 18.16/5.61 U3_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> add_out_aaa(X, Y, Z) 18.16/5.61 U37_aaa(R, S, RSS, add_out_aaa(S, zero(RS), RSS)) -> times_out_aaa(one(R), S, RSS) 18.16/5.61 U35_aaa(R, S, RS, times_out_aaa(R, S, RS)) -> times_out_aaa(zero(R), S, zero(RS)) 18.16/5.61 U36_aag(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aag(R, S, RSS, add_in_aag(S, zero(RS), RSS)) 18.16/5.61 add_in_aag(b, b, b) -> add_out_aag(b, b, b) 18.16/5.61 add_in_aag(X, b, X) -> U1_aag(X, binaryZ_in_g(X)) 18.16/5.61 binaryZ_in_g(zero(X)) -> U29_g(X, binaryZ_in_g(X)) 18.16/5.61 binaryZ_in_g(one(X)) -> U30_g(X, binary_in_g(X)) 18.16/5.61 binary_in_g(b) -> binary_out_g(b) 18.16/5.61 binary_in_g(zero(X)) -> U27_g(X, binaryZ_in_g(X)) 18.16/5.61 U27_g(X, binaryZ_out_g(X)) -> binary_out_g(zero(X)) 18.16/5.61 binary_in_g(one(X)) -> U28_g(X, binary_in_g(X)) 18.16/5.61 U28_g(X, binary_out_g(X)) -> binary_out_g(one(X)) 18.16/5.61 U30_g(X, binary_out_g(X)) -> binaryZ_out_g(one(X)) 18.16/5.61 U29_g(X, binaryZ_out_g(X)) -> binaryZ_out_g(zero(X)) 18.16/5.61 U1_aag(X, binaryZ_out_g(X)) -> add_out_aag(X, b, X) 18.16/5.61 add_in_aag(b, Y, Y) -> U2_aag(Y, binaryZ_in_g(Y)) 18.16/5.61 U2_aag(Y, binaryZ_out_g(Y)) -> add_out_aag(b, Y, Y) 18.16/5.61 add_in_aag(X, Y, Z) -> U3_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.61 addz_in_aag(zero(X), zero(Y), zero(Z)) -> U10_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.61 addz_in_aag(zero(X), one(Y), one(Z)) -> U11_aag(X, Y, Z, addx_in_aag(X, Y, Z)) 18.16/5.61 addx_in_aag(one(X), b, one(X)) -> U4_aag(X, binary_in_g(X)) 18.16/5.61 U4_aag(X, binary_out_g(X)) -> addx_out_aag(one(X), b, one(X)) 18.16/5.61 addx_in_aag(zero(X), b, zero(X)) -> U5_aag(X, binaryZ_in_g(X)) 18.16/5.61 U5_aag(X, binaryZ_out_g(X)) -> addx_out_aag(zero(X), b, zero(X)) 18.16/5.61 addx_in_aag(X, Y, Z) -> U6_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.61 addz_in_aag(one(X), zero(Y), one(Z)) -> U12_aag(X, Y, Z, addy_in_aag(X, Y, Z)) 18.16/5.61 addy_in_aag(b, one(Y), one(Y)) -> U7_aag(Y, binary_in_g(Y)) 18.16/5.61 U7_aag(Y, binary_out_g(Y)) -> addy_out_aag(b, one(Y), one(Y)) 18.16/5.61 addy_in_aag(b, zero(Y), zero(Y)) -> U8_aag(Y, binaryZ_in_g(Y)) 18.16/5.61 U8_aag(Y, binaryZ_out_g(Y)) -> addy_out_aag(b, zero(Y), zero(Y)) 18.16/5.61 addy_in_aag(X, Y, Z) -> U9_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.61 addz_in_aag(one(X), one(Y), zero(Z)) -> U13_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.16/5.61 addc_in_aag(b, b, one(b)) -> addc_out_aag(b, b, one(b)) 18.16/5.61 addc_in_aag(X, b, Z) -> U14_aag(X, Z, succZ_in_ag(X, Z)) 18.16/5.61 succZ_in_ag(zero(X), one(X)) -> U33_ag(X, binaryZ_in_g(X)) 18.16/5.61 U33_ag(X, binaryZ_out_g(X)) -> succZ_out_ag(zero(X), one(X)) 18.16/5.61 succZ_in_ag(one(X), zero(Z)) -> U34_ag(X, Z, succ_in_ag(X, Z)) 18.16/5.61 succ_in_ag(b, one(b)) -> succ_out_ag(b, one(b)) 18.16/5.61 succ_in_ag(zero(X), one(X)) -> U31_ag(X, binaryZ_in_g(X)) 18.16/5.61 U31_ag(X, binaryZ_out_g(X)) -> succ_out_ag(zero(X), one(X)) 18.16/5.61 succ_in_ag(one(X), zero(Z)) -> U32_ag(X, Z, succ_in_ag(X, Z)) 18.16/5.61 U32_ag(X, Z, succ_out_ag(X, Z)) -> succ_out_ag(one(X), zero(Z)) 18.16/5.61 U34_ag(X, Z, succ_out_ag(X, Z)) -> succZ_out_ag(one(X), zero(Z)) 18.16/5.61 U14_aag(X, Z, succZ_out_ag(X, Z)) -> addc_out_aag(X, b, Z) 18.16/5.61 addc_in_aag(b, Y, Z) -> U15_aag(Y, Z, succZ_in_ag(Y, Z)) 18.16/5.61 U15_aag(Y, Z, succZ_out_ag(Y, Z)) -> addc_out_aag(b, Y, Z) 18.16/5.61 addc_in_aag(X, Y, Z) -> U16_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.16/5.61 addC_in_aag(zero(X), zero(Y), one(Z)) -> U23_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.61 U23_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), zero(Y), one(Z)) 18.16/5.61 addC_in_aag(zero(X), one(Y), zero(Z)) -> U24_aag(X, Y, Z, addX_in_aag(X, Y, Z)) 18.16/5.61 addX_in_aag(zero(X), b, one(X)) -> U17_aag(X, binaryZ_in_g(X)) 18.16/5.61 U17_aag(X, binaryZ_out_g(X)) -> addX_out_aag(zero(X), b, one(X)) 18.16/5.61 addX_in_aag(one(X), b, zero(Z)) -> U18_aag(X, Z, succ_in_ag(X, Z)) 18.16/5.61 U18_aag(X, Z, succ_out_ag(X, Z)) -> addX_out_aag(one(X), b, zero(Z)) 18.16/5.61 addX_in_aag(X, Y, Z) -> U19_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.16/5.61 addC_in_aag(one(X), zero(Y), zero(Z)) -> U25_aag(X, Y, Z, addY_in_aag(X, Y, Z)) 18.16/5.61 addY_in_aag(b, zero(Y), one(Y)) -> U20_aag(Y, binaryZ_in_g(Y)) 18.16/5.61 U20_aag(Y, binaryZ_out_g(Y)) -> addY_out_aag(b, zero(Y), one(Y)) 18.16/5.61 addY_in_aag(b, one(Y), zero(Z)) -> U21_aag(Y, Z, succ_in_ag(Y, Z)) 18.16/5.61 U21_aag(Y, Z, succ_out_ag(Y, Z)) -> addY_out_aag(b, one(Y), zero(Z)) 18.16/5.61 addY_in_aag(X, Y, Z) -> U22_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.16/5.61 addC_in_aag(one(X), one(Y), one(Z)) -> U26_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.16/5.61 U26_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addC_out_aag(one(X), one(Y), one(Z)) 18.16/5.61 U22_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addY_out_aag(X, Y, Z) 18.16/5.61 U25_aag(X, Y, Z, addY_out_aag(X, Y, Z)) -> addC_out_aag(one(X), zero(Y), zero(Z)) 18.16/5.61 U19_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addX_out_aag(X, Y, Z) 18.16/5.61 U24_aag(X, Y, Z, addX_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), one(Y), zero(Z)) 18.16/5.61 U16_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addc_out_aag(X, Y, Z) 18.16/5.61 U13_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addz_out_aag(one(X), one(Y), zero(Z)) 18.16/5.61 U9_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addy_out_aag(X, Y, Z) 18.16/5.61 U12_aag(X, Y, Z, addy_out_aag(X, Y, Z)) -> addz_out_aag(one(X), zero(Y), one(Z)) 18.16/5.61 U6_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addx_out_aag(X, Y, Z) 18.16/5.61 U11_aag(X, Y, Z, addx_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), one(Y), one(Z)) 18.16/5.61 U10_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), zero(Y), zero(Z)) 18.16/5.61 U3_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> add_out_aag(X, Y, Z) 18.16/5.61 U37_aag(R, S, RSS, add_out_aag(S, zero(RS), RSS)) -> times_out_aag(one(R), S, RSS) 18.16/5.61 U35_aag(R, S, RS, times_out_aag(R, S, RS)) -> times_out_aag(zero(R), S, zero(RS)) 18.16/5.61 18.16/5.61 The argument filtering Pi contains the following mapping: 18.16/5.61 times_in_aag(x1, x2, x3) = times_in_aag(x3) 18.16/5.61 18.16/5.61 times_out_aag(x1, x2, x3) = times_out_aag(x1, x2, x3) 18.16/5.61 18.16/5.61 zero(x1) = zero(x1) 18.16/5.61 18.16/5.61 U35_aag(x1, x2, x3, x4) = U35_aag(x3, x4) 18.16/5.61 18.16/5.61 U36_aag(x1, x2, x3, x4) = U36_aag(x3, x4) 18.16/5.61 18.16/5.61 times_in_aaa(x1, x2, x3) = times_in_aaa 18.16/5.61 18.16/5.61 times_out_aaa(x1, x2, x3) = times_out_aaa(x1) 18.16/5.61 18.16/5.61 U35_aaa(x1, x2, x3, x4) = U35_aaa(x4) 18.16/5.61 18.16/5.61 U36_aaa(x1, x2, x3, x4) = U36_aaa(x4) 18.16/5.61 18.16/5.61 U37_aaa(x1, x2, x3, x4) = U37_aaa(x1, x4) 18.16/5.61 18.16/5.61 add_in_aaa(x1, x2, x3) = add_in_aaa 18.16/5.61 18.16/5.61 add_out_aaa(x1, x2, x3) = add_out_aaa(x1, x2, x3) 18.16/5.61 18.16/5.61 U1_aaa(x1, x2) = U1_aaa(x2) 18.16/5.61 18.16/5.61 binaryZ_in_a(x1) = binaryZ_in_a 18.16/5.61 18.16/5.61 U29_a(x1, x2) = U29_a(x2) 18.16/5.61 18.16/5.61 U30_a(x1, x2) = U30_a(x2) 18.16/5.61 18.16/5.61 binary_in_a(x1) = binary_in_a 18.16/5.61 18.16/5.61 binary_out_a(x1) = binary_out_a(x1) 18.16/5.61 18.16/5.61 U27_a(x1, x2) = U27_a(x2) 18.16/5.61 18.16/5.61 binaryZ_out_a(x1) = binaryZ_out_a(x1) 18.16/5.61 18.16/5.61 U28_a(x1, x2) = U28_a(x2) 18.16/5.61 18.16/5.61 U2_aaa(x1, x2) = U2_aaa(x2) 18.16/5.61 18.16/5.61 U3_aaa(x1, x2, x3, x4) = U3_aaa(x4) 18.16/5.61 18.16/5.61 addz_in_aaa(x1, x2, x3) = addz_in_aaa 18.16/5.61 18.16/5.61 U10_aaa(x1, x2, x3, x4) = U10_aaa(x4) 18.16/5.61 18.16/5.61 U11_aaa(x1, x2, x3, x4) = U11_aaa(x4) 18.16/5.61 18.16/5.61 addx_in_aaa(x1, x2, x3) = addx_in_aaa 18.16/5.61 18.16/5.61 U4_aaa(x1, x2) = U4_aaa(x2) 18.16/5.61 18.16/5.61 addx_out_aaa(x1, x2, x3) = addx_out_aaa(x1, x2, x3) 18.16/5.61 18.16/5.61 U5_aaa(x1, x2) = U5_aaa(x2) 18.16/5.61 18.16/5.61 U6_aaa(x1, x2, x3, x4) = U6_aaa(x4) 18.16/5.61 18.16/5.61 U12_aaa(x1, x2, x3, x4) = U12_aaa(x4) 18.16/5.61 18.16/5.61 addy_in_aaa(x1, x2, x3) = addy_in_aaa 18.16/5.61 18.16/5.61 U7_aaa(x1, x2) = U7_aaa(x2) 18.16/5.61 18.16/5.61 addy_out_aaa(x1, x2, x3) = addy_out_aaa(x1, x2, x3) 18.16/5.61 18.16/5.61 U8_aaa(x1, x2) = U8_aaa(x2) 18.16/5.61 18.16/5.61 U9_aaa(x1, x2, x3, x4) = U9_aaa(x4) 18.16/5.61 18.16/5.61 U13_aaa(x1, x2, x3, x4) = U13_aaa(x4) 18.16/5.61 18.16/5.61 addc_in_aaa(x1, x2, x3) = addc_in_aaa 18.16/5.61 18.16/5.61 addc_out_aaa(x1, x2, x3) = addc_out_aaa(x1, x2, x3) 18.16/5.61 18.16/5.61 U14_aaa(x1, x2, x3) = U14_aaa(x3) 18.16/5.61 18.16/5.61 succZ_in_aa(x1, x2) = succZ_in_aa 18.16/5.61 18.16/5.61 U33_aa(x1, x2) = U33_aa(x2) 18.16/5.61 18.16/5.61 succZ_out_aa(x1, x2) = succZ_out_aa(x1, x2) 18.16/5.61 18.16/5.61 U34_aa(x1, x2, x3) = U34_aa(x3) 18.16/5.61 18.16/5.61 succ_in_aa(x1, x2) = succ_in_aa 18.16/5.61 18.16/5.61 succ_out_aa(x1, x2) = succ_out_aa(x1, x2) 18.16/5.61 18.16/5.61 U31_aa(x1, x2) = U31_aa(x2) 18.16/5.61 18.16/5.61 U32_aa(x1, x2, x3) = U32_aa(x3) 18.16/5.61 18.16/5.61 U15_aaa(x1, x2, x3) = U15_aaa(x3) 18.16/5.61 18.16/5.61 U16_aaa(x1, x2, x3, x4) = U16_aaa(x4) 18.16/5.61 18.16/5.61 addC_in_aaa(x1, x2, x3) = addC_in_aaa 18.16/5.61 18.16/5.61 U23_aaa(x1, x2, x3, x4) = U23_aaa(x4) 18.16/5.61 18.16/5.61 addz_out_aaa(x1, x2, x3) = addz_out_aaa(x1, x2, x3) 18.16/5.61 18.16/5.61 addC_out_aaa(x1, x2, x3) = addC_out_aaa(x1, x2, x3) 18.16/5.61 18.16/5.61 U24_aaa(x1, x2, x3, x4) = U24_aaa(x4) 18.16/5.61 18.16/5.61 addX_in_aaa(x1, x2, x3) = addX_in_aaa 18.16/5.61 18.16/5.61 U17_aaa(x1, x2) = U17_aaa(x2) 18.16/5.61 18.16/5.61 addX_out_aaa(x1, x2, x3) = addX_out_aaa(x1, x2, x3) 18.16/5.61 18.16/5.61 U18_aaa(x1, x2, x3) = U18_aaa(x3) 18.16/5.61 18.16/5.61 U19_aaa(x1, x2, x3, x4) = U19_aaa(x4) 18.16/5.61 18.16/5.61 U25_aaa(x1, x2, x3, x4) = U25_aaa(x4) 18.16/5.61 18.16/5.61 addY_in_aaa(x1, x2, x3) = addY_in_aaa 18.16/5.61 18.16/5.61 U20_aaa(x1, x2) = U20_aaa(x2) 18.16/5.61 18.16/5.61 addY_out_aaa(x1, x2, x3) = addY_out_aaa(x1, x2, x3) 18.16/5.61 18.16/5.61 U21_aaa(x1, x2, x3) = U21_aaa(x3) 18.16/5.61 18.16/5.61 U22_aaa(x1, x2, x3, x4) = U22_aaa(x4) 18.16/5.61 18.16/5.61 U26_aaa(x1, x2, x3, x4) = U26_aaa(x4) 18.16/5.61 18.16/5.61 U37_aag(x1, x2, x3, x4) = U37_aag(x1, x3, x4) 18.16/5.61 18.16/5.61 add_in_aag(x1, x2, x3) = add_in_aag(x3) 18.16/5.61 18.16/5.61 b = b 18.16/5.61 18.16/5.61 add_out_aag(x1, x2, x3) = add_out_aag(x1, x2, x3) 18.16/5.61 18.16/5.61 U1_aag(x1, x2) = U1_aag(x1, x2) 18.16/5.61 18.16/5.61 binaryZ_in_g(x1) = binaryZ_in_g(x1) 18.16/5.61 18.16/5.61 U29_g(x1, x2) = U29_g(x1, x2) 18.16/5.61 18.16/5.61 one(x1) = one(x1) 18.16/5.61 18.16/5.61 U30_g(x1, x2) = U30_g(x1, x2) 18.16/5.61 18.16/5.61 binary_in_g(x1) = binary_in_g(x1) 18.16/5.61 18.16/5.61 binary_out_g(x1) = binary_out_g(x1) 18.16/5.61 18.16/5.61 U27_g(x1, x2) = U27_g(x1, x2) 18.16/5.61 18.16/5.61 binaryZ_out_g(x1) = binaryZ_out_g(x1) 18.16/5.61 18.16/5.61 U28_g(x1, x2) = U28_g(x1, x2) 18.16/5.61 18.16/5.61 U2_aag(x1, x2) = U2_aag(x1, x2) 18.16/5.61 18.16/5.61 U3_aag(x1, x2, x3, x4) = U3_aag(x3, x4) 18.16/5.61 18.16/5.61 addz_in_aag(x1, x2, x3) = addz_in_aag(x3) 18.16/5.61 18.16/5.61 U10_aag(x1, x2, x3, x4) = U10_aag(x3, x4) 18.16/5.61 18.16/5.61 U11_aag(x1, x2, x3, x4) = U11_aag(x3, x4) 18.16/5.61 18.16/5.61 addx_in_aag(x1, x2, x3) = addx_in_aag(x3) 18.16/5.61 18.16/5.61 U4_aag(x1, x2) = U4_aag(x1, x2) 18.16/5.61 18.16/5.61 addx_out_aag(x1, x2, x3) = addx_out_aag(x1, x2, x3) 18.16/5.61 18.16/5.61 U5_aag(x1, x2) = U5_aag(x1, x2) 18.16/5.61 18.16/5.61 U6_aag(x1, x2, x3, x4) = U6_aag(x3, x4) 18.16/5.61 18.16/5.61 U12_aag(x1, x2, x3, x4) = U12_aag(x3, x4) 18.16/5.61 18.16/5.61 addy_in_aag(x1, x2, x3) = addy_in_aag(x3) 18.16/5.61 18.16/5.61 U7_aag(x1, x2) = U7_aag(x1, x2) 18.16/5.61 18.16/5.61 addy_out_aag(x1, x2, x3) = addy_out_aag(x1, x2, x3) 18.16/5.61 18.16/5.61 U8_aag(x1, x2) = U8_aag(x1, x2) 18.16/5.61 18.16/5.61 U9_aag(x1, x2, x3, x4) = U9_aag(x3, x4) 18.16/5.61 18.16/5.61 U13_aag(x1, x2, x3, x4) = U13_aag(x3, x4) 18.16/5.61 18.16/5.61 addc_in_aag(x1, x2, x3) = addc_in_aag(x3) 18.16/5.61 18.16/5.61 addc_out_aag(x1, x2, x3) = addc_out_aag(x1, x2, x3) 18.16/5.61 18.16/5.61 U14_aag(x1, x2, x3) = U14_aag(x2, x3) 18.16/5.61 18.16/5.61 succZ_in_ag(x1, x2) = succZ_in_ag(x2) 18.16/5.61 18.16/5.61 U33_ag(x1, x2) = U33_ag(x1, x2) 18.16/5.61 18.16/5.61 succZ_out_ag(x1, x2) = succZ_out_ag(x1, x2) 18.16/5.61 18.16/5.61 U34_ag(x1, x2, x3) = U34_ag(x2, x3) 18.16/5.61 18.16/5.61 succ_in_ag(x1, x2) = succ_in_ag(x2) 18.16/5.61 18.16/5.61 succ_out_ag(x1, x2) = succ_out_ag(x1, x2) 18.16/5.61 18.16/5.61 U31_ag(x1, x2) = U31_ag(x1, x2) 18.16/5.61 18.16/5.61 U32_ag(x1, x2, x3) = U32_ag(x2, x3) 18.16/5.61 18.16/5.61 U15_aag(x1, x2, x3) = U15_aag(x2, x3) 18.16/5.61 18.16/5.61 U16_aag(x1, x2, x3, x4) = U16_aag(x3, x4) 18.16/5.61 18.16/5.61 addC_in_aag(x1, x2, x3) = addC_in_aag(x3) 18.16/5.61 18.16/5.61 U23_aag(x1, x2, x3, x4) = U23_aag(x3, x4) 18.16/5.61 18.16/5.61 addz_out_aag(x1, x2, x3) = addz_out_aag(x1, x2, x3) 18.16/5.61 18.16/5.61 addC_out_aag(x1, x2, x3) = addC_out_aag(x1, x2, x3) 18.16/5.61 18.16/5.61 U24_aag(x1, x2, x3, x4) = U24_aag(x3, x4) 18.16/5.61 18.16/5.61 addX_in_aag(x1, x2, x3) = addX_in_aag(x3) 18.16/5.61 18.16/5.61 U17_aag(x1, x2) = U17_aag(x1, x2) 18.16/5.61 18.16/5.61 addX_out_aag(x1, x2, x3) = addX_out_aag(x1, x2, x3) 18.16/5.61 18.16/5.61 U18_aag(x1, x2, x3) = U18_aag(x2, x3) 18.16/5.61 18.16/5.61 U19_aag(x1, x2, x3, x4) = U19_aag(x3, x4) 18.16/5.61 18.16/5.61 U25_aag(x1, x2, x3, x4) = U25_aag(x3, x4) 18.16/5.61 18.16/5.61 addY_in_aag(x1, x2, x3) = addY_in_aag(x3) 18.16/5.61 18.16/5.61 U20_aag(x1, x2) = U20_aag(x1, x2) 18.16/5.61 18.16/5.61 addY_out_aag(x1, x2, x3) = addY_out_aag(x1, x2, x3) 18.16/5.61 18.16/5.61 U21_aag(x1, x2, x3) = U21_aag(x2, x3) 18.16/5.61 18.16/5.61 U22_aag(x1, x2, x3, x4) = U22_aag(x3, x4) 18.16/5.61 18.16/5.61 U26_aag(x1, x2, x3, x4) = U26_aag(x3, x4) 18.16/5.61 18.16/5.61 18.16/5.61 18.16/5.61 ---------------------------------------- 18.16/5.61 18.16/5.61 (3) DependencyPairsProof (EQUIVALENT) 18.16/5.61 Using Dependency Pairs [AG00,LOPSTR] we result in the following initial DP problem: 18.16/5.61 Pi DP problem: 18.16/5.61 The TRS P consists of the following rules: 18.16/5.61 18.16/5.61 TIMES_IN_AAG(zero(R), S, zero(RS)) -> U35_AAG(R, S, RS, times_in_aag(R, S, RS)) 18.16/5.61 TIMES_IN_AAG(zero(R), S, zero(RS)) -> TIMES_IN_AAG(R, S, RS) 18.16/5.61 TIMES_IN_AAG(one(R), S, RSS) -> U36_AAG(R, S, RSS, times_in_aaa(R, S, RS)) 18.16/5.61 TIMES_IN_AAG(one(R), S, RSS) -> TIMES_IN_AAA(R, S, RS) 18.16/5.61 TIMES_IN_AAA(zero(R), S, zero(RS)) -> U35_AAA(R, S, RS, times_in_aaa(R, S, RS)) 18.16/5.61 TIMES_IN_AAA(zero(R), S, zero(RS)) -> TIMES_IN_AAA(R, S, RS) 18.16/5.61 TIMES_IN_AAA(one(R), S, RSS) -> U36_AAA(R, S, RSS, times_in_aaa(R, S, RS)) 18.16/5.61 TIMES_IN_AAA(one(R), S, RSS) -> TIMES_IN_AAA(R, S, RS) 18.16/5.61 U36_AAA(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_AAA(R, S, RSS, add_in_aaa(S, zero(RS), RSS)) 18.16/5.61 U36_AAA(R, S, RSS, times_out_aaa(R, S, RS)) -> ADD_IN_AAA(S, zero(RS), RSS) 18.16/5.61 ADD_IN_AAA(X, b, X) -> U1_AAA(X, binaryZ_in_a(X)) 18.16/5.61 ADD_IN_AAA(X, b, X) -> BINARYZ_IN_A(X) 18.16/5.61 BINARYZ_IN_A(zero(X)) -> U29_A(X, binaryZ_in_a(X)) 18.16/5.61 BINARYZ_IN_A(zero(X)) -> BINARYZ_IN_A(X) 18.16/5.61 BINARYZ_IN_A(one(X)) -> U30_A(X, binary_in_a(X)) 18.16/5.61 BINARYZ_IN_A(one(X)) -> BINARY_IN_A(X) 18.16/5.61 BINARY_IN_A(zero(X)) -> U27_A(X, binaryZ_in_a(X)) 18.16/5.61 BINARY_IN_A(zero(X)) -> BINARYZ_IN_A(X) 18.16/5.61 BINARY_IN_A(one(X)) -> U28_A(X, binary_in_a(X)) 18.16/5.61 BINARY_IN_A(one(X)) -> BINARY_IN_A(X) 18.16/5.61 ADD_IN_AAA(b, Y, Y) -> U2_AAA(Y, binaryZ_in_a(Y)) 18.16/5.61 ADD_IN_AAA(b, Y, Y) -> BINARYZ_IN_A(Y) 18.16/5.61 ADD_IN_AAA(X, Y, Z) -> U3_AAA(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.61 ADD_IN_AAA(X, Y, Z) -> ADDZ_IN_AAA(X, Y, Z) 18.16/5.61 ADDZ_IN_AAA(zero(X), zero(Y), zero(Z)) -> U10_AAA(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.61 ADDZ_IN_AAA(zero(X), zero(Y), zero(Z)) -> ADDZ_IN_AAA(X, Y, Z) 18.16/5.61 ADDZ_IN_AAA(zero(X), one(Y), one(Z)) -> U11_AAA(X, Y, Z, addx_in_aaa(X, Y, Z)) 18.16/5.61 ADDZ_IN_AAA(zero(X), one(Y), one(Z)) -> ADDX_IN_AAA(X, Y, Z) 18.16/5.61 ADDX_IN_AAA(one(X), b, one(X)) -> U4_AAA(X, binary_in_a(X)) 18.16/5.61 ADDX_IN_AAA(one(X), b, one(X)) -> BINARY_IN_A(X) 18.16/5.61 ADDX_IN_AAA(zero(X), b, zero(X)) -> U5_AAA(X, binaryZ_in_a(X)) 18.16/5.61 ADDX_IN_AAA(zero(X), b, zero(X)) -> BINARYZ_IN_A(X) 18.16/5.61 ADDX_IN_AAA(X, Y, Z) -> U6_AAA(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.61 ADDX_IN_AAA(X, Y, Z) -> ADDZ_IN_AAA(X, Y, Z) 18.16/5.61 ADDZ_IN_AAA(one(X), zero(Y), one(Z)) -> U12_AAA(X, Y, Z, addy_in_aaa(X, Y, Z)) 18.16/5.61 ADDZ_IN_AAA(one(X), zero(Y), one(Z)) -> ADDY_IN_AAA(X, Y, Z) 18.16/5.61 ADDY_IN_AAA(b, one(Y), one(Y)) -> U7_AAA(Y, binary_in_a(Y)) 18.16/5.61 ADDY_IN_AAA(b, one(Y), one(Y)) -> BINARY_IN_A(Y) 18.16/5.61 ADDY_IN_AAA(b, zero(Y), zero(Y)) -> U8_AAA(Y, binaryZ_in_a(Y)) 18.16/5.61 ADDY_IN_AAA(b, zero(Y), zero(Y)) -> BINARYZ_IN_A(Y) 18.16/5.61 ADDY_IN_AAA(X, Y, Z) -> U9_AAA(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.61 ADDY_IN_AAA(X, Y, Z) -> ADDZ_IN_AAA(X, Y, Z) 18.16/5.61 ADDZ_IN_AAA(one(X), one(Y), zero(Z)) -> U13_AAA(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.16/5.61 ADDZ_IN_AAA(one(X), one(Y), zero(Z)) -> ADDC_IN_AAA(X, Y, Z) 18.16/5.61 ADDC_IN_AAA(X, b, Z) -> U14_AAA(X, Z, succZ_in_aa(X, Z)) 18.16/5.61 ADDC_IN_AAA(X, b, Z) -> SUCCZ_IN_AA(X, Z) 18.16/5.61 SUCCZ_IN_AA(zero(X), one(X)) -> U33_AA(X, binaryZ_in_a(X)) 18.16/5.61 SUCCZ_IN_AA(zero(X), one(X)) -> BINARYZ_IN_A(X) 18.16/5.61 SUCCZ_IN_AA(one(X), zero(Z)) -> U34_AA(X, Z, succ_in_aa(X, Z)) 18.16/5.61 SUCCZ_IN_AA(one(X), zero(Z)) -> SUCC_IN_AA(X, Z) 18.16/5.61 SUCC_IN_AA(zero(X), one(X)) -> U31_AA(X, binaryZ_in_a(X)) 18.16/5.61 SUCC_IN_AA(zero(X), one(X)) -> BINARYZ_IN_A(X) 18.16/5.61 SUCC_IN_AA(one(X), zero(Z)) -> U32_AA(X, Z, succ_in_aa(X, Z)) 18.16/5.61 SUCC_IN_AA(one(X), zero(Z)) -> SUCC_IN_AA(X, Z) 18.16/5.61 ADDC_IN_AAA(b, Y, Z) -> U15_AAA(Y, Z, succZ_in_aa(Y, Z)) 18.16/5.61 ADDC_IN_AAA(b, Y, Z) -> SUCCZ_IN_AA(Y, Z) 18.16/5.61 ADDC_IN_AAA(X, Y, Z) -> U16_AAA(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.16/5.61 ADDC_IN_AAA(X, Y, Z) -> ADDC_IN_AAA^1(X, Y, Z) 18.16/5.61 ADDC_IN_AAA^1(zero(X), zero(Y), one(Z)) -> U23_AAA(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.61 ADDC_IN_AAA^1(zero(X), zero(Y), one(Z)) -> ADDZ_IN_AAA(X, Y, Z) 18.16/5.61 ADDC_IN_AAA^1(zero(X), one(Y), zero(Z)) -> U24_AAA(X, Y, Z, addX_in_aaa(X, Y, Z)) 18.16/5.61 ADDC_IN_AAA^1(zero(X), one(Y), zero(Z)) -> ADDX_IN_AAA^1(X, Y, Z) 18.16/5.61 ADDX_IN_AAA^1(zero(X), b, one(X)) -> U17_AAA(X, binaryZ_in_a(X)) 18.16/5.61 ADDX_IN_AAA^1(zero(X), b, one(X)) -> BINARYZ_IN_A(X) 18.16/5.61 ADDX_IN_AAA^1(one(X), b, zero(Z)) -> U18_AAA(X, Z, succ_in_aa(X, Z)) 18.16/5.61 ADDX_IN_AAA^1(one(X), b, zero(Z)) -> SUCC_IN_AA(X, Z) 18.16/5.61 ADDX_IN_AAA^1(X, Y, Z) -> U19_AAA(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.16/5.61 ADDX_IN_AAA^1(X, Y, Z) -> ADDC_IN_AAA^1(X, Y, Z) 18.16/5.61 ADDC_IN_AAA^1(one(X), zero(Y), zero(Z)) -> U25_AAA(X, Y, Z, addY_in_aaa(X, Y, Z)) 18.16/5.61 ADDC_IN_AAA^1(one(X), zero(Y), zero(Z)) -> ADDY_IN_AAA^1(X, Y, Z) 18.16/5.61 ADDY_IN_AAA^1(b, zero(Y), one(Y)) -> U20_AAA(Y, binaryZ_in_a(Y)) 18.16/5.61 ADDY_IN_AAA^1(b, zero(Y), one(Y)) -> BINARYZ_IN_A(Y) 18.16/5.61 ADDY_IN_AAA^1(b, one(Y), zero(Z)) -> U21_AAA(Y, Z, succ_in_aa(Y, Z)) 18.16/5.61 ADDY_IN_AAA^1(b, one(Y), zero(Z)) -> SUCC_IN_AA(Y, Z) 18.16/5.61 ADDY_IN_AAA^1(X, Y, Z) -> U22_AAA(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.16/5.61 ADDY_IN_AAA^1(X, Y, Z) -> ADDC_IN_AAA^1(X, Y, Z) 18.16/5.61 ADDC_IN_AAA^1(one(X), one(Y), one(Z)) -> U26_AAA(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.16/5.61 ADDC_IN_AAA^1(one(X), one(Y), one(Z)) -> ADDC_IN_AAA(X, Y, Z) 18.16/5.61 U36_AAG(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_AAG(R, S, RSS, add_in_aag(S, zero(RS), RSS)) 18.16/5.61 U36_AAG(R, S, RSS, times_out_aaa(R, S, RS)) -> ADD_IN_AAG(S, zero(RS), RSS) 18.16/5.61 ADD_IN_AAG(X, b, X) -> U1_AAG(X, binaryZ_in_g(X)) 18.16/5.61 ADD_IN_AAG(X, b, X) -> BINARYZ_IN_G(X) 18.16/5.61 BINARYZ_IN_G(zero(X)) -> U29_G(X, binaryZ_in_g(X)) 18.16/5.61 BINARYZ_IN_G(zero(X)) -> BINARYZ_IN_G(X) 18.16/5.61 BINARYZ_IN_G(one(X)) -> U30_G(X, binary_in_g(X)) 18.16/5.61 BINARYZ_IN_G(one(X)) -> BINARY_IN_G(X) 18.16/5.61 BINARY_IN_G(zero(X)) -> U27_G(X, binaryZ_in_g(X)) 18.16/5.61 BINARY_IN_G(zero(X)) -> BINARYZ_IN_G(X) 18.16/5.61 BINARY_IN_G(one(X)) -> U28_G(X, binary_in_g(X)) 18.16/5.61 BINARY_IN_G(one(X)) -> BINARY_IN_G(X) 18.16/5.61 ADD_IN_AAG(b, Y, Y) -> U2_AAG(Y, binaryZ_in_g(Y)) 18.16/5.61 ADD_IN_AAG(b, Y, Y) -> BINARYZ_IN_G(Y) 18.16/5.61 ADD_IN_AAG(X, Y, Z) -> U3_AAG(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.61 ADD_IN_AAG(X, Y, Z) -> ADDZ_IN_AAG(X, Y, Z) 18.16/5.61 ADDZ_IN_AAG(zero(X), zero(Y), zero(Z)) -> U10_AAG(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.61 ADDZ_IN_AAG(zero(X), zero(Y), zero(Z)) -> ADDZ_IN_AAG(X, Y, Z) 18.16/5.61 ADDZ_IN_AAG(zero(X), one(Y), one(Z)) -> U11_AAG(X, Y, Z, addx_in_aag(X, Y, Z)) 18.16/5.61 ADDZ_IN_AAG(zero(X), one(Y), one(Z)) -> ADDX_IN_AAG(X, Y, Z) 18.16/5.61 ADDX_IN_AAG(one(X), b, one(X)) -> U4_AAG(X, binary_in_g(X)) 18.16/5.61 ADDX_IN_AAG(one(X), b, one(X)) -> BINARY_IN_G(X) 18.16/5.61 ADDX_IN_AAG(zero(X), b, zero(X)) -> U5_AAG(X, binaryZ_in_g(X)) 18.16/5.61 ADDX_IN_AAG(zero(X), b, zero(X)) -> BINARYZ_IN_G(X) 18.16/5.61 ADDX_IN_AAG(X, Y, Z) -> U6_AAG(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.61 ADDX_IN_AAG(X, Y, Z) -> ADDZ_IN_AAG(X, Y, Z) 18.16/5.61 ADDZ_IN_AAG(one(X), zero(Y), one(Z)) -> U12_AAG(X, Y, Z, addy_in_aag(X, Y, Z)) 18.16/5.61 ADDZ_IN_AAG(one(X), zero(Y), one(Z)) -> ADDY_IN_AAG(X, Y, Z) 18.16/5.61 ADDY_IN_AAG(b, one(Y), one(Y)) -> U7_AAG(Y, binary_in_g(Y)) 18.16/5.61 ADDY_IN_AAG(b, one(Y), one(Y)) -> BINARY_IN_G(Y) 18.16/5.61 ADDY_IN_AAG(b, zero(Y), zero(Y)) -> U8_AAG(Y, binaryZ_in_g(Y)) 18.16/5.61 ADDY_IN_AAG(b, zero(Y), zero(Y)) -> BINARYZ_IN_G(Y) 18.16/5.61 ADDY_IN_AAG(X, Y, Z) -> U9_AAG(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.61 ADDY_IN_AAG(X, Y, Z) -> ADDZ_IN_AAG(X, Y, Z) 18.16/5.61 ADDZ_IN_AAG(one(X), one(Y), zero(Z)) -> U13_AAG(X, Y, Z, addc_in_aag(X, Y, Z)) 18.16/5.61 ADDZ_IN_AAG(one(X), one(Y), zero(Z)) -> ADDC_IN_AAG(X, Y, Z) 18.16/5.61 ADDC_IN_AAG(X, b, Z) -> U14_AAG(X, Z, succZ_in_ag(X, Z)) 18.16/5.61 ADDC_IN_AAG(X, b, Z) -> SUCCZ_IN_AG(X, Z) 18.16/5.61 SUCCZ_IN_AG(zero(X), one(X)) -> U33_AG(X, binaryZ_in_g(X)) 18.16/5.61 SUCCZ_IN_AG(zero(X), one(X)) -> BINARYZ_IN_G(X) 18.16/5.61 SUCCZ_IN_AG(one(X), zero(Z)) -> U34_AG(X, Z, succ_in_ag(X, Z)) 18.16/5.61 SUCCZ_IN_AG(one(X), zero(Z)) -> SUCC_IN_AG(X, Z) 18.16/5.61 SUCC_IN_AG(zero(X), one(X)) -> U31_AG(X, binaryZ_in_g(X)) 18.16/5.61 SUCC_IN_AG(zero(X), one(X)) -> BINARYZ_IN_G(X) 18.16/5.61 SUCC_IN_AG(one(X), zero(Z)) -> U32_AG(X, Z, succ_in_ag(X, Z)) 18.16/5.61 SUCC_IN_AG(one(X), zero(Z)) -> SUCC_IN_AG(X, Z) 18.16/5.61 ADDC_IN_AAG(b, Y, Z) -> U15_AAG(Y, Z, succZ_in_ag(Y, Z)) 18.16/5.61 ADDC_IN_AAG(b, Y, Z) -> SUCCZ_IN_AG(Y, Z) 18.16/5.61 ADDC_IN_AAG(X, Y, Z) -> U16_AAG(X, Y, Z, addC_in_aag(X, Y, Z)) 18.16/5.61 ADDC_IN_AAG(X, Y, Z) -> ADDC_IN_AAG^1(X, Y, Z) 18.16/5.61 ADDC_IN_AAG^1(zero(X), zero(Y), one(Z)) -> U23_AAG(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.61 ADDC_IN_AAG^1(zero(X), zero(Y), one(Z)) -> ADDZ_IN_AAG(X, Y, Z) 18.16/5.61 ADDC_IN_AAG^1(zero(X), one(Y), zero(Z)) -> U24_AAG(X, Y, Z, addX_in_aag(X, Y, Z)) 18.16/5.61 ADDC_IN_AAG^1(zero(X), one(Y), zero(Z)) -> ADDX_IN_AAG^1(X, Y, Z) 18.16/5.61 ADDX_IN_AAG^1(zero(X), b, one(X)) -> U17_AAG(X, binaryZ_in_g(X)) 18.16/5.61 ADDX_IN_AAG^1(zero(X), b, one(X)) -> BINARYZ_IN_G(X) 18.16/5.61 ADDX_IN_AAG^1(one(X), b, zero(Z)) -> U18_AAG(X, Z, succ_in_ag(X, Z)) 18.16/5.61 ADDX_IN_AAG^1(one(X), b, zero(Z)) -> SUCC_IN_AG(X, Z) 18.16/5.61 ADDX_IN_AAG^1(X, Y, Z) -> U19_AAG(X, Y, Z, addC_in_aag(X, Y, Z)) 18.16/5.61 ADDX_IN_AAG^1(X, Y, Z) -> ADDC_IN_AAG^1(X, Y, Z) 18.16/5.61 ADDC_IN_AAG^1(one(X), zero(Y), zero(Z)) -> U25_AAG(X, Y, Z, addY_in_aag(X, Y, Z)) 18.16/5.61 ADDC_IN_AAG^1(one(X), zero(Y), zero(Z)) -> ADDY_IN_AAG^1(X, Y, Z) 18.16/5.61 ADDY_IN_AAG^1(b, zero(Y), one(Y)) -> U20_AAG(Y, binaryZ_in_g(Y)) 18.16/5.61 ADDY_IN_AAG^1(b, zero(Y), one(Y)) -> BINARYZ_IN_G(Y) 18.16/5.61 ADDY_IN_AAG^1(b, one(Y), zero(Z)) -> U21_AAG(Y, Z, succ_in_ag(Y, Z)) 18.16/5.61 ADDY_IN_AAG^1(b, one(Y), zero(Z)) -> SUCC_IN_AG(Y, Z) 18.16/5.61 ADDY_IN_AAG^1(X, Y, Z) -> U22_AAG(X, Y, Z, addC_in_aag(X, Y, Z)) 18.16/5.61 ADDY_IN_AAG^1(X, Y, Z) -> ADDC_IN_AAG^1(X, Y, Z) 18.16/5.61 ADDC_IN_AAG^1(one(X), one(Y), one(Z)) -> U26_AAG(X, Y, Z, addc_in_aag(X, Y, Z)) 18.16/5.61 ADDC_IN_AAG^1(one(X), one(Y), one(Z)) -> ADDC_IN_AAG(X, Y, Z) 18.16/5.61 18.16/5.61 The TRS R consists of the following rules: 18.16/5.61 18.16/5.61 times_in_aag(one(b), X, X) -> times_out_aag(one(b), X, X) 18.16/5.61 times_in_aag(zero(R), S, zero(RS)) -> U35_aag(R, S, RS, times_in_aag(R, S, RS)) 18.16/5.61 times_in_aag(one(R), S, RSS) -> U36_aag(R, S, RSS, times_in_aaa(R, S, RS)) 18.16/5.61 times_in_aaa(one(b), X, X) -> times_out_aaa(one(b), X, X) 18.16/5.61 times_in_aaa(zero(R), S, zero(RS)) -> U35_aaa(R, S, RS, times_in_aaa(R, S, RS)) 18.16/5.61 times_in_aaa(one(R), S, RSS) -> U36_aaa(R, S, RSS, times_in_aaa(R, S, RS)) 18.16/5.61 U36_aaa(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aaa(R, S, RSS, add_in_aaa(S, zero(RS), RSS)) 18.16/5.61 add_in_aaa(b, b, b) -> add_out_aaa(b, b, b) 18.16/5.61 add_in_aaa(X, b, X) -> U1_aaa(X, binaryZ_in_a(X)) 18.16/5.61 binaryZ_in_a(zero(X)) -> U29_a(X, binaryZ_in_a(X)) 18.16/5.61 binaryZ_in_a(one(X)) -> U30_a(X, binary_in_a(X)) 18.16/5.61 binary_in_a(b) -> binary_out_a(b) 18.16/5.61 binary_in_a(zero(X)) -> U27_a(X, binaryZ_in_a(X)) 18.16/5.61 U27_a(X, binaryZ_out_a(X)) -> binary_out_a(zero(X)) 18.16/5.61 binary_in_a(one(X)) -> U28_a(X, binary_in_a(X)) 18.16/5.61 U28_a(X, binary_out_a(X)) -> binary_out_a(one(X)) 18.16/5.61 U30_a(X, binary_out_a(X)) -> binaryZ_out_a(one(X)) 18.16/5.61 U29_a(X, binaryZ_out_a(X)) -> binaryZ_out_a(zero(X)) 18.16/5.61 U1_aaa(X, binaryZ_out_a(X)) -> add_out_aaa(X, b, X) 18.16/5.61 add_in_aaa(b, Y, Y) -> U2_aaa(Y, binaryZ_in_a(Y)) 18.16/5.61 U2_aaa(Y, binaryZ_out_a(Y)) -> add_out_aaa(b, Y, Y) 18.16/5.61 add_in_aaa(X, Y, Z) -> U3_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.61 addz_in_aaa(zero(X), zero(Y), zero(Z)) -> U10_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.61 addz_in_aaa(zero(X), one(Y), one(Z)) -> U11_aaa(X, Y, Z, addx_in_aaa(X, Y, Z)) 18.16/5.61 addx_in_aaa(one(X), b, one(X)) -> U4_aaa(X, binary_in_a(X)) 18.16/5.61 U4_aaa(X, binary_out_a(X)) -> addx_out_aaa(one(X), b, one(X)) 18.16/5.61 addx_in_aaa(zero(X), b, zero(X)) -> U5_aaa(X, binaryZ_in_a(X)) 18.16/5.61 U5_aaa(X, binaryZ_out_a(X)) -> addx_out_aaa(zero(X), b, zero(X)) 18.16/5.61 addx_in_aaa(X, Y, Z) -> U6_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.61 addz_in_aaa(one(X), zero(Y), one(Z)) -> U12_aaa(X, Y, Z, addy_in_aaa(X, Y, Z)) 18.16/5.61 addy_in_aaa(b, one(Y), one(Y)) -> U7_aaa(Y, binary_in_a(Y)) 18.16/5.61 U7_aaa(Y, binary_out_a(Y)) -> addy_out_aaa(b, one(Y), one(Y)) 18.16/5.61 addy_in_aaa(b, zero(Y), zero(Y)) -> U8_aaa(Y, binaryZ_in_a(Y)) 18.16/5.61 U8_aaa(Y, binaryZ_out_a(Y)) -> addy_out_aaa(b, zero(Y), zero(Y)) 18.16/5.61 addy_in_aaa(X, Y, Z) -> U9_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.61 addz_in_aaa(one(X), one(Y), zero(Z)) -> U13_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.16/5.61 addc_in_aaa(b, b, one(b)) -> addc_out_aaa(b, b, one(b)) 18.16/5.61 addc_in_aaa(X, b, Z) -> U14_aaa(X, Z, succZ_in_aa(X, Z)) 18.16/5.61 succZ_in_aa(zero(X), one(X)) -> U33_aa(X, binaryZ_in_a(X)) 18.16/5.61 U33_aa(X, binaryZ_out_a(X)) -> succZ_out_aa(zero(X), one(X)) 18.16/5.61 succZ_in_aa(one(X), zero(Z)) -> U34_aa(X, Z, succ_in_aa(X, Z)) 18.16/5.61 succ_in_aa(b, one(b)) -> succ_out_aa(b, one(b)) 18.16/5.61 succ_in_aa(zero(X), one(X)) -> U31_aa(X, binaryZ_in_a(X)) 18.16/5.61 U31_aa(X, binaryZ_out_a(X)) -> succ_out_aa(zero(X), one(X)) 18.16/5.61 succ_in_aa(one(X), zero(Z)) -> U32_aa(X, Z, succ_in_aa(X, Z)) 18.16/5.61 U32_aa(X, Z, succ_out_aa(X, Z)) -> succ_out_aa(one(X), zero(Z)) 18.16/5.61 U34_aa(X, Z, succ_out_aa(X, Z)) -> succZ_out_aa(one(X), zero(Z)) 18.16/5.61 U14_aaa(X, Z, succZ_out_aa(X, Z)) -> addc_out_aaa(X, b, Z) 18.16/5.61 addc_in_aaa(b, Y, Z) -> U15_aaa(Y, Z, succZ_in_aa(Y, Z)) 18.16/5.61 U15_aaa(Y, Z, succZ_out_aa(Y, Z)) -> addc_out_aaa(b, Y, Z) 18.16/5.61 addc_in_aaa(X, Y, Z) -> U16_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.16/5.61 addC_in_aaa(zero(X), zero(Y), one(Z)) -> U23_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.61 U23_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), zero(Y), one(Z)) 18.16/5.61 addC_in_aaa(zero(X), one(Y), zero(Z)) -> U24_aaa(X, Y, Z, addX_in_aaa(X, Y, Z)) 18.16/5.61 addX_in_aaa(zero(X), b, one(X)) -> U17_aaa(X, binaryZ_in_a(X)) 18.16/5.61 U17_aaa(X, binaryZ_out_a(X)) -> addX_out_aaa(zero(X), b, one(X)) 18.16/5.61 addX_in_aaa(one(X), b, zero(Z)) -> U18_aaa(X, Z, succ_in_aa(X, Z)) 18.16/5.61 U18_aaa(X, Z, succ_out_aa(X, Z)) -> addX_out_aaa(one(X), b, zero(Z)) 18.16/5.61 addX_in_aaa(X, Y, Z) -> U19_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.16/5.61 addC_in_aaa(one(X), zero(Y), zero(Z)) -> U25_aaa(X, Y, Z, addY_in_aaa(X, Y, Z)) 18.16/5.61 addY_in_aaa(b, zero(Y), one(Y)) -> U20_aaa(Y, binaryZ_in_a(Y)) 18.16/5.61 U20_aaa(Y, binaryZ_out_a(Y)) -> addY_out_aaa(b, zero(Y), one(Y)) 18.16/5.61 addY_in_aaa(b, one(Y), zero(Z)) -> U21_aaa(Y, Z, succ_in_aa(Y, Z)) 18.16/5.61 U21_aaa(Y, Z, succ_out_aa(Y, Z)) -> addY_out_aaa(b, one(Y), zero(Z)) 18.16/5.61 addY_in_aaa(X, Y, Z) -> U22_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.16/5.61 addC_in_aaa(one(X), one(Y), one(Z)) -> U26_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.16/5.61 U26_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), one(Y), one(Z)) 18.16/5.61 U22_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addY_out_aaa(X, Y, Z) 18.16/5.61 U25_aaa(X, Y, Z, addY_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), zero(Y), zero(Z)) 18.16/5.61 U19_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addX_out_aaa(X, Y, Z) 18.16/5.61 U24_aaa(X, Y, Z, addX_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), one(Y), zero(Z)) 18.16/5.61 U16_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addc_out_aaa(X, Y, Z) 18.16/5.61 U13_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), one(Y), zero(Z)) 18.16/5.61 U9_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addy_out_aaa(X, Y, Z) 18.16/5.61 U12_aaa(X, Y, Z, addy_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), zero(Y), one(Z)) 18.16/5.61 U6_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addx_out_aaa(X, Y, Z) 18.16/5.61 U11_aaa(X, Y, Z, addx_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), one(Y), one(Z)) 18.16/5.61 U10_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), zero(Y), zero(Z)) 18.16/5.62 U3_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> add_out_aaa(X, Y, Z) 18.16/5.62 U37_aaa(R, S, RSS, add_out_aaa(S, zero(RS), RSS)) -> times_out_aaa(one(R), S, RSS) 18.16/5.62 U35_aaa(R, S, RS, times_out_aaa(R, S, RS)) -> times_out_aaa(zero(R), S, zero(RS)) 18.16/5.62 U36_aag(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aag(R, S, RSS, add_in_aag(S, zero(RS), RSS)) 18.16/5.62 add_in_aag(b, b, b) -> add_out_aag(b, b, b) 18.16/5.62 add_in_aag(X, b, X) -> U1_aag(X, binaryZ_in_g(X)) 18.16/5.62 binaryZ_in_g(zero(X)) -> U29_g(X, binaryZ_in_g(X)) 18.16/5.62 binaryZ_in_g(one(X)) -> U30_g(X, binary_in_g(X)) 18.16/5.62 binary_in_g(b) -> binary_out_g(b) 18.16/5.62 binary_in_g(zero(X)) -> U27_g(X, binaryZ_in_g(X)) 18.16/5.62 U27_g(X, binaryZ_out_g(X)) -> binary_out_g(zero(X)) 18.16/5.62 binary_in_g(one(X)) -> U28_g(X, binary_in_g(X)) 18.16/5.62 U28_g(X, binary_out_g(X)) -> binary_out_g(one(X)) 18.16/5.62 U30_g(X, binary_out_g(X)) -> binaryZ_out_g(one(X)) 18.16/5.62 U29_g(X, binaryZ_out_g(X)) -> binaryZ_out_g(zero(X)) 18.16/5.62 U1_aag(X, binaryZ_out_g(X)) -> add_out_aag(X, b, X) 18.16/5.62 add_in_aag(b, Y, Y) -> U2_aag(Y, binaryZ_in_g(Y)) 18.16/5.62 U2_aag(Y, binaryZ_out_g(Y)) -> add_out_aag(b, Y, Y) 18.16/5.62 add_in_aag(X, Y, Z) -> U3_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.62 addz_in_aag(zero(X), zero(Y), zero(Z)) -> U10_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.62 addz_in_aag(zero(X), one(Y), one(Z)) -> U11_aag(X, Y, Z, addx_in_aag(X, Y, Z)) 18.16/5.62 addx_in_aag(one(X), b, one(X)) -> U4_aag(X, binary_in_g(X)) 18.16/5.62 U4_aag(X, binary_out_g(X)) -> addx_out_aag(one(X), b, one(X)) 18.16/5.62 addx_in_aag(zero(X), b, zero(X)) -> U5_aag(X, binaryZ_in_g(X)) 18.16/5.62 U5_aag(X, binaryZ_out_g(X)) -> addx_out_aag(zero(X), b, zero(X)) 18.16/5.62 addx_in_aag(X, Y, Z) -> U6_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.62 addz_in_aag(one(X), zero(Y), one(Z)) -> U12_aag(X, Y, Z, addy_in_aag(X, Y, Z)) 18.16/5.62 addy_in_aag(b, one(Y), one(Y)) -> U7_aag(Y, binary_in_g(Y)) 18.16/5.62 U7_aag(Y, binary_out_g(Y)) -> addy_out_aag(b, one(Y), one(Y)) 18.16/5.62 addy_in_aag(b, zero(Y), zero(Y)) -> U8_aag(Y, binaryZ_in_g(Y)) 18.16/5.62 U8_aag(Y, binaryZ_out_g(Y)) -> addy_out_aag(b, zero(Y), zero(Y)) 18.16/5.62 addy_in_aag(X, Y, Z) -> U9_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.62 addz_in_aag(one(X), one(Y), zero(Z)) -> U13_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.16/5.62 addc_in_aag(b, b, one(b)) -> addc_out_aag(b, b, one(b)) 18.16/5.62 addc_in_aag(X, b, Z) -> U14_aag(X, Z, succZ_in_ag(X, Z)) 18.16/5.62 succZ_in_ag(zero(X), one(X)) -> U33_ag(X, binaryZ_in_g(X)) 18.16/5.62 U33_ag(X, binaryZ_out_g(X)) -> succZ_out_ag(zero(X), one(X)) 18.16/5.62 succZ_in_ag(one(X), zero(Z)) -> U34_ag(X, Z, succ_in_ag(X, Z)) 18.16/5.62 succ_in_ag(b, one(b)) -> succ_out_ag(b, one(b)) 18.16/5.62 succ_in_ag(zero(X), one(X)) -> U31_ag(X, binaryZ_in_g(X)) 18.16/5.62 U31_ag(X, binaryZ_out_g(X)) -> succ_out_ag(zero(X), one(X)) 18.16/5.62 succ_in_ag(one(X), zero(Z)) -> U32_ag(X, Z, succ_in_ag(X, Z)) 18.16/5.62 U32_ag(X, Z, succ_out_ag(X, Z)) -> succ_out_ag(one(X), zero(Z)) 18.16/5.62 U34_ag(X, Z, succ_out_ag(X, Z)) -> succZ_out_ag(one(X), zero(Z)) 18.16/5.62 U14_aag(X, Z, succZ_out_ag(X, Z)) -> addc_out_aag(X, b, Z) 18.16/5.62 addc_in_aag(b, Y, Z) -> U15_aag(Y, Z, succZ_in_ag(Y, Z)) 18.16/5.62 U15_aag(Y, Z, succZ_out_ag(Y, Z)) -> addc_out_aag(b, Y, Z) 18.16/5.62 addc_in_aag(X, Y, Z) -> U16_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.16/5.62 addC_in_aag(zero(X), zero(Y), one(Z)) -> U23_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.62 U23_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), zero(Y), one(Z)) 18.16/5.62 addC_in_aag(zero(X), one(Y), zero(Z)) -> U24_aag(X, Y, Z, addX_in_aag(X, Y, Z)) 18.16/5.62 addX_in_aag(zero(X), b, one(X)) -> U17_aag(X, binaryZ_in_g(X)) 18.16/5.62 U17_aag(X, binaryZ_out_g(X)) -> addX_out_aag(zero(X), b, one(X)) 18.16/5.62 addX_in_aag(one(X), b, zero(Z)) -> U18_aag(X, Z, succ_in_ag(X, Z)) 18.16/5.62 U18_aag(X, Z, succ_out_ag(X, Z)) -> addX_out_aag(one(X), b, zero(Z)) 18.16/5.62 addX_in_aag(X, Y, Z) -> U19_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.16/5.62 addC_in_aag(one(X), zero(Y), zero(Z)) -> U25_aag(X, Y, Z, addY_in_aag(X, Y, Z)) 18.16/5.62 addY_in_aag(b, zero(Y), one(Y)) -> U20_aag(Y, binaryZ_in_g(Y)) 18.16/5.62 U20_aag(Y, binaryZ_out_g(Y)) -> addY_out_aag(b, zero(Y), one(Y)) 18.16/5.62 addY_in_aag(b, one(Y), zero(Z)) -> U21_aag(Y, Z, succ_in_ag(Y, Z)) 18.16/5.62 U21_aag(Y, Z, succ_out_ag(Y, Z)) -> addY_out_aag(b, one(Y), zero(Z)) 18.16/5.62 addY_in_aag(X, Y, Z) -> U22_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.16/5.62 addC_in_aag(one(X), one(Y), one(Z)) -> U26_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.16/5.62 U26_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addC_out_aag(one(X), one(Y), one(Z)) 18.16/5.62 U22_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addY_out_aag(X, Y, Z) 18.16/5.62 U25_aag(X, Y, Z, addY_out_aag(X, Y, Z)) -> addC_out_aag(one(X), zero(Y), zero(Z)) 18.16/5.62 U19_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addX_out_aag(X, Y, Z) 18.16/5.62 U24_aag(X, Y, Z, addX_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), one(Y), zero(Z)) 18.16/5.62 U16_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addc_out_aag(X, Y, Z) 18.16/5.62 U13_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addz_out_aag(one(X), one(Y), zero(Z)) 18.16/5.62 U9_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addy_out_aag(X, Y, Z) 18.16/5.62 U12_aag(X, Y, Z, addy_out_aag(X, Y, Z)) -> addz_out_aag(one(X), zero(Y), one(Z)) 18.16/5.62 U6_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addx_out_aag(X, Y, Z) 18.16/5.62 U11_aag(X, Y, Z, addx_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), one(Y), one(Z)) 18.16/5.62 U10_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), zero(Y), zero(Z)) 18.16/5.62 U3_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> add_out_aag(X, Y, Z) 18.16/5.62 U37_aag(R, S, RSS, add_out_aag(S, zero(RS), RSS)) -> times_out_aag(one(R), S, RSS) 18.16/5.62 U35_aag(R, S, RS, times_out_aag(R, S, RS)) -> times_out_aag(zero(R), S, zero(RS)) 18.16/5.62 18.16/5.62 The argument filtering Pi contains the following mapping: 18.16/5.62 times_in_aag(x1, x2, x3) = times_in_aag(x3) 18.16/5.62 18.16/5.62 times_out_aag(x1, x2, x3) = times_out_aag(x1, x2, x3) 18.16/5.62 18.16/5.62 zero(x1) = zero(x1) 18.16/5.62 18.16/5.62 U35_aag(x1, x2, x3, x4) = U35_aag(x3, x4) 18.16/5.62 18.16/5.62 U36_aag(x1, x2, x3, x4) = U36_aag(x3, x4) 18.16/5.62 18.16/5.62 times_in_aaa(x1, x2, x3) = times_in_aaa 18.16/5.62 18.16/5.62 times_out_aaa(x1, x2, x3) = times_out_aaa(x1) 18.16/5.62 18.16/5.62 U35_aaa(x1, x2, x3, x4) = U35_aaa(x4) 18.16/5.62 18.16/5.62 U36_aaa(x1, x2, x3, x4) = U36_aaa(x4) 18.16/5.62 18.16/5.62 U37_aaa(x1, x2, x3, x4) = U37_aaa(x1, x4) 18.16/5.62 18.16/5.62 add_in_aaa(x1, x2, x3) = add_in_aaa 18.16/5.62 18.16/5.62 add_out_aaa(x1, x2, x3) = add_out_aaa(x1, x2, x3) 18.16/5.62 18.16/5.62 U1_aaa(x1, x2) = U1_aaa(x2) 18.16/5.62 18.16/5.62 binaryZ_in_a(x1) = binaryZ_in_a 18.16/5.62 18.16/5.62 U29_a(x1, x2) = U29_a(x2) 18.16/5.62 18.16/5.62 U30_a(x1, x2) = U30_a(x2) 18.16/5.62 18.16/5.62 binary_in_a(x1) = binary_in_a 18.16/5.62 18.16/5.62 binary_out_a(x1) = binary_out_a(x1) 18.16/5.62 18.16/5.62 U27_a(x1, x2) = U27_a(x2) 18.16/5.62 18.16/5.62 binaryZ_out_a(x1) = binaryZ_out_a(x1) 18.16/5.62 18.16/5.62 U28_a(x1, x2) = U28_a(x2) 18.16/5.62 18.16/5.62 U2_aaa(x1, x2) = U2_aaa(x2) 18.16/5.62 18.16/5.62 U3_aaa(x1, x2, x3, x4) = U3_aaa(x4) 18.16/5.62 18.16/5.62 addz_in_aaa(x1, x2, x3) = addz_in_aaa 18.16/5.62 18.16/5.62 U10_aaa(x1, x2, x3, x4) = U10_aaa(x4) 18.16/5.62 18.16/5.62 U11_aaa(x1, x2, x3, x4) = U11_aaa(x4) 18.16/5.62 18.16/5.62 addx_in_aaa(x1, x2, x3) = addx_in_aaa 18.16/5.62 18.16/5.62 U4_aaa(x1, x2) = U4_aaa(x2) 18.16/5.62 18.16/5.62 addx_out_aaa(x1, x2, x3) = addx_out_aaa(x1, x2, x3) 18.16/5.62 18.16/5.62 U5_aaa(x1, x2) = U5_aaa(x2) 18.16/5.62 18.16/5.62 U6_aaa(x1, x2, x3, x4) = U6_aaa(x4) 18.16/5.62 18.16/5.62 U12_aaa(x1, x2, x3, x4) = U12_aaa(x4) 18.16/5.62 18.16/5.62 addy_in_aaa(x1, x2, x3) = addy_in_aaa 18.16/5.62 18.16/5.62 U7_aaa(x1, x2) = U7_aaa(x2) 18.16/5.62 18.16/5.62 addy_out_aaa(x1, x2, x3) = addy_out_aaa(x1, x2, x3) 18.16/5.62 18.16/5.62 U8_aaa(x1, x2) = U8_aaa(x2) 18.16/5.62 18.16/5.62 U9_aaa(x1, x2, x3, x4) = U9_aaa(x4) 18.16/5.62 18.16/5.62 U13_aaa(x1, x2, x3, x4) = U13_aaa(x4) 18.16/5.62 18.16/5.62 addc_in_aaa(x1, x2, x3) = addc_in_aaa 18.16/5.62 18.16/5.62 addc_out_aaa(x1, x2, x3) = addc_out_aaa(x1, x2, x3) 18.16/5.62 18.16/5.62 U14_aaa(x1, x2, x3) = U14_aaa(x3) 18.16/5.62 18.16/5.62 succZ_in_aa(x1, x2) = succZ_in_aa 18.16/5.62 18.16/5.62 U33_aa(x1, x2) = U33_aa(x2) 18.16/5.62 18.16/5.62 succZ_out_aa(x1, x2) = succZ_out_aa(x1, x2) 18.16/5.62 18.16/5.62 U34_aa(x1, x2, x3) = U34_aa(x3) 18.16/5.62 18.16/5.62 succ_in_aa(x1, x2) = succ_in_aa 18.16/5.62 18.16/5.62 succ_out_aa(x1, x2) = succ_out_aa(x1, x2) 18.16/5.62 18.16/5.62 U31_aa(x1, x2) = U31_aa(x2) 18.16/5.62 18.16/5.62 U32_aa(x1, x2, x3) = U32_aa(x3) 18.16/5.62 18.16/5.62 U15_aaa(x1, x2, x3) = U15_aaa(x3) 18.16/5.62 18.16/5.62 U16_aaa(x1, x2, x3, x4) = U16_aaa(x4) 18.16/5.62 18.16/5.62 addC_in_aaa(x1, x2, x3) = addC_in_aaa 18.16/5.62 18.16/5.62 U23_aaa(x1, x2, x3, x4) = U23_aaa(x4) 18.16/5.62 18.16/5.62 addz_out_aaa(x1, x2, x3) = addz_out_aaa(x1, x2, x3) 18.16/5.62 18.16/5.62 addC_out_aaa(x1, x2, x3) = addC_out_aaa(x1, x2, x3) 18.16/5.62 18.16/5.62 U24_aaa(x1, x2, x3, x4) = U24_aaa(x4) 18.16/5.62 18.16/5.62 addX_in_aaa(x1, x2, x3) = addX_in_aaa 18.16/5.62 18.16/5.62 U17_aaa(x1, x2) = U17_aaa(x2) 18.16/5.62 18.16/5.62 addX_out_aaa(x1, x2, x3) = addX_out_aaa(x1, x2, x3) 18.16/5.62 18.16/5.62 U18_aaa(x1, x2, x3) = U18_aaa(x3) 18.16/5.62 18.16/5.62 U19_aaa(x1, x2, x3, x4) = U19_aaa(x4) 18.16/5.62 18.16/5.62 U25_aaa(x1, x2, x3, x4) = U25_aaa(x4) 18.16/5.62 18.16/5.62 addY_in_aaa(x1, x2, x3) = addY_in_aaa 18.16/5.62 18.16/5.62 U20_aaa(x1, x2) = U20_aaa(x2) 18.16/5.62 18.16/5.62 addY_out_aaa(x1, x2, x3) = addY_out_aaa(x1, x2, x3) 18.16/5.62 18.16/5.62 U21_aaa(x1, x2, x3) = U21_aaa(x3) 18.16/5.62 18.16/5.62 U22_aaa(x1, x2, x3, x4) = U22_aaa(x4) 18.16/5.62 18.16/5.62 U26_aaa(x1, x2, x3, x4) = U26_aaa(x4) 18.16/5.62 18.16/5.62 U37_aag(x1, x2, x3, x4) = U37_aag(x1, x3, x4) 18.16/5.62 18.16/5.62 add_in_aag(x1, x2, x3) = add_in_aag(x3) 18.16/5.62 18.16/5.62 b = b 18.16/5.62 18.16/5.62 add_out_aag(x1, x2, x3) = add_out_aag(x1, x2, x3) 18.16/5.62 18.16/5.62 U1_aag(x1, x2) = U1_aag(x1, x2) 18.16/5.62 18.16/5.62 binaryZ_in_g(x1) = binaryZ_in_g(x1) 18.16/5.62 18.16/5.62 U29_g(x1, x2) = U29_g(x1, x2) 18.16/5.62 18.16/5.62 one(x1) = one(x1) 18.16/5.62 18.16/5.62 U30_g(x1, x2) = U30_g(x1, x2) 18.16/5.62 18.16/5.62 binary_in_g(x1) = binary_in_g(x1) 18.16/5.62 18.16/5.62 binary_out_g(x1) = binary_out_g(x1) 18.16/5.62 18.16/5.62 U27_g(x1, x2) = U27_g(x1, x2) 18.16/5.62 18.16/5.62 binaryZ_out_g(x1) = binaryZ_out_g(x1) 18.16/5.62 18.16/5.62 U28_g(x1, x2) = U28_g(x1, x2) 18.16/5.62 18.16/5.62 U2_aag(x1, x2) = U2_aag(x1, x2) 18.16/5.62 18.16/5.62 U3_aag(x1, x2, x3, x4) = U3_aag(x3, x4) 18.16/5.62 18.16/5.62 addz_in_aag(x1, x2, x3) = addz_in_aag(x3) 18.16/5.62 18.16/5.62 U10_aag(x1, x2, x3, x4) = U10_aag(x3, x4) 18.16/5.62 18.16/5.62 U11_aag(x1, x2, x3, x4) = U11_aag(x3, x4) 18.16/5.62 18.16/5.62 addx_in_aag(x1, x2, x3) = addx_in_aag(x3) 18.16/5.62 18.16/5.62 U4_aag(x1, x2) = U4_aag(x1, x2) 18.16/5.62 18.16/5.62 addx_out_aag(x1, x2, x3) = addx_out_aag(x1, x2, x3) 18.16/5.62 18.16/5.62 U5_aag(x1, x2) = U5_aag(x1, x2) 18.16/5.62 18.16/5.62 U6_aag(x1, x2, x3, x4) = U6_aag(x3, x4) 18.16/5.62 18.16/5.62 U12_aag(x1, x2, x3, x4) = U12_aag(x3, x4) 18.16/5.62 18.16/5.62 addy_in_aag(x1, x2, x3) = addy_in_aag(x3) 18.16/5.62 18.16/5.62 U7_aag(x1, x2) = U7_aag(x1, x2) 18.16/5.62 18.16/5.62 addy_out_aag(x1, x2, x3) = addy_out_aag(x1, x2, x3) 18.16/5.62 18.16/5.62 U8_aag(x1, x2) = U8_aag(x1, x2) 18.16/5.62 18.16/5.62 U9_aag(x1, x2, x3, x4) = U9_aag(x3, x4) 18.16/5.62 18.16/5.62 U13_aag(x1, x2, x3, x4) = U13_aag(x3, x4) 18.16/5.62 18.16/5.62 addc_in_aag(x1, x2, x3) = addc_in_aag(x3) 18.16/5.62 18.16/5.62 addc_out_aag(x1, x2, x3) = addc_out_aag(x1, x2, x3) 18.16/5.62 18.16/5.62 U14_aag(x1, x2, x3) = U14_aag(x2, x3) 18.16/5.62 18.16/5.62 succZ_in_ag(x1, x2) = succZ_in_ag(x2) 18.16/5.62 18.16/5.62 U33_ag(x1, x2) = U33_ag(x1, x2) 18.16/5.62 18.16/5.62 succZ_out_ag(x1, x2) = succZ_out_ag(x1, x2) 18.16/5.62 18.16/5.62 U34_ag(x1, x2, x3) = U34_ag(x2, x3) 18.16/5.62 18.16/5.62 succ_in_ag(x1, x2) = succ_in_ag(x2) 18.16/5.62 18.16/5.62 succ_out_ag(x1, x2) = succ_out_ag(x1, x2) 18.16/5.62 18.16/5.62 U31_ag(x1, x2) = U31_ag(x1, x2) 18.16/5.62 18.16/5.62 U32_ag(x1, x2, x3) = U32_ag(x2, x3) 18.16/5.62 18.16/5.62 U15_aag(x1, x2, x3) = U15_aag(x2, x3) 18.16/5.62 18.16/5.62 U16_aag(x1, x2, x3, x4) = U16_aag(x3, x4) 18.16/5.62 18.16/5.62 addC_in_aag(x1, x2, x3) = addC_in_aag(x3) 18.16/5.62 18.16/5.62 U23_aag(x1, x2, x3, x4) = U23_aag(x3, x4) 18.16/5.62 18.16/5.62 addz_out_aag(x1, x2, x3) = addz_out_aag(x1, x2, x3) 18.16/5.62 18.16/5.62 addC_out_aag(x1, x2, x3) = addC_out_aag(x1, x2, x3) 18.16/5.62 18.16/5.62 U24_aag(x1, x2, x3, x4) = U24_aag(x3, x4) 18.16/5.62 18.16/5.62 addX_in_aag(x1, x2, x3) = addX_in_aag(x3) 18.16/5.62 18.16/5.62 U17_aag(x1, x2) = U17_aag(x1, x2) 18.16/5.62 18.16/5.62 addX_out_aag(x1, x2, x3) = addX_out_aag(x1, x2, x3) 18.16/5.62 18.16/5.62 U18_aag(x1, x2, x3) = U18_aag(x2, x3) 18.16/5.62 18.16/5.62 U19_aag(x1, x2, x3, x4) = U19_aag(x3, x4) 18.16/5.62 18.16/5.62 U25_aag(x1, x2, x3, x4) = U25_aag(x3, x4) 18.16/5.62 18.16/5.62 addY_in_aag(x1, x2, x3) = addY_in_aag(x3) 18.16/5.62 18.16/5.62 U20_aag(x1, x2) = U20_aag(x1, x2) 18.16/5.62 18.16/5.62 addY_out_aag(x1, x2, x3) = addY_out_aag(x1, x2, x3) 18.16/5.62 18.16/5.62 U21_aag(x1, x2, x3) = U21_aag(x2, x3) 18.16/5.62 18.16/5.62 U22_aag(x1, x2, x3, x4) = U22_aag(x3, x4) 18.16/5.62 18.16/5.62 U26_aag(x1, x2, x3, x4) = U26_aag(x3, x4) 18.16/5.62 18.16/5.62 TIMES_IN_AAG(x1, x2, x3) = TIMES_IN_AAG(x3) 18.16/5.62 18.16/5.62 U35_AAG(x1, x2, x3, x4) = U35_AAG(x3, x4) 18.16/5.62 18.16/5.62 U36_AAG(x1, x2, x3, x4) = U36_AAG(x3, x4) 18.16/5.62 18.16/5.62 TIMES_IN_AAA(x1, x2, x3) = TIMES_IN_AAA 18.16/5.62 18.16/5.62 U35_AAA(x1, x2, x3, x4) = U35_AAA(x4) 18.16/5.62 18.16/5.62 U36_AAA(x1, x2, x3, x4) = U36_AAA(x4) 18.16/5.62 18.16/5.62 U37_AAA(x1, x2, x3, x4) = U37_AAA(x1, x4) 18.16/5.62 18.16/5.62 ADD_IN_AAA(x1, x2, x3) = ADD_IN_AAA 18.16/5.62 18.16/5.62 U1_AAA(x1, x2) = U1_AAA(x2) 18.16/5.62 18.16/5.62 BINARYZ_IN_A(x1) = BINARYZ_IN_A 18.16/5.62 18.16/5.62 U29_A(x1, x2) = U29_A(x2) 18.16/5.62 18.16/5.62 U30_A(x1, x2) = U30_A(x2) 18.16/5.62 18.16/5.62 BINARY_IN_A(x1) = BINARY_IN_A 18.16/5.62 18.16/5.62 U27_A(x1, x2) = U27_A(x2) 18.16/5.62 18.16/5.62 U28_A(x1, x2) = U28_A(x2) 18.16/5.62 18.16/5.62 U2_AAA(x1, x2) = U2_AAA(x2) 18.16/5.62 18.16/5.62 U3_AAA(x1, x2, x3, x4) = U3_AAA(x4) 18.16/5.62 18.16/5.62 ADDZ_IN_AAA(x1, x2, x3) = ADDZ_IN_AAA 18.16/5.62 18.16/5.62 U10_AAA(x1, x2, x3, x4) = U10_AAA(x4) 18.16/5.62 18.16/5.62 U11_AAA(x1, x2, x3, x4) = U11_AAA(x4) 18.16/5.62 18.16/5.62 ADDX_IN_AAA(x1, x2, x3) = ADDX_IN_AAA 18.16/5.62 18.16/5.62 U4_AAA(x1, x2) = U4_AAA(x2) 18.16/5.62 18.16/5.62 U5_AAA(x1, x2) = U5_AAA(x2) 18.16/5.62 18.16/5.62 U6_AAA(x1, x2, x3, x4) = U6_AAA(x4) 18.16/5.62 18.16/5.62 U12_AAA(x1, x2, x3, x4) = U12_AAA(x4) 18.16/5.62 18.16/5.62 ADDY_IN_AAA(x1, x2, x3) = ADDY_IN_AAA 18.16/5.62 18.16/5.62 U7_AAA(x1, x2) = U7_AAA(x2) 18.16/5.62 18.16/5.62 U8_AAA(x1, x2) = U8_AAA(x2) 18.16/5.62 18.16/5.62 U9_AAA(x1, x2, x3, x4) = U9_AAA(x4) 18.16/5.62 18.16/5.62 U13_AAA(x1, x2, x3, x4) = U13_AAA(x4) 18.16/5.62 18.16/5.62 ADDC_IN_AAA(x1, x2, x3) = ADDC_IN_AAA 18.16/5.62 18.16/5.62 U14_AAA(x1, x2, x3) = U14_AAA(x3) 18.16/5.62 18.16/5.62 SUCCZ_IN_AA(x1, x2) = SUCCZ_IN_AA 18.16/5.62 18.16/5.62 U33_AA(x1, x2) = U33_AA(x2) 18.16/5.62 18.16/5.62 U34_AA(x1, x2, x3) = U34_AA(x3) 18.16/5.62 18.16/5.62 SUCC_IN_AA(x1, x2) = SUCC_IN_AA 18.16/5.62 18.16/5.62 U31_AA(x1, x2) = U31_AA(x2) 18.16/5.62 18.16/5.62 U32_AA(x1, x2, x3) = U32_AA(x3) 18.16/5.62 18.16/5.62 U15_AAA(x1, x2, x3) = U15_AAA(x3) 18.16/5.62 18.16/5.62 U16_AAA(x1, x2, x3, x4) = U16_AAA(x4) 18.16/5.62 18.16/5.62 ADDC_IN_AAA^1(x1, x2, x3) = ADDC_IN_AAA^1 18.16/5.62 18.16/5.62 U23_AAA(x1, x2, x3, x4) = U23_AAA(x4) 18.16/5.62 18.16/5.62 U24_AAA(x1, x2, x3, x4) = U24_AAA(x4) 18.16/5.62 18.16/5.62 ADDX_IN_AAA^1(x1, x2, x3) = ADDX_IN_AAA^1 18.16/5.62 18.16/5.62 U17_AAA(x1, x2) = U17_AAA(x2) 18.16/5.62 18.16/5.62 U18_AAA(x1, x2, x3) = U18_AAA(x3) 18.16/5.62 18.16/5.62 U19_AAA(x1, x2, x3, x4) = U19_AAA(x4) 18.16/5.62 18.16/5.62 U25_AAA(x1, x2, x3, x4) = U25_AAA(x4) 18.16/5.62 18.16/5.62 ADDY_IN_AAA^1(x1, x2, x3) = ADDY_IN_AAA^1 18.16/5.62 18.16/5.62 U20_AAA(x1, x2) = U20_AAA(x2) 18.16/5.62 18.16/5.62 U21_AAA(x1, x2, x3) = U21_AAA(x3) 18.16/5.62 18.16/5.62 U22_AAA(x1, x2, x3, x4) = U22_AAA(x4) 18.16/5.62 18.16/5.62 U26_AAA(x1, x2, x3, x4) = U26_AAA(x4) 18.16/5.62 18.16/5.62 U37_AAG(x1, x2, x3, x4) = U37_AAG(x1, x3, x4) 18.16/5.62 18.16/5.62 ADD_IN_AAG(x1, x2, x3) = ADD_IN_AAG(x3) 18.16/5.62 18.16/5.62 U1_AAG(x1, x2) = U1_AAG(x1, x2) 18.16/5.62 18.16/5.62 BINARYZ_IN_G(x1) = BINARYZ_IN_G(x1) 18.16/5.62 18.16/5.62 U29_G(x1, x2) = U29_G(x1, x2) 18.16/5.62 18.16/5.62 U30_G(x1, x2) = U30_G(x1, x2) 18.16/5.62 18.16/5.62 BINARY_IN_G(x1) = BINARY_IN_G(x1) 18.16/5.62 18.16/5.62 U27_G(x1, x2) = U27_G(x1, x2) 18.16/5.62 18.16/5.62 U28_G(x1, x2) = U28_G(x1, x2) 18.16/5.62 18.16/5.62 U2_AAG(x1, x2) = U2_AAG(x1, x2) 18.16/5.62 18.16/5.62 U3_AAG(x1, x2, x3, x4) = U3_AAG(x3, x4) 18.16/5.62 18.16/5.62 ADDZ_IN_AAG(x1, x2, x3) = ADDZ_IN_AAG(x3) 18.16/5.62 18.16/5.62 U10_AAG(x1, x2, x3, x4) = U10_AAG(x3, x4) 18.16/5.62 18.16/5.62 U11_AAG(x1, x2, x3, x4) = U11_AAG(x3, x4) 18.16/5.62 18.16/5.62 ADDX_IN_AAG(x1, x2, x3) = ADDX_IN_AAG(x3) 18.16/5.62 18.16/5.62 U4_AAG(x1, x2) = U4_AAG(x1, x2) 18.16/5.62 18.16/5.62 U5_AAG(x1, x2) = U5_AAG(x1, x2) 18.16/5.62 18.16/5.62 U6_AAG(x1, x2, x3, x4) = U6_AAG(x3, x4) 18.16/5.62 18.16/5.62 U12_AAG(x1, x2, x3, x4) = U12_AAG(x3, x4) 18.16/5.62 18.16/5.62 ADDY_IN_AAG(x1, x2, x3) = ADDY_IN_AAG(x3) 18.16/5.62 18.16/5.62 U7_AAG(x1, x2) = U7_AAG(x1, x2) 18.16/5.62 18.16/5.62 U8_AAG(x1, x2) = U8_AAG(x1, x2) 18.16/5.62 18.16/5.62 U9_AAG(x1, x2, x3, x4) = U9_AAG(x3, x4) 18.16/5.62 18.16/5.62 U13_AAG(x1, x2, x3, x4) = U13_AAG(x3, x4) 18.16/5.62 18.16/5.62 ADDC_IN_AAG(x1, x2, x3) = ADDC_IN_AAG(x3) 18.16/5.62 18.16/5.62 U14_AAG(x1, x2, x3) = U14_AAG(x2, x3) 18.16/5.62 18.16/5.62 SUCCZ_IN_AG(x1, x2) = SUCCZ_IN_AG(x2) 18.16/5.62 18.16/5.62 U33_AG(x1, x2) = U33_AG(x1, x2) 18.16/5.62 18.16/5.62 U34_AG(x1, x2, x3) = U34_AG(x2, x3) 18.16/5.62 18.16/5.62 SUCC_IN_AG(x1, x2) = SUCC_IN_AG(x2) 18.16/5.62 18.16/5.62 U31_AG(x1, x2) = U31_AG(x1, x2) 18.16/5.62 18.16/5.62 U32_AG(x1, x2, x3) = U32_AG(x2, x3) 18.16/5.62 18.16/5.62 U15_AAG(x1, x2, x3) = U15_AAG(x2, x3) 18.16/5.62 18.16/5.62 U16_AAG(x1, x2, x3, x4) = U16_AAG(x3, x4) 18.16/5.62 18.16/5.62 ADDC_IN_AAG^1(x1, x2, x3) = ADDC_IN_AAG^1(x3) 18.16/5.62 18.16/5.62 U23_AAG(x1, x2, x3, x4) = U23_AAG(x3, x4) 18.16/5.62 18.16/5.62 U24_AAG(x1, x2, x3, x4) = U24_AAG(x3, x4) 18.16/5.62 18.16/5.62 ADDX_IN_AAG^1(x1, x2, x3) = ADDX_IN_AAG^1(x3) 18.16/5.62 18.16/5.62 U17_AAG(x1, x2) = U17_AAG(x1, x2) 18.16/5.62 18.16/5.62 U18_AAG(x1, x2, x3) = U18_AAG(x2, x3) 18.16/5.62 18.16/5.62 U19_AAG(x1, x2, x3, x4) = U19_AAG(x3, x4) 18.16/5.62 18.16/5.62 U25_AAG(x1, x2, x3, x4) = U25_AAG(x3, x4) 18.16/5.62 18.16/5.62 ADDY_IN_AAG^1(x1, x2, x3) = ADDY_IN_AAG^1(x3) 18.16/5.62 18.16/5.62 U20_AAG(x1, x2) = U20_AAG(x1, x2) 18.16/5.62 18.16/5.62 U21_AAG(x1, x2, x3) = U21_AAG(x2, x3) 18.16/5.62 18.16/5.62 U22_AAG(x1, x2, x3, x4) = U22_AAG(x3, x4) 18.16/5.62 18.16/5.62 U26_AAG(x1, x2, x3, x4) = U26_AAG(x3, x4) 18.16/5.62 18.16/5.62 18.16/5.62 We have to consider all (P,R,Pi)-chains 18.16/5.62 ---------------------------------------- 18.16/5.62 18.16/5.62 (4) 18.16/5.62 Obligation: 18.16/5.62 Pi DP problem: 18.16/5.62 The TRS P consists of the following rules: 18.16/5.62 18.16/5.62 TIMES_IN_AAG(zero(R), S, zero(RS)) -> U35_AAG(R, S, RS, times_in_aag(R, S, RS)) 18.16/5.62 TIMES_IN_AAG(zero(R), S, zero(RS)) -> TIMES_IN_AAG(R, S, RS) 18.16/5.62 TIMES_IN_AAG(one(R), S, RSS) -> U36_AAG(R, S, RSS, times_in_aaa(R, S, RS)) 18.16/5.62 TIMES_IN_AAG(one(R), S, RSS) -> TIMES_IN_AAA(R, S, RS) 18.16/5.62 TIMES_IN_AAA(zero(R), S, zero(RS)) -> U35_AAA(R, S, RS, times_in_aaa(R, S, RS)) 18.16/5.62 TIMES_IN_AAA(zero(R), S, zero(RS)) -> TIMES_IN_AAA(R, S, RS) 18.16/5.62 TIMES_IN_AAA(one(R), S, RSS) -> U36_AAA(R, S, RSS, times_in_aaa(R, S, RS)) 18.16/5.62 TIMES_IN_AAA(one(R), S, RSS) -> TIMES_IN_AAA(R, S, RS) 18.16/5.62 U36_AAA(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_AAA(R, S, RSS, add_in_aaa(S, zero(RS), RSS)) 18.16/5.62 U36_AAA(R, S, RSS, times_out_aaa(R, S, RS)) -> ADD_IN_AAA(S, zero(RS), RSS) 18.16/5.62 ADD_IN_AAA(X, b, X) -> U1_AAA(X, binaryZ_in_a(X)) 18.16/5.62 ADD_IN_AAA(X, b, X) -> BINARYZ_IN_A(X) 18.16/5.62 BINARYZ_IN_A(zero(X)) -> U29_A(X, binaryZ_in_a(X)) 18.16/5.62 BINARYZ_IN_A(zero(X)) -> BINARYZ_IN_A(X) 18.16/5.62 BINARYZ_IN_A(one(X)) -> U30_A(X, binary_in_a(X)) 18.16/5.62 BINARYZ_IN_A(one(X)) -> BINARY_IN_A(X) 18.16/5.62 BINARY_IN_A(zero(X)) -> U27_A(X, binaryZ_in_a(X)) 18.16/5.62 BINARY_IN_A(zero(X)) -> BINARYZ_IN_A(X) 18.16/5.62 BINARY_IN_A(one(X)) -> U28_A(X, binary_in_a(X)) 18.16/5.62 BINARY_IN_A(one(X)) -> BINARY_IN_A(X) 18.16/5.62 ADD_IN_AAA(b, Y, Y) -> U2_AAA(Y, binaryZ_in_a(Y)) 18.16/5.62 ADD_IN_AAA(b, Y, Y) -> BINARYZ_IN_A(Y) 18.16/5.62 ADD_IN_AAA(X, Y, Z) -> U3_AAA(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.62 ADD_IN_AAA(X, Y, Z) -> ADDZ_IN_AAA(X, Y, Z) 18.16/5.62 ADDZ_IN_AAA(zero(X), zero(Y), zero(Z)) -> U10_AAA(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.62 ADDZ_IN_AAA(zero(X), zero(Y), zero(Z)) -> ADDZ_IN_AAA(X, Y, Z) 18.16/5.62 ADDZ_IN_AAA(zero(X), one(Y), one(Z)) -> U11_AAA(X, Y, Z, addx_in_aaa(X, Y, Z)) 18.16/5.62 ADDZ_IN_AAA(zero(X), one(Y), one(Z)) -> ADDX_IN_AAA(X, Y, Z) 18.16/5.62 ADDX_IN_AAA(one(X), b, one(X)) -> U4_AAA(X, binary_in_a(X)) 18.16/5.62 ADDX_IN_AAA(one(X), b, one(X)) -> BINARY_IN_A(X) 18.16/5.62 ADDX_IN_AAA(zero(X), b, zero(X)) -> U5_AAA(X, binaryZ_in_a(X)) 18.16/5.62 ADDX_IN_AAA(zero(X), b, zero(X)) -> BINARYZ_IN_A(X) 18.16/5.62 ADDX_IN_AAA(X, Y, Z) -> U6_AAA(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.62 ADDX_IN_AAA(X, Y, Z) -> ADDZ_IN_AAA(X, Y, Z) 18.16/5.62 ADDZ_IN_AAA(one(X), zero(Y), one(Z)) -> U12_AAA(X, Y, Z, addy_in_aaa(X, Y, Z)) 18.16/5.62 ADDZ_IN_AAA(one(X), zero(Y), one(Z)) -> ADDY_IN_AAA(X, Y, Z) 18.16/5.62 ADDY_IN_AAA(b, one(Y), one(Y)) -> U7_AAA(Y, binary_in_a(Y)) 18.16/5.62 ADDY_IN_AAA(b, one(Y), one(Y)) -> BINARY_IN_A(Y) 18.16/5.62 ADDY_IN_AAA(b, zero(Y), zero(Y)) -> U8_AAA(Y, binaryZ_in_a(Y)) 18.16/5.62 ADDY_IN_AAA(b, zero(Y), zero(Y)) -> BINARYZ_IN_A(Y) 18.16/5.62 ADDY_IN_AAA(X, Y, Z) -> U9_AAA(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.62 ADDY_IN_AAA(X, Y, Z) -> ADDZ_IN_AAA(X, Y, Z) 18.16/5.62 ADDZ_IN_AAA(one(X), one(Y), zero(Z)) -> U13_AAA(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.16/5.62 ADDZ_IN_AAA(one(X), one(Y), zero(Z)) -> ADDC_IN_AAA(X, Y, Z) 18.16/5.62 ADDC_IN_AAA(X, b, Z) -> U14_AAA(X, Z, succZ_in_aa(X, Z)) 18.16/5.62 ADDC_IN_AAA(X, b, Z) -> SUCCZ_IN_AA(X, Z) 18.16/5.62 SUCCZ_IN_AA(zero(X), one(X)) -> U33_AA(X, binaryZ_in_a(X)) 18.16/5.62 SUCCZ_IN_AA(zero(X), one(X)) -> BINARYZ_IN_A(X) 18.16/5.62 SUCCZ_IN_AA(one(X), zero(Z)) -> U34_AA(X, Z, succ_in_aa(X, Z)) 18.16/5.62 SUCCZ_IN_AA(one(X), zero(Z)) -> SUCC_IN_AA(X, Z) 18.16/5.62 SUCC_IN_AA(zero(X), one(X)) -> U31_AA(X, binaryZ_in_a(X)) 18.16/5.62 SUCC_IN_AA(zero(X), one(X)) -> BINARYZ_IN_A(X) 18.16/5.62 SUCC_IN_AA(one(X), zero(Z)) -> U32_AA(X, Z, succ_in_aa(X, Z)) 18.16/5.62 SUCC_IN_AA(one(X), zero(Z)) -> SUCC_IN_AA(X, Z) 18.16/5.62 ADDC_IN_AAA(b, Y, Z) -> U15_AAA(Y, Z, succZ_in_aa(Y, Z)) 18.16/5.62 ADDC_IN_AAA(b, Y, Z) -> SUCCZ_IN_AA(Y, Z) 18.16/5.62 ADDC_IN_AAA(X, Y, Z) -> U16_AAA(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.16/5.62 ADDC_IN_AAA(X, Y, Z) -> ADDC_IN_AAA^1(X, Y, Z) 18.16/5.62 ADDC_IN_AAA^1(zero(X), zero(Y), one(Z)) -> U23_AAA(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.62 ADDC_IN_AAA^1(zero(X), zero(Y), one(Z)) -> ADDZ_IN_AAA(X, Y, Z) 18.16/5.62 ADDC_IN_AAA^1(zero(X), one(Y), zero(Z)) -> U24_AAA(X, Y, Z, addX_in_aaa(X, Y, Z)) 18.16/5.62 ADDC_IN_AAA^1(zero(X), one(Y), zero(Z)) -> ADDX_IN_AAA^1(X, Y, Z) 18.16/5.62 ADDX_IN_AAA^1(zero(X), b, one(X)) -> U17_AAA(X, binaryZ_in_a(X)) 18.16/5.62 ADDX_IN_AAA^1(zero(X), b, one(X)) -> BINARYZ_IN_A(X) 18.16/5.62 ADDX_IN_AAA^1(one(X), b, zero(Z)) -> U18_AAA(X, Z, succ_in_aa(X, Z)) 18.16/5.62 ADDX_IN_AAA^1(one(X), b, zero(Z)) -> SUCC_IN_AA(X, Z) 18.16/5.62 ADDX_IN_AAA^1(X, Y, Z) -> U19_AAA(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.16/5.62 ADDX_IN_AAA^1(X, Y, Z) -> ADDC_IN_AAA^1(X, Y, Z) 18.16/5.62 ADDC_IN_AAA^1(one(X), zero(Y), zero(Z)) -> U25_AAA(X, Y, Z, addY_in_aaa(X, Y, Z)) 18.16/5.62 ADDC_IN_AAA^1(one(X), zero(Y), zero(Z)) -> ADDY_IN_AAA^1(X, Y, Z) 18.16/5.62 ADDY_IN_AAA^1(b, zero(Y), one(Y)) -> U20_AAA(Y, binaryZ_in_a(Y)) 18.16/5.62 ADDY_IN_AAA^1(b, zero(Y), one(Y)) -> BINARYZ_IN_A(Y) 18.16/5.62 ADDY_IN_AAA^1(b, one(Y), zero(Z)) -> U21_AAA(Y, Z, succ_in_aa(Y, Z)) 18.16/5.62 ADDY_IN_AAA^1(b, one(Y), zero(Z)) -> SUCC_IN_AA(Y, Z) 18.16/5.62 ADDY_IN_AAA^1(X, Y, Z) -> U22_AAA(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.16/5.62 ADDY_IN_AAA^1(X, Y, Z) -> ADDC_IN_AAA^1(X, Y, Z) 18.16/5.62 ADDC_IN_AAA^1(one(X), one(Y), one(Z)) -> U26_AAA(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.16/5.62 ADDC_IN_AAA^1(one(X), one(Y), one(Z)) -> ADDC_IN_AAA(X, Y, Z) 18.16/5.62 U36_AAG(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_AAG(R, S, RSS, add_in_aag(S, zero(RS), RSS)) 18.16/5.62 U36_AAG(R, S, RSS, times_out_aaa(R, S, RS)) -> ADD_IN_AAG(S, zero(RS), RSS) 18.16/5.62 ADD_IN_AAG(X, b, X) -> U1_AAG(X, binaryZ_in_g(X)) 18.16/5.62 ADD_IN_AAG(X, b, X) -> BINARYZ_IN_G(X) 18.16/5.62 BINARYZ_IN_G(zero(X)) -> U29_G(X, binaryZ_in_g(X)) 18.16/5.62 BINARYZ_IN_G(zero(X)) -> BINARYZ_IN_G(X) 18.16/5.62 BINARYZ_IN_G(one(X)) -> U30_G(X, binary_in_g(X)) 18.16/5.62 BINARYZ_IN_G(one(X)) -> BINARY_IN_G(X) 18.16/5.62 BINARY_IN_G(zero(X)) -> U27_G(X, binaryZ_in_g(X)) 18.16/5.62 BINARY_IN_G(zero(X)) -> BINARYZ_IN_G(X) 18.16/5.62 BINARY_IN_G(one(X)) -> U28_G(X, binary_in_g(X)) 18.16/5.62 BINARY_IN_G(one(X)) -> BINARY_IN_G(X) 18.16/5.62 ADD_IN_AAG(b, Y, Y) -> U2_AAG(Y, binaryZ_in_g(Y)) 18.16/5.62 ADD_IN_AAG(b, Y, Y) -> BINARYZ_IN_G(Y) 18.16/5.62 ADD_IN_AAG(X, Y, Z) -> U3_AAG(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.62 ADD_IN_AAG(X, Y, Z) -> ADDZ_IN_AAG(X, Y, Z) 18.16/5.62 ADDZ_IN_AAG(zero(X), zero(Y), zero(Z)) -> U10_AAG(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.62 ADDZ_IN_AAG(zero(X), zero(Y), zero(Z)) -> ADDZ_IN_AAG(X, Y, Z) 18.16/5.62 ADDZ_IN_AAG(zero(X), one(Y), one(Z)) -> U11_AAG(X, Y, Z, addx_in_aag(X, Y, Z)) 18.16/5.62 ADDZ_IN_AAG(zero(X), one(Y), one(Z)) -> ADDX_IN_AAG(X, Y, Z) 18.16/5.62 ADDX_IN_AAG(one(X), b, one(X)) -> U4_AAG(X, binary_in_g(X)) 18.16/5.62 ADDX_IN_AAG(one(X), b, one(X)) -> BINARY_IN_G(X) 18.16/5.62 ADDX_IN_AAG(zero(X), b, zero(X)) -> U5_AAG(X, binaryZ_in_g(X)) 18.16/5.62 ADDX_IN_AAG(zero(X), b, zero(X)) -> BINARYZ_IN_G(X) 18.16/5.62 ADDX_IN_AAG(X, Y, Z) -> U6_AAG(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.62 ADDX_IN_AAG(X, Y, Z) -> ADDZ_IN_AAG(X, Y, Z) 18.16/5.62 ADDZ_IN_AAG(one(X), zero(Y), one(Z)) -> U12_AAG(X, Y, Z, addy_in_aag(X, Y, Z)) 18.16/5.62 ADDZ_IN_AAG(one(X), zero(Y), one(Z)) -> ADDY_IN_AAG(X, Y, Z) 18.16/5.62 ADDY_IN_AAG(b, one(Y), one(Y)) -> U7_AAG(Y, binary_in_g(Y)) 18.16/5.62 ADDY_IN_AAG(b, one(Y), one(Y)) -> BINARY_IN_G(Y) 18.16/5.62 ADDY_IN_AAG(b, zero(Y), zero(Y)) -> U8_AAG(Y, binaryZ_in_g(Y)) 18.16/5.62 ADDY_IN_AAG(b, zero(Y), zero(Y)) -> BINARYZ_IN_G(Y) 18.16/5.63 ADDY_IN_AAG(X, Y, Z) -> U9_AAG(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.63 ADDY_IN_AAG(X, Y, Z) -> ADDZ_IN_AAG(X, Y, Z) 18.16/5.63 ADDZ_IN_AAG(one(X), one(Y), zero(Z)) -> U13_AAG(X, Y, Z, addc_in_aag(X, Y, Z)) 18.16/5.63 ADDZ_IN_AAG(one(X), one(Y), zero(Z)) -> ADDC_IN_AAG(X, Y, Z) 18.16/5.63 ADDC_IN_AAG(X, b, Z) -> U14_AAG(X, Z, succZ_in_ag(X, Z)) 18.16/5.63 ADDC_IN_AAG(X, b, Z) -> SUCCZ_IN_AG(X, Z) 18.16/5.63 SUCCZ_IN_AG(zero(X), one(X)) -> U33_AG(X, binaryZ_in_g(X)) 18.16/5.63 SUCCZ_IN_AG(zero(X), one(X)) -> BINARYZ_IN_G(X) 18.16/5.63 SUCCZ_IN_AG(one(X), zero(Z)) -> U34_AG(X, Z, succ_in_ag(X, Z)) 18.16/5.63 SUCCZ_IN_AG(one(X), zero(Z)) -> SUCC_IN_AG(X, Z) 18.16/5.63 SUCC_IN_AG(zero(X), one(X)) -> U31_AG(X, binaryZ_in_g(X)) 18.16/5.63 SUCC_IN_AG(zero(X), one(X)) -> BINARYZ_IN_G(X) 18.16/5.63 SUCC_IN_AG(one(X), zero(Z)) -> U32_AG(X, Z, succ_in_ag(X, Z)) 18.16/5.63 SUCC_IN_AG(one(X), zero(Z)) -> SUCC_IN_AG(X, Z) 18.16/5.63 ADDC_IN_AAG(b, Y, Z) -> U15_AAG(Y, Z, succZ_in_ag(Y, Z)) 18.16/5.63 ADDC_IN_AAG(b, Y, Z) -> SUCCZ_IN_AG(Y, Z) 18.16/5.63 ADDC_IN_AAG(X, Y, Z) -> U16_AAG(X, Y, Z, addC_in_aag(X, Y, Z)) 18.16/5.63 ADDC_IN_AAG(X, Y, Z) -> ADDC_IN_AAG^1(X, Y, Z) 18.16/5.63 ADDC_IN_AAG^1(zero(X), zero(Y), one(Z)) -> U23_AAG(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.63 ADDC_IN_AAG^1(zero(X), zero(Y), one(Z)) -> ADDZ_IN_AAG(X, Y, Z) 18.16/5.63 ADDC_IN_AAG^1(zero(X), one(Y), zero(Z)) -> U24_AAG(X, Y, Z, addX_in_aag(X, Y, Z)) 18.16/5.63 ADDC_IN_AAG^1(zero(X), one(Y), zero(Z)) -> ADDX_IN_AAG^1(X, Y, Z) 18.16/5.63 ADDX_IN_AAG^1(zero(X), b, one(X)) -> U17_AAG(X, binaryZ_in_g(X)) 18.16/5.63 ADDX_IN_AAG^1(zero(X), b, one(X)) -> BINARYZ_IN_G(X) 18.16/5.63 ADDX_IN_AAG^1(one(X), b, zero(Z)) -> U18_AAG(X, Z, succ_in_ag(X, Z)) 18.16/5.63 ADDX_IN_AAG^1(one(X), b, zero(Z)) -> SUCC_IN_AG(X, Z) 18.16/5.63 ADDX_IN_AAG^1(X, Y, Z) -> U19_AAG(X, Y, Z, addC_in_aag(X, Y, Z)) 18.16/5.63 ADDX_IN_AAG^1(X, Y, Z) -> ADDC_IN_AAG^1(X, Y, Z) 18.16/5.63 ADDC_IN_AAG^1(one(X), zero(Y), zero(Z)) -> U25_AAG(X, Y, Z, addY_in_aag(X, Y, Z)) 18.16/5.63 ADDC_IN_AAG^1(one(X), zero(Y), zero(Z)) -> ADDY_IN_AAG^1(X, Y, Z) 18.16/5.63 ADDY_IN_AAG^1(b, zero(Y), one(Y)) -> U20_AAG(Y, binaryZ_in_g(Y)) 18.16/5.63 ADDY_IN_AAG^1(b, zero(Y), one(Y)) -> BINARYZ_IN_G(Y) 18.16/5.63 ADDY_IN_AAG^1(b, one(Y), zero(Z)) -> U21_AAG(Y, Z, succ_in_ag(Y, Z)) 18.16/5.63 ADDY_IN_AAG^1(b, one(Y), zero(Z)) -> SUCC_IN_AG(Y, Z) 18.16/5.63 ADDY_IN_AAG^1(X, Y, Z) -> U22_AAG(X, Y, Z, addC_in_aag(X, Y, Z)) 18.16/5.63 ADDY_IN_AAG^1(X, Y, Z) -> ADDC_IN_AAG^1(X, Y, Z) 18.16/5.63 ADDC_IN_AAG^1(one(X), one(Y), one(Z)) -> U26_AAG(X, Y, Z, addc_in_aag(X, Y, Z)) 18.16/5.63 ADDC_IN_AAG^1(one(X), one(Y), one(Z)) -> ADDC_IN_AAG(X, Y, Z) 18.16/5.63 18.16/5.63 The TRS R consists of the following rules: 18.16/5.63 18.16/5.63 times_in_aag(one(b), X, X) -> times_out_aag(one(b), X, X) 18.16/5.63 times_in_aag(zero(R), S, zero(RS)) -> U35_aag(R, S, RS, times_in_aag(R, S, RS)) 18.16/5.63 times_in_aag(one(R), S, RSS) -> U36_aag(R, S, RSS, times_in_aaa(R, S, RS)) 18.16/5.63 times_in_aaa(one(b), X, X) -> times_out_aaa(one(b), X, X) 18.16/5.63 times_in_aaa(zero(R), S, zero(RS)) -> U35_aaa(R, S, RS, times_in_aaa(R, S, RS)) 18.16/5.63 times_in_aaa(one(R), S, RSS) -> U36_aaa(R, S, RSS, times_in_aaa(R, S, RS)) 18.16/5.63 U36_aaa(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aaa(R, S, RSS, add_in_aaa(S, zero(RS), RSS)) 18.16/5.63 add_in_aaa(b, b, b) -> add_out_aaa(b, b, b) 18.16/5.63 add_in_aaa(X, b, X) -> U1_aaa(X, binaryZ_in_a(X)) 18.16/5.63 binaryZ_in_a(zero(X)) -> U29_a(X, binaryZ_in_a(X)) 18.16/5.63 binaryZ_in_a(one(X)) -> U30_a(X, binary_in_a(X)) 18.16/5.63 binary_in_a(b) -> binary_out_a(b) 18.16/5.63 binary_in_a(zero(X)) -> U27_a(X, binaryZ_in_a(X)) 18.16/5.63 U27_a(X, binaryZ_out_a(X)) -> binary_out_a(zero(X)) 18.16/5.63 binary_in_a(one(X)) -> U28_a(X, binary_in_a(X)) 18.16/5.63 U28_a(X, binary_out_a(X)) -> binary_out_a(one(X)) 18.16/5.63 U30_a(X, binary_out_a(X)) -> binaryZ_out_a(one(X)) 18.16/5.63 U29_a(X, binaryZ_out_a(X)) -> binaryZ_out_a(zero(X)) 18.16/5.63 U1_aaa(X, binaryZ_out_a(X)) -> add_out_aaa(X, b, X) 18.16/5.63 add_in_aaa(b, Y, Y) -> U2_aaa(Y, binaryZ_in_a(Y)) 18.16/5.63 U2_aaa(Y, binaryZ_out_a(Y)) -> add_out_aaa(b, Y, Y) 18.16/5.63 add_in_aaa(X, Y, Z) -> U3_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.63 addz_in_aaa(zero(X), zero(Y), zero(Z)) -> U10_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.63 addz_in_aaa(zero(X), one(Y), one(Z)) -> U11_aaa(X, Y, Z, addx_in_aaa(X, Y, Z)) 18.16/5.63 addx_in_aaa(one(X), b, one(X)) -> U4_aaa(X, binary_in_a(X)) 18.16/5.63 U4_aaa(X, binary_out_a(X)) -> addx_out_aaa(one(X), b, one(X)) 18.16/5.63 addx_in_aaa(zero(X), b, zero(X)) -> U5_aaa(X, binaryZ_in_a(X)) 18.16/5.63 U5_aaa(X, binaryZ_out_a(X)) -> addx_out_aaa(zero(X), b, zero(X)) 18.16/5.63 addx_in_aaa(X, Y, Z) -> U6_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.63 addz_in_aaa(one(X), zero(Y), one(Z)) -> U12_aaa(X, Y, Z, addy_in_aaa(X, Y, Z)) 18.16/5.63 addy_in_aaa(b, one(Y), one(Y)) -> U7_aaa(Y, binary_in_a(Y)) 18.16/5.63 U7_aaa(Y, binary_out_a(Y)) -> addy_out_aaa(b, one(Y), one(Y)) 18.16/5.63 addy_in_aaa(b, zero(Y), zero(Y)) -> U8_aaa(Y, binaryZ_in_a(Y)) 18.16/5.63 U8_aaa(Y, binaryZ_out_a(Y)) -> addy_out_aaa(b, zero(Y), zero(Y)) 18.16/5.63 addy_in_aaa(X, Y, Z) -> U9_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.63 addz_in_aaa(one(X), one(Y), zero(Z)) -> U13_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.16/5.63 addc_in_aaa(b, b, one(b)) -> addc_out_aaa(b, b, one(b)) 18.16/5.63 addc_in_aaa(X, b, Z) -> U14_aaa(X, Z, succZ_in_aa(X, Z)) 18.16/5.63 succZ_in_aa(zero(X), one(X)) -> U33_aa(X, binaryZ_in_a(X)) 18.16/5.63 U33_aa(X, binaryZ_out_a(X)) -> succZ_out_aa(zero(X), one(X)) 18.16/5.63 succZ_in_aa(one(X), zero(Z)) -> U34_aa(X, Z, succ_in_aa(X, Z)) 18.16/5.63 succ_in_aa(b, one(b)) -> succ_out_aa(b, one(b)) 18.16/5.63 succ_in_aa(zero(X), one(X)) -> U31_aa(X, binaryZ_in_a(X)) 18.16/5.63 U31_aa(X, binaryZ_out_a(X)) -> succ_out_aa(zero(X), one(X)) 18.16/5.63 succ_in_aa(one(X), zero(Z)) -> U32_aa(X, Z, succ_in_aa(X, Z)) 18.16/5.63 U32_aa(X, Z, succ_out_aa(X, Z)) -> succ_out_aa(one(X), zero(Z)) 18.16/5.63 U34_aa(X, Z, succ_out_aa(X, Z)) -> succZ_out_aa(one(X), zero(Z)) 18.16/5.63 U14_aaa(X, Z, succZ_out_aa(X, Z)) -> addc_out_aaa(X, b, Z) 18.16/5.63 addc_in_aaa(b, Y, Z) -> U15_aaa(Y, Z, succZ_in_aa(Y, Z)) 18.16/5.63 U15_aaa(Y, Z, succZ_out_aa(Y, Z)) -> addc_out_aaa(b, Y, Z) 18.16/5.63 addc_in_aaa(X, Y, Z) -> U16_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.16/5.63 addC_in_aaa(zero(X), zero(Y), one(Z)) -> U23_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.63 U23_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), zero(Y), one(Z)) 18.16/5.63 addC_in_aaa(zero(X), one(Y), zero(Z)) -> U24_aaa(X, Y, Z, addX_in_aaa(X, Y, Z)) 18.16/5.63 addX_in_aaa(zero(X), b, one(X)) -> U17_aaa(X, binaryZ_in_a(X)) 18.16/5.63 U17_aaa(X, binaryZ_out_a(X)) -> addX_out_aaa(zero(X), b, one(X)) 18.16/5.63 addX_in_aaa(one(X), b, zero(Z)) -> U18_aaa(X, Z, succ_in_aa(X, Z)) 18.16/5.63 U18_aaa(X, Z, succ_out_aa(X, Z)) -> addX_out_aaa(one(X), b, zero(Z)) 18.16/5.63 addX_in_aaa(X, Y, Z) -> U19_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.16/5.63 addC_in_aaa(one(X), zero(Y), zero(Z)) -> U25_aaa(X, Y, Z, addY_in_aaa(X, Y, Z)) 18.16/5.63 addY_in_aaa(b, zero(Y), one(Y)) -> U20_aaa(Y, binaryZ_in_a(Y)) 18.16/5.63 U20_aaa(Y, binaryZ_out_a(Y)) -> addY_out_aaa(b, zero(Y), one(Y)) 18.16/5.63 addY_in_aaa(b, one(Y), zero(Z)) -> U21_aaa(Y, Z, succ_in_aa(Y, Z)) 18.16/5.63 U21_aaa(Y, Z, succ_out_aa(Y, Z)) -> addY_out_aaa(b, one(Y), zero(Z)) 18.16/5.63 addY_in_aaa(X, Y, Z) -> U22_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.16/5.63 addC_in_aaa(one(X), one(Y), one(Z)) -> U26_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.16/5.63 U26_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), one(Y), one(Z)) 18.16/5.63 U22_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addY_out_aaa(X, Y, Z) 18.16/5.63 U25_aaa(X, Y, Z, addY_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), zero(Y), zero(Z)) 18.16/5.63 U19_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addX_out_aaa(X, Y, Z) 18.16/5.63 U24_aaa(X, Y, Z, addX_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), one(Y), zero(Z)) 18.16/5.63 U16_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addc_out_aaa(X, Y, Z) 18.16/5.63 U13_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), one(Y), zero(Z)) 18.16/5.63 U9_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addy_out_aaa(X, Y, Z) 18.16/5.63 U12_aaa(X, Y, Z, addy_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), zero(Y), one(Z)) 18.16/5.63 U6_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addx_out_aaa(X, Y, Z) 18.16/5.63 U11_aaa(X, Y, Z, addx_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), one(Y), one(Z)) 18.16/5.63 U10_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), zero(Y), zero(Z)) 18.16/5.63 U3_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> add_out_aaa(X, Y, Z) 18.16/5.63 U37_aaa(R, S, RSS, add_out_aaa(S, zero(RS), RSS)) -> times_out_aaa(one(R), S, RSS) 18.16/5.63 U35_aaa(R, S, RS, times_out_aaa(R, S, RS)) -> times_out_aaa(zero(R), S, zero(RS)) 18.16/5.63 U36_aag(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aag(R, S, RSS, add_in_aag(S, zero(RS), RSS)) 18.16/5.63 add_in_aag(b, b, b) -> add_out_aag(b, b, b) 18.16/5.63 add_in_aag(X, b, X) -> U1_aag(X, binaryZ_in_g(X)) 18.16/5.63 binaryZ_in_g(zero(X)) -> U29_g(X, binaryZ_in_g(X)) 18.16/5.63 binaryZ_in_g(one(X)) -> U30_g(X, binary_in_g(X)) 18.16/5.63 binary_in_g(b) -> binary_out_g(b) 18.16/5.63 binary_in_g(zero(X)) -> U27_g(X, binaryZ_in_g(X)) 18.16/5.63 U27_g(X, binaryZ_out_g(X)) -> binary_out_g(zero(X)) 18.16/5.63 binary_in_g(one(X)) -> U28_g(X, binary_in_g(X)) 18.16/5.63 U28_g(X, binary_out_g(X)) -> binary_out_g(one(X)) 18.16/5.63 U30_g(X, binary_out_g(X)) -> binaryZ_out_g(one(X)) 18.16/5.63 U29_g(X, binaryZ_out_g(X)) -> binaryZ_out_g(zero(X)) 18.16/5.63 U1_aag(X, binaryZ_out_g(X)) -> add_out_aag(X, b, X) 18.16/5.63 add_in_aag(b, Y, Y) -> U2_aag(Y, binaryZ_in_g(Y)) 18.16/5.63 U2_aag(Y, binaryZ_out_g(Y)) -> add_out_aag(b, Y, Y) 18.16/5.63 add_in_aag(X, Y, Z) -> U3_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.63 addz_in_aag(zero(X), zero(Y), zero(Z)) -> U10_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.63 addz_in_aag(zero(X), one(Y), one(Z)) -> U11_aag(X, Y, Z, addx_in_aag(X, Y, Z)) 18.16/5.63 addx_in_aag(one(X), b, one(X)) -> U4_aag(X, binary_in_g(X)) 18.16/5.63 U4_aag(X, binary_out_g(X)) -> addx_out_aag(one(X), b, one(X)) 18.16/5.63 addx_in_aag(zero(X), b, zero(X)) -> U5_aag(X, binaryZ_in_g(X)) 18.16/5.63 U5_aag(X, binaryZ_out_g(X)) -> addx_out_aag(zero(X), b, zero(X)) 18.16/5.63 addx_in_aag(X, Y, Z) -> U6_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.63 addz_in_aag(one(X), zero(Y), one(Z)) -> U12_aag(X, Y, Z, addy_in_aag(X, Y, Z)) 18.16/5.63 addy_in_aag(b, one(Y), one(Y)) -> U7_aag(Y, binary_in_g(Y)) 18.16/5.63 U7_aag(Y, binary_out_g(Y)) -> addy_out_aag(b, one(Y), one(Y)) 18.16/5.63 addy_in_aag(b, zero(Y), zero(Y)) -> U8_aag(Y, binaryZ_in_g(Y)) 18.16/5.63 U8_aag(Y, binaryZ_out_g(Y)) -> addy_out_aag(b, zero(Y), zero(Y)) 18.16/5.63 addy_in_aag(X, Y, Z) -> U9_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.63 addz_in_aag(one(X), one(Y), zero(Z)) -> U13_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.16/5.63 addc_in_aag(b, b, one(b)) -> addc_out_aag(b, b, one(b)) 18.16/5.63 addc_in_aag(X, b, Z) -> U14_aag(X, Z, succZ_in_ag(X, Z)) 18.16/5.63 succZ_in_ag(zero(X), one(X)) -> U33_ag(X, binaryZ_in_g(X)) 18.16/5.63 U33_ag(X, binaryZ_out_g(X)) -> succZ_out_ag(zero(X), one(X)) 18.16/5.63 succZ_in_ag(one(X), zero(Z)) -> U34_ag(X, Z, succ_in_ag(X, Z)) 18.16/5.63 succ_in_ag(b, one(b)) -> succ_out_ag(b, one(b)) 18.16/5.63 succ_in_ag(zero(X), one(X)) -> U31_ag(X, binaryZ_in_g(X)) 18.16/5.63 U31_ag(X, binaryZ_out_g(X)) -> succ_out_ag(zero(X), one(X)) 18.16/5.63 succ_in_ag(one(X), zero(Z)) -> U32_ag(X, Z, succ_in_ag(X, Z)) 18.16/5.63 U32_ag(X, Z, succ_out_ag(X, Z)) -> succ_out_ag(one(X), zero(Z)) 18.16/5.63 U34_ag(X, Z, succ_out_ag(X, Z)) -> succZ_out_ag(one(X), zero(Z)) 18.16/5.63 U14_aag(X, Z, succZ_out_ag(X, Z)) -> addc_out_aag(X, b, Z) 18.16/5.63 addc_in_aag(b, Y, Z) -> U15_aag(Y, Z, succZ_in_ag(Y, Z)) 18.16/5.63 U15_aag(Y, Z, succZ_out_ag(Y, Z)) -> addc_out_aag(b, Y, Z) 18.16/5.63 addc_in_aag(X, Y, Z) -> U16_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.16/5.63 addC_in_aag(zero(X), zero(Y), one(Z)) -> U23_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.63 U23_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), zero(Y), one(Z)) 18.16/5.63 addC_in_aag(zero(X), one(Y), zero(Z)) -> U24_aag(X, Y, Z, addX_in_aag(X, Y, Z)) 18.16/5.63 addX_in_aag(zero(X), b, one(X)) -> U17_aag(X, binaryZ_in_g(X)) 18.16/5.63 U17_aag(X, binaryZ_out_g(X)) -> addX_out_aag(zero(X), b, one(X)) 18.16/5.63 addX_in_aag(one(X), b, zero(Z)) -> U18_aag(X, Z, succ_in_ag(X, Z)) 18.16/5.63 U18_aag(X, Z, succ_out_ag(X, Z)) -> addX_out_aag(one(X), b, zero(Z)) 18.16/5.63 addX_in_aag(X, Y, Z) -> U19_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.16/5.63 addC_in_aag(one(X), zero(Y), zero(Z)) -> U25_aag(X, Y, Z, addY_in_aag(X, Y, Z)) 18.16/5.63 addY_in_aag(b, zero(Y), one(Y)) -> U20_aag(Y, binaryZ_in_g(Y)) 18.16/5.63 U20_aag(Y, binaryZ_out_g(Y)) -> addY_out_aag(b, zero(Y), one(Y)) 18.16/5.63 addY_in_aag(b, one(Y), zero(Z)) -> U21_aag(Y, Z, succ_in_ag(Y, Z)) 18.16/5.63 U21_aag(Y, Z, succ_out_ag(Y, Z)) -> addY_out_aag(b, one(Y), zero(Z)) 18.16/5.63 addY_in_aag(X, Y, Z) -> U22_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.16/5.63 addC_in_aag(one(X), one(Y), one(Z)) -> U26_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.16/5.63 U26_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addC_out_aag(one(X), one(Y), one(Z)) 18.16/5.63 U22_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addY_out_aag(X, Y, Z) 18.16/5.63 U25_aag(X, Y, Z, addY_out_aag(X, Y, Z)) -> addC_out_aag(one(X), zero(Y), zero(Z)) 18.16/5.63 U19_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addX_out_aag(X, Y, Z) 18.16/5.63 U24_aag(X, Y, Z, addX_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), one(Y), zero(Z)) 18.16/5.63 U16_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addc_out_aag(X, Y, Z) 18.16/5.63 U13_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addz_out_aag(one(X), one(Y), zero(Z)) 18.16/5.63 U9_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addy_out_aag(X, Y, Z) 18.16/5.63 U12_aag(X, Y, Z, addy_out_aag(X, Y, Z)) -> addz_out_aag(one(X), zero(Y), one(Z)) 18.16/5.63 U6_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addx_out_aag(X, Y, Z) 18.16/5.63 U11_aag(X, Y, Z, addx_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), one(Y), one(Z)) 18.16/5.63 U10_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), zero(Y), zero(Z)) 18.16/5.63 U3_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> add_out_aag(X, Y, Z) 18.16/5.63 U37_aag(R, S, RSS, add_out_aag(S, zero(RS), RSS)) -> times_out_aag(one(R), S, RSS) 18.16/5.63 U35_aag(R, S, RS, times_out_aag(R, S, RS)) -> times_out_aag(zero(R), S, zero(RS)) 18.16/5.63 18.16/5.63 The argument filtering Pi contains the following mapping: 18.16/5.63 times_in_aag(x1, x2, x3) = times_in_aag(x3) 18.16/5.63 18.16/5.63 times_out_aag(x1, x2, x3) = times_out_aag(x1, x2, x3) 18.16/5.63 18.16/5.63 zero(x1) = zero(x1) 18.16/5.63 18.16/5.63 U35_aag(x1, x2, x3, x4) = U35_aag(x3, x4) 18.16/5.63 18.16/5.63 U36_aag(x1, x2, x3, x4) = U36_aag(x3, x4) 18.16/5.63 18.16/5.63 times_in_aaa(x1, x2, x3) = times_in_aaa 18.16/5.63 18.16/5.63 times_out_aaa(x1, x2, x3) = times_out_aaa(x1) 18.16/5.63 18.16/5.63 U35_aaa(x1, x2, x3, x4) = U35_aaa(x4) 18.16/5.63 18.16/5.63 U36_aaa(x1, x2, x3, x4) = U36_aaa(x4) 18.16/5.63 18.16/5.63 U37_aaa(x1, x2, x3, x4) = U37_aaa(x1, x4) 18.16/5.63 18.16/5.63 add_in_aaa(x1, x2, x3) = add_in_aaa 18.16/5.63 18.16/5.63 add_out_aaa(x1, x2, x3) = add_out_aaa(x1, x2, x3) 18.16/5.63 18.16/5.63 U1_aaa(x1, x2) = U1_aaa(x2) 18.16/5.63 18.16/5.63 binaryZ_in_a(x1) = binaryZ_in_a 18.16/5.63 18.16/5.63 U29_a(x1, x2) = U29_a(x2) 18.16/5.63 18.16/5.63 U30_a(x1, x2) = U30_a(x2) 18.16/5.63 18.16/5.63 binary_in_a(x1) = binary_in_a 18.16/5.63 18.16/5.63 binary_out_a(x1) = binary_out_a(x1) 18.16/5.63 18.16/5.63 U27_a(x1, x2) = U27_a(x2) 18.16/5.63 18.16/5.63 binaryZ_out_a(x1) = binaryZ_out_a(x1) 18.16/5.63 18.16/5.63 U28_a(x1, x2) = U28_a(x2) 18.16/5.63 18.16/5.63 U2_aaa(x1, x2) = U2_aaa(x2) 18.16/5.63 18.16/5.63 U3_aaa(x1, x2, x3, x4) = U3_aaa(x4) 18.16/5.63 18.16/5.63 addz_in_aaa(x1, x2, x3) = addz_in_aaa 18.16/5.63 18.16/5.63 U10_aaa(x1, x2, x3, x4) = U10_aaa(x4) 18.16/5.63 18.16/5.63 U11_aaa(x1, x2, x3, x4) = U11_aaa(x4) 18.16/5.63 18.16/5.63 addx_in_aaa(x1, x2, x3) = addx_in_aaa 18.16/5.63 18.16/5.63 U4_aaa(x1, x2) = U4_aaa(x2) 18.16/5.63 18.16/5.63 addx_out_aaa(x1, x2, x3) = addx_out_aaa(x1, x2, x3) 18.16/5.63 18.16/5.63 U5_aaa(x1, x2) = U5_aaa(x2) 18.16/5.63 18.16/5.63 U6_aaa(x1, x2, x3, x4) = U6_aaa(x4) 18.16/5.63 18.16/5.63 U12_aaa(x1, x2, x3, x4) = U12_aaa(x4) 18.16/5.63 18.16/5.63 addy_in_aaa(x1, x2, x3) = addy_in_aaa 18.16/5.63 18.16/5.63 U7_aaa(x1, x2) = U7_aaa(x2) 18.16/5.63 18.16/5.63 addy_out_aaa(x1, x2, x3) = addy_out_aaa(x1, x2, x3) 18.16/5.63 18.16/5.63 U8_aaa(x1, x2) = U8_aaa(x2) 18.16/5.63 18.16/5.63 U9_aaa(x1, x2, x3, x4) = U9_aaa(x4) 18.16/5.63 18.16/5.63 U13_aaa(x1, x2, x3, x4) = U13_aaa(x4) 18.16/5.63 18.16/5.63 addc_in_aaa(x1, x2, x3) = addc_in_aaa 18.16/5.63 18.16/5.63 addc_out_aaa(x1, x2, x3) = addc_out_aaa(x1, x2, x3) 18.16/5.63 18.16/5.63 U14_aaa(x1, x2, x3) = U14_aaa(x3) 18.16/5.63 18.16/5.63 succZ_in_aa(x1, x2) = succZ_in_aa 18.16/5.63 18.16/5.63 U33_aa(x1, x2) = U33_aa(x2) 18.16/5.63 18.16/5.63 succZ_out_aa(x1, x2) = succZ_out_aa(x1, x2) 18.16/5.63 18.16/5.63 U34_aa(x1, x2, x3) = U34_aa(x3) 18.16/5.63 18.16/5.63 succ_in_aa(x1, x2) = succ_in_aa 18.16/5.63 18.16/5.63 succ_out_aa(x1, x2) = succ_out_aa(x1, x2) 18.16/5.63 18.16/5.63 U31_aa(x1, x2) = U31_aa(x2) 18.16/5.63 18.16/5.63 U32_aa(x1, x2, x3) = U32_aa(x3) 18.16/5.63 18.16/5.63 U15_aaa(x1, x2, x3) = U15_aaa(x3) 18.16/5.63 18.16/5.63 U16_aaa(x1, x2, x3, x4) = U16_aaa(x4) 18.16/5.63 18.16/5.63 addC_in_aaa(x1, x2, x3) = addC_in_aaa 18.16/5.63 18.16/5.63 U23_aaa(x1, x2, x3, x4) = U23_aaa(x4) 18.16/5.63 18.16/5.63 addz_out_aaa(x1, x2, x3) = addz_out_aaa(x1, x2, x3) 18.16/5.63 18.16/5.63 addC_out_aaa(x1, x2, x3) = addC_out_aaa(x1, x2, x3) 18.16/5.63 18.16/5.63 U24_aaa(x1, x2, x3, x4) = U24_aaa(x4) 18.16/5.63 18.16/5.63 addX_in_aaa(x1, x2, x3) = addX_in_aaa 18.16/5.63 18.16/5.63 U17_aaa(x1, x2) = U17_aaa(x2) 18.16/5.63 18.16/5.63 addX_out_aaa(x1, x2, x3) = addX_out_aaa(x1, x2, x3) 18.16/5.63 18.16/5.63 U18_aaa(x1, x2, x3) = U18_aaa(x3) 18.16/5.63 18.16/5.63 U19_aaa(x1, x2, x3, x4) = U19_aaa(x4) 18.16/5.63 18.16/5.63 U25_aaa(x1, x2, x3, x4) = U25_aaa(x4) 18.16/5.63 18.16/5.63 addY_in_aaa(x1, x2, x3) = addY_in_aaa 18.16/5.63 18.16/5.63 U20_aaa(x1, x2) = U20_aaa(x2) 18.16/5.63 18.16/5.63 addY_out_aaa(x1, x2, x3) = addY_out_aaa(x1, x2, x3) 18.16/5.63 18.16/5.63 U21_aaa(x1, x2, x3) = U21_aaa(x3) 18.16/5.63 18.16/5.63 U22_aaa(x1, x2, x3, x4) = U22_aaa(x4) 18.16/5.63 18.16/5.63 U26_aaa(x1, x2, x3, x4) = U26_aaa(x4) 18.16/5.63 18.16/5.63 U37_aag(x1, x2, x3, x4) = U37_aag(x1, x3, x4) 18.16/5.63 18.16/5.63 add_in_aag(x1, x2, x3) = add_in_aag(x3) 18.16/5.63 18.16/5.63 b = b 18.16/5.63 18.16/5.63 add_out_aag(x1, x2, x3) = add_out_aag(x1, x2, x3) 18.16/5.63 18.16/5.63 U1_aag(x1, x2) = U1_aag(x1, x2) 18.16/5.63 18.16/5.63 binaryZ_in_g(x1) = binaryZ_in_g(x1) 18.16/5.63 18.16/5.63 U29_g(x1, x2) = U29_g(x1, x2) 18.16/5.63 18.16/5.63 one(x1) = one(x1) 18.16/5.63 18.16/5.63 U30_g(x1, x2) = U30_g(x1, x2) 18.16/5.63 18.16/5.63 binary_in_g(x1) = binary_in_g(x1) 18.16/5.63 18.16/5.63 binary_out_g(x1) = binary_out_g(x1) 18.16/5.63 18.16/5.63 U27_g(x1, x2) = U27_g(x1, x2) 18.16/5.63 18.16/5.63 binaryZ_out_g(x1) = binaryZ_out_g(x1) 18.16/5.63 18.16/5.63 U28_g(x1, x2) = U28_g(x1, x2) 18.16/5.63 18.16/5.63 U2_aag(x1, x2) = U2_aag(x1, x2) 18.16/5.63 18.16/5.63 U3_aag(x1, x2, x3, x4) = U3_aag(x3, x4) 18.16/5.63 18.16/5.63 addz_in_aag(x1, x2, x3) = addz_in_aag(x3) 18.16/5.63 18.16/5.63 U10_aag(x1, x2, x3, x4) = U10_aag(x3, x4) 18.16/5.63 18.16/5.63 U11_aag(x1, x2, x3, x4) = U11_aag(x3, x4) 18.16/5.63 18.16/5.63 addx_in_aag(x1, x2, x3) = addx_in_aag(x3) 18.16/5.63 18.16/5.63 U4_aag(x1, x2) = U4_aag(x1, x2) 18.16/5.63 18.16/5.63 addx_out_aag(x1, x2, x3) = addx_out_aag(x1, x2, x3) 18.16/5.63 18.16/5.63 U5_aag(x1, x2) = U5_aag(x1, x2) 18.16/5.63 18.16/5.63 U6_aag(x1, x2, x3, x4) = U6_aag(x3, x4) 18.16/5.63 18.16/5.63 U12_aag(x1, x2, x3, x4) = U12_aag(x3, x4) 18.16/5.63 18.16/5.63 addy_in_aag(x1, x2, x3) = addy_in_aag(x3) 18.16/5.63 18.16/5.63 U7_aag(x1, x2) = U7_aag(x1, x2) 18.16/5.63 18.16/5.63 addy_out_aag(x1, x2, x3) = addy_out_aag(x1, x2, x3) 18.16/5.63 18.16/5.63 U8_aag(x1, x2) = U8_aag(x1, x2) 18.16/5.63 18.16/5.63 U9_aag(x1, x2, x3, x4) = U9_aag(x3, x4) 18.16/5.63 18.16/5.63 U13_aag(x1, x2, x3, x4) = U13_aag(x3, x4) 18.16/5.63 18.16/5.63 addc_in_aag(x1, x2, x3) = addc_in_aag(x3) 18.16/5.63 18.16/5.63 addc_out_aag(x1, x2, x3) = addc_out_aag(x1, x2, x3) 18.16/5.63 18.16/5.63 U14_aag(x1, x2, x3) = U14_aag(x2, x3) 18.16/5.63 18.16/5.63 succZ_in_ag(x1, x2) = succZ_in_ag(x2) 18.16/5.63 18.16/5.63 U33_ag(x1, x2) = U33_ag(x1, x2) 18.16/5.63 18.16/5.63 succZ_out_ag(x1, x2) = succZ_out_ag(x1, x2) 18.16/5.63 18.16/5.63 U34_ag(x1, x2, x3) = U34_ag(x2, x3) 18.16/5.63 18.16/5.63 succ_in_ag(x1, x2) = succ_in_ag(x2) 18.16/5.63 18.16/5.63 succ_out_ag(x1, x2) = succ_out_ag(x1, x2) 18.16/5.63 18.16/5.63 U31_ag(x1, x2) = U31_ag(x1, x2) 18.16/5.63 18.16/5.63 U32_ag(x1, x2, x3) = U32_ag(x2, x3) 18.16/5.63 18.16/5.63 U15_aag(x1, x2, x3) = U15_aag(x2, x3) 18.16/5.63 18.16/5.63 U16_aag(x1, x2, x3, x4) = U16_aag(x3, x4) 18.16/5.63 18.16/5.63 addC_in_aag(x1, x2, x3) = addC_in_aag(x3) 18.16/5.63 18.16/5.63 U23_aag(x1, x2, x3, x4) = U23_aag(x3, x4) 18.16/5.63 18.16/5.63 addz_out_aag(x1, x2, x3) = addz_out_aag(x1, x2, x3) 18.16/5.63 18.16/5.63 addC_out_aag(x1, x2, x3) = addC_out_aag(x1, x2, x3) 18.16/5.63 18.16/5.63 U24_aag(x1, x2, x3, x4) = U24_aag(x3, x4) 18.16/5.63 18.16/5.63 addX_in_aag(x1, x2, x3) = addX_in_aag(x3) 18.16/5.63 18.16/5.63 U17_aag(x1, x2) = U17_aag(x1, x2) 18.16/5.63 18.16/5.63 addX_out_aag(x1, x2, x3) = addX_out_aag(x1, x2, x3) 18.16/5.63 18.16/5.63 U18_aag(x1, x2, x3) = U18_aag(x2, x3) 18.16/5.63 18.16/5.63 U19_aag(x1, x2, x3, x4) = U19_aag(x3, x4) 18.16/5.63 18.16/5.63 U25_aag(x1, x2, x3, x4) = U25_aag(x3, x4) 18.16/5.63 18.16/5.63 addY_in_aag(x1, x2, x3) = addY_in_aag(x3) 18.16/5.63 18.16/5.63 U20_aag(x1, x2) = U20_aag(x1, x2) 18.16/5.63 18.16/5.63 addY_out_aag(x1, x2, x3) = addY_out_aag(x1, x2, x3) 18.16/5.63 18.16/5.63 U21_aag(x1, x2, x3) = U21_aag(x2, x3) 18.16/5.63 18.16/5.63 U22_aag(x1, x2, x3, x4) = U22_aag(x3, x4) 18.16/5.63 18.16/5.63 U26_aag(x1, x2, x3, x4) = U26_aag(x3, x4) 18.16/5.63 18.16/5.63 TIMES_IN_AAG(x1, x2, x3) = TIMES_IN_AAG(x3) 18.16/5.63 18.16/5.63 U35_AAG(x1, x2, x3, x4) = U35_AAG(x3, x4) 18.16/5.63 18.16/5.63 U36_AAG(x1, x2, x3, x4) = U36_AAG(x3, x4) 18.16/5.63 18.16/5.63 TIMES_IN_AAA(x1, x2, x3) = TIMES_IN_AAA 18.16/5.63 18.16/5.63 U35_AAA(x1, x2, x3, x4) = U35_AAA(x4) 18.16/5.63 18.16/5.63 U36_AAA(x1, x2, x3, x4) = U36_AAA(x4) 18.16/5.63 18.16/5.63 U37_AAA(x1, x2, x3, x4) = U37_AAA(x1, x4) 18.16/5.63 18.16/5.63 ADD_IN_AAA(x1, x2, x3) = ADD_IN_AAA 18.16/5.63 18.16/5.63 U1_AAA(x1, x2) = U1_AAA(x2) 18.16/5.63 18.16/5.63 BINARYZ_IN_A(x1) = BINARYZ_IN_A 18.16/5.63 18.16/5.63 U29_A(x1, x2) = U29_A(x2) 18.16/5.63 18.16/5.63 U30_A(x1, x2) = U30_A(x2) 18.16/5.63 18.16/5.63 BINARY_IN_A(x1) = BINARY_IN_A 18.16/5.63 18.16/5.63 U27_A(x1, x2) = U27_A(x2) 18.16/5.63 18.16/5.63 U28_A(x1, x2) = U28_A(x2) 18.16/5.63 18.16/5.63 U2_AAA(x1, x2) = U2_AAA(x2) 18.16/5.63 18.16/5.63 U3_AAA(x1, x2, x3, x4) = U3_AAA(x4) 18.16/5.63 18.16/5.63 ADDZ_IN_AAA(x1, x2, x3) = ADDZ_IN_AAA 18.16/5.63 18.16/5.63 U10_AAA(x1, x2, x3, x4) = U10_AAA(x4) 18.16/5.63 18.16/5.63 U11_AAA(x1, x2, x3, x4) = U11_AAA(x4) 18.16/5.63 18.16/5.63 ADDX_IN_AAA(x1, x2, x3) = ADDX_IN_AAA 18.16/5.63 18.16/5.63 U4_AAA(x1, x2) = U4_AAA(x2) 18.16/5.63 18.16/5.63 U5_AAA(x1, x2) = U5_AAA(x2) 18.16/5.63 18.16/5.63 U6_AAA(x1, x2, x3, x4) = U6_AAA(x4) 18.16/5.63 18.16/5.63 U12_AAA(x1, x2, x3, x4) = U12_AAA(x4) 18.16/5.63 18.16/5.63 ADDY_IN_AAA(x1, x2, x3) = ADDY_IN_AAA 18.16/5.63 18.16/5.63 U7_AAA(x1, x2) = U7_AAA(x2) 18.16/5.63 18.16/5.63 U8_AAA(x1, x2) = U8_AAA(x2) 18.16/5.63 18.16/5.63 U9_AAA(x1, x2, x3, x4) = U9_AAA(x4) 18.16/5.63 18.16/5.63 U13_AAA(x1, x2, x3, x4) = U13_AAA(x4) 18.16/5.63 18.16/5.63 ADDC_IN_AAA(x1, x2, x3) = ADDC_IN_AAA 18.16/5.63 18.16/5.63 U14_AAA(x1, x2, x3) = U14_AAA(x3) 18.16/5.63 18.16/5.63 SUCCZ_IN_AA(x1, x2) = SUCCZ_IN_AA 18.16/5.63 18.16/5.63 U33_AA(x1, x2) = U33_AA(x2) 18.16/5.63 18.16/5.63 U34_AA(x1, x2, x3) = U34_AA(x3) 18.16/5.63 18.16/5.63 SUCC_IN_AA(x1, x2) = SUCC_IN_AA 18.16/5.63 18.16/5.63 U31_AA(x1, x2) = U31_AA(x2) 18.16/5.63 18.16/5.63 U32_AA(x1, x2, x3) = U32_AA(x3) 18.16/5.63 18.16/5.63 U15_AAA(x1, x2, x3) = U15_AAA(x3) 18.16/5.63 18.16/5.63 U16_AAA(x1, x2, x3, x4) = U16_AAA(x4) 18.16/5.63 18.16/5.63 ADDC_IN_AAA^1(x1, x2, x3) = ADDC_IN_AAA^1 18.16/5.63 18.16/5.63 U23_AAA(x1, x2, x3, x4) = U23_AAA(x4) 18.16/5.63 18.16/5.63 U24_AAA(x1, x2, x3, x4) = U24_AAA(x4) 18.16/5.63 18.16/5.63 ADDX_IN_AAA^1(x1, x2, x3) = ADDX_IN_AAA^1 18.16/5.63 18.16/5.63 U17_AAA(x1, x2) = U17_AAA(x2) 18.16/5.63 18.16/5.63 U18_AAA(x1, x2, x3) = U18_AAA(x3) 18.16/5.63 18.16/5.63 U19_AAA(x1, x2, x3, x4) = U19_AAA(x4) 18.16/5.63 18.16/5.63 U25_AAA(x1, x2, x3, x4) = U25_AAA(x4) 18.16/5.63 18.16/5.63 ADDY_IN_AAA^1(x1, x2, x3) = ADDY_IN_AAA^1 18.16/5.63 18.16/5.63 U20_AAA(x1, x2) = U20_AAA(x2) 18.16/5.63 18.16/5.63 U21_AAA(x1, x2, x3) = U21_AAA(x3) 18.16/5.63 18.16/5.63 U22_AAA(x1, x2, x3, x4) = U22_AAA(x4) 18.16/5.63 18.16/5.63 U26_AAA(x1, x2, x3, x4) = U26_AAA(x4) 18.16/5.63 18.16/5.63 U37_AAG(x1, x2, x3, x4) = U37_AAG(x1, x3, x4) 18.16/5.63 18.16/5.63 ADD_IN_AAG(x1, x2, x3) = ADD_IN_AAG(x3) 18.16/5.63 18.16/5.63 U1_AAG(x1, x2) = U1_AAG(x1, x2) 18.16/5.63 18.16/5.63 BINARYZ_IN_G(x1) = BINARYZ_IN_G(x1) 18.16/5.63 18.16/5.63 U29_G(x1, x2) = U29_G(x1, x2) 18.16/5.63 18.16/5.63 U30_G(x1, x2) = U30_G(x1, x2) 18.16/5.63 18.16/5.63 BINARY_IN_G(x1) = BINARY_IN_G(x1) 18.16/5.63 18.16/5.63 U27_G(x1, x2) = U27_G(x1, x2) 18.16/5.63 18.16/5.63 U28_G(x1, x2) = U28_G(x1, x2) 18.16/5.63 18.16/5.63 U2_AAG(x1, x2) = U2_AAG(x1, x2) 18.16/5.63 18.16/5.63 U3_AAG(x1, x2, x3, x4) = U3_AAG(x3, x4) 18.16/5.63 18.16/5.63 ADDZ_IN_AAG(x1, x2, x3) = ADDZ_IN_AAG(x3) 18.16/5.63 18.16/5.63 U10_AAG(x1, x2, x3, x4) = U10_AAG(x3, x4) 18.16/5.63 18.16/5.63 U11_AAG(x1, x2, x3, x4) = U11_AAG(x3, x4) 18.16/5.63 18.16/5.63 ADDX_IN_AAG(x1, x2, x3) = ADDX_IN_AAG(x3) 18.16/5.63 18.16/5.63 U4_AAG(x1, x2) = U4_AAG(x1, x2) 18.16/5.63 18.16/5.63 U5_AAG(x1, x2) = U5_AAG(x1, x2) 18.16/5.63 18.16/5.63 U6_AAG(x1, x2, x3, x4) = U6_AAG(x3, x4) 18.16/5.63 18.16/5.63 U12_AAG(x1, x2, x3, x4) = U12_AAG(x3, x4) 18.16/5.63 18.16/5.63 ADDY_IN_AAG(x1, x2, x3) = ADDY_IN_AAG(x3) 18.16/5.63 18.16/5.63 U7_AAG(x1, x2) = U7_AAG(x1, x2) 18.16/5.63 18.16/5.63 U8_AAG(x1, x2) = U8_AAG(x1, x2) 18.16/5.63 18.16/5.63 U9_AAG(x1, x2, x3, x4) = U9_AAG(x3, x4) 18.16/5.63 18.16/5.63 U13_AAG(x1, x2, x3, x4) = U13_AAG(x3, x4) 18.16/5.63 18.16/5.63 ADDC_IN_AAG(x1, x2, x3) = ADDC_IN_AAG(x3) 18.16/5.63 18.16/5.63 U14_AAG(x1, x2, x3) = U14_AAG(x2, x3) 18.16/5.63 18.16/5.63 SUCCZ_IN_AG(x1, x2) = SUCCZ_IN_AG(x2) 18.16/5.63 18.16/5.63 U33_AG(x1, x2) = U33_AG(x1, x2) 18.16/5.63 18.16/5.63 U34_AG(x1, x2, x3) = U34_AG(x2, x3) 18.16/5.63 18.16/5.63 SUCC_IN_AG(x1, x2) = SUCC_IN_AG(x2) 18.16/5.63 18.16/5.63 U31_AG(x1, x2) = U31_AG(x1, x2) 18.16/5.63 18.16/5.63 U32_AG(x1, x2, x3) = U32_AG(x2, x3) 18.16/5.63 18.16/5.63 U15_AAG(x1, x2, x3) = U15_AAG(x2, x3) 18.16/5.63 18.16/5.63 U16_AAG(x1, x2, x3, x4) = U16_AAG(x3, x4) 18.16/5.63 18.16/5.63 ADDC_IN_AAG^1(x1, x2, x3) = ADDC_IN_AAG^1(x3) 18.16/5.63 18.16/5.63 U23_AAG(x1, x2, x3, x4) = U23_AAG(x3, x4) 18.16/5.63 18.16/5.63 U24_AAG(x1, x2, x3, x4) = U24_AAG(x3, x4) 18.16/5.63 18.16/5.63 ADDX_IN_AAG^1(x1, x2, x3) = ADDX_IN_AAG^1(x3) 18.16/5.63 18.16/5.63 U17_AAG(x1, x2) = U17_AAG(x1, x2) 18.16/5.63 18.16/5.63 U18_AAG(x1, x2, x3) = U18_AAG(x2, x3) 18.16/5.63 18.16/5.63 U19_AAG(x1, x2, x3, x4) = U19_AAG(x3, x4) 18.16/5.63 18.16/5.63 U25_AAG(x1, x2, x3, x4) = U25_AAG(x3, x4) 18.16/5.63 18.16/5.63 ADDY_IN_AAG^1(x1, x2, x3) = ADDY_IN_AAG^1(x3) 18.16/5.63 18.16/5.63 U20_AAG(x1, x2) = U20_AAG(x1, x2) 18.16/5.63 18.16/5.63 U21_AAG(x1, x2, x3) = U21_AAG(x2, x3) 18.16/5.63 18.16/5.63 U22_AAG(x1, x2, x3, x4) = U22_AAG(x3, x4) 18.16/5.63 18.16/5.63 U26_AAG(x1, x2, x3, x4) = U26_AAG(x3, x4) 18.16/5.63 18.16/5.63 18.16/5.63 We have to consider all (P,R,Pi)-chains 18.16/5.63 ---------------------------------------- 18.16/5.63 18.16/5.63 (5) DependencyGraphProof (EQUIVALENT) 18.16/5.63 The approximation of the Dependency Graph [LOPSTR] contains 8 SCCs with 109 less nodes. 18.16/5.63 ---------------------------------------- 18.16/5.63 18.16/5.63 (6) 18.16/5.63 Complex Obligation (AND) 18.16/5.63 18.16/5.63 ---------------------------------------- 18.16/5.63 18.16/5.63 (7) 18.16/5.63 Obligation: 18.16/5.63 Pi DP problem: 18.16/5.63 The TRS P consists of the following rules: 18.16/5.63 18.16/5.63 BINARYZ_IN_G(one(X)) -> BINARY_IN_G(X) 18.16/5.63 BINARY_IN_G(zero(X)) -> BINARYZ_IN_G(X) 18.16/5.63 BINARYZ_IN_G(zero(X)) -> BINARYZ_IN_G(X) 18.16/5.63 BINARY_IN_G(one(X)) -> BINARY_IN_G(X) 18.16/5.63 18.16/5.63 The TRS R consists of the following rules: 18.16/5.63 18.16/5.63 times_in_aag(one(b), X, X) -> times_out_aag(one(b), X, X) 18.16/5.63 times_in_aag(zero(R), S, zero(RS)) -> U35_aag(R, S, RS, times_in_aag(R, S, RS)) 18.16/5.63 times_in_aag(one(R), S, RSS) -> U36_aag(R, S, RSS, times_in_aaa(R, S, RS)) 18.16/5.63 times_in_aaa(one(b), X, X) -> times_out_aaa(one(b), X, X) 18.16/5.63 times_in_aaa(zero(R), S, zero(RS)) -> U35_aaa(R, S, RS, times_in_aaa(R, S, RS)) 18.16/5.63 times_in_aaa(one(R), S, RSS) -> U36_aaa(R, S, RSS, times_in_aaa(R, S, RS)) 18.16/5.63 U36_aaa(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aaa(R, S, RSS, add_in_aaa(S, zero(RS), RSS)) 18.16/5.63 add_in_aaa(b, b, b) -> add_out_aaa(b, b, b) 18.16/5.63 add_in_aaa(X, b, X) -> U1_aaa(X, binaryZ_in_a(X)) 18.16/5.63 binaryZ_in_a(zero(X)) -> U29_a(X, binaryZ_in_a(X)) 18.16/5.63 binaryZ_in_a(one(X)) -> U30_a(X, binary_in_a(X)) 18.16/5.63 binary_in_a(b) -> binary_out_a(b) 18.16/5.63 binary_in_a(zero(X)) -> U27_a(X, binaryZ_in_a(X)) 18.16/5.63 U27_a(X, binaryZ_out_a(X)) -> binary_out_a(zero(X)) 18.16/5.63 binary_in_a(one(X)) -> U28_a(X, binary_in_a(X)) 18.16/5.63 U28_a(X, binary_out_a(X)) -> binary_out_a(one(X)) 18.16/5.63 U30_a(X, binary_out_a(X)) -> binaryZ_out_a(one(X)) 18.16/5.63 U29_a(X, binaryZ_out_a(X)) -> binaryZ_out_a(zero(X)) 18.16/5.63 U1_aaa(X, binaryZ_out_a(X)) -> add_out_aaa(X, b, X) 18.16/5.63 add_in_aaa(b, Y, Y) -> U2_aaa(Y, binaryZ_in_a(Y)) 18.16/5.63 U2_aaa(Y, binaryZ_out_a(Y)) -> add_out_aaa(b, Y, Y) 18.16/5.63 add_in_aaa(X, Y, Z) -> U3_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.63 addz_in_aaa(zero(X), zero(Y), zero(Z)) -> U10_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.63 addz_in_aaa(zero(X), one(Y), one(Z)) -> U11_aaa(X, Y, Z, addx_in_aaa(X, Y, Z)) 18.16/5.63 addx_in_aaa(one(X), b, one(X)) -> U4_aaa(X, binary_in_a(X)) 18.16/5.63 U4_aaa(X, binary_out_a(X)) -> addx_out_aaa(one(X), b, one(X)) 18.16/5.63 addx_in_aaa(zero(X), b, zero(X)) -> U5_aaa(X, binaryZ_in_a(X)) 18.16/5.63 U5_aaa(X, binaryZ_out_a(X)) -> addx_out_aaa(zero(X), b, zero(X)) 18.16/5.63 addx_in_aaa(X, Y, Z) -> U6_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.63 addz_in_aaa(one(X), zero(Y), one(Z)) -> U12_aaa(X, Y, Z, addy_in_aaa(X, Y, Z)) 18.16/5.63 addy_in_aaa(b, one(Y), one(Y)) -> U7_aaa(Y, binary_in_a(Y)) 18.16/5.63 U7_aaa(Y, binary_out_a(Y)) -> addy_out_aaa(b, one(Y), one(Y)) 18.16/5.63 addy_in_aaa(b, zero(Y), zero(Y)) -> U8_aaa(Y, binaryZ_in_a(Y)) 18.16/5.63 U8_aaa(Y, binaryZ_out_a(Y)) -> addy_out_aaa(b, zero(Y), zero(Y)) 18.16/5.63 addy_in_aaa(X, Y, Z) -> U9_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.63 addz_in_aaa(one(X), one(Y), zero(Z)) -> U13_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.16/5.63 addc_in_aaa(b, b, one(b)) -> addc_out_aaa(b, b, one(b)) 18.16/5.63 addc_in_aaa(X, b, Z) -> U14_aaa(X, Z, succZ_in_aa(X, Z)) 18.16/5.63 succZ_in_aa(zero(X), one(X)) -> U33_aa(X, binaryZ_in_a(X)) 18.16/5.63 U33_aa(X, binaryZ_out_a(X)) -> succZ_out_aa(zero(X), one(X)) 18.16/5.63 succZ_in_aa(one(X), zero(Z)) -> U34_aa(X, Z, succ_in_aa(X, Z)) 18.16/5.63 succ_in_aa(b, one(b)) -> succ_out_aa(b, one(b)) 18.16/5.63 succ_in_aa(zero(X), one(X)) -> U31_aa(X, binaryZ_in_a(X)) 18.16/5.63 U31_aa(X, binaryZ_out_a(X)) -> succ_out_aa(zero(X), one(X)) 18.16/5.63 succ_in_aa(one(X), zero(Z)) -> U32_aa(X, Z, succ_in_aa(X, Z)) 18.16/5.63 U32_aa(X, Z, succ_out_aa(X, Z)) -> succ_out_aa(one(X), zero(Z)) 18.16/5.63 U34_aa(X, Z, succ_out_aa(X, Z)) -> succZ_out_aa(one(X), zero(Z)) 18.16/5.63 U14_aaa(X, Z, succZ_out_aa(X, Z)) -> addc_out_aaa(X, b, Z) 18.16/5.63 addc_in_aaa(b, Y, Z) -> U15_aaa(Y, Z, succZ_in_aa(Y, Z)) 18.16/5.63 U15_aaa(Y, Z, succZ_out_aa(Y, Z)) -> addc_out_aaa(b, Y, Z) 18.16/5.63 addc_in_aaa(X, Y, Z) -> U16_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.16/5.63 addC_in_aaa(zero(X), zero(Y), one(Z)) -> U23_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.63 U23_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), zero(Y), one(Z)) 18.16/5.63 addC_in_aaa(zero(X), one(Y), zero(Z)) -> U24_aaa(X, Y, Z, addX_in_aaa(X, Y, Z)) 18.16/5.63 addX_in_aaa(zero(X), b, one(X)) -> U17_aaa(X, binaryZ_in_a(X)) 18.16/5.63 U17_aaa(X, binaryZ_out_a(X)) -> addX_out_aaa(zero(X), b, one(X)) 18.16/5.63 addX_in_aaa(one(X), b, zero(Z)) -> U18_aaa(X, Z, succ_in_aa(X, Z)) 18.16/5.63 U18_aaa(X, Z, succ_out_aa(X, Z)) -> addX_out_aaa(one(X), b, zero(Z)) 18.16/5.63 addX_in_aaa(X, Y, Z) -> U19_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.16/5.63 addC_in_aaa(one(X), zero(Y), zero(Z)) -> U25_aaa(X, Y, Z, addY_in_aaa(X, Y, Z)) 18.16/5.63 addY_in_aaa(b, zero(Y), one(Y)) -> U20_aaa(Y, binaryZ_in_a(Y)) 18.16/5.63 U20_aaa(Y, binaryZ_out_a(Y)) -> addY_out_aaa(b, zero(Y), one(Y)) 18.16/5.63 addY_in_aaa(b, one(Y), zero(Z)) -> U21_aaa(Y, Z, succ_in_aa(Y, Z)) 18.16/5.63 U21_aaa(Y, Z, succ_out_aa(Y, Z)) -> addY_out_aaa(b, one(Y), zero(Z)) 18.16/5.63 addY_in_aaa(X, Y, Z) -> U22_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.16/5.63 addC_in_aaa(one(X), one(Y), one(Z)) -> U26_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.16/5.63 U26_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), one(Y), one(Z)) 18.16/5.63 U22_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addY_out_aaa(X, Y, Z) 18.16/5.63 U25_aaa(X, Y, Z, addY_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), zero(Y), zero(Z)) 18.16/5.63 U19_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addX_out_aaa(X, Y, Z) 18.16/5.63 U24_aaa(X, Y, Z, addX_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), one(Y), zero(Z)) 18.16/5.63 U16_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addc_out_aaa(X, Y, Z) 18.16/5.63 U13_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), one(Y), zero(Z)) 18.16/5.63 U9_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addy_out_aaa(X, Y, Z) 18.16/5.63 U12_aaa(X, Y, Z, addy_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), zero(Y), one(Z)) 18.16/5.63 U6_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addx_out_aaa(X, Y, Z) 18.16/5.63 U11_aaa(X, Y, Z, addx_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), one(Y), one(Z)) 18.16/5.63 U10_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), zero(Y), zero(Z)) 18.16/5.63 U3_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> add_out_aaa(X, Y, Z) 18.16/5.63 U37_aaa(R, S, RSS, add_out_aaa(S, zero(RS), RSS)) -> times_out_aaa(one(R), S, RSS) 18.16/5.63 U35_aaa(R, S, RS, times_out_aaa(R, S, RS)) -> times_out_aaa(zero(R), S, zero(RS)) 18.16/5.63 U36_aag(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aag(R, S, RSS, add_in_aag(S, zero(RS), RSS)) 18.16/5.63 add_in_aag(b, b, b) -> add_out_aag(b, b, b) 18.16/5.63 add_in_aag(X, b, X) -> U1_aag(X, binaryZ_in_g(X)) 18.16/5.63 binaryZ_in_g(zero(X)) -> U29_g(X, binaryZ_in_g(X)) 18.16/5.63 binaryZ_in_g(one(X)) -> U30_g(X, binary_in_g(X)) 18.16/5.63 binary_in_g(b) -> binary_out_g(b) 18.16/5.63 binary_in_g(zero(X)) -> U27_g(X, binaryZ_in_g(X)) 18.16/5.63 U27_g(X, binaryZ_out_g(X)) -> binary_out_g(zero(X)) 18.16/5.63 binary_in_g(one(X)) -> U28_g(X, binary_in_g(X)) 18.16/5.63 U28_g(X, binary_out_g(X)) -> binary_out_g(one(X)) 18.16/5.63 U30_g(X, binary_out_g(X)) -> binaryZ_out_g(one(X)) 18.16/5.63 U29_g(X, binaryZ_out_g(X)) -> binaryZ_out_g(zero(X)) 18.16/5.63 U1_aag(X, binaryZ_out_g(X)) -> add_out_aag(X, b, X) 18.16/5.63 add_in_aag(b, Y, Y) -> U2_aag(Y, binaryZ_in_g(Y)) 18.16/5.63 U2_aag(Y, binaryZ_out_g(Y)) -> add_out_aag(b, Y, Y) 18.16/5.63 add_in_aag(X, Y, Z) -> U3_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.63 addz_in_aag(zero(X), zero(Y), zero(Z)) -> U10_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.63 addz_in_aag(zero(X), one(Y), one(Z)) -> U11_aag(X, Y, Z, addx_in_aag(X, Y, Z)) 18.16/5.63 addx_in_aag(one(X), b, one(X)) -> U4_aag(X, binary_in_g(X)) 18.16/5.63 U4_aag(X, binary_out_g(X)) -> addx_out_aag(one(X), b, one(X)) 18.16/5.63 addx_in_aag(zero(X), b, zero(X)) -> U5_aag(X, binaryZ_in_g(X)) 18.16/5.63 U5_aag(X, binaryZ_out_g(X)) -> addx_out_aag(zero(X), b, zero(X)) 18.16/5.63 addx_in_aag(X, Y, Z) -> U6_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.63 addz_in_aag(one(X), zero(Y), one(Z)) -> U12_aag(X, Y, Z, addy_in_aag(X, Y, Z)) 18.16/5.63 addy_in_aag(b, one(Y), one(Y)) -> U7_aag(Y, binary_in_g(Y)) 18.16/5.63 U7_aag(Y, binary_out_g(Y)) -> addy_out_aag(b, one(Y), one(Y)) 18.16/5.63 addy_in_aag(b, zero(Y), zero(Y)) -> U8_aag(Y, binaryZ_in_g(Y)) 18.16/5.63 U8_aag(Y, binaryZ_out_g(Y)) -> addy_out_aag(b, zero(Y), zero(Y)) 18.16/5.63 addy_in_aag(X, Y, Z) -> U9_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.63 addz_in_aag(one(X), one(Y), zero(Z)) -> U13_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.16/5.63 addc_in_aag(b, b, one(b)) -> addc_out_aag(b, b, one(b)) 18.16/5.63 addc_in_aag(X, b, Z) -> U14_aag(X, Z, succZ_in_ag(X, Z)) 18.16/5.63 succZ_in_ag(zero(X), one(X)) -> U33_ag(X, binaryZ_in_g(X)) 18.16/5.63 U33_ag(X, binaryZ_out_g(X)) -> succZ_out_ag(zero(X), one(X)) 18.16/5.63 succZ_in_ag(one(X), zero(Z)) -> U34_ag(X, Z, succ_in_ag(X, Z)) 18.16/5.63 succ_in_ag(b, one(b)) -> succ_out_ag(b, one(b)) 18.16/5.63 succ_in_ag(zero(X), one(X)) -> U31_ag(X, binaryZ_in_g(X)) 18.16/5.63 U31_ag(X, binaryZ_out_g(X)) -> succ_out_ag(zero(X), one(X)) 18.16/5.63 succ_in_ag(one(X), zero(Z)) -> U32_ag(X, Z, succ_in_ag(X, Z)) 18.16/5.63 U32_ag(X, Z, succ_out_ag(X, Z)) -> succ_out_ag(one(X), zero(Z)) 18.16/5.63 U34_ag(X, Z, succ_out_ag(X, Z)) -> succZ_out_ag(one(X), zero(Z)) 18.16/5.63 U14_aag(X, Z, succZ_out_ag(X, Z)) -> addc_out_aag(X, b, Z) 18.16/5.63 addc_in_aag(b, Y, Z) -> U15_aag(Y, Z, succZ_in_ag(Y, Z)) 18.16/5.63 U15_aag(Y, Z, succZ_out_ag(Y, Z)) -> addc_out_aag(b, Y, Z) 18.16/5.63 addc_in_aag(X, Y, Z) -> U16_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.16/5.63 addC_in_aag(zero(X), zero(Y), one(Z)) -> U23_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.63 U23_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), zero(Y), one(Z)) 18.16/5.63 addC_in_aag(zero(X), one(Y), zero(Z)) -> U24_aag(X, Y, Z, addX_in_aag(X, Y, Z)) 18.16/5.63 addX_in_aag(zero(X), b, one(X)) -> U17_aag(X, binaryZ_in_g(X)) 18.16/5.63 U17_aag(X, binaryZ_out_g(X)) -> addX_out_aag(zero(X), b, one(X)) 18.16/5.63 addX_in_aag(one(X), b, zero(Z)) -> U18_aag(X, Z, succ_in_ag(X, Z)) 18.16/5.63 U18_aag(X, Z, succ_out_ag(X, Z)) -> addX_out_aag(one(X), b, zero(Z)) 18.16/5.63 addX_in_aag(X, Y, Z) -> U19_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.16/5.63 addC_in_aag(one(X), zero(Y), zero(Z)) -> U25_aag(X, Y, Z, addY_in_aag(X, Y, Z)) 18.16/5.63 addY_in_aag(b, zero(Y), one(Y)) -> U20_aag(Y, binaryZ_in_g(Y)) 18.16/5.63 U20_aag(Y, binaryZ_out_g(Y)) -> addY_out_aag(b, zero(Y), one(Y)) 18.16/5.63 addY_in_aag(b, one(Y), zero(Z)) -> U21_aag(Y, Z, succ_in_ag(Y, Z)) 18.16/5.63 U21_aag(Y, Z, succ_out_ag(Y, Z)) -> addY_out_aag(b, one(Y), zero(Z)) 18.16/5.63 addY_in_aag(X, Y, Z) -> U22_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.16/5.63 addC_in_aag(one(X), one(Y), one(Z)) -> U26_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.16/5.63 U26_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addC_out_aag(one(X), one(Y), one(Z)) 18.16/5.63 U22_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addY_out_aag(X, Y, Z) 18.16/5.63 U25_aag(X, Y, Z, addY_out_aag(X, Y, Z)) -> addC_out_aag(one(X), zero(Y), zero(Z)) 18.16/5.63 U19_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addX_out_aag(X, Y, Z) 18.16/5.63 U24_aag(X, Y, Z, addX_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), one(Y), zero(Z)) 18.16/5.63 U16_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addc_out_aag(X, Y, Z) 18.16/5.63 U13_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addz_out_aag(one(X), one(Y), zero(Z)) 18.16/5.63 U9_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addy_out_aag(X, Y, Z) 18.16/5.63 U12_aag(X, Y, Z, addy_out_aag(X, Y, Z)) -> addz_out_aag(one(X), zero(Y), one(Z)) 18.16/5.63 U6_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addx_out_aag(X, Y, Z) 18.16/5.63 U11_aag(X, Y, Z, addx_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), one(Y), one(Z)) 18.16/5.63 U10_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), zero(Y), zero(Z)) 18.16/5.63 U3_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> add_out_aag(X, Y, Z) 18.16/5.63 U37_aag(R, S, RSS, add_out_aag(S, zero(RS), RSS)) -> times_out_aag(one(R), S, RSS) 18.16/5.63 U35_aag(R, S, RS, times_out_aag(R, S, RS)) -> times_out_aag(zero(R), S, zero(RS)) 18.16/5.63 18.16/5.63 The argument filtering Pi contains the following mapping: 18.16/5.63 times_in_aag(x1, x2, x3) = times_in_aag(x3) 18.16/5.63 18.16/5.63 times_out_aag(x1, x2, x3) = times_out_aag(x1, x2, x3) 18.16/5.63 18.16/5.63 zero(x1) = zero(x1) 18.16/5.63 18.16/5.63 U35_aag(x1, x2, x3, x4) = U35_aag(x3, x4) 18.16/5.63 18.16/5.63 U36_aag(x1, x2, x3, x4) = U36_aag(x3, x4) 18.16/5.63 18.16/5.63 times_in_aaa(x1, x2, x3) = times_in_aaa 18.16/5.63 18.16/5.63 times_out_aaa(x1, x2, x3) = times_out_aaa(x1) 18.16/5.63 18.16/5.63 U35_aaa(x1, x2, x3, x4) = U35_aaa(x4) 18.16/5.63 18.16/5.63 U36_aaa(x1, x2, x3, x4) = U36_aaa(x4) 18.16/5.63 18.16/5.63 U37_aaa(x1, x2, x3, x4) = U37_aaa(x1, x4) 18.16/5.63 18.16/5.63 add_in_aaa(x1, x2, x3) = add_in_aaa 18.16/5.63 18.16/5.63 add_out_aaa(x1, x2, x3) = add_out_aaa(x1, x2, x3) 18.16/5.63 18.16/5.63 U1_aaa(x1, x2) = U1_aaa(x2) 18.16/5.63 18.16/5.63 binaryZ_in_a(x1) = binaryZ_in_a 18.16/5.63 18.16/5.63 U29_a(x1, x2) = U29_a(x2) 18.16/5.63 18.16/5.63 U30_a(x1, x2) = U30_a(x2) 18.16/5.63 18.16/5.63 binary_in_a(x1) = binary_in_a 18.16/5.63 18.16/5.63 binary_out_a(x1) = binary_out_a(x1) 18.16/5.63 18.16/5.63 U27_a(x1, x2) = U27_a(x2) 18.16/5.63 18.16/5.63 binaryZ_out_a(x1) = binaryZ_out_a(x1) 18.16/5.63 18.16/5.63 U28_a(x1, x2) = U28_a(x2) 18.16/5.63 18.16/5.63 U2_aaa(x1, x2) = U2_aaa(x2) 18.16/5.63 18.16/5.63 U3_aaa(x1, x2, x3, x4) = U3_aaa(x4) 18.16/5.63 18.16/5.63 addz_in_aaa(x1, x2, x3) = addz_in_aaa 18.16/5.63 18.16/5.63 U10_aaa(x1, x2, x3, x4) = U10_aaa(x4) 18.16/5.63 18.16/5.63 U11_aaa(x1, x2, x3, x4) = U11_aaa(x4) 18.16/5.63 18.16/5.63 addx_in_aaa(x1, x2, x3) = addx_in_aaa 18.16/5.63 18.16/5.63 U4_aaa(x1, x2) = U4_aaa(x2) 18.16/5.63 18.16/5.63 addx_out_aaa(x1, x2, x3) = addx_out_aaa(x1, x2, x3) 18.16/5.63 18.16/5.63 U5_aaa(x1, x2) = U5_aaa(x2) 18.16/5.63 18.16/5.63 U6_aaa(x1, x2, x3, x4) = U6_aaa(x4) 18.16/5.63 18.16/5.63 U12_aaa(x1, x2, x3, x4) = U12_aaa(x4) 18.16/5.63 18.16/5.63 addy_in_aaa(x1, x2, x3) = addy_in_aaa 18.16/5.63 18.16/5.63 U7_aaa(x1, x2) = U7_aaa(x2) 18.16/5.63 18.16/5.63 addy_out_aaa(x1, x2, x3) = addy_out_aaa(x1, x2, x3) 18.16/5.63 18.16/5.63 U8_aaa(x1, x2) = U8_aaa(x2) 18.16/5.63 18.16/5.63 U9_aaa(x1, x2, x3, x4) = U9_aaa(x4) 18.16/5.63 18.16/5.63 U13_aaa(x1, x2, x3, x4) = U13_aaa(x4) 18.16/5.63 18.16/5.63 addc_in_aaa(x1, x2, x3) = addc_in_aaa 18.16/5.63 18.16/5.63 addc_out_aaa(x1, x2, x3) = addc_out_aaa(x1, x2, x3) 18.16/5.63 18.16/5.63 U14_aaa(x1, x2, x3) = U14_aaa(x3) 18.16/5.63 18.16/5.63 succZ_in_aa(x1, x2) = succZ_in_aa 18.16/5.63 18.16/5.63 U33_aa(x1, x2) = U33_aa(x2) 18.16/5.63 18.16/5.63 succZ_out_aa(x1, x2) = succZ_out_aa(x1, x2) 18.16/5.63 18.16/5.63 U34_aa(x1, x2, x3) = U34_aa(x3) 18.16/5.63 18.16/5.63 succ_in_aa(x1, x2) = succ_in_aa 18.16/5.63 18.16/5.63 succ_out_aa(x1, x2) = succ_out_aa(x1, x2) 18.16/5.63 18.16/5.63 U31_aa(x1, x2) = U31_aa(x2) 18.16/5.63 18.16/5.63 U32_aa(x1, x2, x3) = U32_aa(x3) 18.16/5.63 18.16/5.63 U15_aaa(x1, x2, x3) = U15_aaa(x3) 18.16/5.63 18.16/5.63 U16_aaa(x1, x2, x3, x4) = U16_aaa(x4) 18.16/5.63 18.16/5.63 addC_in_aaa(x1, x2, x3) = addC_in_aaa 18.16/5.63 18.16/5.63 U23_aaa(x1, x2, x3, x4) = U23_aaa(x4) 18.16/5.63 18.16/5.63 addz_out_aaa(x1, x2, x3) = addz_out_aaa(x1, x2, x3) 18.16/5.63 18.16/5.63 addC_out_aaa(x1, x2, x3) = addC_out_aaa(x1, x2, x3) 18.16/5.63 18.16/5.63 U24_aaa(x1, x2, x3, x4) = U24_aaa(x4) 18.16/5.63 18.16/5.63 addX_in_aaa(x1, x2, x3) = addX_in_aaa 18.16/5.63 18.16/5.63 U17_aaa(x1, x2) = U17_aaa(x2) 18.16/5.63 18.16/5.63 addX_out_aaa(x1, x2, x3) = addX_out_aaa(x1, x2, x3) 18.16/5.63 18.16/5.63 U18_aaa(x1, x2, x3) = U18_aaa(x3) 18.16/5.63 18.16/5.63 U19_aaa(x1, x2, x3, x4) = U19_aaa(x4) 18.16/5.63 18.16/5.63 U25_aaa(x1, x2, x3, x4) = U25_aaa(x4) 18.16/5.63 18.16/5.63 addY_in_aaa(x1, x2, x3) = addY_in_aaa 18.16/5.63 18.16/5.63 U20_aaa(x1, x2) = U20_aaa(x2) 18.16/5.63 18.16/5.63 addY_out_aaa(x1, x2, x3) = addY_out_aaa(x1, x2, x3) 18.16/5.63 18.16/5.63 U21_aaa(x1, x2, x3) = U21_aaa(x3) 18.16/5.63 18.16/5.63 U22_aaa(x1, x2, x3, x4) = U22_aaa(x4) 18.16/5.63 18.16/5.63 U26_aaa(x1, x2, x3, x4) = U26_aaa(x4) 18.16/5.63 18.16/5.63 U37_aag(x1, x2, x3, x4) = U37_aag(x1, x3, x4) 18.16/5.63 18.16/5.63 add_in_aag(x1, x2, x3) = add_in_aag(x3) 18.16/5.63 18.16/5.63 b = b 18.16/5.63 18.16/5.63 add_out_aag(x1, x2, x3) = add_out_aag(x1, x2, x3) 18.16/5.63 18.16/5.63 U1_aag(x1, x2) = U1_aag(x1, x2) 18.16/5.63 18.16/5.63 binaryZ_in_g(x1) = binaryZ_in_g(x1) 18.16/5.63 18.16/5.63 U29_g(x1, x2) = U29_g(x1, x2) 18.16/5.63 18.16/5.63 one(x1) = one(x1) 18.16/5.63 18.16/5.63 U30_g(x1, x2) = U30_g(x1, x2) 18.16/5.63 18.16/5.63 binary_in_g(x1) = binary_in_g(x1) 18.16/5.63 18.16/5.63 binary_out_g(x1) = binary_out_g(x1) 18.16/5.63 18.16/5.63 U27_g(x1, x2) = U27_g(x1, x2) 18.16/5.63 18.16/5.63 binaryZ_out_g(x1) = binaryZ_out_g(x1) 18.16/5.63 18.16/5.63 U28_g(x1, x2) = U28_g(x1, x2) 18.16/5.63 18.16/5.63 U2_aag(x1, x2) = U2_aag(x1, x2) 18.16/5.63 18.16/5.63 U3_aag(x1, x2, x3, x4) = U3_aag(x3, x4) 18.16/5.63 18.16/5.63 addz_in_aag(x1, x2, x3) = addz_in_aag(x3) 18.16/5.63 18.16/5.63 U10_aag(x1, x2, x3, x4) = U10_aag(x3, x4) 18.16/5.63 18.16/5.63 U11_aag(x1, x2, x3, x4) = U11_aag(x3, x4) 18.16/5.63 18.16/5.63 addx_in_aag(x1, x2, x3) = addx_in_aag(x3) 18.16/5.63 18.16/5.63 U4_aag(x1, x2) = U4_aag(x1, x2) 18.16/5.63 18.16/5.63 addx_out_aag(x1, x2, x3) = addx_out_aag(x1, x2, x3) 18.16/5.63 18.16/5.63 U5_aag(x1, x2) = U5_aag(x1, x2) 18.16/5.63 18.16/5.63 U6_aag(x1, x2, x3, x4) = U6_aag(x3, x4) 18.16/5.63 18.16/5.63 U12_aag(x1, x2, x3, x4) = U12_aag(x3, x4) 18.16/5.63 18.16/5.63 addy_in_aag(x1, x2, x3) = addy_in_aag(x3) 18.16/5.63 18.16/5.63 U7_aag(x1, x2) = U7_aag(x1, x2) 18.16/5.63 18.16/5.63 addy_out_aag(x1, x2, x3) = addy_out_aag(x1, x2, x3) 18.16/5.63 18.16/5.63 U8_aag(x1, x2) = U8_aag(x1, x2) 18.16/5.63 18.16/5.63 U9_aag(x1, x2, x3, x4) = U9_aag(x3, x4) 18.16/5.63 18.16/5.63 U13_aag(x1, x2, x3, x4) = U13_aag(x3, x4) 18.16/5.63 18.16/5.63 addc_in_aag(x1, x2, x3) = addc_in_aag(x3) 18.16/5.63 18.16/5.63 addc_out_aag(x1, x2, x3) = addc_out_aag(x1, x2, x3) 18.16/5.63 18.16/5.63 U14_aag(x1, x2, x3) = U14_aag(x2, x3) 18.16/5.63 18.16/5.63 succZ_in_ag(x1, x2) = succZ_in_ag(x2) 18.16/5.63 18.16/5.63 U33_ag(x1, x2) = U33_ag(x1, x2) 18.16/5.63 18.16/5.63 succZ_out_ag(x1, x2) = succZ_out_ag(x1, x2) 18.16/5.63 18.16/5.63 U34_ag(x1, x2, x3) = U34_ag(x2, x3) 18.16/5.63 18.16/5.63 succ_in_ag(x1, x2) = succ_in_ag(x2) 18.16/5.63 18.16/5.63 succ_out_ag(x1, x2) = succ_out_ag(x1, x2) 18.16/5.63 18.16/5.63 U31_ag(x1, x2) = U31_ag(x1, x2) 18.16/5.63 18.16/5.63 U32_ag(x1, x2, x3) = U32_ag(x2, x3) 18.16/5.63 18.16/5.63 U15_aag(x1, x2, x3) = U15_aag(x2, x3) 18.16/5.63 18.16/5.63 U16_aag(x1, x2, x3, x4) = U16_aag(x3, x4) 18.16/5.63 18.16/5.63 addC_in_aag(x1, x2, x3) = addC_in_aag(x3) 18.16/5.63 18.16/5.63 U23_aag(x1, x2, x3, x4) = U23_aag(x3, x4) 18.16/5.63 18.16/5.63 addz_out_aag(x1, x2, x3) = addz_out_aag(x1, x2, x3) 18.16/5.63 18.16/5.63 addC_out_aag(x1, x2, x3) = addC_out_aag(x1, x2, x3) 18.16/5.63 18.16/5.63 U24_aag(x1, x2, x3, x4) = U24_aag(x3, x4) 18.16/5.63 18.16/5.63 addX_in_aag(x1, x2, x3) = addX_in_aag(x3) 18.16/5.63 18.16/5.63 U17_aag(x1, x2) = U17_aag(x1, x2) 18.16/5.63 18.16/5.63 addX_out_aag(x1, x2, x3) = addX_out_aag(x1, x2, x3) 18.16/5.63 18.16/5.63 U18_aag(x1, x2, x3) = U18_aag(x2, x3) 18.16/5.63 18.16/5.63 U19_aag(x1, x2, x3, x4) = U19_aag(x3, x4) 18.16/5.63 18.16/5.63 U25_aag(x1, x2, x3, x4) = U25_aag(x3, x4) 18.16/5.63 18.16/5.63 addY_in_aag(x1, x2, x3) = addY_in_aag(x3) 18.16/5.63 18.16/5.63 U20_aag(x1, x2) = U20_aag(x1, x2) 18.16/5.63 18.16/5.63 addY_out_aag(x1, x2, x3) = addY_out_aag(x1, x2, x3) 18.16/5.63 18.16/5.63 U21_aag(x1, x2, x3) = U21_aag(x2, x3) 18.16/5.63 18.16/5.63 U22_aag(x1, x2, x3, x4) = U22_aag(x3, x4) 18.16/5.63 18.16/5.63 U26_aag(x1, x2, x3, x4) = U26_aag(x3, x4) 18.16/5.63 18.16/5.63 BINARYZ_IN_G(x1) = BINARYZ_IN_G(x1) 18.16/5.63 18.16/5.63 BINARY_IN_G(x1) = BINARY_IN_G(x1) 18.16/5.63 18.16/5.63 18.16/5.63 We have to consider all (P,R,Pi)-chains 18.16/5.63 ---------------------------------------- 18.16/5.63 18.16/5.63 (8) UsableRulesProof (EQUIVALENT) 18.16/5.63 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 18.16/5.63 ---------------------------------------- 18.16/5.63 18.16/5.63 (9) 18.16/5.63 Obligation: 18.16/5.63 Pi DP problem: 18.16/5.63 The TRS P consists of the following rules: 18.16/5.63 18.16/5.63 BINARYZ_IN_G(one(X)) -> BINARY_IN_G(X) 18.16/5.63 BINARY_IN_G(zero(X)) -> BINARYZ_IN_G(X) 18.16/5.63 BINARYZ_IN_G(zero(X)) -> BINARYZ_IN_G(X) 18.16/5.63 BINARY_IN_G(one(X)) -> BINARY_IN_G(X) 18.16/5.63 18.16/5.63 R is empty. 18.16/5.63 Pi is empty. 18.16/5.63 We have to consider all (P,R,Pi)-chains 18.16/5.63 ---------------------------------------- 18.16/5.63 18.16/5.63 (10) PiDPToQDPProof (EQUIVALENT) 18.16/5.63 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 18.16/5.63 ---------------------------------------- 18.16/5.63 18.16/5.63 (11) 18.16/5.63 Obligation: 18.16/5.63 Q DP problem: 18.16/5.63 The TRS P consists of the following rules: 18.16/5.63 18.16/5.63 BINARYZ_IN_G(one(X)) -> BINARY_IN_G(X) 18.16/5.63 BINARY_IN_G(zero(X)) -> BINARYZ_IN_G(X) 18.16/5.63 BINARYZ_IN_G(zero(X)) -> BINARYZ_IN_G(X) 18.16/5.63 BINARY_IN_G(one(X)) -> BINARY_IN_G(X) 18.16/5.63 18.16/5.63 R is empty. 18.16/5.63 Q is empty. 18.16/5.63 We have to consider all (P,Q,R)-chains. 18.16/5.63 ---------------------------------------- 18.16/5.63 18.16/5.63 (12) QDPSizeChangeProof (EQUIVALENT) 18.16/5.63 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 18.16/5.63 18.16/5.63 From the DPs we obtained the following set of size-change graphs: 18.16/5.63 *BINARY_IN_G(zero(X)) -> BINARYZ_IN_G(X) 18.16/5.63 The graph contains the following edges 1 > 1 18.16/5.63 18.16/5.63 18.16/5.63 *BINARY_IN_G(one(X)) -> BINARY_IN_G(X) 18.16/5.63 The graph contains the following edges 1 > 1 18.16/5.63 18.16/5.63 18.16/5.63 *BINARYZ_IN_G(zero(X)) -> BINARYZ_IN_G(X) 18.16/5.63 The graph contains the following edges 1 > 1 18.16/5.63 18.16/5.63 18.16/5.63 *BINARYZ_IN_G(one(X)) -> BINARY_IN_G(X) 18.16/5.63 The graph contains the following edges 1 > 1 18.16/5.63 18.16/5.63 18.16/5.63 ---------------------------------------- 18.16/5.63 18.16/5.63 (13) 18.16/5.63 YES 18.16/5.63 18.16/5.63 ---------------------------------------- 18.16/5.63 18.16/5.63 (14) 18.16/5.63 Obligation: 18.16/5.63 Pi DP problem: 18.16/5.63 The TRS P consists of the following rules: 18.16/5.63 18.16/5.63 SUCC_IN_AG(one(X), zero(Z)) -> SUCC_IN_AG(X, Z) 18.16/5.63 18.16/5.63 The TRS R consists of the following rules: 18.16/5.63 18.16/5.63 times_in_aag(one(b), X, X) -> times_out_aag(one(b), X, X) 18.16/5.63 times_in_aag(zero(R), S, zero(RS)) -> U35_aag(R, S, RS, times_in_aag(R, S, RS)) 18.16/5.63 times_in_aag(one(R), S, RSS) -> U36_aag(R, S, RSS, times_in_aaa(R, S, RS)) 18.16/5.63 times_in_aaa(one(b), X, X) -> times_out_aaa(one(b), X, X) 18.16/5.63 times_in_aaa(zero(R), S, zero(RS)) -> U35_aaa(R, S, RS, times_in_aaa(R, S, RS)) 18.16/5.63 times_in_aaa(one(R), S, RSS) -> U36_aaa(R, S, RSS, times_in_aaa(R, S, RS)) 18.16/5.63 U36_aaa(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aaa(R, S, RSS, add_in_aaa(S, zero(RS), RSS)) 18.16/5.63 add_in_aaa(b, b, b) -> add_out_aaa(b, b, b) 18.16/5.63 add_in_aaa(X, b, X) -> U1_aaa(X, binaryZ_in_a(X)) 18.16/5.63 binaryZ_in_a(zero(X)) -> U29_a(X, binaryZ_in_a(X)) 18.16/5.63 binaryZ_in_a(one(X)) -> U30_a(X, binary_in_a(X)) 18.16/5.63 binary_in_a(b) -> binary_out_a(b) 18.16/5.63 binary_in_a(zero(X)) -> U27_a(X, binaryZ_in_a(X)) 18.16/5.63 U27_a(X, binaryZ_out_a(X)) -> binary_out_a(zero(X)) 18.16/5.63 binary_in_a(one(X)) -> U28_a(X, binary_in_a(X)) 18.16/5.63 U28_a(X, binary_out_a(X)) -> binary_out_a(one(X)) 18.16/5.63 U30_a(X, binary_out_a(X)) -> binaryZ_out_a(one(X)) 18.16/5.63 U29_a(X, binaryZ_out_a(X)) -> binaryZ_out_a(zero(X)) 18.16/5.63 U1_aaa(X, binaryZ_out_a(X)) -> add_out_aaa(X, b, X) 18.16/5.63 add_in_aaa(b, Y, Y) -> U2_aaa(Y, binaryZ_in_a(Y)) 18.16/5.63 U2_aaa(Y, binaryZ_out_a(Y)) -> add_out_aaa(b, Y, Y) 18.16/5.63 add_in_aaa(X, Y, Z) -> U3_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.63 addz_in_aaa(zero(X), zero(Y), zero(Z)) -> U10_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.63 addz_in_aaa(zero(X), one(Y), one(Z)) -> U11_aaa(X, Y, Z, addx_in_aaa(X, Y, Z)) 18.16/5.63 addx_in_aaa(one(X), b, one(X)) -> U4_aaa(X, binary_in_a(X)) 18.16/5.63 U4_aaa(X, binary_out_a(X)) -> addx_out_aaa(one(X), b, one(X)) 18.16/5.63 addx_in_aaa(zero(X), b, zero(X)) -> U5_aaa(X, binaryZ_in_a(X)) 18.16/5.63 U5_aaa(X, binaryZ_out_a(X)) -> addx_out_aaa(zero(X), b, zero(X)) 18.16/5.63 addx_in_aaa(X, Y, Z) -> U6_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.63 addz_in_aaa(one(X), zero(Y), one(Z)) -> U12_aaa(X, Y, Z, addy_in_aaa(X, Y, Z)) 18.16/5.63 addy_in_aaa(b, one(Y), one(Y)) -> U7_aaa(Y, binary_in_a(Y)) 18.16/5.63 U7_aaa(Y, binary_out_a(Y)) -> addy_out_aaa(b, one(Y), one(Y)) 18.16/5.63 addy_in_aaa(b, zero(Y), zero(Y)) -> U8_aaa(Y, binaryZ_in_a(Y)) 18.16/5.63 U8_aaa(Y, binaryZ_out_a(Y)) -> addy_out_aaa(b, zero(Y), zero(Y)) 18.16/5.63 addy_in_aaa(X, Y, Z) -> U9_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.63 addz_in_aaa(one(X), one(Y), zero(Z)) -> U13_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.16/5.63 addc_in_aaa(b, b, one(b)) -> addc_out_aaa(b, b, one(b)) 18.16/5.63 addc_in_aaa(X, b, Z) -> U14_aaa(X, Z, succZ_in_aa(X, Z)) 18.16/5.63 succZ_in_aa(zero(X), one(X)) -> U33_aa(X, binaryZ_in_a(X)) 18.16/5.63 U33_aa(X, binaryZ_out_a(X)) -> succZ_out_aa(zero(X), one(X)) 18.16/5.63 succZ_in_aa(one(X), zero(Z)) -> U34_aa(X, Z, succ_in_aa(X, Z)) 18.16/5.63 succ_in_aa(b, one(b)) -> succ_out_aa(b, one(b)) 18.16/5.63 succ_in_aa(zero(X), one(X)) -> U31_aa(X, binaryZ_in_a(X)) 18.16/5.63 U31_aa(X, binaryZ_out_a(X)) -> succ_out_aa(zero(X), one(X)) 18.16/5.63 succ_in_aa(one(X), zero(Z)) -> U32_aa(X, Z, succ_in_aa(X, Z)) 18.16/5.63 U32_aa(X, Z, succ_out_aa(X, Z)) -> succ_out_aa(one(X), zero(Z)) 18.16/5.63 U34_aa(X, Z, succ_out_aa(X, Z)) -> succZ_out_aa(one(X), zero(Z)) 18.16/5.63 U14_aaa(X, Z, succZ_out_aa(X, Z)) -> addc_out_aaa(X, b, Z) 18.16/5.63 addc_in_aaa(b, Y, Z) -> U15_aaa(Y, Z, succZ_in_aa(Y, Z)) 18.16/5.63 U15_aaa(Y, Z, succZ_out_aa(Y, Z)) -> addc_out_aaa(b, Y, Z) 18.16/5.63 addc_in_aaa(X, Y, Z) -> U16_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.16/5.63 addC_in_aaa(zero(X), zero(Y), one(Z)) -> U23_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.16/5.63 U23_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), zero(Y), one(Z)) 18.16/5.63 addC_in_aaa(zero(X), one(Y), zero(Z)) -> U24_aaa(X, Y, Z, addX_in_aaa(X, Y, Z)) 18.16/5.63 addX_in_aaa(zero(X), b, one(X)) -> U17_aaa(X, binaryZ_in_a(X)) 18.16/5.63 U17_aaa(X, binaryZ_out_a(X)) -> addX_out_aaa(zero(X), b, one(X)) 18.16/5.63 addX_in_aaa(one(X), b, zero(Z)) -> U18_aaa(X, Z, succ_in_aa(X, Z)) 18.16/5.63 U18_aaa(X, Z, succ_out_aa(X, Z)) -> addX_out_aaa(one(X), b, zero(Z)) 18.16/5.63 addX_in_aaa(X, Y, Z) -> U19_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.16/5.63 addC_in_aaa(one(X), zero(Y), zero(Z)) -> U25_aaa(X, Y, Z, addY_in_aaa(X, Y, Z)) 18.16/5.63 addY_in_aaa(b, zero(Y), one(Y)) -> U20_aaa(Y, binaryZ_in_a(Y)) 18.16/5.63 U20_aaa(Y, binaryZ_out_a(Y)) -> addY_out_aaa(b, zero(Y), one(Y)) 18.16/5.63 addY_in_aaa(b, one(Y), zero(Z)) -> U21_aaa(Y, Z, succ_in_aa(Y, Z)) 18.16/5.63 U21_aaa(Y, Z, succ_out_aa(Y, Z)) -> addY_out_aaa(b, one(Y), zero(Z)) 18.16/5.63 addY_in_aaa(X, Y, Z) -> U22_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.16/5.63 addC_in_aaa(one(X), one(Y), one(Z)) -> U26_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.16/5.63 U26_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), one(Y), one(Z)) 18.16/5.63 U22_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addY_out_aaa(X, Y, Z) 18.16/5.63 U25_aaa(X, Y, Z, addY_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), zero(Y), zero(Z)) 18.16/5.63 U19_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addX_out_aaa(X, Y, Z) 18.16/5.63 U24_aaa(X, Y, Z, addX_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), one(Y), zero(Z)) 18.16/5.63 U16_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addc_out_aaa(X, Y, Z) 18.16/5.63 U13_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), one(Y), zero(Z)) 18.16/5.63 U9_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addy_out_aaa(X, Y, Z) 18.16/5.63 U12_aaa(X, Y, Z, addy_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), zero(Y), one(Z)) 18.16/5.63 U6_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addx_out_aaa(X, Y, Z) 18.16/5.63 U11_aaa(X, Y, Z, addx_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), one(Y), one(Z)) 18.16/5.63 U10_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), zero(Y), zero(Z)) 18.16/5.63 U3_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> add_out_aaa(X, Y, Z) 18.16/5.63 U37_aaa(R, S, RSS, add_out_aaa(S, zero(RS), RSS)) -> times_out_aaa(one(R), S, RSS) 18.16/5.63 U35_aaa(R, S, RS, times_out_aaa(R, S, RS)) -> times_out_aaa(zero(R), S, zero(RS)) 18.16/5.63 U36_aag(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aag(R, S, RSS, add_in_aag(S, zero(RS), RSS)) 18.16/5.63 add_in_aag(b, b, b) -> add_out_aag(b, b, b) 18.16/5.63 add_in_aag(X, b, X) -> U1_aag(X, binaryZ_in_g(X)) 18.16/5.63 binaryZ_in_g(zero(X)) -> U29_g(X, binaryZ_in_g(X)) 18.16/5.63 binaryZ_in_g(one(X)) -> U30_g(X, binary_in_g(X)) 18.16/5.63 binary_in_g(b) -> binary_out_g(b) 18.16/5.63 binary_in_g(zero(X)) -> U27_g(X, binaryZ_in_g(X)) 18.16/5.63 U27_g(X, binaryZ_out_g(X)) -> binary_out_g(zero(X)) 18.16/5.63 binary_in_g(one(X)) -> U28_g(X, binary_in_g(X)) 18.16/5.63 U28_g(X, binary_out_g(X)) -> binary_out_g(one(X)) 18.16/5.63 U30_g(X, binary_out_g(X)) -> binaryZ_out_g(one(X)) 18.16/5.63 U29_g(X, binaryZ_out_g(X)) -> binaryZ_out_g(zero(X)) 18.16/5.63 U1_aag(X, binaryZ_out_g(X)) -> add_out_aag(X, b, X) 18.16/5.63 add_in_aag(b, Y, Y) -> U2_aag(Y, binaryZ_in_g(Y)) 18.16/5.63 U2_aag(Y, binaryZ_out_g(Y)) -> add_out_aag(b, Y, Y) 18.16/5.63 add_in_aag(X, Y, Z) -> U3_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.63 addz_in_aag(zero(X), zero(Y), zero(Z)) -> U10_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.63 addz_in_aag(zero(X), one(Y), one(Z)) -> U11_aag(X, Y, Z, addx_in_aag(X, Y, Z)) 18.16/5.63 addx_in_aag(one(X), b, one(X)) -> U4_aag(X, binary_in_g(X)) 18.16/5.63 U4_aag(X, binary_out_g(X)) -> addx_out_aag(one(X), b, one(X)) 18.16/5.63 addx_in_aag(zero(X), b, zero(X)) -> U5_aag(X, binaryZ_in_g(X)) 18.16/5.63 U5_aag(X, binaryZ_out_g(X)) -> addx_out_aag(zero(X), b, zero(X)) 18.16/5.63 addx_in_aag(X, Y, Z) -> U6_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.63 addz_in_aag(one(X), zero(Y), one(Z)) -> U12_aag(X, Y, Z, addy_in_aag(X, Y, Z)) 18.16/5.63 addy_in_aag(b, one(Y), one(Y)) -> U7_aag(Y, binary_in_g(Y)) 18.16/5.63 U7_aag(Y, binary_out_g(Y)) -> addy_out_aag(b, one(Y), one(Y)) 18.16/5.63 addy_in_aag(b, zero(Y), zero(Y)) -> U8_aag(Y, binaryZ_in_g(Y)) 18.16/5.63 U8_aag(Y, binaryZ_out_g(Y)) -> addy_out_aag(b, zero(Y), zero(Y)) 18.16/5.63 addy_in_aag(X, Y, Z) -> U9_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.63 addz_in_aag(one(X), one(Y), zero(Z)) -> U13_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.16/5.63 addc_in_aag(b, b, one(b)) -> addc_out_aag(b, b, one(b)) 18.16/5.63 addc_in_aag(X, b, Z) -> U14_aag(X, Z, succZ_in_ag(X, Z)) 18.16/5.63 succZ_in_ag(zero(X), one(X)) -> U33_ag(X, binaryZ_in_g(X)) 18.16/5.63 U33_ag(X, binaryZ_out_g(X)) -> succZ_out_ag(zero(X), one(X)) 18.16/5.63 succZ_in_ag(one(X), zero(Z)) -> U34_ag(X, Z, succ_in_ag(X, Z)) 18.16/5.63 succ_in_ag(b, one(b)) -> succ_out_ag(b, one(b)) 18.16/5.63 succ_in_ag(zero(X), one(X)) -> U31_ag(X, binaryZ_in_g(X)) 18.16/5.63 U31_ag(X, binaryZ_out_g(X)) -> succ_out_ag(zero(X), one(X)) 18.16/5.63 succ_in_ag(one(X), zero(Z)) -> U32_ag(X, Z, succ_in_ag(X, Z)) 18.16/5.63 U32_ag(X, Z, succ_out_ag(X, Z)) -> succ_out_ag(one(X), zero(Z)) 18.16/5.63 U34_ag(X, Z, succ_out_ag(X, Z)) -> succZ_out_ag(one(X), zero(Z)) 18.16/5.63 U14_aag(X, Z, succZ_out_ag(X, Z)) -> addc_out_aag(X, b, Z) 18.16/5.63 addc_in_aag(b, Y, Z) -> U15_aag(Y, Z, succZ_in_ag(Y, Z)) 18.16/5.63 U15_aag(Y, Z, succZ_out_ag(Y, Z)) -> addc_out_aag(b, Y, Z) 18.16/5.63 addc_in_aag(X, Y, Z) -> U16_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.16/5.63 addC_in_aag(zero(X), zero(Y), one(Z)) -> U23_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.16/5.63 U23_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), zero(Y), one(Z)) 18.16/5.63 addC_in_aag(zero(X), one(Y), zero(Z)) -> U24_aag(X, Y, Z, addX_in_aag(X, Y, Z)) 18.16/5.63 addX_in_aag(zero(X), b, one(X)) -> U17_aag(X, binaryZ_in_g(X)) 18.16/5.63 U17_aag(X, binaryZ_out_g(X)) -> addX_out_aag(zero(X), b, one(X)) 18.16/5.63 addX_in_aag(one(X), b, zero(Z)) -> U18_aag(X, Z, succ_in_ag(X, Z)) 18.16/5.63 U18_aag(X, Z, succ_out_ag(X, Z)) -> addX_out_aag(one(X), b, zero(Z)) 18.16/5.63 addX_in_aag(X, Y, Z) -> U19_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.16/5.63 addC_in_aag(one(X), zero(Y), zero(Z)) -> U25_aag(X, Y, Z, addY_in_aag(X, Y, Z)) 18.16/5.63 addY_in_aag(b, zero(Y), one(Y)) -> U20_aag(Y, binaryZ_in_g(Y)) 18.16/5.63 U20_aag(Y, binaryZ_out_g(Y)) -> addY_out_aag(b, zero(Y), one(Y)) 18.16/5.63 addY_in_aag(b, one(Y), zero(Z)) -> U21_aag(Y, Z, succ_in_ag(Y, Z)) 18.16/5.63 U21_aag(Y, Z, succ_out_ag(Y, Z)) -> addY_out_aag(b, one(Y), zero(Z)) 18.16/5.63 addY_in_aag(X, Y, Z) -> U22_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.16/5.63 addC_in_aag(one(X), one(Y), one(Z)) -> U26_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.16/5.63 U26_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addC_out_aag(one(X), one(Y), one(Z)) 18.16/5.63 U22_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addY_out_aag(X, Y, Z) 18.16/5.63 U25_aag(X, Y, Z, addY_out_aag(X, Y, Z)) -> addC_out_aag(one(X), zero(Y), zero(Z)) 18.16/5.63 U19_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addX_out_aag(X, Y, Z) 18.16/5.63 U24_aag(X, Y, Z, addX_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), one(Y), zero(Z)) 18.16/5.63 U16_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addc_out_aag(X, Y, Z) 18.16/5.63 U13_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addz_out_aag(one(X), one(Y), zero(Z)) 18.16/5.63 U9_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addy_out_aag(X, Y, Z) 18.16/5.63 U12_aag(X, Y, Z, addy_out_aag(X, Y, Z)) -> addz_out_aag(one(X), zero(Y), one(Z)) 18.16/5.63 U6_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addx_out_aag(X, Y, Z) 18.16/5.63 U11_aag(X, Y, Z, addx_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), one(Y), one(Z)) 18.16/5.63 U10_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), zero(Y), zero(Z)) 18.16/5.63 U3_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> add_out_aag(X, Y, Z) 18.16/5.63 U37_aag(R, S, RSS, add_out_aag(S, zero(RS), RSS)) -> times_out_aag(one(R), S, RSS) 18.16/5.63 U35_aag(R, S, RS, times_out_aag(R, S, RS)) -> times_out_aag(zero(R), S, zero(RS)) 18.16/5.63 18.16/5.63 The argument filtering Pi contains the following mapping: 18.16/5.63 times_in_aag(x1, x2, x3) = times_in_aag(x3) 18.16/5.63 18.16/5.63 times_out_aag(x1, x2, x3) = times_out_aag(x1, x2, x3) 18.16/5.63 18.16/5.63 zero(x1) = zero(x1) 18.16/5.63 18.16/5.63 U35_aag(x1, x2, x3, x4) = U35_aag(x3, x4) 18.16/5.63 18.16/5.63 U36_aag(x1, x2, x3, x4) = U36_aag(x3, x4) 18.16/5.63 18.16/5.63 times_in_aaa(x1, x2, x3) = times_in_aaa 18.16/5.63 18.16/5.63 times_out_aaa(x1, x2, x3) = times_out_aaa(x1) 18.16/5.63 18.16/5.63 U35_aaa(x1, x2, x3, x4) = U35_aaa(x4) 18.16/5.63 18.16/5.63 U36_aaa(x1, x2, x3, x4) = U36_aaa(x4) 18.16/5.63 18.16/5.63 U37_aaa(x1, x2, x3, x4) = U37_aaa(x1, x4) 18.16/5.63 18.16/5.63 add_in_aaa(x1, x2, x3) = add_in_aaa 18.16/5.63 18.16/5.63 add_out_aaa(x1, x2, x3) = add_out_aaa(x1, x2, x3) 18.16/5.63 18.16/5.63 U1_aaa(x1, x2) = U1_aaa(x2) 18.38/5.63 18.38/5.63 binaryZ_in_a(x1) = binaryZ_in_a 18.38/5.63 18.38/5.63 U29_a(x1, x2) = U29_a(x2) 18.38/5.63 18.38/5.63 U30_a(x1, x2) = U30_a(x2) 18.38/5.63 18.38/5.63 binary_in_a(x1) = binary_in_a 18.38/5.63 18.38/5.63 binary_out_a(x1) = binary_out_a(x1) 18.38/5.63 18.38/5.63 U27_a(x1, x2) = U27_a(x2) 18.38/5.63 18.38/5.63 binaryZ_out_a(x1) = binaryZ_out_a(x1) 18.38/5.63 18.38/5.63 U28_a(x1, x2) = U28_a(x2) 18.38/5.63 18.38/5.63 U2_aaa(x1, x2) = U2_aaa(x2) 18.38/5.63 18.38/5.63 U3_aaa(x1, x2, x3, x4) = U3_aaa(x4) 18.38/5.63 18.38/5.63 addz_in_aaa(x1, x2, x3) = addz_in_aaa 18.38/5.63 18.38/5.63 U10_aaa(x1, x2, x3, x4) = U10_aaa(x4) 18.38/5.63 18.38/5.63 U11_aaa(x1, x2, x3, x4) = U11_aaa(x4) 18.38/5.63 18.38/5.63 addx_in_aaa(x1, x2, x3) = addx_in_aaa 18.38/5.63 18.38/5.63 U4_aaa(x1, x2) = U4_aaa(x2) 18.38/5.63 18.38/5.63 addx_out_aaa(x1, x2, x3) = addx_out_aaa(x1, x2, x3) 18.38/5.63 18.38/5.63 U5_aaa(x1, x2) = U5_aaa(x2) 18.38/5.63 18.38/5.63 U6_aaa(x1, x2, x3, x4) = U6_aaa(x4) 18.38/5.63 18.38/5.63 U12_aaa(x1, x2, x3, x4) = U12_aaa(x4) 18.38/5.63 18.38/5.63 addy_in_aaa(x1, x2, x3) = addy_in_aaa 18.38/5.63 18.38/5.63 U7_aaa(x1, x2) = U7_aaa(x2) 18.38/5.63 18.38/5.63 addy_out_aaa(x1, x2, x3) = addy_out_aaa(x1, x2, x3) 18.38/5.63 18.38/5.63 U8_aaa(x1, x2) = U8_aaa(x2) 18.38/5.63 18.38/5.63 U9_aaa(x1, x2, x3, x4) = U9_aaa(x4) 18.38/5.63 18.38/5.63 U13_aaa(x1, x2, x3, x4) = U13_aaa(x4) 18.38/5.63 18.38/5.63 addc_in_aaa(x1, x2, x3) = addc_in_aaa 18.38/5.63 18.38/5.63 addc_out_aaa(x1, x2, x3) = addc_out_aaa(x1, x2, x3) 18.38/5.63 18.38/5.63 U14_aaa(x1, x2, x3) = U14_aaa(x3) 18.38/5.63 18.38/5.63 succZ_in_aa(x1, x2) = succZ_in_aa 18.38/5.63 18.38/5.63 U33_aa(x1, x2) = U33_aa(x2) 18.38/5.63 18.38/5.63 succZ_out_aa(x1, x2) = succZ_out_aa(x1, x2) 18.38/5.63 18.38/5.63 U34_aa(x1, x2, x3) = U34_aa(x3) 18.38/5.63 18.38/5.63 succ_in_aa(x1, x2) = succ_in_aa 18.38/5.63 18.38/5.63 succ_out_aa(x1, x2) = succ_out_aa(x1, x2) 18.38/5.63 18.38/5.63 U31_aa(x1, x2) = U31_aa(x2) 18.38/5.63 18.38/5.63 U32_aa(x1, x2, x3) = U32_aa(x3) 18.38/5.63 18.38/5.63 U15_aaa(x1, x2, x3) = U15_aaa(x3) 18.38/5.63 18.38/5.63 U16_aaa(x1, x2, x3, x4) = U16_aaa(x4) 18.38/5.63 18.38/5.63 addC_in_aaa(x1, x2, x3) = addC_in_aaa 18.38/5.63 18.38/5.63 U23_aaa(x1, x2, x3, x4) = U23_aaa(x4) 18.38/5.63 18.38/5.63 addz_out_aaa(x1, x2, x3) = addz_out_aaa(x1, x2, x3) 18.38/5.63 18.38/5.63 addC_out_aaa(x1, x2, x3) = addC_out_aaa(x1, x2, x3) 18.38/5.63 18.38/5.63 U24_aaa(x1, x2, x3, x4) = U24_aaa(x4) 18.38/5.63 18.38/5.63 addX_in_aaa(x1, x2, x3) = addX_in_aaa 18.38/5.63 18.38/5.63 U17_aaa(x1, x2) = U17_aaa(x2) 18.38/5.63 18.38/5.63 addX_out_aaa(x1, x2, x3) = addX_out_aaa(x1, x2, x3) 18.38/5.63 18.38/5.63 U18_aaa(x1, x2, x3) = U18_aaa(x3) 18.38/5.63 18.38/5.63 U19_aaa(x1, x2, x3, x4) = U19_aaa(x4) 18.38/5.63 18.38/5.63 U25_aaa(x1, x2, x3, x4) = U25_aaa(x4) 18.38/5.63 18.38/5.63 addY_in_aaa(x1, x2, x3) = addY_in_aaa 18.38/5.63 18.38/5.63 U20_aaa(x1, x2) = U20_aaa(x2) 18.38/5.63 18.38/5.63 addY_out_aaa(x1, x2, x3) = addY_out_aaa(x1, x2, x3) 18.38/5.63 18.38/5.63 U21_aaa(x1, x2, x3) = U21_aaa(x3) 18.38/5.63 18.38/5.63 U22_aaa(x1, x2, x3, x4) = U22_aaa(x4) 18.38/5.63 18.38/5.63 U26_aaa(x1, x2, x3, x4) = U26_aaa(x4) 18.38/5.63 18.38/5.63 U37_aag(x1, x2, x3, x4) = U37_aag(x1, x3, x4) 18.38/5.63 18.38/5.63 add_in_aag(x1, x2, x3) = add_in_aag(x3) 18.38/5.63 18.38/5.63 b = b 18.38/5.63 18.38/5.63 add_out_aag(x1, x2, x3) = add_out_aag(x1, x2, x3) 18.38/5.63 18.38/5.63 U1_aag(x1, x2) = U1_aag(x1, x2) 18.38/5.63 18.38/5.63 binaryZ_in_g(x1) = binaryZ_in_g(x1) 18.38/5.63 18.38/5.63 U29_g(x1, x2) = U29_g(x1, x2) 18.38/5.63 18.38/5.63 one(x1) = one(x1) 18.38/5.63 18.38/5.63 U30_g(x1, x2) = U30_g(x1, x2) 18.38/5.63 18.38/5.63 binary_in_g(x1) = binary_in_g(x1) 18.38/5.63 18.38/5.63 binary_out_g(x1) = binary_out_g(x1) 18.38/5.63 18.38/5.63 U27_g(x1, x2) = U27_g(x1, x2) 18.38/5.63 18.38/5.63 binaryZ_out_g(x1) = binaryZ_out_g(x1) 18.38/5.63 18.38/5.63 U28_g(x1, x2) = U28_g(x1, x2) 18.38/5.63 18.38/5.63 U2_aag(x1, x2) = U2_aag(x1, x2) 18.38/5.63 18.38/5.63 U3_aag(x1, x2, x3, x4) = U3_aag(x3, x4) 18.38/5.63 18.38/5.63 addz_in_aag(x1, x2, x3) = addz_in_aag(x3) 18.38/5.63 18.38/5.63 U10_aag(x1, x2, x3, x4) = U10_aag(x3, x4) 18.38/5.63 18.38/5.63 U11_aag(x1, x2, x3, x4) = U11_aag(x3, x4) 18.38/5.63 18.38/5.63 addx_in_aag(x1, x2, x3) = addx_in_aag(x3) 18.38/5.63 18.38/5.63 U4_aag(x1, x2) = U4_aag(x1, x2) 18.38/5.63 18.38/5.63 addx_out_aag(x1, x2, x3) = addx_out_aag(x1, x2, x3) 18.38/5.63 18.38/5.63 U5_aag(x1, x2) = U5_aag(x1, x2) 18.38/5.63 18.38/5.63 U6_aag(x1, x2, x3, x4) = U6_aag(x3, x4) 18.38/5.63 18.38/5.63 U12_aag(x1, x2, x3, x4) = U12_aag(x3, x4) 18.38/5.63 18.38/5.63 addy_in_aag(x1, x2, x3) = addy_in_aag(x3) 18.38/5.63 18.38/5.63 U7_aag(x1, x2) = U7_aag(x1, x2) 18.38/5.63 18.38/5.63 addy_out_aag(x1, x2, x3) = addy_out_aag(x1, x2, x3) 18.38/5.63 18.38/5.63 U8_aag(x1, x2) = U8_aag(x1, x2) 18.38/5.63 18.38/5.63 U9_aag(x1, x2, x3, x4) = U9_aag(x3, x4) 18.38/5.63 18.38/5.63 U13_aag(x1, x2, x3, x4) = U13_aag(x3, x4) 18.38/5.63 18.38/5.63 addc_in_aag(x1, x2, x3) = addc_in_aag(x3) 18.38/5.63 18.38/5.63 addc_out_aag(x1, x2, x3) = addc_out_aag(x1, x2, x3) 18.38/5.63 18.38/5.63 U14_aag(x1, x2, x3) = U14_aag(x2, x3) 18.38/5.63 18.38/5.63 succZ_in_ag(x1, x2) = succZ_in_ag(x2) 18.38/5.63 18.38/5.63 U33_ag(x1, x2) = U33_ag(x1, x2) 18.38/5.63 18.38/5.63 succZ_out_ag(x1, x2) = succZ_out_ag(x1, x2) 18.38/5.63 18.38/5.63 U34_ag(x1, x2, x3) = U34_ag(x2, x3) 18.38/5.63 18.38/5.63 succ_in_ag(x1, x2) = succ_in_ag(x2) 18.38/5.63 18.38/5.63 succ_out_ag(x1, x2) = succ_out_ag(x1, x2) 18.38/5.63 18.38/5.63 U31_ag(x1, x2) = U31_ag(x1, x2) 18.38/5.63 18.38/5.63 U32_ag(x1, x2, x3) = U32_ag(x2, x3) 18.38/5.63 18.38/5.63 U15_aag(x1, x2, x3) = U15_aag(x2, x3) 18.38/5.63 18.38/5.63 U16_aag(x1, x2, x3, x4) = U16_aag(x3, x4) 18.38/5.63 18.38/5.63 addC_in_aag(x1, x2, x3) = addC_in_aag(x3) 18.38/5.63 18.38/5.63 U23_aag(x1, x2, x3, x4) = U23_aag(x3, x4) 18.38/5.63 18.38/5.63 addz_out_aag(x1, x2, x3) = addz_out_aag(x1, x2, x3) 18.38/5.63 18.38/5.63 addC_out_aag(x1, x2, x3) = addC_out_aag(x1, x2, x3) 18.38/5.63 18.38/5.63 U24_aag(x1, x2, x3, x4) = U24_aag(x3, x4) 18.38/5.63 18.38/5.63 addX_in_aag(x1, x2, x3) = addX_in_aag(x3) 18.38/5.63 18.38/5.63 U17_aag(x1, x2) = U17_aag(x1, x2) 18.38/5.63 18.38/5.63 addX_out_aag(x1, x2, x3) = addX_out_aag(x1, x2, x3) 18.38/5.63 18.38/5.63 U18_aag(x1, x2, x3) = U18_aag(x2, x3) 18.38/5.63 18.38/5.63 U19_aag(x1, x2, x3, x4) = U19_aag(x3, x4) 18.38/5.63 18.38/5.63 U25_aag(x1, x2, x3, x4) = U25_aag(x3, x4) 18.38/5.63 18.38/5.63 addY_in_aag(x1, x2, x3) = addY_in_aag(x3) 18.38/5.63 18.38/5.63 U20_aag(x1, x2) = U20_aag(x1, x2) 18.38/5.63 18.38/5.63 addY_out_aag(x1, x2, x3) = addY_out_aag(x1, x2, x3) 18.38/5.63 18.38/5.63 U21_aag(x1, x2, x3) = U21_aag(x2, x3) 18.38/5.63 18.38/5.63 U22_aag(x1, x2, x3, x4) = U22_aag(x3, x4) 18.38/5.63 18.38/5.63 U26_aag(x1, x2, x3, x4) = U26_aag(x3, x4) 18.38/5.63 18.38/5.63 SUCC_IN_AG(x1, x2) = SUCC_IN_AG(x2) 18.38/5.63 18.38/5.63 18.38/5.63 We have to consider all (P,R,Pi)-chains 18.38/5.63 ---------------------------------------- 18.38/5.63 18.38/5.63 (15) UsableRulesProof (EQUIVALENT) 18.38/5.63 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 18.38/5.63 ---------------------------------------- 18.38/5.63 18.38/5.63 (16) 18.38/5.63 Obligation: 18.38/5.63 Pi DP problem: 18.38/5.63 The TRS P consists of the following rules: 18.38/5.63 18.38/5.63 SUCC_IN_AG(one(X), zero(Z)) -> SUCC_IN_AG(X, Z) 18.38/5.63 18.38/5.63 R is empty. 18.38/5.63 The argument filtering Pi contains the following mapping: 18.38/5.63 zero(x1) = zero(x1) 18.38/5.63 18.38/5.63 one(x1) = one(x1) 18.38/5.63 18.38/5.63 SUCC_IN_AG(x1, x2) = SUCC_IN_AG(x2) 18.38/5.63 18.38/5.63 18.38/5.63 We have to consider all (P,R,Pi)-chains 18.38/5.63 ---------------------------------------- 18.38/5.63 18.38/5.63 (17) PiDPToQDPProof (SOUND) 18.38/5.63 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 18.38/5.63 ---------------------------------------- 18.38/5.63 18.38/5.63 (18) 18.38/5.63 Obligation: 18.38/5.63 Q DP problem: 18.38/5.63 The TRS P consists of the following rules: 18.38/5.63 18.38/5.63 SUCC_IN_AG(zero(Z)) -> SUCC_IN_AG(Z) 18.38/5.63 18.38/5.63 R is empty. 18.38/5.63 Q is empty. 18.38/5.63 We have to consider all (P,Q,R)-chains. 18.38/5.63 ---------------------------------------- 18.38/5.63 18.38/5.63 (19) QDPSizeChangeProof (EQUIVALENT) 18.38/5.63 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 18.38/5.63 18.38/5.63 From the DPs we obtained the following set of size-change graphs: 18.38/5.63 *SUCC_IN_AG(zero(Z)) -> SUCC_IN_AG(Z) 18.38/5.63 The graph contains the following edges 1 > 1 18.38/5.63 18.38/5.63 18.38/5.63 ---------------------------------------- 18.38/5.63 18.38/5.63 (20) 18.38/5.63 YES 18.38/5.63 18.38/5.63 ---------------------------------------- 18.38/5.63 18.38/5.63 (21) 18.38/5.63 Obligation: 18.38/5.63 Pi DP problem: 18.38/5.63 The TRS P consists of the following rules: 18.38/5.63 18.38/5.63 ADDX_IN_AAG(X, Y, Z) -> ADDZ_IN_AAG(X, Y, Z) 18.38/5.63 ADDZ_IN_AAG(zero(X), zero(Y), zero(Z)) -> ADDZ_IN_AAG(X, Y, Z) 18.38/5.63 ADDZ_IN_AAG(zero(X), one(Y), one(Z)) -> ADDX_IN_AAG(X, Y, Z) 18.38/5.63 ADDZ_IN_AAG(one(X), zero(Y), one(Z)) -> ADDY_IN_AAG(X, Y, Z) 18.38/5.63 ADDY_IN_AAG(X, Y, Z) -> ADDZ_IN_AAG(X, Y, Z) 18.38/5.63 ADDZ_IN_AAG(one(X), one(Y), zero(Z)) -> ADDC_IN_AAG(X, Y, Z) 18.38/5.63 ADDC_IN_AAG(X, Y, Z) -> ADDC_IN_AAG^1(X, Y, Z) 18.38/5.63 ADDC_IN_AAG^1(zero(X), zero(Y), one(Z)) -> ADDZ_IN_AAG(X, Y, Z) 18.38/5.63 ADDC_IN_AAG^1(zero(X), one(Y), zero(Z)) -> ADDX_IN_AAG^1(X, Y, Z) 18.38/5.63 ADDX_IN_AAG^1(X, Y, Z) -> ADDC_IN_AAG^1(X, Y, Z) 18.38/5.63 ADDC_IN_AAG^1(one(X), zero(Y), zero(Z)) -> ADDY_IN_AAG^1(X, Y, Z) 18.38/5.63 ADDY_IN_AAG^1(X, Y, Z) -> ADDC_IN_AAG^1(X, Y, Z) 18.38/5.63 ADDC_IN_AAG^1(one(X), one(Y), one(Z)) -> ADDC_IN_AAG(X, Y, Z) 18.38/5.63 18.38/5.63 The TRS R consists of the following rules: 18.38/5.63 18.38/5.63 times_in_aag(one(b), X, X) -> times_out_aag(one(b), X, X) 18.38/5.63 times_in_aag(zero(R), S, zero(RS)) -> U35_aag(R, S, RS, times_in_aag(R, S, RS)) 18.38/5.63 times_in_aag(one(R), S, RSS) -> U36_aag(R, S, RSS, times_in_aaa(R, S, RS)) 18.38/5.63 times_in_aaa(one(b), X, X) -> times_out_aaa(one(b), X, X) 18.38/5.63 times_in_aaa(zero(R), S, zero(RS)) -> U35_aaa(R, S, RS, times_in_aaa(R, S, RS)) 18.38/5.63 times_in_aaa(one(R), S, RSS) -> U36_aaa(R, S, RSS, times_in_aaa(R, S, RS)) 18.38/5.63 U36_aaa(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aaa(R, S, RSS, add_in_aaa(S, zero(RS), RSS)) 18.38/5.63 add_in_aaa(b, b, b) -> add_out_aaa(b, b, b) 18.38/5.63 add_in_aaa(X, b, X) -> U1_aaa(X, binaryZ_in_a(X)) 18.38/5.63 binaryZ_in_a(zero(X)) -> U29_a(X, binaryZ_in_a(X)) 18.38/5.63 binaryZ_in_a(one(X)) -> U30_a(X, binary_in_a(X)) 18.38/5.63 binary_in_a(b) -> binary_out_a(b) 18.38/5.63 binary_in_a(zero(X)) -> U27_a(X, binaryZ_in_a(X)) 18.38/5.63 U27_a(X, binaryZ_out_a(X)) -> binary_out_a(zero(X)) 18.38/5.63 binary_in_a(one(X)) -> U28_a(X, binary_in_a(X)) 18.38/5.63 U28_a(X, binary_out_a(X)) -> binary_out_a(one(X)) 18.38/5.63 U30_a(X, binary_out_a(X)) -> binaryZ_out_a(one(X)) 18.38/5.63 U29_a(X, binaryZ_out_a(X)) -> binaryZ_out_a(zero(X)) 18.38/5.63 U1_aaa(X, binaryZ_out_a(X)) -> add_out_aaa(X, b, X) 18.38/5.63 add_in_aaa(b, Y, Y) -> U2_aaa(Y, binaryZ_in_a(Y)) 18.38/5.63 U2_aaa(Y, binaryZ_out_a(Y)) -> add_out_aaa(b, Y, Y) 18.38/5.63 add_in_aaa(X, Y, Z) -> U3_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.63 addz_in_aaa(zero(X), zero(Y), zero(Z)) -> U10_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.63 addz_in_aaa(zero(X), one(Y), one(Z)) -> U11_aaa(X, Y, Z, addx_in_aaa(X, Y, Z)) 18.38/5.63 addx_in_aaa(one(X), b, one(X)) -> U4_aaa(X, binary_in_a(X)) 18.38/5.63 U4_aaa(X, binary_out_a(X)) -> addx_out_aaa(one(X), b, one(X)) 18.38/5.63 addx_in_aaa(zero(X), b, zero(X)) -> U5_aaa(X, binaryZ_in_a(X)) 18.38/5.63 U5_aaa(X, binaryZ_out_a(X)) -> addx_out_aaa(zero(X), b, zero(X)) 18.38/5.63 addx_in_aaa(X, Y, Z) -> U6_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.63 addz_in_aaa(one(X), zero(Y), one(Z)) -> U12_aaa(X, Y, Z, addy_in_aaa(X, Y, Z)) 18.38/5.63 addy_in_aaa(b, one(Y), one(Y)) -> U7_aaa(Y, binary_in_a(Y)) 18.38/5.63 U7_aaa(Y, binary_out_a(Y)) -> addy_out_aaa(b, one(Y), one(Y)) 18.38/5.63 addy_in_aaa(b, zero(Y), zero(Y)) -> U8_aaa(Y, binaryZ_in_a(Y)) 18.38/5.63 U8_aaa(Y, binaryZ_out_a(Y)) -> addy_out_aaa(b, zero(Y), zero(Y)) 18.38/5.63 addy_in_aaa(X, Y, Z) -> U9_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.63 addz_in_aaa(one(X), one(Y), zero(Z)) -> U13_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.38/5.63 addc_in_aaa(b, b, one(b)) -> addc_out_aaa(b, b, one(b)) 18.38/5.63 addc_in_aaa(X, b, Z) -> U14_aaa(X, Z, succZ_in_aa(X, Z)) 18.38/5.63 succZ_in_aa(zero(X), one(X)) -> U33_aa(X, binaryZ_in_a(X)) 18.38/5.63 U33_aa(X, binaryZ_out_a(X)) -> succZ_out_aa(zero(X), one(X)) 18.38/5.63 succZ_in_aa(one(X), zero(Z)) -> U34_aa(X, Z, succ_in_aa(X, Z)) 18.38/5.63 succ_in_aa(b, one(b)) -> succ_out_aa(b, one(b)) 18.38/5.63 succ_in_aa(zero(X), one(X)) -> U31_aa(X, binaryZ_in_a(X)) 18.38/5.63 U31_aa(X, binaryZ_out_a(X)) -> succ_out_aa(zero(X), one(X)) 18.38/5.63 succ_in_aa(one(X), zero(Z)) -> U32_aa(X, Z, succ_in_aa(X, Z)) 18.38/5.63 U32_aa(X, Z, succ_out_aa(X, Z)) -> succ_out_aa(one(X), zero(Z)) 18.38/5.63 U34_aa(X, Z, succ_out_aa(X, Z)) -> succZ_out_aa(one(X), zero(Z)) 18.38/5.63 U14_aaa(X, Z, succZ_out_aa(X, Z)) -> addc_out_aaa(X, b, Z) 18.38/5.63 addc_in_aaa(b, Y, Z) -> U15_aaa(Y, Z, succZ_in_aa(Y, Z)) 18.38/5.63 U15_aaa(Y, Z, succZ_out_aa(Y, Z)) -> addc_out_aaa(b, Y, Z) 18.38/5.63 addc_in_aaa(X, Y, Z) -> U16_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.63 addC_in_aaa(zero(X), zero(Y), one(Z)) -> U23_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.63 U23_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), zero(Y), one(Z)) 18.38/5.63 addC_in_aaa(zero(X), one(Y), zero(Z)) -> U24_aaa(X, Y, Z, addX_in_aaa(X, Y, Z)) 18.38/5.63 addX_in_aaa(zero(X), b, one(X)) -> U17_aaa(X, binaryZ_in_a(X)) 18.38/5.63 U17_aaa(X, binaryZ_out_a(X)) -> addX_out_aaa(zero(X), b, one(X)) 18.38/5.63 addX_in_aaa(one(X), b, zero(Z)) -> U18_aaa(X, Z, succ_in_aa(X, Z)) 18.38/5.63 U18_aaa(X, Z, succ_out_aa(X, Z)) -> addX_out_aaa(one(X), b, zero(Z)) 18.38/5.63 addX_in_aaa(X, Y, Z) -> U19_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.63 addC_in_aaa(one(X), zero(Y), zero(Z)) -> U25_aaa(X, Y, Z, addY_in_aaa(X, Y, Z)) 18.38/5.63 addY_in_aaa(b, zero(Y), one(Y)) -> U20_aaa(Y, binaryZ_in_a(Y)) 18.38/5.63 U20_aaa(Y, binaryZ_out_a(Y)) -> addY_out_aaa(b, zero(Y), one(Y)) 18.38/5.63 addY_in_aaa(b, one(Y), zero(Z)) -> U21_aaa(Y, Z, succ_in_aa(Y, Z)) 18.38/5.63 U21_aaa(Y, Z, succ_out_aa(Y, Z)) -> addY_out_aaa(b, one(Y), zero(Z)) 18.38/5.63 addY_in_aaa(X, Y, Z) -> U22_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.63 addC_in_aaa(one(X), one(Y), one(Z)) -> U26_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.38/5.63 U26_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), one(Y), one(Z)) 18.38/5.63 U22_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addY_out_aaa(X, Y, Z) 18.38/5.63 U25_aaa(X, Y, Z, addY_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), zero(Y), zero(Z)) 18.38/5.63 U19_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addX_out_aaa(X, Y, Z) 18.38/5.63 U24_aaa(X, Y, Z, addX_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), one(Y), zero(Z)) 18.38/5.63 U16_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addc_out_aaa(X, Y, Z) 18.38/5.63 U13_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), one(Y), zero(Z)) 18.38/5.63 U9_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addy_out_aaa(X, Y, Z) 18.38/5.63 U12_aaa(X, Y, Z, addy_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), zero(Y), one(Z)) 18.38/5.63 U6_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addx_out_aaa(X, Y, Z) 18.38/5.63 U11_aaa(X, Y, Z, addx_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), one(Y), one(Z)) 18.38/5.63 U10_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), zero(Y), zero(Z)) 18.38/5.63 U3_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> add_out_aaa(X, Y, Z) 18.38/5.63 U37_aaa(R, S, RSS, add_out_aaa(S, zero(RS), RSS)) -> times_out_aaa(one(R), S, RSS) 18.38/5.63 U35_aaa(R, S, RS, times_out_aaa(R, S, RS)) -> times_out_aaa(zero(R), S, zero(RS)) 18.38/5.63 U36_aag(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aag(R, S, RSS, add_in_aag(S, zero(RS), RSS)) 18.38/5.63 add_in_aag(b, b, b) -> add_out_aag(b, b, b) 18.38/5.63 add_in_aag(X, b, X) -> U1_aag(X, binaryZ_in_g(X)) 18.38/5.63 binaryZ_in_g(zero(X)) -> U29_g(X, binaryZ_in_g(X)) 18.38/5.63 binaryZ_in_g(one(X)) -> U30_g(X, binary_in_g(X)) 18.38/5.63 binary_in_g(b) -> binary_out_g(b) 18.38/5.63 binary_in_g(zero(X)) -> U27_g(X, binaryZ_in_g(X)) 18.38/5.63 U27_g(X, binaryZ_out_g(X)) -> binary_out_g(zero(X)) 18.38/5.63 binary_in_g(one(X)) -> U28_g(X, binary_in_g(X)) 18.38/5.63 U28_g(X, binary_out_g(X)) -> binary_out_g(one(X)) 18.38/5.63 U30_g(X, binary_out_g(X)) -> binaryZ_out_g(one(X)) 18.38/5.63 U29_g(X, binaryZ_out_g(X)) -> binaryZ_out_g(zero(X)) 18.38/5.63 U1_aag(X, binaryZ_out_g(X)) -> add_out_aag(X, b, X) 18.38/5.63 add_in_aag(b, Y, Y) -> U2_aag(Y, binaryZ_in_g(Y)) 18.38/5.63 U2_aag(Y, binaryZ_out_g(Y)) -> add_out_aag(b, Y, Y) 18.38/5.63 add_in_aag(X, Y, Z) -> U3_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.63 addz_in_aag(zero(X), zero(Y), zero(Z)) -> U10_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.63 addz_in_aag(zero(X), one(Y), one(Z)) -> U11_aag(X, Y, Z, addx_in_aag(X, Y, Z)) 18.38/5.63 addx_in_aag(one(X), b, one(X)) -> U4_aag(X, binary_in_g(X)) 18.38/5.63 U4_aag(X, binary_out_g(X)) -> addx_out_aag(one(X), b, one(X)) 18.38/5.63 addx_in_aag(zero(X), b, zero(X)) -> U5_aag(X, binaryZ_in_g(X)) 18.38/5.63 U5_aag(X, binaryZ_out_g(X)) -> addx_out_aag(zero(X), b, zero(X)) 18.38/5.63 addx_in_aag(X, Y, Z) -> U6_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.63 addz_in_aag(one(X), zero(Y), one(Z)) -> U12_aag(X, Y, Z, addy_in_aag(X, Y, Z)) 18.38/5.63 addy_in_aag(b, one(Y), one(Y)) -> U7_aag(Y, binary_in_g(Y)) 18.38/5.63 U7_aag(Y, binary_out_g(Y)) -> addy_out_aag(b, one(Y), one(Y)) 18.38/5.63 addy_in_aag(b, zero(Y), zero(Y)) -> U8_aag(Y, binaryZ_in_g(Y)) 18.38/5.63 U8_aag(Y, binaryZ_out_g(Y)) -> addy_out_aag(b, zero(Y), zero(Y)) 18.38/5.63 addy_in_aag(X, Y, Z) -> U9_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.63 addz_in_aag(one(X), one(Y), zero(Z)) -> U13_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.38/5.63 addc_in_aag(b, b, one(b)) -> addc_out_aag(b, b, one(b)) 18.38/5.63 addc_in_aag(X, b, Z) -> U14_aag(X, Z, succZ_in_ag(X, Z)) 18.38/5.63 succZ_in_ag(zero(X), one(X)) -> U33_ag(X, binaryZ_in_g(X)) 18.38/5.63 U33_ag(X, binaryZ_out_g(X)) -> succZ_out_ag(zero(X), one(X)) 18.38/5.63 succZ_in_ag(one(X), zero(Z)) -> U34_ag(X, Z, succ_in_ag(X, Z)) 18.38/5.63 succ_in_ag(b, one(b)) -> succ_out_ag(b, one(b)) 18.38/5.63 succ_in_ag(zero(X), one(X)) -> U31_ag(X, binaryZ_in_g(X)) 18.38/5.63 U31_ag(X, binaryZ_out_g(X)) -> succ_out_ag(zero(X), one(X)) 18.38/5.63 succ_in_ag(one(X), zero(Z)) -> U32_ag(X, Z, succ_in_ag(X, Z)) 18.38/5.63 U32_ag(X, Z, succ_out_ag(X, Z)) -> succ_out_ag(one(X), zero(Z)) 18.38/5.63 U34_ag(X, Z, succ_out_ag(X, Z)) -> succZ_out_ag(one(X), zero(Z)) 18.38/5.63 U14_aag(X, Z, succZ_out_ag(X, Z)) -> addc_out_aag(X, b, Z) 18.38/5.63 addc_in_aag(b, Y, Z) -> U15_aag(Y, Z, succZ_in_ag(Y, Z)) 18.38/5.63 U15_aag(Y, Z, succZ_out_ag(Y, Z)) -> addc_out_aag(b, Y, Z) 18.38/5.63 addc_in_aag(X, Y, Z) -> U16_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.63 addC_in_aag(zero(X), zero(Y), one(Z)) -> U23_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.63 U23_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), zero(Y), one(Z)) 18.38/5.63 addC_in_aag(zero(X), one(Y), zero(Z)) -> U24_aag(X, Y, Z, addX_in_aag(X, Y, Z)) 18.38/5.63 addX_in_aag(zero(X), b, one(X)) -> U17_aag(X, binaryZ_in_g(X)) 18.38/5.63 U17_aag(X, binaryZ_out_g(X)) -> addX_out_aag(zero(X), b, one(X)) 18.38/5.63 addX_in_aag(one(X), b, zero(Z)) -> U18_aag(X, Z, succ_in_ag(X, Z)) 18.38/5.63 U18_aag(X, Z, succ_out_ag(X, Z)) -> addX_out_aag(one(X), b, zero(Z)) 18.38/5.63 addX_in_aag(X, Y, Z) -> U19_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.63 addC_in_aag(one(X), zero(Y), zero(Z)) -> U25_aag(X, Y, Z, addY_in_aag(X, Y, Z)) 18.38/5.63 addY_in_aag(b, zero(Y), one(Y)) -> U20_aag(Y, binaryZ_in_g(Y)) 18.38/5.63 U20_aag(Y, binaryZ_out_g(Y)) -> addY_out_aag(b, zero(Y), one(Y)) 18.38/5.63 addY_in_aag(b, one(Y), zero(Z)) -> U21_aag(Y, Z, succ_in_ag(Y, Z)) 18.38/5.63 U21_aag(Y, Z, succ_out_ag(Y, Z)) -> addY_out_aag(b, one(Y), zero(Z)) 18.38/5.63 addY_in_aag(X, Y, Z) -> U22_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.63 addC_in_aag(one(X), one(Y), one(Z)) -> U26_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.38/5.63 U26_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addC_out_aag(one(X), one(Y), one(Z)) 18.38/5.63 U22_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addY_out_aag(X, Y, Z) 18.38/5.63 U25_aag(X, Y, Z, addY_out_aag(X, Y, Z)) -> addC_out_aag(one(X), zero(Y), zero(Z)) 18.38/5.63 U19_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addX_out_aag(X, Y, Z) 18.38/5.63 U24_aag(X, Y, Z, addX_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), one(Y), zero(Z)) 18.38/5.63 U16_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addc_out_aag(X, Y, Z) 18.38/5.63 U13_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addz_out_aag(one(X), one(Y), zero(Z)) 18.38/5.63 U9_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addy_out_aag(X, Y, Z) 18.38/5.63 U12_aag(X, Y, Z, addy_out_aag(X, Y, Z)) -> addz_out_aag(one(X), zero(Y), one(Z)) 18.38/5.63 U6_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addx_out_aag(X, Y, Z) 18.38/5.63 U11_aag(X, Y, Z, addx_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), one(Y), one(Z)) 18.38/5.64 U10_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), zero(Y), zero(Z)) 18.38/5.64 U3_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> add_out_aag(X, Y, Z) 18.38/5.64 U37_aag(R, S, RSS, add_out_aag(S, zero(RS), RSS)) -> times_out_aag(one(R), S, RSS) 18.38/5.64 U35_aag(R, S, RS, times_out_aag(R, S, RS)) -> times_out_aag(zero(R), S, zero(RS)) 18.38/5.64 18.38/5.64 The argument filtering Pi contains the following mapping: 18.38/5.64 times_in_aag(x1, x2, x3) = times_in_aag(x3) 18.38/5.64 18.38/5.64 times_out_aag(x1, x2, x3) = times_out_aag(x1, x2, x3) 18.38/5.64 18.38/5.64 zero(x1) = zero(x1) 18.38/5.64 18.38/5.64 U35_aag(x1, x2, x3, x4) = U35_aag(x3, x4) 18.38/5.64 18.38/5.64 U36_aag(x1, x2, x3, x4) = U36_aag(x3, x4) 18.38/5.64 18.38/5.64 times_in_aaa(x1, x2, x3) = times_in_aaa 18.38/5.64 18.38/5.64 times_out_aaa(x1, x2, x3) = times_out_aaa(x1) 18.38/5.64 18.38/5.64 U35_aaa(x1, x2, x3, x4) = U35_aaa(x4) 18.38/5.64 18.38/5.64 U36_aaa(x1, x2, x3, x4) = U36_aaa(x4) 18.38/5.64 18.38/5.64 U37_aaa(x1, x2, x3, x4) = U37_aaa(x1, x4) 18.38/5.64 18.38/5.64 add_in_aaa(x1, x2, x3) = add_in_aaa 18.38/5.64 18.38/5.64 add_out_aaa(x1, x2, x3) = add_out_aaa(x1, x2, x3) 18.38/5.64 18.38/5.64 U1_aaa(x1, x2) = U1_aaa(x2) 18.38/5.64 18.38/5.64 binaryZ_in_a(x1) = binaryZ_in_a 18.38/5.64 18.38/5.64 U29_a(x1, x2) = U29_a(x2) 18.38/5.64 18.38/5.64 U30_a(x1, x2) = U30_a(x2) 18.38/5.64 18.38/5.64 binary_in_a(x1) = binary_in_a 18.38/5.64 18.38/5.64 binary_out_a(x1) = binary_out_a(x1) 18.38/5.64 18.38/5.64 U27_a(x1, x2) = U27_a(x2) 18.38/5.64 18.38/5.64 binaryZ_out_a(x1) = binaryZ_out_a(x1) 18.38/5.64 18.38/5.64 U28_a(x1, x2) = U28_a(x2) 18.38/5.64 18.38/5.64 U2_aaa(x1, x2) = U2_aaa(x2) 18.38/5.64 18.38/5.64 U3_aaa(x1, x2, x3, x4) = U3_aaa(x4) 18.38/5.64 18.38/5.64 addz_in_aaa(x1, x2, x3) = addz_in_aaa 18.38/5.64 18.38/5.64 U10_aaa(x1, x2, x3, x4) = U10_aaa(x4) 18.38/5.64 18.38/5.64 U11_aaa(x1, x2, x3, x4) = U11_aaa(x4) 18.38/5.64 18.38/5.64 addx_in_aaa(x1, x2, x3) = addx_in_aaa 18.38/5.64 18.38/5.64 U4_aaa(x1, x2) = U4_aaa(x2) 18.38/5.64 18.38/5.64 addx_out_aaa(x1, x2, x3) = addx_out_aaa(x1, x2, x3) 18.38/5.64 18.38/5.64 U5_aaa(x1, x2) = U5_aaa(x2) 18.38/5.64 18.38/5.64 U6_aaa(x1, x2, x3, x4) = U6_aaa(x4) 18.38/5.64 18.38/5.64 U12_aaa(x1, x2, x3, x4) = U12_aaa(x4) 18.38/5.64 18.38/5.64 addy_in_aaa(x1, x2, x3) = addy_in_aaa 18.38/5.64 18.38/5.64 U7_aaa(x1, x2) = U7_aaa(x2) 18.38/5.64 18.38/5.64 addy_out_aaa(x1, x2, x3) = addy_out_aaa(x1, x2, x3) 18.38/5.64 18.38/5.64 U8_aaa(x1, x2) = U8_aaa(x2) 18.38/5.64 18.38/5.64 U9_aaa(x1, x2, x3, x4) = U9_aaa(x4) 18.38/5.64 18.38/5.64 U13_aaa(x1, x2, x3, x4) = U13_aaa(x4) 18.38/5.64 18.38/5.64 addc_in_aaa(x1, x2, x3) = addc_in_aaa 18.38/5.64 18.38/5.64 addc_out_aaa(x1, x2, x3) = addc_out_aaa(x1, x2, x3) 18.38/5.64 18.38/5.64 U14_aaa(x1, x2, x3) = U14_aaa(x3) 18.38/5.64 18.38/5.64 succZ_in_aa(x1, x2) = succZ_in_aa 18.38/5.64 18.38/5.64 U33_aa(x1, x2) = U33_aa(x2) 18.38/5.64 18.38/5.64 succZ_out_aa(x1, x2) = succZ_out_aa(x1, x2) 18.38/5.64 18.38/5.64 U34_aa(x1, x2, x3) = U34_aa(x3) 18.38/5.64 18.38/5.64 succ_in_aa(x1, x2) = succ_in_aa 18.38/5.64 18.38/5.64 succ_out_aa(x1, x2) = succ_out_aa(x1, x2) 18.38/5.64 18.38/5.64 U31_aa(x1, x2) = U31_aa(x2) 18.38/5.64 18.38/5.64 U32_aa(x1, x2, x3) = U32_aa(x3) 18.38/5.64 18.38/5.64 U15_aaa(x1, x2, x3) = U15_aaa(x3) 18.38/5.64 18.38/5.64 U16_aaa(x1, x2, x3, x4) = U16_aaa(x4) 18.38/5.64 18.38/5.64 addC_in_aaa(x1, x2, x3) = addC_in_aaa 18.38/5.64 18.38/5.64 U23_aaa(x1, x2, x3, x4) = U23_aaa(x4) 18.38/5.64 18.38/5.64 addz_out_aaa(x1, x2, x3) = addz_out_aaa(x1, x2, x3) 18.38/5.64 18.38/5.64 addC_out_aaa(x1, x2, x3) = addC_out_aaa(x1, x2, x3) 18.38/5.64 18.38/5.64 U24_aaa(x1, x2, x3, x4) = U24_aaa(x4) 18.38/5.64 18.38/5.64 addX_in_aaa(x1, x2, x3) = addX_in_aaa 18.38/5.64 18.38/5.64 U17_aaa(x1, x2) = U17_aaa(x2) 18.38/5.64 18.38/5.64 addX_out_aaa(x1, x2, x3) = addX_out_aaa(x1, x2, x3) 18.38/5.64 18.38/5.64 U18_aaa(x1, x2, x3) = U18_aaa(x3) 18.38/5.64 18.38/5.64 U19_aaa(x1, x2, x3, x4) = U19_aaa(x4) 18.38/5.64 18.38/5.64 U25_aaa(x1, x2, x3, x4) = U25_aaa(x4) 18.38/5.64 18.38/5.64 addY_in_aaa(x1, x2, x3) = addY_in_aaa 18.38/5.64 18.38/5.64 U20_aaa(x1, x2) = U20_aaa(x2) 18.38/5.64 18.38/5.64 addY_out_aaa(x1, x2, x3) = addY_out_aaa(x1, x2, x3) 18.38/5.64 18.38/5.64 U21_aaa(x1, x2, x3) = U21_aaa(x3) 18.38/5.64 18.38/5.64 U22_aaa(x1, x2, x3, x4) = U22_aaa(x4) 18.38/5.64 18.38/5.64 U26_aaa(x1, x2, x3, x4) = U26_aaa(x4) 18.38/5.64 18.38/5.64 U37_aag(x1, x2, x3, x4) = U37_aag(x1, x3, x4) 18.38/5.64 18.38/5.64 add_in_aag(x1, x2, x3) = add_in_aag(x3) 18.38/5.64 18.38/5.64 b = b 18.38/5.64 18.38/5.64 add_out_aag(x1, x2, x3) = add_out_aag(x1, x2, x3) 18.38/5.64 18.38/5.64 U1_aag(x1, x2) = U1_aag(x1, x2) 18.38/5.64 18.38/5.64 binaryZ_in_g(x1) = binaryZ_in_g(x1) 18.38/5.64 18.38/5.64 U29_g(x1, x2) = U29_g(x1, x2) 18.38/5.64 18.38/5.64 one(x1) = one(x1) 18.38/5.64 18.38/5.64 U30_g(x1, x2) = U30_g(x1, x2) 18.38/5.64 18.38/5.64 binary_in_g(x1) = binary_in_g(x1) 18.38/5.64 18.38/5.64 binary_out_g(x1) = binary_out_g(x1) 18.38/5.64 18.38/5.64 U27_g(x1, x2) = U27_g(x1, x2) 18.38/5.64 18.38/5.64 binaryZ_out_g(x1) = binaryZ_out_g(x1) 18.38/5.64 18.38/5.64 U28_g(x1, x2) = U28_g(x1, x2) 18.38/5.64 18.38/5.64 U2_aag(x1, x2) = U2_aag(x1, x2) 18.38/5.64 18.38/5.64 U3_aag(x1, x2, x3, x4) = U3_aag(x3, x4) 18.38/5.64 18.38/5.64 addz_in_aag(x1, x2, x3) = addz_in_aag(x3) 18.38/5.64 18.38/5.64 U10_aag(x1, x2, x3, x4) = U10_aag(x3, x4) 18.38/5.64 18.38/5.64 U11_aag(x1, x2, x3, x4) = U11_aag(x3, x4) 18.38/5.64 18.38/5.64 addx_in_aag(x1, x2, x3) = addx_in_aag(x3) 18.38/5.64 18.38/5.64 U4_aag(x1, x2) = U4_aag(x1, x2) 18.38/5.64 18.38/5.64 addx_out_aag(x1, x2, x3) = addx_out_aag(x1, x2, x3) 18.38/5.64 18.38/5.64 U5_aag(x1, x2) = U5_aag(x1, x2) 18.38/5.64 18.38/5.64 U6_aag(x1, x2, x3, x4) = U6_aag(x3, x4) 18.38/5.64 18.38/5.64 U12_aag(x1, x2, x3, x4) = U12_aag(x3, x4) 18.38/5.64 18.38/5.64 addy_in_aag(x1, x2, x3) = addy_in_aag(x3) 18.38/5.64 18.38/5.64 U7_aag(x1, x2) = U7_aag(x1, x2) 18.38/5.64 18.38/5.64 addy_out_aag(x1, x2, x3) = addy_out_aag(x1, x2, x3) 18.38/5.64 18.38/5.64 U8_aag(x1, x2) = U8_aag(x1, x2) 18.38/5.64 18.38/5.64 U9_aag(x1, x2, x3, x4) = U9_aag(x3, x4) 18.38/5.64 18.38/5.64 U13_aag(x1, x2, x3, x4) = U13_aag(x3, x4) 18.38/5.64 18.38/5.64 addc_in_aag(x1, x2, x3) = addc_in_aag(x3) 18.38/5.64 18.38/5.64 addc_out_aag(x1, x2, x3) = addc_out_aag(x1, x2, x3) 18.38/5.64 18.38/5.64 U14_aag(x1, x2, x3) = U14_aag(x2, x3) 18.38/5.64 18.38/5.64 succZ_in_ag(x1, x2) = succZ_in_ag(x2) 18.38/5.64 18.38/5.64 U33_ag(x1, x2) = U33_ag(x1, x2) 18.38/5.64 18.38/5.64 succZ_out_ag(x1, x2) = succZ_out_ag(x1, x2) 18.38/5.64 18.38/5.64 U34_ag(x1, x2, x3) = U34_ag(x2, x3) 18.38/5.64 18.38/5.64 succ_in_ag(x1, x2) = succ_in_ag(x2) 18.38/5.64 18.38/5.64 succ_out_ag(x1, x2) = succ_out_ag(x1, x2) 18.38/5.64 18.38/5.64 U31_ag(x1, x2) = U31_ag(x1, x2) 18.38/5.64 18.38/5.64 U32_ag(x1, x2, x3) = U32_ag(x2, x3) 18.38/5.64 18.38/5.64 U15_aag(x1, x2, x3) = U15_aag(x2, x3) 18.38/5.64 18.38/5.64 U16_aag(x1, x2, x3, x4) = U16_aag(x3, x4) 18.38/5.64 18.38/5.64 addC_in_aag(x1, x2, x3) = addC_in_aag(x3) 18.38/5.64 18.38/5.64 U23_aag(x1, x2, x3, x4) = U23_aag(x3, x4) 18.38/5.64 18.38/5.64 addz_out_aag(x1, x2, x3) = addz_out_aag(x1, x2, x3) 18.38/5.64 18.38/5.64 addC_out_aag(x1, x2, x3) = addC_out_aag(x1, x2, x3) 18.38/5.64 18.38/5.64 U24_aag(x1, x2, x3, x4) = U24_aag(x3, x4) 18.38/5.64 18.38/5.64 addX_in_aag(x1, x2, x3) = addX_in_aag(x3) 18.38/5.64 18.38/5.64 U17_aag(x1, x2) = U17_aag(x1, x2) 18.38/5.64 18.38/5.64 addX_out_aag(x1, x2, x3) = addX_out_aag(x1, x2, x3) 18.38/5.64 18.38/5.64 U18_aag(x1, x2, x3) = U18_aag(x2, x3) 18.38/5.64 18.38/5.64 U19_aag(x1, x2, x3, x4) = U19_aag(x3, x4) 18.38/5.64 18.38/5.64 U25_aag(x1, x2, x3, x4) = U25_aag(x3, x4) 18.38/5.64 18.38/5.64 addY_in_aag(x1, x2, x3) = addY_in_aag(x3) 18.38/5.64 18.38/5.64 U20_aag(x1, x2) = U20_aag(x1, x2) 18.38/5.64 18.38/5.64 addY_out_aag(x1, x2, x3) = addY_out_aag(x1, x2, x3) 18.38/5.64 18.38/5.64 U21_aag(x1, x2, x3) = U21_aag(x2, x3) 18.38/5.64 18.38/5.64 U22_aag(x1, x2, x3, x4) = U22_aag(x3, x4) 18.38/5.64 18.38/5.64 U26_aag(x1, x2, x3, x4) = U26_aag(x3, x4) 18.38/5.64 18.38/5.64 ADDZ_IN_AAG(x1, x2, x3) = ADDZ_IN_AAG(x3) 18.38/5.64 18.38/5.64 ADDX_IN_AAG(x1, x2, x3) = ADDX_IN_AAG(x3) 18.38/5.64 18.38/5.64 ADDY_IN_AAG(x1, x2, x3) = ADDY_IN_AAG(x3) 18.38/5.64 18.38/5.64 ADDC_IN_AAG(x1, x2, x3) = ADDC_IN_AAG(x3) 18.38/5.64 18.38/5.64 ADDC_IN_AAG^1(x1, x2, x3) = ADDC_IN_AAG^1(x3) 18.38/5.64 18.38/5.64 ADDX_IN_AAG^1(x1, x2, x3) = ADDX_IN_AAG^1(x3) 18.38/5.64 18.38/5.64 ADDY_IN_AAG^1(x1, x2, x3) = ADDY_IN_AAG^1(x3) 18.38/5.64 18.38/5.64 18.38/5.64 We have to consider all (P,R,Pi)-chains 18.38/5.64 ---------------------------------------- 18.38/5.64 18.38/5.64 (22) UsableRulesProof (EQUIVALENT) 18.38/5.64 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 18.38/5.64 ---------------------------------------- 18.38/5.64 18.38/5.64 (23) 18.38/5.64 Obligation: 18.38/5.64 Pi DP problem: 18.38/5.64 The TRS P consists of the following rules: 18.38/5.64 18.38/5.64 ADDX_IN_AAG(X, Y, Z) -> ADDZ_IN_AAG(X, Y, Z) 18.38/5.64 ADDZ_IN_AAG(zero(X), zero(Y), zero(Z)) -> ADDZ_IN_AAG(X, Y, Z) 18.38/5.64 ADDZ_IN_AAG(zero(X), one(Y), one(Z)) -> ADDX_IN_AAG(X, Y, Z) 18.38/5.64 ADDZ_IN_AAG(one(X), zero(Y), one(Z)) -> ADDY_IN_AAG(X, Y, Z) 18.38/5.64 ADDY_IN_AAG(X, Y, Z) -> ADDZ_IN_AAG(X, Y, Z) 18.38/5.64 ADDZ_IN_AAG(one(X), one(Y), zero(Z)) -> ADDC_IN_AAG(X, Y, Z) 18.38/5.64 ADDC_IN_AAG(X, Y, Z) -> ADDC_IN_AAG^1(X, Y, Z) 18.38/5.64 ADDC_IN_AAG^1(zero(X), zero(Y), one(Z)) -> ADDZ_IN_AAG(X, Y, Z) 18.38/5.64 ADDC_IN_AAG^1(zero(X), one(Y), zero(Z)) -> ADDX_IN_AAG^1(X, Y, Z) 18.38/5.64 ADDX_IN_AAG^1(X, Y, Z) -> ADDC_IN_AAG^1(X, Y, Z) 18.38/5.64 ADDC_IN_AAG^1(one(X), zero(Y), zero(Z)) -> ADDY_IN_AAG^1(X, Y, Z) 18.38/5.64 ADDY_IN_AAG^1(X, Y, Z) -> ADDC_IN_AAG^1(X, Y, Z) 18.38/5.64 ADDC_IN_AAG^1(one(X), one(Y), one(Z)) -> ADDC_IN_AAG(X, Y, Z) 18.38/5.64 18.38/5.64 R is empty. 18.38/5.64 The argument filtering Pi contains the following mapping: 18.38/5.64 zero(x1) = zero(x1) 18.38/5.64 18.38/5.64 one(x1) = one(x1) 18.38/5.64 18.38/5.64 ADDZ_IN_AAG(x1, x2, x3) = ADDZ_IN_AAG(x3) 18.38/5.64 18.38/5.64 ADDX_IN_AAG(x1, x2, x3) = ADDX_IN_AAG(x3) 18.38/5.64 18.38/5.64 ADDY_IN_AAG(x1, x2, x3) = ADDY_IN_AAG(x3) 18.38/5.64 18.38/5.64 ADDC_IN_AAG(x1, x2, x3) = ADDC_IN_AAG(x3) 18.38/5.64 18.38/5.64 ADDC_IN_AAG^1(x1, x2, x3) = ADDC_IN_AAG^1(x3) 18.38/5.64 18.38/5.64 ADDX_IN_AAG^1(x1, x2, x3) = ADDX_IN_AAG^1(x3) 18.38/5.64 18.38/5.64 ADDY_IN_AAG^1(x1, x2, x3) = ADDY_IN_AAG^1(x3) 18.38/5.64 18.38/5.64 18.38/5.64 We have to consider all (P,R,Pi)-chains 18.38/5.64 ---------------------------------------- 18.38/5.64 18.38/5.64 (24) PiDPToQDPProof (SOUND) 18.38/5.64 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 18.38/5.64 ---------------------------------------- 18.38/5.64 18.38/5.64 (25) 18.38/5.64 Obligation: 18.38/5.64 Q DP problem: 18.38/5.64 The TRS P consists of the following rules: 18.38/5.64 18.38/5.64 ADDX_IN_AAG(Z) -> ADDZ_IN_AAG(Z) 18.38/5.64 ADDZ_IN_AAG(zero(Z)) -> ADDZ_IN_AAG(Z) 18.38/5.64 ADDZ_IN_AAG(one(Z)) -> ADDX_IN_AAG(Z) 18.38/5.64 ADDZ_IN_AAG(one(Z)) -> ADDY_IN_AAG(Z) 18.38/5.64 ADDY_IN_AAG(Z) -> ADDZ_IN_AAG(Z) 18.38/5.64 ADDZ_IN_AAG(zero(Z)) -> ADDC_IN_AAG(Z) 18.38/5.64 ADDC_IN_AAG(Z) -> ADDC_IN_AAG^1(Z) 18.38/5.64 ADDC_IN_AAG^1(one(Z)) -> ADDZ_IN_AAG(Z) 18.38/5.64 ADDC_IN_AAG^1(zero(Z)) -> ADDX_IN_AAG^1(Z) 18.38/5.64 ADDX_IN_AAG^1(Z) -> ADDC_IN_AAG^1(Z) 18.38/5.64 ADDC_IN_AAG^1(zero(Z)) -> ADDY_IN_AAG^1(Z) 18.38/5.64 ADDY_IN_AAG^1(Z) -> ADDC_IN_AAG^1(Z) 18.38/5.64 ADDC_IN_AAG^1(one(Z)) -> ADDC_IN_AAG(Z) 18.38/5.64 18.38/5.64 R is empty. 18.38/5.64 Q is empty. 18.38/5.64 We have to consider all (P,Q,R)-chains. 18.38/5.64 ---------------------------------------- 18.38/5.64 18.38/5.64 (26) QDPSizeChangeProof (EQUIVALENT) 18.38/5.64 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 18.38/5.64 18.38/5.64 From the DPs we obtained the following set of size-change graphs: 18.38/5.64 *ADDZ_IN_AAG(one(Z)) -> ADDX_IN_AAG(Z) 18.38/5.64 The graph contains the following edges 1 > 1 18.38/5.64 18.38/5.64 18.38/5.64 *ADDZ_IN_AAG(zero(Z)) -> ADDZ_IN_AAG(Z) 18.38/5.64 The graph contains the following edges 1 > 1 18.38/5.64 18.38/5.64 18.38/5.64 *ADDX_IN_AAG(Z) -> ADDZ_IN_AAG(Z) 18.38/5.64 The graph contains the following edges 1 >= 1 18.38/5.64 18.38/5.64 18.38/5.64 *ADDY_IN_AAG(Z) -> ADDZ_IN_AAG(Z) 18.38/5.64 The graph contains the following edges 1 >= 1 18.38/5.64 18.38/5.64 18.38/5.64 *ADDC_IN_AAG^1(one(Z)) -> ADDZ_IN_AAG(Z) 18.38/5.64 The graph contains the following edges 1 > 1 18.38/5.64 18.38/5.64 18.38/5.64 *ADDZ_IN_AAG(one(Z)) -> ADDY_IN_AAG(Z) 18.38/5.64 The graph contains the following edges 1 > 1 18.38/5.64 18.38/5.64 18.38/5.64 *ADDZ_IN_AAG(zero(Z)) -> ADDC_IN_AAG(Z) 18.38/5.64 The graph contains the following edges 1 > 1 18.38/5.64 18.38/5.64 18.38/5.64 *ADDC_IN_AAG(Z) -> ADDC_IN_AAG^1(Z) 18.38/5.64 The graph contains the following edges 1 >= 1 18.38/5.64 18.38/5.64 18.38/5.64 *ADDC_IN_AAG^1(one(Z)) -> ADDC_IN_AAG(Z) 18.38/5.64 The graph contains the following edges 1 > 1 18.38/5.64 18.38/5.64 18.38/5.64 *ADDX_IN_AAG^1(Z) -> ADDC_IN_AAG^1(Z) 18.38/5.64 The graph contains the following edges 1 >= 1 18.38/5.64 18.38/5.64 18.38/5.64 *ADDY_IN_AAG^1(Z) -> ADDC_IN_AAG^1(Z) 18.38/5.64 The graph contains the following edges 1 >= 1 18.38/5.64 18.38/5.64 18.38/5.64 *ADDC_IN_AAG^1(zero(Z)) -> ADDX_IN_AAG^1(Z) 18.38/5.64 The graph contains the following edges 1 > 1 18.38/5.64 18.38/5.64 18.38/5.64 *ADDC_IN_AAG^1(zero(Z)) -> ADDY_IN_AAG^1(Z) 18.38/5.64 The graph contains the following edges 1 > 1 18.38/5.64 18.38/5.64 18.38/5.64 ---------------------------------------- 18.38/5.64 18.38/5.64 (27) 18.38/5.64 YES 18.38/5.64 18.38/5.64 ---------------------------------------- 18.38/5.64 18.38/5.64 (28) 18.38/5.64 Obligation: 18.38/5.64 Pi DP problem: 18.38/5.64 The TRS P consists of the following rules: 18.38/5.64 18.38/5.64 BINARYZ_IN_A(one(X)) -> BINARY_IN_A(X) 18.38/5.64 BINARY_IN_A(zero(X)) -> BINARYZ_IN_A(X) 18.38/5.64 BINARYZ_IN_A(zero(X)) -> BINARYZ_IN_A(X) 18.38/5.64 BINARY_IN_A(one(X)) -> BINARY_IN_A(X) 18.38/5.64 18.38/5.64 The TRS R consists of the following rules: 18.38/5.64 18.38/5.64 times_in_aag(one(b), X, X) -> times_out_aag(one(b), X, X) 18.38/5.64 times_in_aag(zero(R), S, zero(RS)) -> U35_aag(R, S, RS, times_in_aag(R, S, RS)) 18.38/5.64 times_in_aag(one(R), S, RSS) -> U36_aag(R, S, RSS, times_in_aaa(R, S, RS)) 18.38/5.64 times_in_aaa(one(b), X, X) -> times_out_aaa(one(b), X, X) 18.38/5.64 times_in_aaa(zero(R), S, zero(RS)) -> U35_aaa(R, S, RS, times_in_aaa(R, S, RS)) 18.38/5.64 times_in_aaa(one(R), S, RSS) -> U36_aaa(R, S, RSS, times_in_aaa(R, S, RS)) 18.38/5.64 U36_aaa(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aaa(R, S, RSS, add_in_aaa(S, zero(RS), RSS)) 18.38/5.64 add_in_aaa(b, b, b) -> add_out_aaa(b, b, b) 18.38/5.64 add_in_aaa(X, b, X) -> U1_aaa(X, binaryZ_in_a(X)) 18.38/5.64 binaryZ_in_a(zero(X)) -> U29_a(X, binaryZ_in_a(X)) 18.38/5.64 binaryZ_in_a(one(X)) -> U30_a(X, binary_in_a(X)) 18.38/5.64 binary_in_a(b) -> binary_out_a(b) 18.38/5.64 binary_in_a(zero(X)) -> U27_a(X, binaryZ_in_a(X)) 18.38/5.64 U27_a(X, binaryZ_out_a(X)) -> binary_out_a(zero(X)) 18.38/5.64 binary_in_a(one(X)) -> U28_a(X, binary_in_a(X)) 18.38/5.64 U28_a(X, binary_out_a(X)) -> binary_out_a(one(X)) 18.38/5.64 U30_a(X, binary_out_a(X)) -> binaryZ_out_a(one(X)) 18.38/5.64 U29_a(X, binaryZ_out_a(X)) -> binaryZ_out_a(zero(X)) 18.38/5.64 U1_aaa(X, binaryZ_out_a(X)) -> add_out_aaa(X, b, X) 18.38/5.64 add_in_aaa(b, Y, Y) -> U2_aaa(Y, binaryZ_in_a(Y)) 18.38/5.64 U2_aaa(Y, binaryZ_out_a(Y)) -> add_out_aaa(b, Y, Y) 18.38/5.64 add_in_aaa(X, Y, Z) -> U3_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.64 addz_in_aaa(zero(X), zero(Y), zero(Z)) -> U10_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.64 addz_in_aaa(zero(X), one(Y), one(Z)) -> U11_aaa(X, Y, Z, addx_in_aaa(X, Y, Z)) 18.38/5.64 addx_in_aaa(one(X), b, one(X)) -> U4_aaa(X, binary_in_a(X)) 18.38/5.64 U4_aaa(X, binary_out_a(X)) -> addx_out_aaa(one(X), b, one(X)) 18.38/5.64 addx_in_aaa(zero(X), b, zero(X)) -> U5_aaa(X, binaryZ_in_a(X)) 18.38/5.64 U5_aaa(X, binaryZ_out_a(X)) -> addx_out_aaa(zero(X), b, zero(X)) 18.38/5.64 addx_in_aaa(X, Y, Z) -> U6_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.64 addz_in_aaa(one(X), zero(Y), one(Z)) -> U12_aaa(X, Y, Z, addy_in_aaa(X, Y, Z)) 18.38/5.64 addy_in_aaa(b, one(Y), one(Y)) -> U7_aaa(Y, binary_in_a(Y)) 18.38/5.64 U7_aaa(Y, binary_out_a(Y)) -> addy_out_aaa(b, one(Y), one(Y)) 18.38/5.64 addy_in_aaa(b, zero(Y), zero(Y)) -> U8_aaa(Y, binaryZ_in_a(Y)) 18.38/5.64 U8_aaa(Y, binaryZ_out_a(Y)) -> addy_out_aaa(b, zero(Y), zero(Y)) 18.38/5.64 addy_in_aaa(X, Y, Z) -> U9_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.64 addz_in_aaa(one(X), one(Y), zero(Z)) -> U13_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.38/5.64 addc_in_aaa(b, b, one(b)) -> addc_out_aaa(b, b, one(b)) 18.38/5.64 addc_in_aaa(X, b, Z) -> U14_aaa(X, Z, succZ_in_aa(X, Z)) 18.38/5.64 succZ_in_aa(zero(X), one(X)) -> U33_aa(X, binaryZ_in_a(X)) 18.38/5.64 U33_aa(X, binaryZ_out_a(X)) -> succZ_out_aa(zero(X), one(X)) 18.38/5.64 succZ_in_aa(one(X), zero(Z)) -> U34_aa(X, Z, succ_in_aa(X, Z)) 18.38/5.64 succ_in_aa(b, one(b)) -> succ_out_aa(b, one(b)) 18.38/5.64 succ_in_aa(zero(X), one(X)) -> U31_aa(X, binaryZ_in_a(X)) 18.38/5.64 U31_aa(X, binaryZ_out_a(X)) -> succ_out_aa(zero(X), one(X)) 18.38/5.64 succ_in_aa(one(X), zero(Z)) -> U32_aa(X, Z, succ_in_aa(X, Z)) 18.38/5.64 U32_aa(X, Z, succ_out_aa(X, Z)) -> succ_out_aa(one(X), zero(Z)) 18.38/5.64 U34_aa(X, Z, succ_out_aa(X, Z)) -> succZ_out_aa(one(X), zero(Z)) 18.38/5.64 U14_aaa(X, Z, succZ_out_aa(X, Z)) -> addc_out_aaa(X, b, Z) 18.38/5.64 addc_in_aaa(b, Y, Z) -> U15_aaa(Y, Z, succZ_in_aa(Y, Z)) 18.38/5.64 U15_aaa(Y, Z, succZ_out_aa(Y, Z)) -> addc_out_aaa(b, Y, Z) 18.38/5.64 addc_in_aaa(X, Y, Z) -> U16_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.64 addC_in_aaa(zero(X), zero(Y), one(Z)) -> U23_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.64 U23_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), zero(Y), one(Z)) 18.38/5.64 addC_in_aaa(zero(X), one(Y), zero(Z)) -> U24_aaa(X, Y, Z, addX_in_aaa(X, Y, Z)) 18.38/5.64 addX_in_aaa(zero(X), b, one(X)) -> U17_aaa(X, binaryZ_in_a(X)) 18.38/5.64 U17_aaa(X, binaryZ_out_a(X)) -> addX_out_aaa(zero(X), b, one(X)) 18.38/5.64 addX_in_aaa(one(X), b, zero(Z)) -> U18_aaa(X, Z, succ_in_aa(X, Z)) 18.38/5.64 U18_aaa(X, Z, succ_out_aa(X, Z)) -> addX_out_aaa(one(X), b, zero(Z)) 18.38/5.64 addX_in_aaa(X, Y, Z) -> U19_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.64 addC_in_aaa(one(X), zero(Y), zero(Z)) -> U25_aaa(X, Y, Z, addY_in_aaa(X, Y, Z)) 18.38/5.64 addY_in_aaa(b, zero(Y), one(Y)) -> U20_aaa(Y, binaryZ_in_a(Y)) 18.38/5.64 U20_aaa(Y, binaryZ_out_a(Y)) -> addY_out_aaa(b, zero(Y), one(Y)) 18.38/5.64 addY_in_aaa(b, one(Y), zero(Z)) -> U21_aaa(Y, Z, succ_in_aa(Y, Z)) 18.38/5.64 U21_aaa(Y, Z, succ_out_aa(Y, Z)) -> addY_out_aaa(b, one(Y), zero(Z)) 18.38/5.64 addY_in_aaa(X, Y, Z) -> U22_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.64 addC_in_aaa(one(X), one(Y), one(Z)) -> U26_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.38/5.64 U26_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), one(Y), one(Z)) 18.38/5.64 U22_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addY_out_aaa(X, Y, Z) 18.38/5.64 U25_aaa(X, Y, Z, addY_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), zero(Y), zero(Z)) 18.38/5.64 U19_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addX_out_aaa(X, Y, Z) 18.38/5.64 U24_aaa(X, Y, Z, addX_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), one(Y), zero(Z)) 18.38/5.64 U16_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addc_out_aaa(X, Y, Z) 18.38/5.64 U13_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), one(Y), zero(Z)) 18.38/5.64 U9_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addy_out_aaa(X, Y, Z) 18.38/5.64 U12_aaa(X, Y, Z, addy_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), zero(Y), one(Z)) 18.38/5.64 U6_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addx_out_aaa(X, Y, Z) 18.38/5.64 U11_aaa(X, Y, Z, addx_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), one(Y), one(Z)) 18.38/5.64 U10_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), zero(Y), zero(Z)) 18.38/5.64 U3_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> add_out_aaa(X, Y, Z) 18.38/5.64 U37_aaa(R, S, RSS, add_out_aaa(S, zero(RS), RSS)) -> times_out_aaa(one(R), S, RSS) 18.38/5.64 U35_aaa(R, S, RS, times_out_aaa(R, S, RS)) -> times_out_aaa(zero(R), S, zero(RS)) 18.38/5.64 U36_aag(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aag(R, S, RSS, add_in_aag(S, zero(RS), RSS)) 18.38/5.64 add_in_aag(b, b, b) -> add_out_aag(b, b, b) 18.38/5.64 add_in_aag(X, b, X) -> U1_aag(X, binaryZ_in_g(X)) 18.38/5.64 binaryZ_in_g(zero(X)) -> U29_g(X, binaryZ_in_g(X)) 18.38/5.64 binaryZ_in_g(one(X)) -> U30_g(X, binary_in_g(X)) 18.38/5.64 binary_in_g(b) -> binary_out_g(b) 18.38/5.64 binary_in_g(zero(X)) -> U27_g(X, binaryZ_in_g(X)) 18.38/5.64 U27_g(X, binaryZ_out_g(X)) -> binary_out_g(zero(X)) 18.38/5.64 binary_in_g(one(X)) -> U28_g(X, binary_in_g(X)) 18.38/5.64 U28_g(X, binary_out_g(X)) -> binary_out_g(one(X)) 18.38/5.64 U30_g(X, binary_out_g(X)) -> binaryZ_out_g(one(X)) 18.38/5.64 U29_g(X, binaryZ_out_g(X)) -> binaryZ_out_g(zero(X)) 18.38/5.64 U1_aag(X, binaryZ_out_g(X)) -> add_out_aag(X, b, X) 18.38/5.64 add_in_aag(b, Y, Y) -> U2_aag(Y, binaryZ_in_g(Y)) 18.38/5.64 U2_aag(Y, binaryZ_out_g(Y)) -> add_out_aag(b, Y, Y) 18.38/5.64 add_in_aag(X, Y, Z) -> U3_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.64 addz_in_aag(zero(X), zero(Y), zero(Z)) -> U10_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.64 addz_in_aag(zero(X), one(Y), one(Z)) -> U11_aag(X, Y, Z, addx_in_aag(X, Y, Z)) 18.38/5.64 addx_in_aag(one(X), b, one(X)) -> U4_aag(X, binary_in_g(X)) 18.38/5.64 U4_aag(X, binary_out_g(X)) -> addx_out_aag(one(X), b, one(X)) 18.38/5.64 addx_in_aag(zero(X), b, zero(X)) -> U5_aag(X, binaryZ_in_g(X)) 18.38/5.64 U5_aag(X, binaryZ_out_g(X)) -> addx_out_aag(zero(X), b, zero(X)) 18.38/5.64 addx_in_aag(X, Y, Z) -> U6_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.64 addz_in_aag(one(X), zero(Y), one(Z)) -> U12_aag(X, Y, Z, addy_in_aag(X, Y, Z)) 18.38/5.64 addy_in_aag(b, one(Y), one(Y)) -> U7_aag(Y, binary_in_g(Y)) 18.38/5.64 U7_aag(Y, binary_out_g(Y)) -> addy_out_aag(b, one(Y), one(Y)) 18.38/5.64 addy_in_aag(b, zero(Y), zero(Y)) -> U8_aag(Y, binaryZ_in_g(Y)) 18.38/5.64 U8_aag(Y, binaryZ_out_g(Y)) -> addy_out_aag(b, zero(Y), zero(Y)) 18.38/5.64 addy_in_aag(X, Y, Z) -> U9_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.64 addz_in_aag(one(X), one(Y), zero(Z)) -> U13_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.38/5.64 addc_in_aag(b, b, one(b)) -> addc_out_aag(b, b, one(b)) 18.38/5.64 addc_in_aag(X, b, Z) -> U14_aag(X, Z, succZ_in_ag(X, Z)) 18.38/5.64 succZ_in_ag(zero(X), one(X)) -> U33_ag(X, binaryZ_in_g(X)) 18.38/5.64 U33_ag(X, binaryZ_out_g(X)) -> succZ_out_ag(zero(X), one(X)) 18.38/5.64 succZ_in_ag(one(X), zero(Z)) -> U34_ag(X, Z, succ_in_ag(X, Z)) 18.38/5.64 succ_in_ag(b, one(b)) -> succ_out_ag(b, one(b)) 18.38/5.64 succ_in_ag(zero(X), one(X)) -> U31_ag(X, binaryZ_in_g(X)) 18.38/5.64 U31_ag(X, binaryZ_out_g(X)) -> succ_out_ag(zero(X), one(X)) 18.38/5.64 succ_in_ag(one(X), zero(Z)) -> U32_ag(X, Z, succ_in_ag(X, Z)) 18.38/5.64 U32_ag(X, Z, succ_out_ag(X, Z)) -> succ_out_ag(one(X), zero(Z)) 18.38/5.64 U34_ag(X, Z, succ_out_ag(X, Z)) -> succZ_out_ag(one(X), zero(Z)) 18.38/5.64 U14_aag(X, Z, succZ_out_ag(X, Z)) -> addc_out_aag(X, b, Z) 18.38/5.64 addc_in_aag(b, Y, Z) -> U15_aag(Y, Z, succZ_in_ag(Y, Z)) 18.38/5.64 U15_aag(Y, Z, succZ_out_ag(Y, Z)) -> addc_out_aag(b, Y, Z) 18.38/5.64 addc_in_aag(X, Y, Z) -> U16_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.64 addC_in_aag(zero(X), zero(Y), one(Z)) -> U23_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.64 U23_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), zero(Y), one(Z)) 18.38/5.64 addC_in_aag(zero(X), one(Y), zero(Z)) -> U24_aag(X, Y, Z, addX_in_aag(X, Y, Z)) 18.38/5.64 addX_in_aag(zero(X), b, one(X)) -> U17_aag(X, binaryZ_in_g(X)) 18.38/5.64 U17_aag(X, binaryZ_out_g(X)) -> addX_out_aag(zero(X), b, one(X)) 18.38/5.64 addX_in_aag(one(X), b, zero(Z)) -> U18_aag(X, Z, succ_in_ag(X, Z)) 18.38/5.64 U18_aag(X, Z, succ_out_ag(X, Z)) -> addX_out_aag(one(X), b, zero(Z)) 18.38/5.64 addX_in_aag(X, Y, Z) -> U19_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.64 addC_in_aag(one(X), zero(Y), zero(Z)) -> U25_aag(X, Y, Z, addY_in_aag(X, Y, Z)) 18.38/5.64 addY_in_aag(b, zero(Y), one(Y)) -> U20_aag(Y, binaryZ_in_g(Y)) 18.38/5.64 U20_aag(Y, binaryZ_out_g(Y)) -> addY_out_aag(b, zero(Y), one(Y)) 18.38/5.64 addY_in_aag(b, one(Y), zero(Z)) -> U21_aag(Y, Z, succ_in_ag(Y, Z)) 18.38/5.64 U21_aag(Y, Z, succ_out_ag(Y, Z)) -> addY_out_aag(b, one(Y), zero(Z)) 18.38/5.64 addY_in_aag(X, Y, Z) -> U22_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.64 addC_in_aag(one(X), one(Y), one(Z)) -> U26_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.38/5.64 U26_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addC_out_aag(one(X), one(Y), one(Z)) 18.38/5.64 U22_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addY_out_aag(X, Y, Z) 18.38/5.64 U25_aag(X, Y, Z, addY_out_aag(X, Y, Z)) -> addC_out_aag(one(X), zero(Y), zero(Z)) 18.38/5.64 U19_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addX_out_aag(X, Y, Z) 18.38/5.64 U24_aag(X, Y, Z, addX_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), one(Y), zero(Z)) 18.38/5.64 U16_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addc_out_aag(X, Y, Z) 18.38/5.64 U13_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addz_out_aag(one(X), one(Y), zero(Z)) 18.38/5.64 U9_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addy_out_aag(X, Y, Z) 18.38/5.64 U12_aag(X, Y, Z, addy_out_aag(X, Y, Z)) -> addz_out_aag(one(X), zero(Y), one(Z)) 18.38/5.64 U6_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addx_out_aag(X, Y, Z) 18.38/5.64 U11_aag(X, Y, Z, addx_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), one(Y), one(Z)) 18.38/5.64 U10_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), zero(Y), zero(Z)) 18.38/5.64 U3_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> add_out_aag(X, Y, Z) 18.38/5.64 U37_aag(R, S, RSS, add_out_aag(S, zero(RS), RSS)) -> times_out_aag(one(R), S, RSS) 18.38/5.64 U35_aag(R, S, RS, times_out_aag(R, S, RS)) -> times_out_aag(zero(R), S, zero(RS)) 18.38/5.64 18.38/5.64 The argument filtering Pi contains the following mapping: 18.38/5.64 times_in_aag(x1, x2, x3) = times_in_aag(x3) 18.38/5.64 18.38/5.64 times_out_aag(x1, x2, x3) = times_out_aag(x1, x2, x3) 18.38/5.64 18.38/5.64 zero(x1) = zero(x1) 18.38/5.64 18.38/5.64 U35_aag(x1, x2, x3, x4) = U35_aag(x3, x4) 18.38/5.64 18.38/5.64 U36_aag(x1, x2, x3, x4) = U36_aag(x3, x4) 18.38/5.64 18.38/5.64 times_in_aaa(x1, x2, x3) = times_in_aaa 18.38/5.64 18.38/5.64 times_out_aaa(x1, x2, x3) = times_out_aaa(x1) 18.38/5.64 18.38/5.64 U35_aaa(x1, x2, x3, x4) = U35_aaa(x4) 18.38/5.64 18.38/5.64 U36_aaa(x1, x2, x3, x4) = U36_aaa(x4) 18.38/5.64 18.38/5.64 U37_aaa(x1, x2, x3, x4) = U37_aaa(x1, x4) 18.38/5.64 18.38/5.64 add_in_aaa(x1, x2, x3) = add_in_aaa 18.38/5.64 18.38/5.64 add_out_aaa(x1, x2, x3) = add_out_aaa(x1, x2, x3) 18.38/5.64 18.38/5.64 U1_aaa(x1, x2) = U1_aaa(x2) 18.38/5.64 18.38/5.64 binaryZ_in_a(x1) = binaryZ_in_a 18.38/5.64 18.38/5.64 U29_a(x1, x2) = U29_a(x2) 18.38/5.64 18.38/5.64 U30_a(x1, x2) = U30_a(x2) 18.38/5.64 18.38/5.64 binary_in_a(x1) = binary_in_a 18.38/5.64 18.38/5.64 binary_out_a(x1) = binary_out_a(x1) 18.38/5.64 18.38/5.64 U27_a(x1, x2) = U27_a(x2) 18.38/5.64 18.38/5.64 binaryZ_out_a(x1) = binaryZ_out_a(x1) 18.38/5.64 18.38/5.64 U28_a(x1, x2) = U28_a(x2) 18.38/5.64 18.38/5.64 U2_aaa(x1, x2) = U2_aaa(x2) 18.38/5.64 18.38/5.64 U3_aaa(x1, x2, x3, x4) = U3_aaa(x4) 18.38/5.64 18.38/5.64 addz_in_aaa(x1, x2, x3) = addz_in_aaa 18.38/5.64 18.38/5.64 U10_aaa(x1, x2, x3, x4) = U10_aaa(x4) 18.38/5.64 18.38/5.64 U11_aaa(x1, x2, x3, x4) = U11_aaa(x4) 18.38/5.64 18.38/5.64 addx_in_aaa(x1, x2, x3) = addx_in_aaa 18.38/5.64 18.38/5.64 U4_aaa(x1, x2) = U4_aaa(x2) 18.38/5.64 18.38/5.64 addx_out_aaa(x1, x2, x3) = addx_out_aaa(x1, x2, x3) 18.38/5.64 18.38/5.64 U5_aaa(x1, x2) = U5_aaa(x2) 18.38/5.64 18.38/5.64 U6_aaa(x1, x2, x3, x4) = U6_aaa(x4) 18.38/5.64 18.38/5.64 U12_aaa(x1, x2, x3, x4) = U12_aaa(x4) 18.38/5.64 18.38/5.64 addy_in_aaa(x1, x2, x3) = addy_in_aaa 18.38/5.64 18.38/5.64 U7_aaa(x1, x2) = U7_aaa(x2) 18.38/5.64 18.38/5.64 addy_out_aaa(x1, x2, x3) = addy_out_aaa(x1, x2, x3) 18.38/5.64 18.38/5.64 U8_aaa(x1, x2) = U8_aaa(x2) 18.38/5.64 18.38/5.64 U9_aaa(x1, x2, x3, x4) = U9_aaa(x4) 18.38/5.64 18.38/5.64 U13_aaa(x1, x2, x3, x4) = U13_aaa(x4) 18.38/5.64 18.38/5.64 addc_in_aaa(x1, x2, x3) = addc_in_aaa 18.38/5.64 18.38/5.64 addc_out_aaa(x1, x2, x3) = addc_out_aaa(x1, x2, x3) 18.38/5.64 18.38/5.64 U14_aaa(x1, x2, x3) = U14_aaa(x3) 18.38/5.64 18.38/5.64 succZ_in_aa(x1, x2) = succZ_in_aa 18.38/5.64 18.38/5.64 U33_aa(x1, x2) = U33_aa(x2) 18.38/5.64 18.38/5.64 succZ_out_aa(x1, x2) = succZ_out_aa(x1, x2) 18.38/5.64 18.38/5.64 U34_aa(x1, x2, x3) = U34_aa(x3) 18.38/5.64 18.38/5.64 succ_in_aa(x1, x2) = succ_in_aa 18.38/5.64 18.38/5.64 succ_out_aa(x1, x2) = succ_out_aa(x1, x2) 18.38/5.64 18.38/5.64 U31_aa(x1, x2) = U31_aa(x2) 18.38/5.64 18.38/5.64 U32_aa(x1, x2, x3) = U32_aa(x3) 18.38/5.64 18.38/5.64 U15_aaa(x1, x2, x3) = U15_aaa(x3) 18.38/5.64 18.38/5.64 U16_aaa(x1, x2, x3, x4) = U16_aaa(x4) 18.38/5.64 18.38/5.64 addC_in_aaa(x1, x2, x3) = addC_in_aaa 18.38/5.64 18.38/5.64 U23_aaa(x1, x2, x3, x4) = U23_aaa(x4) 18.38/5.64 18.38/5.64 addz_out_aaa(x1, x2, x3) = addz_out_aaa(x1, x2, x3) 18.38/5.64 18.38/5.64 addC_out_aaa(x1, x2, x3) = addC_out_aaa(x1, x2, x3) 18.38/5.64 18.38/5.64 U24_aaa(x1, x2, x3, x4) = U24_aaa(x4) 18.38/5.64 18.38/5.64 addX_in_aaa(x1, x2, x3) = addX_in_aaa 18.38/5.64 18.38/5.64 U17_aaa(x1, x2) = U17_aaa(x2) 18.38/5.64 18.38/5.64 addX_out_aaa(x1, x2, x3) = addX_out_aaa(x1, x2, x3) 18.38/5.64 18.38/5.64 U18_aaa(x1, x2, x3) = U18_aaa(x3) 18.38/5.64 18.38/5.64 U19_aaa(x1, x2, x3, x4) = U19_aaa(x4) 18.38/5.64 18.38/5.64 U25_aaa(x1, x2, x3, x4) = U25_aaa(x4) 18.38/5.64 18.38/5.64 addY_in_aaa(x1, x2, x3) = addY_in_aaa 18.38/5.64 18.38/5.64 U20_aaa(x1, x2) = U20_aaa(x2) 18.38/5.64 18.38/5.64 addY_out_aaa(x1, x2, x3) = addY_out_aaa(x1, x2, x3) 18.38/5.64 18.38/5.64 U21_aaa(x1, x2, x3) = U21_aaa(x3) 18.38/5.64 18.38/5.64 U22_aaa(x1, x2, x3, x4) = U22_aaa(x4) 18.38/5.64 18.38/5.64 U26_aaa(x1, x2, x3, x4) = U26_aaa(x4) 18.38/5.64 18.38/5.64 U37_aag(x1, x2, x3, x4) = U37_aag(x1, x3, x4) 18.38/5.64 18.38/5.64 add_in_aag(x1, x2, x3) = add_in_aag(x3) 18.38/5.64 18.38/5.64 b = b 18.38/5.64 18.38/5.64 add_out_aag(x1, x2, x3) = add_out_aag(x1, x2, x3) 18.38/5.64 18.38/5.64 U1_aag(x1, x2) = U1_aag(x1, x2) 18.38/5.64 18.38/5.64 binaryZ_in_g(x1) = binaryZ_in_g(x1) 18.38/5.64 18.38/5.64 U29_g(x1, x2) = U29_g(x1, x2) 18.38/5.64 18.38/5.64 one(x1) = one(x1) 18.38/5.64 18.38/5.64 U30_g(x1, x2) = U30_g(x1, x2) 18.38/5.64 18.38/5.64 binary_in_g(x1) = binary_in_g(x1) 18.38/5.64 18.38/5.64 binary_out_g(x1) = binary_out_g(x1) 18.38/5.64 18.38/5.64 U27_g(x1, x2) = U27_g(x1, x2) 18.38/5.64 18.38/5.64 binaryZ_out_g(x1) = binaryZ_out_g(x1) 18.38/5.64 18.38/5.64 U28_g(x1, x2) = U28_g(x1, x2) 18.38/5.64 18.38/5.64 U2_aag(x1, x2) = U2_aag(x1, x2) 18.38/5.64 18.38/5.64 U3_aag(x1, x2, x3, x4) = U3_aag(x3, x4) 18.38/5.64 18.38/5.64 addz_in_aag(x1, x2, x3) = addz_in_aag(x3) 18.38/5.64 18.38/5.64 U10_aag(x1, x2, x3, x4) = U10_aag(x3, x4) 18.38/5.64 18.38/5.64 U11_aag(x1, x2, x3, x4) = U11_aag(x3, x4) 18.38/5.64 18.38/5.64 addx_in_aag(x1, x2, x3) = addx_in_aag(x3) 18.38/5.64 18.38/5.64 U4_aag(x1, x2) = U4_aag(x1, x2) 18.38/5.64 18.38/5.64 addx_out_aag(x1, x2, x3) = addx_out_aag(x1, x2, x3) 18.38/5.64 18.38/5.64 U5_aag(x1, x2) = U5_aag(x1, x2) 18.38/5.64 18.38/5.64 U6_aag(x1, x2, x3, x4) = U6_aag(x3, x4) 18.38/5.64 18.38/5.64 U12_aag(x1, x2, x3, x4) = U12_aag(x3, x4) 18.38/5.64 18.38/5.64 addy_in_aag(x1, x2, x3) = addy_in_aag(x3) 18.38/5.64 18.38/5.64 U7_aag(x1, x2) = U7_aag(x1, x2) 18.38/5.64 18.38/5.64 addy_out_aag(x1, x2, x3) = addy_out_aag(x1, x2, x3) 18.38/5.64 18.38/5.64 U8_aag(x1, x2) = U8_aag(x1, x2) 18.38/5.64 18.38/5.64 U9_aag(x1, x2, x3, x4) = U9_aag(x3, x4) 18.38/5.64 18.38/5.64 U13_aag(x1, x2, x3, x4) = U13_aag(x3, x4) 18.38/5.64 18.38/5.64 addc_in_aag(x1, x2, x3) = addc_in_aag(x3) 18.38/5.64 18.38/5.64 addc_out_aag(x1, x2, x3) = addc_out_aag(x1, x2, x3) 18.38/5.64 18.38/5.64 U14_aag(x1, x2, x3) = U14_aag(x2, x3) 18.38/5.64 18.38/5.64 succZ_in_ag(x1, x2) = succZ_in_ag(x2) 18.38/5.64 18.38/5.64 U33_ag(x1, x2) = U33_ag(x1, x2) 18.38/5.64 18.38/5.64 succZ_out_ag(x1, x2) = succZ_out_ag(x1, x2) 18.38/5.64 18.38/5.64 U34_ag(x1, x2, x3) = U34_ag(x2, x3) 18.38/5.64 18.38/5.64 succ_in_ag(x1, x2) = succ_in_ag(x2) 18.38/5.64 18.38/5.64 succ_out_ag(x1, x2) = succ_out_ag(x1, x2) 18.38/5.64 18.38/5.64 U31_ag(x1, x2) = U31_ag(x1, x2) 18.38/5.64 18.38/5.64 U32_ag(x1, x2, x3) = U32_ag(x2, x3) 18.38/5.64 18.38/5.64 U15_aag(x1, x2, x3) = U15_aag(x2, x3) 18.38/5.64 18.38/5.64 U16_aag(x1, x2, x3, x4) = U16_aag(x3, x4) 18.38/5.64 18.38/5.64 addC_in_aag(x1, x2, x3) = addC_in_aag(x3) 18.38/5.64 18.38/5.64 U23_aag(x1, x2, x3, x4) = U23_aag(x3, x4) 18.38/5.64 18.38/5.64 addz_out_aag(x1, x2, x3) = addz_out_aag(x1, x2, x3) 18.38/5.64 18.38/5.64 addC_out_aag(x1, x2, x3) = addC_out_aag(x1, x2, x3) 18.38/5.64 18.38/5.64 U24_aag(x1, x2, x3, x4) = U24_aag(x3, x4) 18.38/5.64 18.38/5.64 addX_in_aag(x1, x2, x3) = addX_in_aag(x3) 18.38/5.64 18.38/5.64 U17_aag(x1, x2) = U17_aag(x1, x2) 18.38/5.64 18.38/5.64 addX_out_aag(x1, x2, x3) = addX_out_aag(x1, x2, x3) 18.38/5.64 18.38/5.64 U18_aag(x1, x2, x3) = U18_aag(x2, x3) 18.38/5.64 18.38/5.64 U19_aag(x1, x2, x3, x4) = U19_aag(x3, x4) 18.38/5.64 18.38/5.64 U25_aag(x1, x2, x3, x4) = U25_aag(x3, x4) 18.38/5.64 18.38/5.64 addY_in_aag(x1, x2, x3) = addY_in_aag(x3) 18.38/5.64 18.38/5.64 U20_aag(x1, x2) = U20_aag(x1, x2) 18.38/5.64 18.38/5.64 addY_out_aag(x1, x2, x3) = addY_out_aag(x1, x2, x3) 18.38/5.64 18.38/5.64 U21_aag(x1, x2, x3) = U21_aag(x2, x3) 18.38/5.64 18.38/5.64 U22_aag(x1, x2, x3, x4) = U22_aag(x3, x4) 18.38/5.64 18.38/5.64 U26_aag(x1, x2, x3, x4) = U26_aag(x3, x4) 18.38/5.64 18.38/5.64 BINARYZ_IN_A(x1) = BINARYZ_IN_A 18.38/5.64 18.38/5.64 BINARY_IN_A(x1) = BINARY_IN_A 18.38/5.64 18.38/5.64 18.38/5.64 We have to consider all (P,R,Pi)-chains 18.38/5.64 ---------------------------------------- 18.38/5.64 18.38/5.64 (29) UsableRulesProof (EQUIVALENT) 18.38/5.64 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 18.38/5.64 ---------------------------------------- 18.38/5.64 18.38/5.64 (30) 18.38/5.64 Obligation: 18.38/5.64 Pi DP problem: 18.38/5.64 The TRS P consists of the following rules: 18.38/5.64 18.38/5.64 BINARYZ_IN_A(one(X)) -> BINARY_IN_A(X) 18.38/5.64 BINARY_IN_A(zero(X)) -> BINARYZ_IN_A(X) 18.38/5.64 BINARYZ_IN_A(zero(X)) -> BINARYZ_IN_A(X) 18.38/5.64 BINARY_IN_A(one(X)) -> BINARY_IN_A(X) 18.38/5.64 18.38/5.64 R is empty. 18.38/5.64 The argument filtering Pi contains the following mapping: 18.38/5.64 zero(x1) = zero(x1) 18.38/5.64 18.38/5.64 one(x1) = one(x1) 18.38/5.64 18.38/5.64 BINARYZ_IN_A(x1) = BINARYZ_IN_A 18.38/5.64 18.38/5.64 BINARY_IN_A(x1) = BINARY_IN_A 18.38/5.64 18.38/5.64 18.38/5.64 We have to consider all (P,R,Pi)-chains 18.38/5.64 ---------------------------------------- 18.38/5.64 18.38/5.64 (31) PiDPToQDPProof (SOUND) 18.38/5.64 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 18.38/5.64 ---------------------------------------- 18.38/5.64 18.38/5.64 (32) 18.38/5.64 Obligation: 18.38/5.64 Q DP problem: 18.38/5.64 The TRS P consists of the following rules: 18.38/5.64 18.38/5.64 BINARYZ_IN_A -> BINARY_IN_A 18.38/5.64 BINARY_IN_A -> BINARYZ_IN_A 18.38/5.64 BINARYZ_IN_A -> BINARYZ_IN_A 18.38/5.64 BINARY_IN_A -> BINARY_IN_A 18.38/5.64 18.38/5.64 R is empty. 18.38/5.64 Q is empty. 18.38/5.64 We have to consider all (P,Q,R)-chains. 18.38/5.64 ---------------------------------------- 18.38/5.64 18.38/5.64 (33) NonTerminationLoopProof (COMPLETE) 18.38/5.64 We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. 18.38/5.64 Found a loop by semiunifying a rule from P directly. 18.38/5.64 18.38/5.64 s = BINARYZ_IN_A evaluates to t =BINARYZ_IN_A 18.38/5.64 18.38/5.64 Thus s starts an infinite chain as s semiunifies with t with the following substitutions: 18.38/5.64 * Matcher: [ ] 18.38/5.64 * Semiunifier: [ ] 18.38/5.64 18.38/5.64 -------------------------------------------------------------------------------- 18.38/5.64 Rewriting sequence 18.38/5.64 18.38/5.64 The DP semiunifies directly so there is only one rewrite step from BINARYZ_IN_A to BINARYZ_IN_A. 18.38/5.64 18.38/5.64 18.38/5.64 18.38/5.64 18.38/5.64 ---------------------------------------- 18.38/5.64 18.38/5.64 (34) 18.38/5.64 NO 18.38/5.64 18.38/5.64 ---------------------------------------- 18.38/5.64 18.38/5.64 (35) 18.38/5.64 Obligation: 18.38/5.64 Pi DP problem: 18.38/5.64 The TRS P consists of the following rules: 18.38/5.64 18.38/5.64 SUCC_IN_AA(one(X), zero(Z)) -> SUCC_IN_AA(X, Z) 18.38/5.64 18.38/5.64 The TRS R consists of the following rules: 18.38/5.64 18.38/5.64 times_in_aag(one(b), X, X) -> times_out_aag(one(b), X, X) 18.38/5.64 times_in_aag(zero(R), S, zero(RS)) -> U35_aag(R, S, RS, times_in_aag(R, S, RS)) 18.38/5.64 times_in_aag(one(R), S, RSS) -> U36_aag(R, S, RSS, times_in_aaa(R, S, RS)) 18.38/5.64 times_in_aaa(one(b), X, X) -> times_out_aaa(one(b), X, X) 18.38/5.64 times_in_aaa(zero(R), S, zero(RS)) -> U35_aaa(R, S, RS, times_in_aaa(R, S, RS)) 18.38/5.64 times_in_aaa(one(R), S, RSS) -> U36_aaa(R, S, RSS, times_in_aaa(R, S, RS)) 18.38/5.64 U36_aaa(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aaa(R, S, RSS, add_in_aaa(S, zero(RS), RSS)) 18.38/5.64 add_in_aaa(b, b, b) -> add_out_aaa(b, b, b) 18.38/5.64 add_in_aaa(X, b, X) -> U1_aaa(X, binaryZ_in_a(X)) 18.38/5.64 binaryZ_in_a(zero(X)) -> U29_a(X, binaryZ_in_a(X)) 18.38/5.64 binaryZ_in_a(one(X)) -> U30_a(X, binary_in_a(X)) 18.38/5.64 binary_in_a(b) -> binary_out_a(b) 18.38/5.64 binary_in_a(zero(X)) -> U27_a(X, binaryZ_in_a(X)) 18.38/5.64 U27_a(X, binaryZ_out_a(X)) -> binary_out_a(zero(X)) 18.38/5.64 binary_in_a(one(X)) -> U28_a(X, binary_in_a(X)) 18.38/5.64 U28_a(X, binary_out_a(X)) -> binary_out_a(one(X)) 18.38/5.64 U30_a(X, binary_out_a(X)) -> binaryZ_out_a(one(X)) 18.38/5.64 U29_a(X, binaryZ_out_a(X)) -> binaryZ_out_a(zero(X)) 18.38/5.64 U1_aaa(X, binaryZ_out_a(X)) -> add_out_aaa(X, b, X) 18.38/5.64 add_in_aaa(b, Y, Y) -> U2_aaa(Y, binaryZ_in_a(Y)) 18.38/5.64 U2_aaa(Y, binaryZ_out_a(Y)) -> add_out_aaa(b, Y, Y) 18.38/5.64 add_in_aaa(X, Y, Z) -> U3_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.64 addz_in_aaa(zero(X), zero(Y), zero(Z)) -> U10_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.64 addz_in_aaa(zero(X), one(Y), one(Z)) -> U11_aaa(X, Y, Z, addx_in_aaa(X, Y, Z)) 18.38/5.64 addx_in_aaa(one(X), b, one(X)) -> U4_aaa(X, binary_in_a(X)) 18.38/5.64 U4_aaa(X, binary_out_a(X)) -> addx_out_aaa(one(X), b, one(X)) 18.38/5.64 addx_in_aaa(zero(X), b, zero(X)) -> U5_aaa(X, binaryZ_in_a(X)) 18.38/5.64 U5_aaa(X, binaryZ_out_a(X)) -> addx_out_aaa(zero(X), b, zero(X)) 18.38/5.64 addx_in_aaa(X, Y, Z) -> U6_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.64 addz_in_aaa(one(X), zero(Y), one(Z)) -> U12_aaa(X, Y, Z, addy_in_aaa(X, Y, Z)) 18.38/5.64 addy_in_aaa(b, one(Y), one(Y)) -> U7_aaa(Y, binary_in_a(Y)) 18.38/5.64 U7_aaa(Y, binary_out_a(Y)) -> addy_out_aaa(b, one(Y), one(Y)) 18.38/5.64 addy_in_aaa(b, zero(Y), zero(Y)) -> U8_aaa(Y, binaryZ_in_a(Y)) 18.38/5.64 U8_aaa(Y, binaryZ_out_a(Y)) -> addy_out_aaa(b, zero(Y), zero(Y)) 18.38/5.64 addy_in_aaa(X, Y, Z) -> U9_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.64 addz_in_aaa(one(X), one(Y), zero(Z)) -> U13_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.38/5.64 addc_in_aaa(b, b, one(b)) -> addc_out_aaa(b, b, one(b)) 18.38/5.64 addc_in_aaa(X, b, Z) -> U14_aaa(X, Z, succZ_in_aa(X, Z)) 18.38/5.64 succZ_in_aa(zero(X), one(X)) -> U33_aa(X, binaryZ_in_a(X)) 18.38/5.64 U33_aa(X, binaryZ_out_a(X)) -> succZ_out_aa(zero(X), one(X)) 18.38/5.64 succZ_in_aa(one(X), zero(Z)) -> U34_aa(X, Z, succ_in_aa(X, Z)) 18.38/5.64 succ_in_aa(b, one(b)) -> succ_out_aa(b, one(b)) 18.38/5.64 succ_in_aa(zero(X), one(X)) -> U31_aa(X, binaryZ_in_a(X)) 18.38/5.64 U31_aa(X, binaryZ_out_a(X)) -> succ_out_aa(zero(X), one(X)) 18.38/5.64 succ_in_aa(one(X), zero(Z)) -> U32_aa(X, Z, succ_in_aa(X, Z)) 18.38/5.64 U32_aa(X, Z, succ_out_aa(X, Z)) -> succ_out_aa(one(X), zero(Z)) 18.38/5.64 U34_aa(X, Z, succ_out_aa(X, Z)) -> succZ_out_aa(one(X), zero(Z)) 18.38/5.64 U14_aaa(X, Z, succZ_out_aa(X, Z)) -> addc_out_aaa(X, b, Z) 18.38/5.64 addc_in_aaa(b, Y, Z) -> U15_aaa(Y, Z, succZ_in_aa(Y, Z)) 18.38/5.64 U15_aaa(Y, Z, succZ_out_aa(Y, Z)) -> addc_out_aaa(b, Y, Z) 18.38/5.64 addc_in_aaa(X, Y, Z) -> U16_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.64 addC_in_aaa(zero(X), zero(Y), one(Z)) -> U23_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.64 U23_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), zero(Y), one(Z)) 18.38/5.64 addC_in_aaa(zero(X), one(Y), zero(Z)) -> U24_aaa(X, Y, Z, addX_in_aaa(X, Y, Z)) 18.38/5.64 addX_in_aaa(zero(X), b, one(X)) -> U17_aaa(X, binaryZ_in_a(X)) 18.38/5.64 U17_aaa(X, binaryZ_out_a(X)) -> addX_out_aaa(zero(X), b, one(X)) 18.38/5.64 addX_in_aaa(one(X), b, zero(Z)) -> U18_aaa(X, Z, succ_in_aa(X, Z)) 18.38/5.64 U18_aaa(X, Z, succ_out_aa(X, Z)) -> addX_out_aaa(one(X), b, zero(Z)) 18.38/5.64 addX_in_aaa(X, Y, Z) -> U19_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.64 addC_in_aaa(one(X), zero(Y), zero(Z)) -> U25_aaa(X, Y, Z, addY_in_aaa(X, Y, Z)) 18.38/5.64 addY_in_aaa(b, zero(Y), one(Y)) -> U20_aaa(Y, binaryZ_in_a(Y)) 18.38/5.64 U20_aaa(Y, binaryZ_out_a(Y)) -> addY_out_aaa(b, zero(Y), one(Y)) 18.38/5.64 addY_in_aaa(b, one(Y), zero(Z)) -> U21_aaa(Y, Z, succ_in_aa(Y, Z)) 18.38/5.64 U21_aaa(Y, Z, succ_out_aa(Y, Z)) -> addY_out_aaa(b, one(Y), zero(Z)) 18.38/5.64 addY_in_aaa(X, Y, Z) -> U22_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.64 addC_in_aaa(one(X), one(Y), one(Z)) -> U26_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.38/5.64 U26_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), one(Y), one(Z)) 18.38/5.64 U22_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addY_out_aaa(X, Y, Z) 18.38/5.64 U25_aaa(X, Y, Z, addY_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), zero(Y), zero(Z)) 18.38/5.64 U19_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addX_out_aaa(X, Y, Z) 18.38/5.64 U24_aaa(X, Y, Z, addX_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), one(Y), zero(Z)) 18.38/5.64 U16_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addc_out_aaa(X, Y, Z) 18.38/5.64 U13_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), one(Y), zero(Z)) 18.38/5.64 U9_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addy_out_aaa(X, Y, Z) 18.38/5.64 U12_aaa(X, Y, Z, addy_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), zero(Y), one(Z)) 18.38/5.64 U6_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addx_out_aaa(X, Y, Z) 18.38/5.64 U11_aaa(X, Y, Z, addx_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), one(Y), one(Z)) 18.38/5.64 U10_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), zero(Y), zero(Z)) 18.38/5.64 U3_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> add_out_aaa(X, Y, Z) 18.38/5.64 U37_aaa(R, S, RSS, add_out_aaa(S, zero(RS), RSS)) -> times_out_aaa(one(R), S, RSS) 18.38/5.64 U35_aaa(R, S, RS, times_out_aaa(R, S, RS)) -> times_out_aaa(zero(R), S, zero(RS)) 18.38/5.64 U36_aag(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aag(R, S, RSS, add_in_aag(S, zero(RS), RSS)) 18.38/5.64 add_in_aag(b, b, b) -> add_out_aag(b, b, b) 18.38/5.64 add_in_aag(X, b, X) -> U1_aag(X, binaryZ_in_g(X)) 18.38/5.64 binaryZ_in_g(zero(X)) -> U29_g(X, binaryZ_in_g(X)) 18.38/5.64 binaryZ_in_g(one(X)) -> U30_g(X, binary_in_g(X)) 18.38/5.64 binary_in_g(b) -> binary_out_g(b) 18.38/5.64 binary_in_g(zero(X)) -> U27_g(X, binaryZ_in_g(X)) 18.38/5.64 U27_g(X, binaryZ_out_g(X)) -> binary_out_g(zero(X)) 18.38/5.64 binary_in_g(one(X)) -> U28_g(X, binary_in_g(X)) 18.38/5.64 U28_g(X, binary_out_g(X)) -> binary_out_g(one(X)) 18.38/5.64 U30_g(X, binary_out_g(X)) -> binaryZ_out_g(one(X)) 18.38/5.64 U29_g(X, binaryZ_out_g(X)) -> binaryZ_out_g(zero(X)) 18.38/5.64 U1_aag(X, binaryZ_out_g(X)) -> add_out_aag(X, b, X) 18.38/5.64 add_in_aag(b, Y, Y) -> U2_aag(Y, binaryZ_in_g(Y)) 18.38/5.64 U2_aag(Y, binaryZ_out_g(Y)) -> add_out_aag(b, Y, Y) 18.38/5.64 add_in_aag(X, Y, Z) -> U3_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.64 addz_in_aag(zero(X), zero(Y), zero(Z)) -> U10_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.64 addz_in_aag(zero(X), one(Y), one(Z)) -> U11_aag(X, Y, Z, addx_in_aag(X, Y, Z)) 18.38/5.64 addx_in_aag(one(X), b, one(X)) -> U4_aag(X, binary_in_g(X)) 18.38/5.64 U4_aag(X, binary_out_g(X)) -> addx_out_aag(one(X), b, one(X)) 18.38/5.64 addx_in_aag(zero(X), b, zero(X)) -> U5_aag(X, binaryZ_in_g(X)) 18.38/5.64 U5_aag(X, binaryZ_out_g(X)) -> addx_out_aag(zero(X), b, zero(X)) 18.38/5.64 addx_in_aag(X, Y, Z) -> U6_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.64 addz_in_aag(one(X), zero(Y), one(Z)) -> U12_aag(X, Y, Z, addy_in_aag(X, Y, Z)) 18.38/5.64 addy_in_aag(b, one(Y), one(Y)) -> U7_aag(Y, binary_in_g(Y)) 18.38/5.64 U7_aag(Y, binary_out_g(Y)) -> addy_out_aag(b, one(Y), one(Y)) 18.38/5.64 addy_in_aag(b, zero(Y), zero(Y)) -> U8_aag(Y, binaryZ_in_g(Y)) 18.38/5.64 U8_aag(Y, binaryZ_out_g(Y)) -> addy_out_aag(b, zero(Y), zero(Y)) 18.38/5.64 addy_in_aag(X, Y, Z) -> U9_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.64 addz_in_aag(one(X), one(Y), zero(Z)) -> U13_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.38/5.64 addc_in_aag(b, b, one(b)) -> addc_out_aag(b, b, one(b)) 18.38/5.64 addc_in_aag(X, b, Z) -> U14_aag(X, Z, succZ_in_ag(X, Z)) 18.38/5.64 succZ_in_ag(zero(X), one(X)) -> U33_ag(X, binaryZ_in_g(X)) 18.38/5.64 U33_ag(X, binaryZ_out_g(X)) -> succZ_out_ag(zero(X), one(X)) 18.38/5.64 succZ_in_ag(one(X), zero(Z)) -> U34_ag(X, Z, succ_in_ag(X, Z)) 18.38/5.64 succ_in_ag(b, one(b)) -> succ_out_ag(b, one(b)) 18.38/5.64 succ_in_ag(zero(X), one(X)) -> U31_ag(X, binaryZ_in_g(X)) 18.38/5.64 U31_ag(X, binaryZ_out_g(X)) -> succ_out_ag(zero(X), one(X)) 18.38/5.64 succ_in_ag(one(X), zero(Z)) -> U32_ag(X, Z, succ_in_ag(X, Z)) 18.38/5.64 U32_ag(X, Z, succ_out_ag(X, Z)) -> succ_out_ag(one(X), zero(Z)) 18.38/5.64 U34_ag(X, Z, succ_out_ag(X, Z)) -> succZ_out_ag(one(X), zero(Z)) 18.38/5.64 U14_aag(X, Z, succZ_out_ag(X, Z)) -> addc_out_aag(X, b, Z) 18.38/5.64 addc_in_aag(b, Y, Z) -> U15_aag(Y, Z, succZ_in_ag(Y, Z)) 18.38/5.64 U15_aag(Y, Z, succZ_out_ag(Y, Z)) -> addc_out_aag(b, Y, Z) 18.38/5.64 addc_in_aag(X, Y, Z) -> U16_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.64 addC_in_aag(zero(X), zero(Y), one(Z)) -> U23_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.64 U23_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), zero(Y), one(Z)) 18.38/5.64 addC_in_aag(zero(X), one(Y), zero(Z)) -> U24_aag(X, Y, Z, addX_in_aag(X, Y, Z)) 18.38/5.64 addX_in_aag(zero(X), b, one(X)) -> U17_aag(X, binaryZ_in_g(X)) 18.38/5.64 U17_aag(X, binaryZ_out_g(X)) -> addX_out_aag(zero(X), b, one(X)) 18.38/5.64 addX_in_aag(one(X), b, zero(Z)) -> U18_aag(X, Z, succ_in_ag(X, Z)) 18.38/5.64 U18_aag(X, Z, succ_out_ag(X, Z)) -> addX_out_aag(one(X), b, zero(Z)) 18.38/5.64 addX_in_aag(X, Y, Z) -> U19_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.64 addC_in_aag(one(X), zero(Y), zero(Z)) -> U25_aag(X, Y, Z, addY_in_aag(X, Y, Z)) 18.38/5.64 addY_in_aag(b, zero(Y), one(Y)) -> U20_aag(Y, binaryZ_in_g(Y)) 18.38/5.64 U20_aag(Y, binaryZ_out_g(Y)) -> addY_out_aag(b, zero(Y), one(Y)) 18.38/5.64 addY_in_aag(b, one(Y), zero(Z)) -> U21_aag(Y, Z, succ_in_ag(Y, Z)) 18.38/5.64 U21_aag(Y, Z, succ_out_ag(Y, Z)) -> addY_out_aag(b, one(Y), zero(Z)) 18.38/5.64 addY_in_aag(X, Y, Z) -> U22_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.64 addC_in_aag(one(X), one(Y), one(Z)) -> U26_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.38/5.64 U26_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addC_out_aag(one(X), one(Y), one(Z)) 18.38/5.64 U22_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addY_out_aag(X, Y, Z) 18.38/5.64 U25_aag(X, Y, Z, addY_out_aag(X, Y, Z)) -> addC_out_aag(one(X), zero(Y), zero(Z)) 18.38/5.64 U19_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addX_out_aag(X, Y, Z) 18.38/5.64 U24_aag(X, Y, Z, addX_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), one(Y), zero(Z)) 18.38/5.64 U16_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addc_out_aag(X, Y, Z) 18.38/5.64 U13_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addz_out_aag(one(X), one(Y), zero(Z)) 18.38/5.64 U9_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addy_out_aag(X, Y, Z) 18.38/5.64 U12_aag(X, Y, Z, addy_out_aag(X, Y, Z)) -> addz_out_aag(one(X), zero(Y), one(Z)) 18.38/5.64 U6_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addx_out_aag(X, Y, Z) 18.38/5.64 U11_aag(X, Y, Z, addx_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), one(Y), one(Z)) 18.38/5.64 U10_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), zero(Y), zero(Z)) 18.38/5.64 U3_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> add_out_aag(X, Y, Z) 18.38/5.64 U37_aag(R, S, RSS, add_out_aag(S, zero(RS), RSS)) -> times_out_aag(one(R), S, RSS) 18.38/5.64 U35_aag(R, S, RS, times_out_aag(R, S, RS)) -> times_out_aag(zero(R), S, zero(RS)) 18.38/5.64 18.38/5.64 The argument filtering Pi contains the following mapping: 18.38/5.64 times_in_aag(x1, x2, x3) = times_in_aag(x3) 18.38/5.64 18.38/5.64 times_out_aag(x1, x2, x3) = times_out_aag(x1, x2, x3) 18.38/5.64 18.38/5.64 zero(x1) = zero(x1) 18.38/5.64 18.38/5.64 U35_aag(x1, x2, x3, x4) = U35_aag(x3, x4) 18.38/5.64 18.38/5.64 U36_aag(x1, x2, x3, x4) = U36_aag(x3, x4) 18.38/5.64 18.38/5.64 times_in_aaa(x1, x2, x3) = times_in_aaa 18.38/5.64 18.38/5.64 times_out_aaa(x1, x2, x3) = times_out_aaa(x1) 18.38/5.64 18.38/5.64 U35_aaa(x1, x2, x3, x4) = U35_aaa(x4) 18.38/5.64 18.38/5.64 U36_aaa(x1, x2, x3, x4) = U36_aaa(x4) 18.38/5.64 18.38/5.64 U37_aaa(x1, x2, x3, x4) = U37_aaa(x1, x4) 18.38/5.64 18.38/5.64 add_in_aaa(x1, x2, x3) = add_in_aaa 18.38/5.64 18.38/5.64 add_out_aaa(x1, x2, x3) = add_out_aaa(x1, x2, x3) 18.38/5.64 18.38/5.64 U1_aaa(x1, x2) = U1_aaa(x2) 18.38/5.64 18.38/5.64 binaryZ_in_a(x1) = binaryZ_in_a 18.38/5.64 18.38/5.64 U29_a(x1, x2) = U29_a(x2) 18.38/5.64 18.38/5.64 U30_a(x1, x2) = U30_a(x2) 18.38/5.64 18.38/5.64 binary_in_a(x1) = binary_in_a 18.38/5.64 18.38/5.64 binary_out_a(x1) = binary_out_a(x1) 18.38/5.64 18.38/5.64 U27_a(x1, x2) = U27_a(x2) 18.38/5.64 18.38/5.64 binaryZ_out_a(x1) = binaryZ_out_a(x1) 18.38/5.64 18.38/5.64 U28_a(x1, x2) = U28_a(x2) 18.38/5.64 18.38/5.64 U2_aaa(x1, x2) = U2_aaa(x2) 18.38/5.64 18.38/5.64 U3_aaa(x1, x2, x3, x4) = U3_aaa(x4) 18.38/5.64 18.38/5.64 addz_in_aaa(x1, x2, x3) = addz_in_aaa 18.38/5.64 18.38/5.64 U10_aaa(x1, x2, x3, x4) = U10_aaa(x4) 18.38/5.64 18.38/5.64 U11_aaa(x1, x2, x3, x4) = U11_aaa(x4) 18.38/5.64 18.38/5.64 addx_in_aaa(x1, x2, x3) = addx_in_aaa 18.38/5.64 18.38/5.64 U4_aaa(x1, x2) = U4_aaa(x2) 18.38/5.64 18.38/5.64 addx_out_aaa(x1, x2, x3) = addx_out_aaa(x1, x2, x3) 18.38/5.64 18.38/5.64 U5_aaa(x1, x2) = U5_aaa(x2) 18.38/5.64 18.38/5.64 U6_aaa(x1, x2, x3, x4) = U6_aaa(x4) 18.38/5.64 18.38/5.64 U12_aaa(x1, x2, x3, x4) = U12_aaa(x4) 18.38/5.64 18.38/5.64 addy_in_aaa(x1, x2, x3) = addy_in_aaa 18.38/5.64 18.38/5.64 U7_aaa(x1, x2) = U7_aaa(x2) 18.38/5.64 18.38/5.64 addy_out_aaa(x1, x2, x3) = addy_out_aaa(x1, x2, x3) 18.38/5.64 18.38/5.64 U8_aaa(x1, x2) = U8_aaa(x2) 18.38/5.64 18.38/5.64 U9_aaa(x1, x2, x3, x4) = U9_aaa(x4) 18.38/5.64 18.38/5.64 U13_aaa(x1, x2, x3, x4) = U13_aaa(x4) 18.38/5.64 18.38/5.64 addc_in_aaa(x1, x2, x3) = addc_in_aaa 18.38/5.64 18.38/5.64 addc_out_aaa(x1, x2, x3) = addc_out_aaa(x1, x2, x3) 18.38/5.64 18.38/5.64 U14_aaa(x1, x2, x3) = U14_aaa(x3) 18.38/5.64 18.38/5.64 succZ_in_aa(x1, x2) = succZ_in_aa 18.38/5.64 18.38/5.64 U33_aa(x1, x2) = U33_aa(x2) 18.38/5.64 18.38/5.64 succZ_out_aa(x1, x2) = succZ_out_aa(x1, x2) 18.38/5.64 18.38/5.64 U34_aa(x1, x2, x3) = U34_aa(x3) 18.38/5.64 18.38/5.64 succ_in_aa(x1, x2) = succ_in_aa 18.38/5.64 18.38/5.64 succ_out_aa(x1, x2) = succ_out_aa(x1, x2) 18.38/5.64 18.38/5.64 U31_aa(x1, x2) = U31_aa(x2) 18.38/5.64 18.38/5.64 U32_aa(x1, x2, x3) = U32_aa(x3) 18.38/5.64 18.38/5.64 U15_aaa(x1, x2, x3) = U15_aaa(x3) 18.38/5.64 18.38/5.64 U16_aaa(x1, x2, x3, x4) = U16_aaa(x4) 18.38/5.64 18.38/5.64 addC_in_aaa(x1, x2, x3) = addC_in_aaa 18.38/5.64 18.38/5.64 U23_aaa(x1, x2, x3, x4) = U23_aaa(x4) 18.38/5.64 18.38/5.64 addz_out_aaa(x1, x2, x3) = addz_out_aaa(x1, x2, x3) 18.38/5.64 18.38/5.64 addC_out_aaa(x1, x2, x3) = addC_out_aaa(x1, x2, x3) 18.38/5.64 18.38/5.64 U24_aaa(x1, x2, x3, x4) = U24_aaa(x4) 18.38/5.64 18.38/5.64 addX_in_aaa(x1, x2, x3) = addX_in_aaa 18.38/5.64 18.38/5.64 U17_aaa(x1, x2) = U17_aaa(x2) 18.38/5.64 18.38/5.64 addX_out_aaa(x1, x2, x3) = addX_out_aaa(x1, x2, x3) 18.38/5.64 18.38/5.64 U18_aaa(x1, x2, x3) = U18_aaa(x3) 18.38/5.64 18.38/5.64 U19_aaa(x1, x2, x3, x4) = U19_aaa(x4) 18.38/5.64 18.38/5.64 U25_aaa(x1, x2, x3, x4) = U25_aaa(x4) 18.38/5.64 18.38/5.64 addY_in_aaa(x1, x2, x3) = addY_in_aaa 18.38/5.64 18.38/5.64 U20_aaa(x1, x2) = U20_aaa(x2) 18.38/5.64 18.38/5.64 addY_out_aaa(x1, x2, x3) = addY_out_aaa(x1, x2, x3) 18.38/5.64 18.38/5.64 U21_aaa(x1, x2, x3) = U21_aaa(x3) 18.38/5.64 18.38/5.64 U22_aaa(x1, x2, x3, x4) = U22_aaa(x4) 18.38/5.64 18.38/5.64 U26_aaa(x1, x2, x3, x4) = U26_aaa(x4) 18.38/5.64 18.38/5.64 U37_aag(x1, x2, x3, x4) = U37_aag(x1, x3, x4) 18.38/5.64 18.38/5.64 add_in_aag(x1, x2, x3) = add_in_aag(x3) 18.38/5.64 18.38/5.64 b = b 18.38/5.64 18.38/5.64 add_out_aag(x1, x2, x3) = add_out_aag(x1, x2, x3) 18.38/5.64 18.38/5.64 U1_aag(x1, x2) = U1_aag(x1, x2) 18.38/5.64 18.38/5.64 binaryZ_in_g(x1) = binaryZ_in_g(x1) 18.38/5.64 18.38/5.64 U29_g(x1, x2) = U29_g(x1, x2) 18.38/5.64 18.38/5.64 one(x1) = one(x1) 18.38/5.64 18.38/5.64 U30_g(x1, x2) = U30_g(x1, x2) 18.38/5.64 18.38/5.64 binary_in_g(x1) = binary_in_g(x1) 18.38/5.64 18.38/5.64 binary_out_g(x1) = binary_out_g(x1) 18.38/5.64 18.38/5.64 U27_g(x1, x2) = U27_g(x1, x2) 18.38/5.64 18.38/5.64 binaryZ_out_g(x1) = binaryZ_out_g(x1) 18.38/5.64 18.38/5.64 U28_g(x1, x2) = U28_g(x1, x2) 18.38/5.64 18.38/5.64 U2_aag(x1, x2) = U2_aag(x1, x2) 18.38/5.64 18.38/5.64 U3_aag(x1, x2, x3, x4) = U3_aag(x3, x4) 18.38/5.64 18.38/5.64 addz_in_aag(x1, x2, x3) = addz_in_aag(x3) 18.38/5.64 18.38/5.64 U10_aag(x1, x2, x3, x4) = U10_aag(x3, x4) 18.38/5.64 18.38/5.64 U11_aag(x1, x2, x3, x4) = U11_aag(x3, x4) 18.38/5.64 18.38/5.64 addx_in_aag(x1, x2, x3) = addx_in_aag(x3) 18.38/5.64 18.38/5.64 U4_aag(x1, x2) = U4_aag(x1, x2) 18.38/5.64 18.38/5.64 addx_out_aag(x1, x2, x3) = addx_out_aag(x1, x2, x3) 18.38/5.64 18.38/5.64 U5_aag(x1, x2) = U5_aag(x1, x2) 18.38/5.64 18.38/5.64 U6_aag(x1, x2, x3, x4) = U6_aag(x3, x4) 18.38/5.64 18.38/5.64 U12_aag(x1, x2, x3, x4) = U12_aag(x3, x4) 18.38/5.64 18.38/5.64 addy_in_aag(x1, x2, x3) = addy_in_aag(x3) 18.38/5.64 18.38/5.64 U7_aag(x1, x2) = U7_aag(x1, x2) 18.38/5.64 18.38/5.64 addy_out_aag(x1, x2, x3) = addy_out_aag(x1, x2, x3) 18.38/5.64 18.38/5.64 U8_aag(x1, x2) = U8_aag(x1, x2) 18.38/5.64 18.38/5.64 U9_aag(x1, x2, x3, x4) = U9_aag(x3, x4) 18.38/5.64 18.38/5.64 U13_aag(x1, x2, x3, x4) = U13_aag(x3, x4) 18.38/5.64 18.38/5.64 addc_in_aag(x1, x2, x3) = addc_in_aag(x3) 18.38/5.64 18.38/5.64 addc_out_aag(x1, x2, x3) = addc_out_aag(x1, x2, x3) 18.38/5.64 18.38/5.64 U14_aag(x1, x2, x3) = U14_aag(x2, x3) 18.38/5.64 18.38/5.64 succZ_in_ag(x1, x2) = succZ_in_ag(x2) 18.38/5.64 18.38/5.64 U33_ag(x1, x2) = U33_ag(x1, x2) 18.38/5.64 18.38/5.64 succZ_out_ag(x1, x2) = succZ_out_ag(x1, x2) 18.38/5.64 18.38/5.64 U34_ag(x1, x2, x3) = U34_ag(x2, x3) 18.38/5.64 18.38/5.64 succ_in_ag(x1, x2) = succ_in_ag(x2) 18.38/5.64 18.38/5.64 succ_out_ag(x1, x2) = succ_out_ag(x1, x2) 18.38/5.64 18.38/5.64 U31_ag(x1, x2) = U31_ag(x1, x2) 18.38/5.64 18.38/5.64 U32_ag(x1, x2, x3) = U32_ag(x2, x3) 18.38/5.64 18.38/5.64 U15_aag(x1, x2, x3) = U15_aag(x2, x3) 18.38/5.64 18.38/5.64 U16_aag(x1, x2, x3, x4) = U16_aag(x3, x4) 18.38/5.64 18.38/5.64 addC_in_aag(x1, x2, x3) = addC_in_aag(x3) 18.38/5.64 18.38/5.64 U23_aag(x1, x2, x3, x4) = U23_aag(x3, x4) 18.38/5.64 18.38/5.64 addz_out_aag(x1, x2, x3) = addz_out_aag(x1, x2, x3) 18.38/5.64 18.38/5.64 addC_out_aag(x1, x2, x3) = addC_out_aag(x1, x2, x3) 18.38/5.64 18.38/5.64 U24_aag(x1, x2, x3, x4) = U24_aag(x3, x4) 18.38/5.64 18.38/5.64 addX_in_aag(x1, x2, x3) = addX_in_aag(x3) 18.38/5.64 18.38/5.64 U17_aag(x1, x2) = U17_aag(x1, x2) 18.38/5.64 18.38/5.64 addX_out_aag(x1, x2, x3) = addX_out_aag(x1, x2, x3) 18.38/5.64 18.38/5.64 U18_aag(x1, x2, x3) = U18_aag(x2, x3) 18.38/5.64 18.38/5.64 U19_aag(x1, x2, x3, x4) = U19_aag(x3, x4) 18.38/5.64 18.38/5.64 U25_aag(x1, x2, x3, x4) = U25_aag(x3, x4) 18.38/5.64 18.38/5.64 addY_in_aag(x1, x2, x3) = addY_in_aag(x3) 18.38/5.64 18.38/5.64 U20_aag(x1, x2) = U20_aag(x1, x2) 18.38/5.64 18.38/5.64 addY_out_aag(x1, x2, x3) = addY_out_aag(x1, x2, x3) 18.38/5.64 18.38/5.64 U21_aag(x1, x2, x3) = U21_aag(x2, x3) 18.38/5.64 18.38/5.64 U22_aag(x1, x2, x3, x4) = U22_aag(x3, x4) 18.38/5.64 18.38/5.64 U26_aag(x1, x2, x3, x4) = U26_aag(x3, x4) 18.38/5.64 18.38/5.64 SUCC_IN_AA(x1, x2) = SUCC_IN_AA 18.38/5.64 18.38/5.64 18.38/5.64 We have to consider all (P,R,Pi)-chains 18.38/5.64 ---------------------------------------- 18.38/5.64 18.38/5.64 (36) UsableRulesProof (EQUIVALENT) 18.38/5.64 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 18.38/5.64 ---------------------------------------- 18.38/5.64 18.38/5.64 (37) 18.38/5.64 Obligation: 18.38/5.64 Pi DP problem: 18.38/5.64 The TRS P consists of the following rules: 18.38/5.64 18.38/5.64 SUCC_IN_AA(one(X), zero(Z)) -> SUCC_IN_AA(X, Z) 18.38/5.64 18.38/5.64 R is empty. 18.38/5.64 The argument filtering Pi contains the following mapping: 18.38/5.64 zero(x1) = zero(x1) 18.38/5.64 18.38/5.64 one(x1) = one(x1) 18.38/5.64 18.38/5.64 SUCC_IN_AA(x1, x2) = SUCC_IN_AA 18.38/5.64 18.38/5.64 18.38/5.64 We have to consider all (P,R,Pi)-chains 18.38/5.64 ---------------------------------------- 18.38/5.64 18.38/5.64 (38) PiDPToQDPProof (SOUND) 18.38/5.64 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 18.38/5.64 ---------------------------------------- 18.38/5.64 18.38/5.64 (39) 18.38/5.64 Obligation: 18.38/5.64 Q DP problem: 18.38/5.64 The TRS P consists of the following rules: 18.38/5.64 18.38/5.64 SUCC_IN_AA -> SUCC_IN_AA 18.38/5.64 18.38/5.64 R is empty. 18.38/5.64 Q is empty. 18.38/5.64 We have to consider all (P,Q,R)-chains. 18.38/5.64 ---------------------------------------- 18.38/5.64 18.38/5.64 (40) 18.38/5.64 Obligation: 18.38/5.64 Pi DP problem: 18.38/5.64 The TRS P consists of the following rules: 18.38/5.64 18.38/5.64 ADDX_IN_AAA(X, Y, Z) -> ADDZ_IN_AAA(X, Y, Z) 18.38/5.64 ADDZ_IN_AAA(zero(X), zero(Y), zero(Z)) -> ADDZ_IN_AAA(X, Y, Z) 18.38/5.64 ADDZ_IN_AAA(zero(X), one(Y), one(Z)) -> ADDX_IN_AAA(X, Y, Z) 18.38/5.64 ADDZ_IN_AAA(one(X), zero(Y), one(Z)) -> ADDY_IN_AAA(X, Y, Z) 18.38/5.64 ADDY_IN_AAA(X, Y, Z) -> ADDZ_IN_AAA(X, Y, Z) 18.38/5.64 ADDZ_IN_AAA(one(X), one(Y), zero(Z)) -> ADDC_IN_AAA(X, Y, Z) 18.38/5.64 ADDC_IN_AAA(X, Y, Z) -> ADDC_IN_AAA^1(X, Y, Z) 18.38/5.64 ADDC_IN_AAA^1(zero(X), zero(Y), one(Z)) -> ADDZ_IN_AAA(X, Y, Z) 18.38/5.64 ADDC_IN_AAA^1(zero(X), one(Y), zero(Z)) -> ADDX_IN_AAA^1(X, Y, Z) 18.38/5.64 ADDX_IN_AAA^1(X, Y, Z) -> ADDC_IN_AAA^1(X, Y, Z) 18.38/5.64 ADDC_IN_AAA^1(one(X), zero(Y), zero(Z)) -> ADDY_IN_AAA^1(X, Y, Z) 18.38/5.64 ADDY_IN_AAA^1(X, Y, Z) -> ADDC_IN_AAA^1(X, Y, Z) 18.38/5.64 ADDC_IN_AAA^1(one(X), one(Y), one(Z)) -> ADDC_IN_AAA(X, Y, Z) 18.38/5.64 18.38/5.64 The TRS R consists of the following rules: 18.38/5.64 18.38/5.64 times_in_aag(one(b), X, X) -> times_out_aag(one(b), X, X) 18.38/5.64 times_in_aag(zero(R), S, zero(RS)) -> U35_aag(R, S, RS, times_in_aag(R, S, RS)) 18.38/5.64 times_in_aag(one(R), S, RSS) -> U36_aag(R, S, RSS, times_in_aaa(R, S, RS)) 18.38/5.64 times_in_aaa(one(b), X, X) -> times_out_aaa(one(b), X, X) 18.38/5.64 times_in_aaa(zero(R), S, zero(RS)) -> U35_aaa(R, S, RS, times_in_aaa(R, S, RS)) 18.38/5.64 times_in_aaa(one(R), S, RSS) -> U36_aaa(R, S, RSS, times_in_aaa(R, S, RS)) 18.38/5.64 U36_aaa(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aaa(R, S, RSS, add_in_aaa(S, zero(RS), RSS)) 18.38/5.64 add_in_aaa(b, b, b) -> add_out_aaa(b, b, b) 18.38/5.64 add_in_aaa(X, b, X) -> U1_aaa(X, binaryZ_in_a(X)) 18.38/5.64 binaryZ_in_a(zero(X)) -> U29_a(X, binaryZ_in_a(X)) 18.38/5.64 binaryZ_in_a(one(X)) -> U30_a(X, binary_in_a(X)) 18.38/5.64 binary_in_a(b) -> binary_out_a(b) 18.38/5.64 binary_in_a(zero(X)) -> U27_a(X, binaryZ_in_a(X)) 18.38/5.64 U27_a(X, binaryZ_out_a(X)) -> binary_out_a(zero(X)) 18.38/5.64 binary_in_a(one(X)) -> U28_a(X, binary_in_a(X)) 18.38/5.64 U28_a(X, binary_out_a(X)) -> binary_out_a(one(X)) 18.38/5.64 U30_a(X, binary_out_a(X)) -> binaryZ_out_a(one(X)) 18.38/5.64 U29_a(X, binaryZ_out_a(X)) -> binaryZ_out_a(zero(X)) 18.38/5.64 U1_aaa(X, binaryZ_out_a(X)) -> add_out_aaa(X, b, X) 18.38/5.64 add_in_aaa(b, Y, Y) -> U2_aaa(Y, binaryZ_in_a(Y)) 18.38/5.64 U2_aaa(Y, binaryZ_out_a(Y)) -> add_out_aaa(b, Y, Y) 18.38/5.64 add_in_aaa(X, Y, Z) -> U3_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.64 addz_in_aaa(zero(X), zero(Y), zero(Z)) -> U10_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.64 addz_in_aaa(zero(X), one(Y), one(Z)) -> U11_aaa(X, Y, Z, addx_in_aaa(X, Y, Z)) 18.38/5.64 addx_in_aaa(one(X), b, one(X)) -> U4_aaa(X, binary_in_a(X)) 18.38/5.64 U4_aaa(X, binary_out_a(X)) -> addx_out_aaa(one(X), b, one(X)) 18.38/5.64 addx_in_aaa(zero(X), b, zero(X)) -> U5_aaa(X, binaryZ_in_a(X)) 18.38/5.64 U5_aaa(X, binaryZ_out_a(X)) -> addx_out_aaa(zero(X), b, zero(X)) 18.38/5.64 addx_in_aaa(X, Y, Z) -> U6_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.64 addz_in_aaa(one(X), zero(Y), one(Z)) -> U12_aaa(X, Y, Z, addy_in_aaa(X, Y, Z)) 18.38/5.64 addy_in_aaa(b, one(Y), one(Y)) -> U7_aaa(Y, binary_in_a(Y)) 18.38/5.64 U7_aaa(Y, binary_out_a(Y)) -> addy_out_aaa(b, one(Y), one(Y)) 18.38/5.64 addy_in_aaa(b, zero(Y), zero(Y)) -> U8_aaa(Y, binaryZ_in_a(Y)) 18.38/5.64 U8_aaa(Y, binaryZ_out_a(Y)) -> addy_out_aaa(b, zero(Y), zero(Y)) 18.38/5.64 addy_in_aaa(X, Y, Z) -> U9_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.64 addz_in_aaa(one(X), one(Y), zero(Z)) -> U13_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.38/5.64 addc_in_aaa(b, b, one(b)) -> addc_out_aaa(b, b, one(b)) 18.38/5.64 addc_in_aaa(X, b, Z) -> U14_aaa(X, Z, succZ_in_aa(X, Z)) 18.38/5.64 succZ_in_aa(zero(X), one(X)) -> U33_aa(X, binaryZ_in_a(X)) 18.38/5.64 U33_aa(X, binaryZ_out_a(X)) -> succZ_out_aa(zero(X), one(X)) 18.38/5.64 succZ_in_aa(one(X), zero(Z)) -> U34_aa(X, Z, succ_in_aa(X, Z)) 18.38/5.64 succ_in_aa(b, one(b)) -> succ_out_aa(b, one(b)) 18.38/5.64 succ_in_aa(zero(X), one(X)) -> U31_aa(X, binaryZ_in_a(X)) 18.38/5.64 U31_aa(X, binaryZ_out_a(X)) -> succ_out_aa(zero(X), one(X)) 18.38/5.64 succ_in_aa(one(X), zero(Z)) -> U32_aa(X, Z, succ_in_aa(X, Z)) 18.38/5.64 U32_aa(X, Z, succ_out_aa(X, Z)) -> succ_out_aa(one(X), zero(Z)) 18.38/5.64 U34_aa(X, Z, succ_out_aa(X, Z)) -> succZ_out_aa(one(X), zero(Z)) 18.38/5.64 U14_aaa(X, Z, succZ_out_aa(X, Z)) -> addc_out_aaa(X, b, Z) 18.38/5.64 addc_in_aaa(b, Y, Z) -> U15_aaa(Y, Z, succZ_in_aa(Y, Z)) 18.38/5.64 U15_aaa(Y, Z, succZ_out_aa(Y, Z)) -> addc_out_aaa(b, Y, Z) 18.38/5.64 addc_in_aaa(X, Y, Z) -> U16_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.64 addC_in_aaa(zero(X), zero(Y), one(Z)) -> U23_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.64 U23_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), zero(Y), one(Z)) 18.38/5.64 addC_in_aaa(zero(X), one(Y), zero(Z)) -> U24_aaa(X, Y, Z, addX_in_aaa(X, Y, Z)) 18.38/5.64 addX_in_aaa(zero(X), b, one(X)) -> U17_aaa(X, binaryZ_in_a(X)) 18.38/5.64 U17_aaa(X, binaryZ_out_a(X)) -> addX_out_aaa(zero(X), b, one(X)) 18.38/5.64 addX_in_aaa(one(X), b, zero(Z)) -> U18_aaa(X, Z, succ_in_aa(X, Z)) 18.38/5.64 U18_aaa(X, Z, succ_out_aa(X, Z)) -> addX_out_aaa(one(X), b, zero(Z)) 18.38/5.64 addX_in_aaa(X, Y, Z) -> U19_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.64 addC_in_aaa(one(X), zero(Y), zero(Z)) -> U25_aaa(X, Y, Z, addY_in_aaa(X, Y, Z)) 18.38/5.64 addY_in_aaa(b, zero(Y), one(Y)) -> U20_aaa(Y, binaryZ_in_a(Y)) 18.38/5.64 U20_aaa(Y, binaryZ_out_a(Y)) -> addY_out_aaa(b, zero(Y), one(Y)) 18.38/5.64 addY_in_aaa(b, one(Y), zero(Z)) -> U21_aaa(Y, Z, succ_in_aa(Y, Z)) 18.38/5.64 U21_aaa(Y, Z, succ_out_aa(Y, Z)) -> addY_out_aaa(b, one(Y), zero(Z)) 18.38/5.64 addY_in_aaa(X, Y, Z) -> U22_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.64 addC_in_aaa(one(X), one(Y), one(Z)) -> U26_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.38/5.64 U26_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), one(Y), one(Z)) 18.38/5.64 U22_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addY_out_aaa(X, Y, Z) 18.38/5.64 U25_aaa(X, Y, Z, addY_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), zero(Y), zero(Z)) 18.38/5.64 U19_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addX_out_aaa(X, Y, Z) 18.38/5.64 U24_aaa(X, Y, Z, addX_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), one(Y), zero(Z)) 18.38/5.64 U16_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addc_out_aaa(X, Y, Z) 18.38/5.64 U13_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), one(Y), zero(Z)) 18.38/5.64 U9_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addy_out_aaa(X, Y, Z) 18.38/5.64 U12_aaa(X, Y, Z, addy_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), zero(Y), one(Z)) 18.38/5.64 U6_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addx_out_aaa(X, Y, Z) 18.38/5.64 U11_aaa(X, Y, Z, addx_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), one(Y), one(Z)) 18.38/5.64 U10_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), zero(Y), zero(Z)) 18.38/5.64 U3_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> add_out_aaa(X, Y, Z) 18.38/5.64 U37_aaa(R, S, RSS, add_out_aaa(S, zero(RS), RSS)) -> times_out_aaa(one(R), S, RSS) 18.38/5.64 U35_aaa(R, S, RS, times_out_aaa(R, S, RS)) -> times_out_aaa(zero(R), S, zero(RS)) 18.38/5.64 U36_aag(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aag(R, S, RSS, add_in_aag(S, zero(RS), RSS)) 18.38/5.64 add_in_aag(b, b, b) -> add_out_aag(b, b, b) 18.38/5.64 add_in_aag(X, b, X) -> U1_aag(X, binaryZ_in_g(X)) 18.38/5.64 binaryZ_in_g(zero(X)) -> U29_g(X, binaryZ_in_g(X)) 18.38/5.64 binaryZ_in_g(one(X)) -> U30_g(X, binary_in_g(X)) 18.38/5.64 binary_in_g(b) -> binary_out_g(b) 18.38/5.64 binary_in_g(zero(X)) -> U27_g(X, binaryZ_in_g(X)) 18.38/5.64 U27_g(X, binaryZ_out_g(X)) -> binary_out_g(zero(X)) 18.38/5.64 binary_in_g(one(X)) -> U28_g(X, binary_in_g(X)) 18.38/5.64 U28_g(X, binary_out_g(X)) -> binary_out_g(one(X)) 18.38/5.64 U30_g(X, binary_out_g(X)) -> binaryZ_out_g(one(X)) 18.38/5.64 U29_g(X, binaryZ_out_g(X)) -> binaryZ_out_g(zero(X)) 18.38/5.64 U1_aag(X, binaryZ_out_g(X)) -> add_out_aag(X, b, X) 18.38/5.64 add_in_aag(b, Y, Y) -> U2_aag(Y, binaryZ_in_g(Y)) 18.38/5.64 U2_aag(Y, binaryZ_out_g(Y)) -> add_out_aag(b, Y, Y) 18.38/5.64 add_in_aag(X, Y, Z) -> U3_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.64 addz_in_aag(zero(X), zero(Y), zero(Z)) -> U10_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.64 addz_in_aag(zero(X), one(Y), one(Z)) -> U11_aag(X, Y, Z, addx_in_aag(X, Y, Z)) 18.38/5.64 addx_in_aag(one(X), b, one(X)) -> U4_aag(X, binary_in_g(X)) 18.38/5.64 U4_aag(X, binary_out_g(X)) -> addx_out_aag(one(X), b, one(X)) 18.38/5.64 addx_in_aag(zero(X), b, zero(X)) -> U5_aag(X, binaryZ_in_g(X)) 18.38/5.64 U5_aag(X, binaryZ_out_g(X)) -> addx_out_aag(zero(X), b, zero(X)) 18.38/5.64 addx_in_aag(X, Y, Z) -> U6_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.64 addz_in_aag(one(X), zero(Y), one(Z)) -> U12_aag(X, Y, Z, addy_in_aag(X, Y, Z)) 18.38/5.64 addy_in_aag(b, one(Y), one(Y)) -> U7_aag(Y, binary_in_g(Y)) 18.38/5.64 U7_aag(Y, binary_out_g(Y)) -> addy_out_aag(b, one(Y), one(Y)) 18.38/5.64 addy_in_aag(b, zero(Y), zero(Y)) -> U8_aag(Y, binaryZ_in_g(Y)) 18.38/5.64 U8_aag(Y, binaryZ_out_g(Y)) -> addy_out_aag(b, zero(Y), zero(Y)) 18.38/5.64 addy_in_aag(X, Y, Z) -> U9_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.64 addz_in_aag(one(X), one(Y), zero(Z)) -> U13_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.38/5.64 addc_in_aag(b, b, one(b)) -> addc_out_aag(b, b, one(b)) 18.38/5.64 addc_in_aag(X, b, Z) -> U14_aag(X, Z, succZ_in_ag(X, Z)) 18.38/5.64 succZ_in_ag(zero(X), one(X)) -> U33_ag(X, binaryZ_in_g(X)) 18.38/5.64 U33_ag(X, binaryZ_out_g(X)) -> succZ_out_ag(zero(X), one(X)) 18.38/5.64 succZ_in_ag(one(X), zero(Z)) -> U34_ag(X, Z, succ_in_ag(X, Z)) 18.38/5.64 succ_in_ag(b, one(b)) -> succ_out_ag(b, one(b)) 18.38/5.64 succ_in_ag(zero(X), one(X)) -> U31_ag(X, binaryZ_in_g(X)) 18.38/5.64 U31_ag(X, binaryZ_out_g(X)) -> succ_out_ag(zero(X), one(X)) 18.38/5.64 succ_in_ag(one(X), zero(Z)) -> U32_ag(X, Z, succ_in_ag(X, Z)) 18.38/5.64 U32_ag(X, Z, succ_out_ag(X, Z)) -> succ_out_ag(one(X), zero(Z)) 18.38/5.64 U34_ag(X, Z, succ_out_ag(X, Z)) -> succZ_out_ag(one(X), zero(Z)) 18.38/5.64 U14_aag(X, Z, succZ_out_ag(X, Z)) -> addc_out_aag(X, b, Z) 18.38/5.64 addc_in_aag(b, Y, Z) -> U15_aag(Y, Z, succZ_in_ag(Y, Z)) 18.38/5.64 U15_aag(Y, Z, succZ_out_ag(Y, Z)) -> addc_out_aag(b, Y, Z) 18.38/5.64 addc_in_aag(X, Y, Z) -> U16_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.64 addC_in_aag(zero(X), zero(Y), one(Z)) -> U23_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.64 U23_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), zero(Y), one(Z)) 18.38/5.64 addC_in_aag(zero(X), one(Y), zero(Z)) -> U24_aag(X, Y, Z, addX_in_aag(X, Y, Z)) 18.38/5.64 addX_in_aag(zero(X), b, one(X)) -> U17_aag(X, binaryZ_in_g(X)) 18.38/5.64 U17_aag(X, binaryZ_out_g(X)) -> addX_out_aag(zero(X), b, one(X)) 18.38/5.64 addX_in_aag(one(X), b, zero(Z)) -> U18_aag(X, Z, succ_in_ag(X, Z)) 18.38/5.64 U18_aag(X, Z, succ_out_ag(X, Z)) -> addX_out_aag(one(X), b, zero(Z)) 18.38/5.64 addX_in_aag(X, Y, Z) -> U19_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.64 addC_in_aag(one(X), zero(Y), zero(Z)) -> U25_aag(X, Y, Z, addY_in_aag(X, Y, Z)) 18.38/5.64 addY_in_aag(b, zero(Y), one(Y)) -> U20_aag(Y, binaryZ_in_g(Y)) 18.38/5.64 U20_aag(Y, binaryZ_out_g(Y)) -> addY_out_aag(b, zero(Y), one(Y)) 18.38/5.64 addY_in_aag(b, one(Y), zero(Z)) -> U21_aag(Y, Z, succ_in_ag(Y, Z)) 18.38/5.64 U21_aag(Y, Z, succ_out_ag(Y, Z)) -> addY_out_aag(b, one(Y), zero(Z)) 18.38/5.64 addY_in_aag(X, Y, Z) -> U22_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.64 addC_in_aag(one(X), one(Y), one(Z)) -> U26_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.38/5.64 U26_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addC_out_aag(one(X), one(Y), one(Z)) 18.38/5.64 U22_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addY_out_aag(X, Y, Z) 18.38/5.64 U25_aag(X, Y, Z, addY_out_aag(X, Y, Z)) -> addC_out_aag(one(X), zero(Y), zero(Z)) 18.38/5.64 U19_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addX_out_aag(X, Y, Z) 18.38/5.64 U24_aag(X, Y, Z, addX_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), one(Y), zero(Z)) 18.38/5.64 U16_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addc_out_aag(X, Y, Z) 18.38/5.64 U13_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addz_out_aag(one(X), one(Y), zero(Z)) 18.38/5.64 U9_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addy_out_aag(X, Y, Z) 18.38/5.64 U12_aag(X, Y, Z, addy_out_aag(X, Y, Z)) -> addz_out_aag(one(X), zero(Y), one(Z)) 18.38/5.64 U6_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addx_out_aag(X, Y, Z) 18.38/5.64 U11_aag(X, Y, Z, addx_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), one(Y), one(Z)) 18.38/5.64 U10_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), zero(Y), zero(Z)) 18.38/5.64 U3_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> add_out_aag(X, Y, Z) 18.38/5.64 U37_aag(R, S, RSS, add_out_aag(S, zero(RS), RSS)) -> times_out_aag(one(R), S, RSS) 18.38/5.64 U35_aag(R, S, RS, times_out_aag(R, S, RS)) -> times_out_aag(zero(R), S, zero(RS)) 18.38/5.64 18.38/5.64 The argument filtering Pi contains the following mapping: 18.38/5.64 times_in_aag(x1, x2, x3) = times_in_aag(x3) 18.38/5.64 18.38/5.64 times_out_aag(x1, x2, x3) = times_out_aag(x1, x2, x3) 18.38/5.64 18.38/5.64 zero(x1) = zero(x1) 18.38/5.64 18.38/5.64 U35_aag(x1, x2, x3, x4) = U35_aag(x3, x4) 18.38/5.64 18.38/5.64 U36_aag(x1, x2, x3, x4) = U36_aag(x3, x4) 18.38/5.64 18.38/5.64 times_in_aaa(x1, x2, x3) = times_in_aaa 18.38/5.64 18.38/5.64 times_out_aaa(x1, x2, x3) = times_out_aaa(x1) 18.38/5.64 18.38/5.64 U35_aaa(x1, x2, x3, x4) = U35_aaa(x4) 18.38/5.64 18.38/5.64 U36_aaa(x1, x2, x3, x4) = U36_aaa(x4) 18.38/5.64 18.38/5.64 U37_aaa(x1, x2, x3, x4) = U37_aaa(x1, x4) 18.38/5.64 18.38/5.64 add_in_aaa(x1, x2, x3) = add_in_aaa 18.38/5.64 18.38/5.64 add_out_aaa(x1, x2, x3) = add_out_aaa(x1, x2, x3) 18.38/5.64 18.38/5.64 U1_aaa(x1, x2) = U1_aaa(x2) 18.38/5.64 18.38/5.64 binaryZ_in_a(x1) = binaryZ_in_a 18.38/5.64 18.38/5.64 U29_a(x1, x2) = U29_a(x2) 18.38/5.64 18.38/5.64 U30_a(x1, x2) = U30_a(x2) 18.38/5.64 18.38/5.64 binary_in_a(x1) = binary_in_a 18.38/5.64 18.38/5.64 binary_out_a(x1) = binary_out_a(x1) 18.38/5.64 18.38/5.64 U27_a(x1, x2) = U27_a(x2) 18.38/5.64 18.38/5.64 binaryZ_out_a(x1) = binaryZ_out_a(x1) 18.38/5.64 18.38/5.64 U28_a(x1, x2) = U28_a(x2) 18.38/5.64 18.38/5.64 U2_aaa(x1, x2) = U2_aaa(x2) 18.38/5.64 18.38/5.64 U3_aaa(x1, x2, x3, x4) = U3_aaa(x4) 18.38/5.64 18.38/5.64 addz_in_aaa(x1, x2, x3) = addz_in_aaa 18.38/5.64 18.38/5.64 U10_aaa(x1, x2, x3, x4) = U10_aaa(x4) 18.38/5.64 18.38/5.64 U11_aaa(x1, x2, x3, x4) = U11_aaa(x4) 18.38/5.64 18.38/5.64 addx_in_aaa(x1, x2, x3) = addx_in_aaa 18.38/5.64 18.38/5.64 U4_aaa(x1, x2) = U4_aaa(x2) 18.38/5.64 18.38/5.64 addx_out_aaa(x1, x2, x3) = addx_out_aaa(x1, x2, x3) 18.38/5.64 18.38/5.64 U5_aaa(x1, x2) = U5_aaa(x2) 18.38/5.64 18.38/5.64 U6_aaa(x1, x2, x3, x4) = U6_aaa(x4) 18.38/5.64 18.38/5.64 U12_aaa(x1, x2, x3, x4) = U12_aaa(x4) 18.38/5.64 18.38/5.64 addy_in_aaa(x1, x2, x3) = addy_in_aaa 18.38/5.64 18.38/5.64 U7_aaa(x1, x2) = U7_aaa(x2) 18.38/5.64 18.38/5.64 addy_out_aaa(x1, x2, x3) = addy_out_aaa(x1, x2, x3) 18.38/5.64 18.38/5.64 U8_aaa(x1, x2) = U8_aaa(x2) 18.38/5.64 18.38/5.64 U9_aaa(x1, x2, x3, x4) = U9_aaa(x4) 18.38/5.64 18.38/5.64 U13_aaa(x1, x2, x3, x4) = U13_aaa(x4) 18.38/5.64 18.38/5.64 addc_in_aaa(x1, x2, x3) = addc_in_aaa 18.38/5.64 18.38/5.64 addc_out_aaa(x1, x2, x3) = addc_out_aaa(x1, x2, x3) 18.38/5.64 18.38/5.64 U14_aaa(x1, x2, x3) = U14_aaa(x3) 18.38/5.64 18.38/5.64 succZ_in_aa(x1, x2) = succZ_in_aa 18.38/5.64 18.38/5.64 U33_aa(x1, x2) = U33_aa(x2) 18.38/5.64 18.38/5.64 succZ_out_aa(x1, x2) = succZ_out_aa(x1, x2) 18.38/5.64 18.38/5.64 U34_aa(x1, x2, x3) = U34_aa(x3) 18.38/5.64 18.38/5.64 succ_in_aa(x1, x2) = succ_in_aa 18.38/5.64 18.38/5.64 succ_out_aa(x1, x2) = succ_out_aa(x1, x2) 18.38/5.64 18.38/5.64 U31_aa(x1, x2) = U31_aa(x2) 18.38/5.64 18.38/5.64 U32_aa(x1, x2, x3) = U32_aa(x3) 18.38/5.64 18.38/5.64 U15_aaa(x1, x2, x3) = U15_aaa(x3) 18.38/5.64 18.38/5.64 U16_aaa(x1, x2, x3, x4) = U16_aaa(x4) 18.38/5.64 18.38/5.64 addC_in_aaa(x1, x2, x3) = addC_in_aaa 18.38/5.64 18.38/5.64 U23_aaa(x1, x2, x3, x4) = U23_aaa(x4) 18.38/5.64 18.38/5.64 addz_out_aaa(x1, x2, x3) = addz_out_aaa(x1, x2, x3) 18.38/5.64 18.38/5.64 addC_out_aaa(x1, x2, x3) = addC_out_aaa(x1, x2, x3) 18.38/5.64 18.38/5.64 U24_aaa(x1, x2, x3, x4) = U24_aaa(x4) 18.38/5.64 18.38/5.64 addX_in_aaa(x1, x2, x3) = addX_in_aaa 18.38/5.64 18.38/5.64 U17_aaa(x1, x2) = U17_aaa(x2) 18.38/5.64 18.38/5.64 addX_out_aaa(x1, x2, x3) = addX_out_aaa(x1, x2, x3) 18.38/5.64 18.38/5.64 U18_aaa(x1, x2, x3) = U18_aaa(x3) 18.38/5.64 18.38/5.64 U19_aaa(x1, x2, x3, x4) = U19_aaa(x4) 18.38/5.64 18.38/5.64 U25_aaa(x1, x2, x3, x4) = U25_aaa(x4) 18.38/5.64 18.38/5.64 addY_in_aaa(x1, x2, x3) = addY_in_aaa 18.38/5.64 18.38/5.64 U20_aaa(x1, x2) = U20_aaa(x2) 18.38/5.64 18.38/5.64 addY_out_aaa(x1, x2, x3) = addY_out_aaa(x1, x2, x3) 18.38/5.64 18.38/5.64 U21_aaa(x1, x2, x3) = U21_aaa(x3) 18.38/5.64 18.38/5.64 U22_aaa(x1, x2, x3, x4) = U22_aaa(x4) 18.38/5.64 18.38/5.64 U26_aaa(x1, x2, x3, x4) = U26_aaa(x4) 18.38/5.64 18.38/5.64 U37_aag(x1, x2, x3, x4) = U37_aag(x1, x3, x4) 18.38/5.64 18.38/5.64 add_in_aag(x1, x2, x3) = add_in_aag(x3) 18.38/5.64 18.38/5.64 b = b 18.38/5.64 18.38/5.64 add_out_aag(x1, x2, x3) = add_out_aag(x1, x2, x3) 18.38/5.64 18.38/5.64 U1_aag(x1, x2) = U1_aag(x1, x2) 18.38/5.64 18.38/5.64 binaryZ_in_g(x1) = binaryZ_in_g(x1) 18.38/5.64 18.38/5.64 U29_g(x1, x2) = U29_g(x1, x2) 18.38/5.64 18.38/5.64 one(x1) = one(x1) 18.38/5.64 18.38/5.64 U30_g(x1, x2) = U30_g(x1, x2) 18.38/5.64 18.38/5.64 binary_in_g(x1) = binary_in_g(x1) 18.38/5.64 18.38/5.64 binary_out_g(x1) = binary_out_g(x1) 18.38/5.64 18.38/5.64 U27_g(x1, x2) = U27_g(x1, x2) 18.38/5.64 18.38/5.64 binaryZ_out_g(x1) = binaryZ_out_g(x1) 18.38/5.64 18.38/5.64 U28_g(x1, x2) = U28_g(x1, x2) 18.38/5.64 18.38/5.64 U2_aag(x1, x2) = U2_aag(x1, x2) 18.38/5.64 18.38/5.64 U3_aag(x1, x2, x3, x4) = U3_aag(x3, x4) 18.38/5.64 18.38/5.64 addz_in_aag(x1, x2, x3) = addz_in_aag(x3) 18.38/5.64 18.38/5.64 U10_aag(x1, x2, x3, x4) = U10_aag(x3, x4) 18.38/5.64 18.38/5.64 U11_aag(x1, x2, x3, x4) = U11_aag(x3, x4) 18.38/5.64 18.38/5.64 addx_in_aag(x1, x2, x3) = addx_in_aag(x3) 18.38/5.64 18.38/5.64 U4_aag(x1, x2) = U4_aag(x1, x2) 18.38/5.64 18.38/5.64 addx_out_aag(x1, x2, x3) = addx_out_aag(x1, x2, x3) 18.38/5.64 18.38/5.64 U5_aag(x1, x2) = U5_aag(x1, x2) 18.38/5.64 18.38/5.64 U6_aag(x1, x2, x3, x4) = U6_aag(x3, x4) 18.38/5.64 18.38/5.64 U12_aag(x1, x2, x3, x4) = U12_aag(x3, x4) 18.38/5.64 18.38/5.64 addy_in_aag(x1, x2, x3) = addy_in_aag(x3) 18.38/5.64 18.38/5.64 U7_aag(x1, x2) = U7_aag(x1, x2) 18.38/5.64 18.38/5.64 addy_out_aag(x1, x2, x3) = addy_out_aag(x1, x2, x3) 18.38/5.64 18.38/5.64 U8_aag(x1, x2) = U8_aag(x1, x2) 18.38/5.64 18.38/5.64 U9_aag(x1, x2, x3, x4) = U9_aag(x3, x4) 18.38/5.64 18.38/5.64 U13_aag(x1, x2, x3, x4) = U13_aag(x3, x4) 18.38/5.64 18.38/5.64 addc_in_aag(x1, x2, x3) = addc_in_aag(x3) 18.38/5.64 18.38/5.64 addc_out_aag(x1, x2, x3) = addc_out_aag(x1, x2, x3) 18.38/5.64 18.38/5.64 U14_aag(x1, x2, x3) = U14_aag(x2, x3) 18.38/5.64 18.38/5.64 succZ_in_ag(x1, x2) = succZ_in_ag(x2) 18.38/5.64 18.38/5.64 U33_ag(x1, x2) = U33_ag(x1, x2) 18.38/5.64 18.38/5.64 succZ_out_ag(x1, x2) = succZ_out_ag(x1, x2) 18.38/5.64 18.38/5.64 U34_ag(x1, x2, x3) = U34_ag(x2, x3) 18.38/5.64 18.38/5.64 succ_in_ag(x1, x2) = succ_in_ag(x2) 18.38/5.64 18.38/5.64 succ_out_ag(x1, x2) = succ_out_ag(x1, x2) 18.38/5.64 18.38/5.64 U31_ag(x1, x2) = U31_ag(x1, x2) 18.38/5.64 18.38/5.64 U32_ag(x1, x2, x3) = U32_ag(x2, x3) 18.38/5.64 18.38/5.64 U15_aag(x1, x2, x3) = U15_aag(x2, x3) 18.38/5.64 18.38/5.64 U16_aag(x1, x2, x3, x4) = U16_aag(x3, x4) 18.38/5.64 18.38/5.64 addC_in_aag(x1, x2, x3) = addC_in_aag(x3) 18.38/5.64 18.38/5.64 U23_aag(x1, x2, x3, x4) = U23_aag(x3, x4) 18.38/5.64 18.38/5.64 addz_out_aag(x1, x2, x3) = addz_out_aag(x1, x2, x3) 18.38/5.64 18.38/5.64 addC_out_aag(x1, x2, x3) = addC_out_aag(x1, x2, x3) 18.38/5.64 18.38/5.64 U24_aag(x1, x2, x3, x4) = U24_aag(x3, x4) 18.38/5.64 18.38/5.64 addX_in_aag(x1, x2, x3) = addX_in_aag(x3) 18.38/5.64 18.38/5.64 U17_aag(x1, x2) = U17_aag(x1, x2) 18.38/5.64 18.38/5.64 addX_out_aag(x1, x2, x3) = addX_out_aag(x1, x2, x3) 18.38/5.64 18.38/5.64 U18_aag(x1, x2, x3) = U18_aag(x2, x3) 18.38/5.64 18.38/5.64 U19_aag(x1, x2, x3, x4) = U19_aag(x3, x4) 18.38/5.64 18.38/5.64 U25_aag(x1, x2, x3, x4) = U25_aag(x3, x4) 18.38/5.64 18.38/5.64 addY_in_aag(x1, x2, x3) = addY_in_aag(x3) 18.38/5.64 18.38/5.64 U20_aag(x1, x2) = U20_aag(x1, x2) 18.38/5.64 18.38/5.64 addY_out_aag(x1, x2, x3) = addY_out_aag(x1, x2, x3) 18.38/5.64 18.38/5.64 U21_aag(x1, x2, x3) = U21_aag(x2, x3) 18.38/5.64 18.38/5.64 U22_aag(x1, x2, x3, x4) = U22_aag(x3, x4) 18.38/5.64 18.38/5.64 U26_aag(x1, x2, x3, x4) = U26_aag(x3, x4) 18.38/5.64 18.38/5.64 ADDZ_IN_AAA(x1, x2, x3) = ADDZ_IN_AAA 18.38/5.64 18.38/5.64 ADDX_IN_AAA(x1, x2, x3) = ADDX_IN_AAA 18.38/5.64 18.38/5.64 ADDY_IN_AAA(x1, x2, x3) = ADDY_IN_AAA 18.38/5.64 18.38/5.64 ADDC_IN_AAA(x1, x2, x3) = ADDC_IN_AAA 18.38/5.64 18.38/5.64 ADDC_IN_AAA^1(x1, x2, x3) = ADDC_IN_AAA^1 18.38/5.64 18.38/5.64 ADDX_IN_AAA^1(x1, x2, x3) = ADDX_IN_AAA^1 18.38/5.64 18.38/5.64 ADDY_IN_AAA^1(x1, x2, x3) = ADDY_IN_AAA^1 18.38/5.64 18.38/5.64 18.38/5.64 We have to consider all (P,R,Pi)-chains 18.38/5.64 ---------------------------------------- 18.38/5.64 18.38/5.64 (41) UsableRulesProof (EQUIVALENT) 18.38/5.64 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 18.38/5.64 ---------------------------------------- 18.38/5.64 18.38/5.64 (42) 18.38/5.64 Obligation: 18.38/5.64 Pi DP problem: 18.38/5.64 The TRS P consists of the following rules: 18.38/5.64 18.38/5.64 ADDX_IN_AAA(X, Y, Z) -> ADDZ_IN_AAA(X, Y, Z) 18.38/5.64 ADDZ_IN_AAA(zero(X), zero(Y), zero(Z)) -> ADDZ_IN_AAA(X, Y, Z) 18.38/5.64 ADDZ_IN_AAA(zero(X), one(Y), one(Z)) -> ADDX_IN_AAA(X, Y, Z) 18.38/5.64 ADDZ_IN_AAA(one(X), zero(Y), one(Z)) -> ADDY_IN_AAA(X, Y, Z) 18.38/5.64 ADDY_IN_AAA(X, Y, Z) -> ADDZ_IN_AAA(X, Y, Z) 18.38/5.64 ADDZ_IN_AAA(one(X), one(Y), zero(Z)) -> ADDC_IN_AAA(X, Y, Z) 18.38/5.64 ADDC_IN_AAA(X, Y, Z) -> ADDC_IN_AAA^1(X, Y, Z) 18.38/5.64 ADDC_IN_AAA^1(zero(X), zero(Y), one(Z)) -> ADDZ_IN_AAA(X, Y, Z) 18.38/5.64 ADDC_IN_AAA^1(zero(X), one(Y), zero(Z)) -> ADDX_IN_AAA^1(X, Y, Z) 18.38/5.64 ADDX_IN_AAA^1(X, Y, Z) -> ADDC_IN_AAA^1(X, Y, Z) 18.38/5.64 ADDC_IN_AAA^1(one(X), zero(Y), zero(Z)) -> ADDY_IN_AAA^1(X, Y, Z) 18.38/5.64 ADDY_IN_AAA^1(X, Y, Z) -> ADDC_IN_AAA^1(X, Y, Z) 18.38/5.64 ADDC_IN_AAA^1(one(X), one(Y), one(Z)) -> ADDC_IN_AAA(X, Y, Z) 18.38/5.64 18.38/5.64 R is empty. 18.38/5.64 The argument filtering Pi contains the following mapping: 18.38/5.64 zero(x1) = zero(x1) 18.38/5.64 18.38/5.64 one(x1) = one(x1) 18.38/5.64 18.38/5.64 ADDZ_IN_AAA(x1, x2, x3) = ADDZ_IN_AAA 18.38/5.64 18.38/5.64 ADDX_IN_AAA(x1, x2, x3) = ADDX_IN_AAA 18.38/5.64 18.38/5.64 ADDY_IN_AAA(x1, x2, x3) = ADDY_IN_AAA 18.38/5.64 18.38/5.64 ADDC_IN_AAA(x1, x2, x3) = ADDC_IN_AAA 18.38/5.64 18.38/5.64 ADDC_IN_AAA^1(x1, x2, x3) = ADDC_IN_AAA^1 18.38/5.64 18.38/5.64 ADDX_IN_AAA^1(x1, x2, x3) = ADDX_IN_AAA^1 18.38/5.64 18.38/5.64 ADDY_IN_AAA^1(x1, x2, x3) = ADDY_IN_AAA^1 18.38/5.64 18.38/5.64 18.38/5.64 We have to consider all (P,R,Pi)-chains 18.38/5.64 ---------------------------------------- 18.38/5.64 18.38/5.64 (43) 18.38/5.64 Obligation: 18.38/5.64 Pi DP problem: 18.38/5.64 The TRS P consists of the following rules: 18.38/5.64 18.38/5.64 TIMES_IN_AAA(one(R), S, RSS) -> TIMES_IN_AAA(R, S, RS) 18.38/5.64 TIMES_IN_AAA(zero(R), S, zero(RS)) -> TIMES_IN_AAA(R, S, RS) 18.38/5.64 18.38/5.64 The TRS R consists of the following rules: 18.38/5.64 18.38/5.64 times_in_aag(one(b), X, X) -> times_out_aag(one(b), X, X) 18.38/5.64 times_in_aag(zero(R), S, zero(RS)) -> U35_aag(R, S, RS, times_in_aag(R, S, RS)) 18.38/5.64 times_in_aag(one(R), S, RSS) -> U36_aag(R, S, RSS, times_in_aaa(R, S, RS)) 18.38/5.64 times_in_aaa(one(b), X, X) -> times_out_aaa(one(b), X, X) 18.38/5.64 times_in_aaa(zero(R), S, zero(RS)) -> U35_aaa(R, S, RS, times_in_aaa(R, S, RS)) 18.38/5.64 times_in_aaa(one(R), S, RSS) -> U36_aaa(R, S, RSS, times_in_aaa(R, S, RS)) 18.38/5.64 U36_aaa(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aaa(R, S, RSS, add_in_aaa(S, zero(RS), RSS)) 18.38/5.64 add_in_aaa(b, b, b) -> add_out_aaa(b, b, b) 18.38/5.64 add_in_aaa(X, b, X) -> U1_aaa(X, binaryZ_in_a(X)) 18.38/5.64 binaryZ_in_a(zero(X)) -> U29_a(X, binaryZ_in_a(X)) 18.38/5.64 binaryZ_in_a(one(X)) -> U30_a(X, binary_in_a(X)) 18.38/5.64 binary_in_a(b) -> binary_out_a(b) 18.38/5.64 binary_in_a(zero(X)) -> U27_a(X, binaryZ_in_a(X)) 18.38/5.64 U27_a(X, binaryZ_out_a(X)) -> binary_out_a(zero(X)) 18.38/5.64 binary_in_a(one(X)) -> U28_a(X, binary_in_a(X)) 18.38/5.64 U28_a(X, binary_out_a(X)) -> binary_out_a(one(X)) 18.38/5.64 U30_a(X, binary_out_a(X)) -> binaryZ_out_a(one(X)) 18.38/5.64 U29_a(X, binaryZ_out_a(X)) -> binaryZ_out_a(zero(X)) 18.38/5.64 U1_aaa(X, binaryZ_out_a(X)) -> add_out_aaa(X, b, X) 18.38/5.64 add_in_aaa(b, Y, Y) -> U2_aaa(Y, binaryZ_in_a(Y)) 18.38/5.64 U2_aaa(Y, binaryZ_out_a(Y)) -> add_out_aaa(b, Y, Y) 18.38/5.64 add_in_aaa(X, Y, Z) -> U3_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.64 addz_in_aaa(zero(X), zero(Y), zero(Z)) -> U10_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.64 addz_in_aaa(zero(X), one(Y), one(Z)) -> U11_aaa(X, Y, Z, addx_in_aaa(X, Y, Z)) 18.38/5.64 addx_in_aaa(one(X), b, one(X)) -> U4_aaa(X, binary_in_a(X)) 18.38/5.64 U4_aaa(X, binary_out_a(X)) -> addx_out_aaa(one(X), b, one(X)) 18.38/5.64 addx_in_aaa(zero(X), b, zero(X)) -> U5_aaa(X, binaryZ_in_a(X)) 18.38/5.64 U5_aaa(X, binaryZ_out_a(X)) -> addx_out_aaa(zero(X), b, zero(X)) 18.38/5.64 addx_in_aaa(X, Y, Z) -> U6_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.64 addz_in_aaa(one(X), zero(Y), one(Z)) -> U12_aaa(X, Y, Z, addy_in_aaa(X, Y, Z)) 18.38/5.64 addy_in_aaa(b, one(Y), one(Y)) -> U7_aaa(Y, binary_in_a(Y)) 18.38/5.64 U7_aaa(Y, binary_out_a(Y)) -> addy_out_aaa(b, one(Y), one(Y)) 18.38/5.64 addy_in_aaa(b, zero(Y), zero(Y)) -> U8_aaa(Y, binaryZ_in_a(Y)) 18.38/5.64 U8_aaa(Y, binaryZ_out_a(Y)) -> addy_out_aaa(b, zero(Y), zero(Y)) 18.38/5.65 addy_in_aaa(X, Y, Z) -> U9_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.65 addz_in_aaa(one(X), one(Y), zero(Z)) -> U13_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.38/5.65 addc_in_aaa(b, b, one(b)) -> addc_out_aaa(b, b, one(b)) 18.38/5.65 addc_in_aaa(X, b, Z) -> U14_aaa(X, Z, succZ_in_aa(X, Z)) 18.38/5.65 succZ_in_aa(zero(X), one(X)) -> U33_aa(X, binaryZ_in_a(X)) 18.38/5.65 U33_aa(X, binaryZ_out_a(X)) -> succZ_out_aa(zero(X), one(X)) 18.38/5.65 succZ_in_aa(one(X), zero(Z)) -> U34_aa(X, Z, succ_in_aa(X, Z)) 18.38/5.65 succ_in_aa(b, one(b)) -> succ_out_aa(b, one(b)) 18.38/5.65 succ_in_aa(zero(X), one(X)) -> U31_aa(X, binaryZ_in_a(X)) 18.38/5.65 U31_aa(X, binaryZ_out_a(X)) -> succ_out_aa(zero(X), one(X)) 18.38/5.65 succ_in_aa(one(X), zero(Z)) -> U32_aa(X, Z, succ_in_aa(X, Z)) 18.38/5.65 U32_aa(X, Z, succ_out_aa(X, Z)) -> succ_out_aa(one(X), zero(Z)) 18.38/5.65 U34_aa(X, Z, succ_out_aa(X, Z)) -> succZ_out_aa(one(X), zero(Z)) 18.38/5.65 U14_aaa(X, Z, succZ_out_aa(X, Z)) -> addc_out_aaa(X, b, Z) 18.38/5.65 addc_in_aaa(b, Y, Z) -> U15_aaa(Y, Z, succZ_in_aa(Y, Z)) 18.38/5.65 U15_aaa(Y, Z, succZ_out_aa(Y, Z)) -> addc_out_aaa(b, Y, Z) 18.38/5.65 addc_in_aaa(X, Y, Z) -> U16_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.65 addC_in_aaa(zero(X), zero(Y), one(Z)) -> U23_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.65 U23_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), zero(Y), one(Z)) 18.38/5.65 addC_in_aaa(zero(X), one(Y), zero(Z)) -> U24_aaa(X, Y, Z, addX_in_aaa(X, Y, Z)) 18.38/5.65 addX_in_aaa(zero(X), b, one(X)) -> U17_aaa(X, binaryZ_in_a(X)) 18.38/5.65 U17_aaa(X, binaryZ_out_a(X)) -> addX_out_aaa(zero(X), b, one(X)) 18.38/5.65 addX_in_aaa(one(X), b, zero(Z)) -> U18_aaa(X, Z, succ_in_aa(X, Z)) 18.38/5.65 U18_aaa(X, Z, succ_out_aa(X, Z)) -> addX_out_aaa(one(X), b, zero(Z)) 18.38/5.65 addX_in_aaa(X, Y, Z) -> U19_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.65 addC_in_aaa(one(X), zero(Y), zero(Z)) -> U25_aaa(X, Y, Z, addY_in_aaa(X, Y, Z)) 18.38/5.65 addY_in_aaa(b, zero(Y), one(Y)) -> U20_aaa(Y, binaryZ_in_a(Y)) 18.38/5.65 U20_aaa(Y, binaryZ_out_a(Y)) -> addY_out_aaa(b, zero(Y), one(Y)) 18.38/5.65 addY_in_aaa(b, one(Y), zero(Z)) -> U21_aaa(Y, Z, succ_in_aa(Y, Z)) 18.38/5.65 U21_aaa(Y, Z, succ_out_aa(Y, Z)) -> addY_out_aaa(b, one(Y), zero(Z)) 18.38/5.65 addY_in_aaa(X, Y, Z) -> U22_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.65 addC_in_aaa(one(X), one(Y), one(Z)) -> U26_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.38/5.65 U26_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), one(Y), one(Z)) 18.38/5.65 U22_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addY_out_aaa(X, Y, Z) 18.38/5.65 U25_aaa(X, Y, Z, addY_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), zero(Y), zero(Z)) 18.38/5.65 U19_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addX_out_aaa(X, Y, Z) 18.38/5.65 U24_aaa(X, Y, Z, addX_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), one(Y), zero(Z)) 18.38/5.65 U16_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addc_out_aaa(X, Y, Z) 18.38/5.65 U13_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), one(Y), zero(Z)) 18.38/5.65 U9_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addy_out_aaa(X, Y, Z) 18.38/5.65 U12_aaa(X, Y, Z, addy_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), zero(Y), one(Z)) 18.38/5.65 U6_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addx_out_aaa(X, Y, Z) 18.38/5.65 U11_aaa(X, Y, Z, addx_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), one(Y), one(Z)) 18.38/5.65 U10_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), zero(Y), zero(Z)) 18.38/5.65 U3_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> add_out_aaa(X, Y, Z) 18.38/5.65 U37_aaa(R, S, RSS, add_out_aaa(S, zero(RS), RSS)) -> times_out_aaa(one(R), S, RSS) 18.38/5.65 U35_aaa(R, S, RS, times_out_aaa(R, S, RS)) -> times_out_aaa(zero(R), S, zero(RS)) 18.38/5.65 U36_aag(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aag(R, S, RSS, add_in_aag(S, zero(RS), RSS)) 18.38/5.65 add_in_aag(b, b, b) -> add_out_aag(b, b, b) 18.38/5.65 add_in_aag(X, b, X) -> U1_aag(X, binaryZ_in_g(X)) 18.38/5.65 binaryZ_in_g(zero(X)) -> U29_g(X, binaryZ_in_g(X)) 18.38/5.65 binaryZ_in_g(one(X)) -> U30_g(X, binary_in_g(X)) 18.38/5.65 binary_in_g(b) -> binary_out_g(b) 18.38/5.65 binary_in_g(zero(X)) -> U27_g(X, binaryZ_in_g(X)) 18.38/5.65 U27_g(X, binaryZ_out_g(X)) -> binary_out_g(zero(X)) 18.38/5.65 binary_in_g(one(X)) -> U28_g(X, binary_in_g(X)) 18.38/5.65 U28_g(X, binary_out_g(X)) -> binary_out_g(one(X)) 18.38/5.65 U30_g(X, binary_out_g(X)) -> binaryZ_out_g(one(X)) 18.38/5.65 U29_g(X, binaryZ_out_g(X)) -> binaryZ_out_g(zero(X)) 18.38/5.65 U1_aag(X, binaryZ_out_g(X)) -> add_out_aag(X, b, X) 18.38/5.65 add_in_aag(b, Y, Y) -> U2_aag(Y, binaryZ_in_g(Y)) 18.38/5.65 U2_aag(Y, binaryZ_out_g(Y)) -> add_out_aag(b, Y, Y) 18.38/5.65 add_in_aag(X, Y, Z) -> U3_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.65 addz_in_aag(zero(X), zero(Y), zero(Z)) -> U10_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.65 addz_in_aag(zero(X), one(Y), one(Z)) -> U11_aag(X, Y, Z, addx_in_aag(X, Y, Z)) 18.38/5.65 addx_in_aag(one(X), b, one(X)) -> U4_aag(X, binary_in_g(X)) 18.38/5.65 U4_aag(X, binary_out_g(X)) -> addx_out_aag(one(X), b, one(X)) 18.38/5.65 addx_in_aag(zero(X), b, zero(X)) -> U5_aag(X, binaryZ_in_g(X)) 18.38/5.65 U5_aag(X, binaryZ_out_g(X)) -> addx_out_aag(zero(X), b, zero(X)) 18.38/5.65 addx_in_aag(X, Y, Z) -> U6_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.65 addz_in_aag(one(X), zero(Y), one(Z)) -> U12_aag(X, Y, Z, addy_in_aag(X, Y, Z)) 18.38/5.65 addy_in_aag(b, one(Y), one(Y)) -> U7_aag(Y, binary_in_g(Y)) 18.38/5.65 U7_aag(Y, binary_out_g(Y)) -> addy_out_aag(b, one(Y), one(Y)) 18.38/5.65 addy_in_aag(b, zero(Y), zero(Y)) -> U8_aag(Y, binaryZ_in_g(Y)) 18.38/5.65 U8_aag(Y, binaryZ_out_g(Y)) -> addy_out_aag(b, zero(Y), zero(Y)) 18.38/5.65 addy_in_aag(X, Y, Z) -> U9_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.65 addz_in_aag(one(X), one(Y), zero(Z)) -> U13_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.38/5.65 addc_in_aag(b, b, one(b)) -> addc_out_aag(b, b, one(b)) 18.38/5.65 addc_in_aag(X, b, Z) -> U14_aag(X, Z, succZ_in_ag(X, Z)) 18.38/5.65 succZ_in_ag(zero(X), one(X)) -> U33_ag(X, binaryZ_in_g(X)) 18.38/5.65 U33_ag(X, binaryZ_out_g(X)) -> succZ_out_ag(zero(X), one(X)) 18.38/5.65 succZ_in_ag(one(X), zero(Z)) -> U34_ag(X, Z, succ_in_ag(X, Z)) 18.38/5.65 succ_in_ag(b, one(b)) -> succ_out_ag(b, one(b)) 18.38/5.65 succ_in_ag(zero(X), one(X)) -> U31_ag(X, binaryZ_in_g(X)) 18.38/5.65 U31_ag(X, binaryZ_out_g(X)) -> succ_out_ag(zero(X), one(X)) 18.38/5.65 succ_in_ag(one(X), zero(Z)) -> U32_ag(X, Z, succ_in_ag(X, Z)) 18.38/5.65 U32_ag(X, Z, succ_out_ag(X, Z)) -> succ_out_ag(one(X), zero(Z)) 18.38/5.65 U34_ag(X, Z, succ_out_ag(X, Z)) -> succZ_out_ag(one(X), zero(Z)) 18.38/5.65 U14_aag(X, Z, succZ_out_ag(X, Z)) -> addc_out_aag(X, b, Z) 18.38/5.65 addc_in_aag(b, Y, Z) -> U15_aag(Y, Z, succZ_in_ag(Y, Z)) 18.38/5.65 U15_aag(Y, Z, succZ_out_ag(Y, Z)) -> addc_out_aag(b, Y, Z) 18.38/5.65 addc_in_aag(X, Y, Z) -> U16_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.65 addC_in_aag(zero(X), zero(Y), one(Z)) -> U23_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.65 U23_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), zero(Y), one(Z)) 18.38/5.65 addC_in_aag(zero(X), one(Y), zero(Z)) -> U24_aag(X, Y, Z, addX_in_aag(X, Y, Z)) 18.38/5.65 addX_in_aag(zero(X), b, one(X)) -> U17_aag(X, binaryZ_in_g(X)) 18.38/5.65 U17_aag(X, binaryZ_out_g(X)) -> addX_out_aag(zero(X), b, one(X)) 18.38/5.65 addX_in_aag(one(X), b, zero(Z)) -> U18_aag(X, Z, succ_in_ag(X, Z)) 18.38/5.65 U18_aag(X, Z, succ_out_ag(X, Z)) -> addX_out_aag(one(X), b, zero(Z)) 18.38/5.65 addX_in_aag(X, Y, Z) -> U19_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.65 addC_in_aag(one(X), zero(Y), zero(Z)) -> U25_aag(X, Y, Z, addY_in_aag(X, Y, Z)) 18.38/5.65 addY_in_aag(b, zero(Y), one(Y)) -> U20_aag(Y, binaryZ_in_g(Y)) 18.38/5.65 U20_aag(Y, binaryZ_out_g(Y)) -> addY_out_aag(b, zero(Y), one(Y)) 18.38/5.65 addY_in_aag(b, one(Y), zero(Z)) -> U21_aag(Y, Z, succ_in_ag(Y, Z)) 18.38/5.65 U21_aag(Y, Z, succ_out_ag(Y, Z)) -> addY_out_aag(b, one(Y), zero(Z)) 18.38/5.65 addY_in_aag(X, Y, Z) -> U22_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.65 addC_in_aag(one(X), one(Y), one(Z)) -> U26_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.38/5.65 U26_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addC_out_aag(one(X), one(Y), one(Z)) 18.38/5.65 U22_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addY_out_aag(X, Y, Z) 18.38/5.65 U25_aag(X, Y, Z, addY_out_aag(X, Y, Z)) -> addC_out_aag(one(X), zero(Y), zero(Z)) 18.38/5.65 U19_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addX_out_aag(X, Y, Z) 18.38/5.65 U24_aag(X, Y, Z, addX_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), one(Y), zero(Z)) 18.38/5.65 U16_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addc_out_aag(X, Y, Z) 18.38/5.65 U13_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addz_out_aag(one(X), one(Y), zero(Z)) 18.38/5.65 U9_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addy_out_aag(X, Y, Z) 18.38/5.65 U12_aag(X, Y, Z, addy_out_aag(X, Y, Z)) -> addz_out_aag(one(X), zero(Y), one(Z)) 18.38/5.65 U6_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addx_out_aag(X, Y, Z) 18.38/5.65 U11_aag(X, Y, Z, addx_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), one(Y), one(Z)) 18.38/5.65 U10_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), zero(Y), zero(Z)) 18.38/5.65 U3_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> add_out_aag(X, Y, Z) 18.38/5.65 U37_aag(R, S, RSS, add_out_aag(S, zero(RS), RSS)) -> times_out_aag(one(R), S, RSS) 18.38/5.65 U35_aag(R, S, RS, times_out_aag(R, S, RS)) -> times_out_aag(zero(R), S, zero(RS)) 18.38/5.65 18.38/5.65 The argument filtering Pi contains the following mapping: 18.38/5.65 times_in_aag(x1, x2, x3) = times_in_aag(x3) 18.38/5.65 18.38/5.65 times_out_aag(x1, x2, x3) = times_out_aag(x1, x2, x3) 18.38/5.65 18.38/5.65 zero(x1) = zero(x1) 18.38/5.65 18.38/5.65 U35_aag(x1, x2, x3, x4) = U35_aag(x3, x4) 18.38/5.65 18.38/5.65 U36_aag(x1, x2, x3, x4) = U36_aag(x3, x4) 18.38/5.65 18.38/5.65 times_in_aaa(x1, x2, x3) = times_in_aaa 18.38/5.65 18.38/5.65 times_out_aaa(x1, x2, x3) = times_out_aaa(x1) 18.38/5.65 18.38/5.65 U35_aaa(x1, x2, x3, x4) = U35_aaa(x4) 18.38/5.65 18.38/5.65 U36_aaa(x1, x2, x3, x4) = U36_aaa(x4) 18.38/5.65 18.38/5.65 U37_aaa(x1, x2, x3, x4) = U37_aaa(x1, x4) 18.38/5.65 18.38/5.65 add_in_aaa(x1, x2, x3) = add_in_aaa 18.38/5.65 18.38/5.65 add_out_aaa(x1, x2, x3) = add_out_aaa(x1, x2, x3) 18.38/5.65 18.38/5.65 U1_aaa(x1, x2) = U1_aaa(x2) 18.38/5.65 18.38/5.65 binaryZ_in_a(x1) = binaryZ_in_a 18.38/5.65 18.38/5.65 U29_a(x1, x2) = U29_a(x2) 18.38/5.65 18.38/5.65 U30_a(x1, x2) = U30_a(x2) 18.38/5.65 18.38/5.65 binary_in_a(x1) = binary_in_a 18.38/5.65 18.38/5.65 binary_out_a(x1) = binary_out_a(x1) 18.38/5.65 18.38/5.65 U27_a(x1, x2) = U27_a(x2) 18.38/5.65 18.38/5.65 binaryZ_out_a(x1) = binaryZ_out_a(x1) 18.38/5.65 18.38/5.65 U28_a(x1, x2) = U28_a(x2) 18.38/5.65 18.38/5.65 U2_aaa(x1, x2) = U2_aaa(x2) 18.38/5.65 18.38/5.65 U3_aaa(x1, x2, x3, x4) = U3_aaa(x4) 18.38/5.65 18.38/5.65 addz_in_aaa(x1, x2, x3) = addz_in_aaa 18.38/5.65 18.38/5.65 U10_aaa(x1, x2, x3, x4) = U10_aaa(x4) 18.38/5.65 18.38/5.65 U11_aaa(x1, x2, x3, x4) = U11_aaa(x4) 18.38/5.65 18.38/5.65 addx_in_aaa(x1, x2, x3) = addx_in_aaa 18.38/5.65 18.38/5.65 U4_aaa(x1, x2) = U4_aaa(x2) 18.38/5.65 18.38/5.65 addx_out_aaa(x1, x2, x3) = addx_out_aaa(x1, x2, x3) 18.38/5.65 18.38/5.65 U5_aaa(x1, x2) = U5_aaa(x2) 18.38/5.65 18.38/5.65 U6_aaa(x1, x2, x3, x4) = U6_aaa(x4) 18.38/5.65 18.38/5.65 U12_aaa(x1, x2, x3, x4) = U12_aaa(x4) 18.38/5.65 18.38/5.65 addy_in_aaa(x1, x2, x3) = addy_in_aaa 18.38/5.65 18.38/5.65 U7_aaa(x1, x2) = U7_aaa(x2) 18.38/5.65 18.38/5.65 addy_out_aaa(x1, x2, x3) = addy_out_aaa(x1, x2, x3) 18.38/5.65 18.38/5.65 U8_aaa(x1, x2) = U8_aaa(x2) 18.38/5.65 18.38/5.65 U9_aaa(x1, x2, x3, x4) = U9_aaa(x4) 18.38/5.65 18.38/5.65 U13_aaa(x1, x2, x3, x4) = U13_aaa(x4) 18.38/5.65 18.38/5.65 addc_in_aaa(x1, x2, x3) = addc_in_aaa 18.38/5.65 18.38/5.65 addc_out_aaa(x1, x2, x3) = addc_out_aaa(x1, x2, x3) 18.38/5.65 18.38/5.65 U14_aaa(x1, x2, x3) = U14_aaa(x3) 18.38/5.65 18.38/5.65 succZ_in_aa(x1, x2) = succZ_in_aa 18.38/5.65 18.38/5.65 U33_aa(x1, x2) = U33_aa(x2) 18.38/5.65 18.38/5.65 succZ_out_aa(x1, x2) = succZ_out_aa(x1, x2) 18.38/5.65 18.38/5.65 U34_aa(x1, x2, x3) = U34_aa(x3) 18.38/5.65 18.38/5.65 succ_in_aa(x1, x2) = succ_in_aa 18.38/5.65 18.38/5.65 succ_out_aa(x1, x2) = succ_out_aa(x1, x2) 18.38/5.65 18.38/5.65 U31_aa(x1, x2) = U31_aa(x2) 18.38/5.65 18.38/5.65 U32_aa(x1, x2, x3) = U32_aa(x3) 18.38/5.65 18.38/5.65 U15_aaa(x1, x2, x3) = U15_aaa(x3) 18.38/5.65 18.38/5.65 U16_aaa(x1, x2, x3, x4) = U16_aaa(x4) 18.38/5.65 18.38/5.65 addC_in_aaa(x1, x2, x3) = addC_in_aaa 18.38/5.65 18.38/5.65 U23_aaa(x1, x2, x3, x4) = U23_aaa(x4) 18.38/5.65 18.38/5.65 addz_out_aaa(x1, x2, x3) = addz_out_aaa(x1, x2, x3) 18.38/5.65 18.38/5.65 addC_out_aaa(x1, x2, x3) = addC_out_aaa(x1, x2, x3) 18.38/5.65 18.38/5.65 U24_aaa(x1, x2, x3, x4) = U24_aaa(x4) 18.38/5.65 18.38/5.65 addX_in_aaa(x1, x2, x3) = addX_in_aaa 18.38/5.65 18.38/5.65 U17_aaa(x1, x2) = U17_aaa(x2) 18.38/5.65 18.38/5.65 addX_out_aaa(x1, x2, x3) = addX_out_aaa(x1, x2, x3) 18.38/5.65 18.38/5.65 U18_aaa(x1, x2, x3) = U18_aaa(x3) 18.38/5.65 18.38/5.65 U19_aaa(x1, x2, x3, x4) = U19_aaa(x4) 18.38/5.65 18.38/5.65 U25_aaa(x1, x2, x3, x4) = U25_aaa(x4) 18.38/5.65 18.38/5.65 addY_in_aaa(x1, x2, x3) = addY_in_aaa 18.38/5.65 18.38/5.65 U20_aaa(x1, x2) = U20_aaa(x2) 18.38/5.65 18.38/5.65 addY_out_aaa(x1, x2, x3) = addY_out_aaa(x1, x2, x3) 18.38/5.65 18.38/5.65 U21_aaa(x1, x2, x3) = U21_aaa(x3) 18.38/5.65 18.38/5.65 U22_aaa(x1, x2, x3, x4) = U22_aaa(x4) 18.38/5.65 18.38/5.65 U26_aaa(x1, x2, x3, x4) = U26_aaa(x4) 18.38/5.65 18.38/5.65 U37_aag(x1, x2, x3, x4) = U37_aag(x1, x3, x4) 18.38/5.65 18.38/5.65 add_in_aag(x1, x2, x3) = add_in_aag(x3) 18.38/5.65 18.38/5.65 b = b 18.38/5.65 18.38/5.65 add_out_aag(x1, x2, x3) = add_out_aag(x1, x2, x3) 18.38/5.65 18.38/5.65 U1_aag(x1, x2) = U1_aag(x1, x2) 18.38/5.65 18.38/5.65 binaryZ_in_g(x1) = binaryZ_in_g(x1) 18.38/5.65 18.38/5.65 U29_g(x1, x2) = U29_g(x1, x2) 18.38/5.65 18.38/5.65 one(x1) = one(x1) 18.38/5.65 18.38/5.65 U30_g(x1, x2) = U30_g(x1, x2) 18.38/5.65 18.38/5.65 binary_in_g(x1) = binary_in_g(x1) 18.38/5.65 18.38/5.65 binary_out_g(x1) = binary_out_g(x1) 18.38/5.65 18.38/5.65 U27_g(x1, x2) = U27_g(x1, x2) 18.38/5.65 18.38/5.65 binaryZ_out_g(x1) = binaryZ_out_g(x1) 18.38/5.65 18.38/5.65 U28_g(x1, x2) = U28_g(x1, x2) 18.38/5.65 18.38/5.65 U2_aag(x1, x2) = U2_aag(x1, x2) 18.38/5.65 18.38/5.65 U3_aag(x1, x2, x3, x4) = U3_aag(x3, x4) 18.38/5.65 18.38/5.65 addz_in_aag(x1, x2, x3) = addz_in_aag(x3) 18.38/5.65 18.38/5.65 U10_aag(x1, x2, x3, x4) = U10_aag(x3, x4) 18.38/5.65 18.38/5.65 U11_aag(x1, x2, x3, x4) = U11_aag(x3, x4) 18.38/5.65 18.38/5.65 addx_in_aag(x1, x2, x3) = addx_in_aag(x3) 18.38/5.65 18.38/5.65 U4_aag(x1, x2) = U4_aag(x1, x2) 18.38/5.65 18.38/5.65 addx_out_aag(x1, x2, x3) = addx_out_aag(x1, x2, x3) 18.38/5.65 18.38/5.65 U5_aag(x1, x2) = U5_aag(x1, x2) 18.38/5.65 18.38/5.65 U6_aag(x1, x2, x3, x4) = U6_aag(x3, x4) 18.38/5.65 18.38/5.65 U12_aag(x1, x2, x3, x4) = U12_aag(x3, x4) 18.38/5.65 18.38/5.65 addy_in_aag(x1, x2, x3) = addy_in_aag(x3) 18.38/5.65 18.38/5.65 U7_aag(x1, x2) = U7_aag(x1, x2) 18.38/5.65 18.38/5.65 addy_out_aag(x1, x2, x3) = addy_out_aag(x1, x2, x3) 18.38/5.65 18.38/5.65 U8_aag(x1, x2) = U8_aag(x1, x2) 18.38/5.65 18.38/5.65 U9_aag(x1, x2, x3, x4) = U9_aag(x3, x4) 18.38/5.65 18.38/5.65 U13_aag(x1, x2, x3, x4) = U13_aag(x3, x4) 18.38/5.65 18.38/5.65 addc_in_aag(x1, x2, x3) = addc_in_aag(x3) 18.38/5.65 18.38/5.65 addc_out_aag(x1, x2, x3) = addc_out_aag(x1, x2, x3) 18.38/5.65 18.38/5.65 U14_aag(x1, x2, x3) = U14_aag(x2, x3) 18.38/5.65 18.38/5.65 succZ_in_ag(x1, x2) = succZ_in_ag(x2) 18.38/5.65 18.38/5.65 U33_ag(x1, x2) = U33_ag(x1, x2) 18.38/5.65 18.38/5.65 succZ_out_ag(x1, x2) = succZ_out_ag(x1, x2) 18.38/5.65 18.38/5.65 U34_ag(x1, x2, x3) = U34_ag(x2, x3) 18.38/5.65 18.38/5.65 succ_in_ag(x1, x2) = succ_in_ag(x2) 18.38/5.65 18.38/5.65 succ_out_ag(x1, x2) = succ_out_ag(x1, x2) 18.38/5.65 18.38/5.65 U31_ag(x1, x2) = U31_ag(x1, x2) 18.38/5.65 18.38/5.65 U32_ag(x1, x2, x3) = U32_ag(x2, x3) 18.38/5.65 18.38/5.65 U15_aag(x1, x2, x3) = U15_aag(x2, x3) 18.38/5.65 18.38/5.65 U16_aag(x1, x2, x3, x4) = U16_aag(x3, x4) 18.38/5.65 18.38/5.65 addC_in_aag(x1, x2, x3) = addC_in_aag(x3) 18.38/5.65 18.38/5.65 U23_aag(x1, x2, x3, x4) = U23_aag(x3, x4) 18.38/5.65 18.38/5.65 addz_out_aag(x1, x2, x3) = addz_out_aag(x1, x2, x3) 18.38/5.65 18.38/5.65 addC_out_aag(x1, x2, x3) = addC_out_aag(x1, x2, x3) 18.38/5.65 18.38/5.65 U24_aag(x1, x2, x3, x4) = U24_aag(x3, x4) 18.38/5.65 18.38/5.65 addX_in_aag(x1, x2, x3) = addX_in_aag(x3) 18.38/5.65 18.38/5.65 U17_aag(x1, x2) = U17_aag(x1, x2) 18.38/5.65 18.38/5.65 addX_out_aag(x1, x2, x3) = addX_out_aag(x1, x2, x3) 18.38/5.65 18.38/5.65 U18_aag(x1, x2, x3) = U18_aag(x2, x3) 18.38/5.65 18.38/5.65 U19_aag(x1, x2, x3, x4) = U19_aag(x3, x4) 18.38/5.65 18.38/5.65 U25_aag(x1, x2, x3, x4) = U25_aag(x3, x4) 18.38/5.65 18.38/5.65 addY_in_aag(x1, x2, x3) = addY_in_aag(x3) 18.38/5.65 18.38/5.65 U20_aag(x1, x2) = U20_aag(x1, x2) 18.38/5.65 18.38/5.65 addY_out_aag(x1, x2, x3) = addY_out_aag(x1, x2, x3) 18.38/5.65 18.38/5.65 U21_aag(x1, x2, x3) = U21_aag(x2, x3) 18.38/5.65 18.38/5.65 U22_aag(x1, x2, x3, x4) = U22_aag(x3, x4) 18.38/5.65 18.38/5.65 U26_aag(x1, x2, x3, x4) = U26_aag(x3, x4) 18.38/5.65 18.38/5.65 TIMES_IN_AAA(x1, x2, x3) = TIMES_IN_AAA 18.38/5.65 18.38/5.65 18.38/5.65 We have to consider all (P,R,Pi)-chains 18.38/5.65 ---------------------------------------- 18.38/5.65 18.38/5.65 (44) UsableRulesProof (EQUIVALENT) 18.38/5.65 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 18.38/5.65 ---------------------------------------- 18.38/5.65 18.38/5.65 (45) 18.38/5.65 Obligation: 18.38/5.65 Pi DP problem: 18.38/5.65 The TRS P consists of the following rules: 18.38/5.65 18.38/5.65 TIMES_IN_AAA(one(R), S, RSS) -> TIMES_IN_AAA(R, S, RS) 18.38/5.65 TIMES_IN_AAA(zero(R), S, zero(RS)) -> TIMES_IN_AAA(R, S, RS) 18.38/5.65 18.38/5.65 R is empty. 18.38/5.65 The argument filtering Pi contains the following mapping: 18.38/5.65 zero(x1) = zero(x1) 18.38/5.65 18.38/5.65 one(x1) = one(x1) 18.38/5.65 18.38/5.65 TIMES_IN_AAA(x1, x2, x3) = TIMES_IN_AAA 18.38/5.65 18.38/5.65 18.38/5.65 We have to consider all (P,R,Pi)-chains 18.38/5.65 ---------------------------------------- 18.38/5.65 18.38/5.65 (46) 18.38/5.65 Obligation: 18.38/5.65 Pi DP problem: 18.38/5.65 The TRS P consists of the following rules: 18.38/5.65 18.38/5.65 TIMES_IN_AAG(zero(R), S, zero(RS)) -> TIMES_IN_AAG(R, S, RS) 18.38/5.65 18.38/5.65 The TRS R consists of the following rules: 18.38/5.65 18.38/5.65 times_in_aag(one(b), X, X) -> times_out_aag(one(b), X, X) 18.38/5.65 times_in_aag(zero(R), S, zero(RS)) -> U35_aag(R, S, RS, times_in_aag(R, S, RS)) 18.38/5.65 times_in_aag(one(R), S, RSS) -> U36_aag(R, S, RSS, times_in_aaa(R, S, RS)) 18.38/5.65 times_in_aaa(one(b), X, X) -> times_out_aaa(one(b), X, X) 18.38/5.65 times_in_aaa(zero(R), S, zero(RS)) -> U35_aaa(R, S, RS, times_in_aaa(R, S, RS)) 18.38/5.65 times_in_aaa(one(R), S, RSS) -> U36_aaa(R, S, RSS, times_in_aaa(R, S, RS)) 18.38/5.65 U36_aaa(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aaa(R, S, RSS, add_in_aaa(S, zero(RS), RSS)) 18.38/5.65 add_in_aaa(b, b, b) -> add_out_aaa(b, b, b) 18.38/5.65 add_in_aaa(X, b, X) -> U1_aaa(X, binaryZ_in_a(X)) 18.38/5.65 binaryZ_in_a(zero(X)) -> U29_a(X, binaryZ_in_a(X)) 18.38/5.65 binaryZ_in_a(one(X)) -> U30_a(X, binary_in_a(X)) 18.38/5.65 binary_in_a(b) -> binary_out_a(b) 18.38/5.65 binary_in_a(zero(X)) -> U27_a(X, binaryZ_in_a(X)) 18.38/5.65 U27_a(X, binaryZ_out_a(X)) -> binary_out_a(zero(X)) 18.38/5.65 binary_in_a(one(X)) -> U28_a(X, binary_in_a(X)) 18.38/5.65 U28_a(X, binary_out_a(X)) -> binary_out_a(one(X)) 18.38/5.65 U30_a(X, binary_out_a(X)) -> binaryZ_out_a(one(X)) 18.38/5.65 U29_a(X, binaryZ_out_a(X)) -> binaryZ_out_a(zero(X)) 18.38/5.65 U1_aaa(X, binaryZ_out_a(X)) -> add_out_aaa(X, b, X) 18.38/5.65 add_in_aaa(b, Y, Y) -> U2_aaa(Y, binaryZ_in_a(Y)) 18.38/5.65 U2_aaa(Y, binaryZ_out_a(Y)) -> add_out_aaa(b, Y, Y) 18.38/5.65 add_in_aaa(X, Y, Z) -> U3_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.65 addz_in_aaa(zero(X), zero(Y), zero(Z)) -> U10_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.65 addz_in_aaa(zero(X), one(Y), one(Z)) -> U11_aaa(X, Y, Z, addx_in_aaa(X, Y, Z)) 18.38/5.65 addx_in_aaa(one(X), b, one(X)) -> U4_aaa(X, binary_in_a(X)) 18.38/5.65 U4_aaa(X, binary_out_a(X)) -> addx_out_aaa(one(X), b, one(X)) 18.38/5.65 addx_in_aaa(zero(X), b, zero(X)) -> U5_aaa(X, binaryZ_in_a(X)) 18.38/5.65 U5_aaa(X, binaryZ_out_a(X)) -> addx_out_aaa(zero(X), b, zero(X)) 18.38/5.65 addx_in_aaa(X, Y, Z) -> U6_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.65 addz_in_aaa(one(X), zero(Y), one(Z)) -> U12_aaa(X, Y, Z, addy_in_aaa(X, Y, Z)) 18.38/5.65 addy_in_aaa(b, one(Y), one(Y)) -> U7_aaa(Y, binary_in_a(Y)) 18.38/5.65 U7_aaa(Y, binary_out_a(Y)) -> addy_out_aaa(b, one(Y), one(Y)) 18.38/5.65 addy_in_aaa(b, zero(Y), zero(Y)) -> U8_aaa(Y, binaryZ_in_a(Y)) 18.38/5.65 U8_aaa(Y, binaryZ_out_a(Y)) -> addy_out_aaa(b, zero(Y), zero(Y)) 18.38/5.65 addy_in_aaa(X, Y, Z) -> U9_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.65 addz_in_aaa(one(X), one(Y), zero(Z)) -> U13_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.38/5.65 addc_in_aaa(b, b, one(b)) -> addc_out_aaa(b, b, one(b)) 18.38/5.65 addc_in_aaa(X, b, Z) -> U14_aaa(X, Z, succZ_in_aa(X, Z)) 18.38/5.65 succZ_in_aa(zero(X), one(X)) -> U33_aa(X, binaryZ_in_a(X)) 18.38/5.65 U33_aa(X, binaryZ_out_a(X)) -> succZ_out_aa(zero(X), one(X)) 18.38/5.65 succZ_in_aa(one(X), zero(Z)) -> U34_aa(X, Z, succ_in_aa(X, Z)) 18.38/5.65 succ_in_aa(b, one(b)) -> succ_out_aa(b, one(b)) 18.38/5.65 succ_in_aa(zero(X), one(X)) -> U31_aa(X, binaryZ_in_a(X)) 18.38/5.65 U31_aa(X, binaryZ_out_a(X)) -> succ_out_aa(zero(X), one(X)) 18.38/5.65 succ_in_aa(one(X), zero(Z)) -> U32_aa(X, Z, succ_in_aa(X, Z)) 18.38/5.65 U32_aa(X, Z, succ_out_aa(X, Z)) -> succ_out_aa(one(X), zero(Z)) 18.38/5.65 U34_aa(X, Z, succ_out_aa(X, Z)) -> succZ_out_aa(one(X), zero(Z)) 18.38/5.65 U14_aaa(X, Z, succZ_out_aa(X, Z)) -> addc_out_aaa(X, b, Z) 18.38/5.65 addc_in_aaa(b, Y, Z) -> U15_aaa(Y, Z, succZ_in_aa(Y, Z)) 18.38/5.65 U15_aaa(Y, Z, succZ_out_aa(Y, Z)) -> addc_out_aaa(b, Y, Z) 18.38/5.65 addc_in_aaa(X, Y, Z) -> U16_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.65 addC_in_aaa(zero(X), zero(Y), one(Z)) -> U23_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.65 U23_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), zero(Y), one(Z)) 18.38/5.65 addC_in_aaa(zero(X), one(Y), zero(Z)) -> U24_aaa(X, Y, Z, addX_in_aaa(X, Y, Z)) 18.38/5.65 addX_in_aaa(zero(X), b, one(X)) -> U17_aaa(X, binaryZ_in_a(X)) 18.38/5.65 U17_aaa(X, binaryZ_out_a(X)) -> addX_out_aaa(zero(X), b, one(X)) 18.38/5.65 addX_in_aaa(one(X), b, zero(Z)) -> U18_aaa(X, Z, succ_in_aa(X, Z)) 18.38/5.65 U18_aaa(X, Z, succ_out_aa(X, Z)) -> addX_out_aaa(one(X), b, zero(Z)) 18.38/5.65 addX_in_aaa(X, Y, Z) -> U19_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.65 addC_in_aaa(one(X), zero(Y), zero(Z)) -> U25_aaa(X, Y, Z, addY_in_aaa(X, Y, Z)) 18.38/5.65 addY_in_aaa(b, zero(Y), one(Y)) -> U20_aaa(Y, binaryZ_in_a(Y)) 18.38/5.65 U20_aaa(Y, binaryZ_out_a(Y)) -> addY_out_aaa(b, zero(Y), one(Y)) 18.38/5.65 addY_in_aaa(b, one(Y), zero(Z)) -> U21_aaa(Y, Z, succ_in_aa(Y, Z)) 18.38/5.65 U21_aaa(Y, Z, succ_out_aa(Y, Z)) -> addY_out_aaa(b, one(Y), zero(Z)) 18.38/5.65 addY_in_aaa(X, Y, Z) -> U22_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.65 addC_in_aaa(one(X), one(Y), one(Z)) -> U26_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.38/5.65 U26_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), one(Y), one(Z)) 18.38/5.65 U22_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addY_out_aaa(X, Y, Z) 18.38/5.65 U25_aaa(X, Y, Z, addY_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), zero(Y), zero(Z)) 18.38/5.65 U19_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addX_out_aaa(X, Y, Z) 18.38/5.65 U24_aaa(X, Y, Z, addX_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), one(Y), zero(Z)) 18.38/5.65 U16_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addc_out_aaa(X, Y, Z) 18.38/5.65 U13_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), one(Y), zero(Z)) 18.38/5.65 U9_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addy_out_aaa(X, Y, Z) 18.38/5.65 U12_aaa(X, Y, Z, addy_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), zero(Y), one(Z)) 18.38/5.65 U6_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addx_out_aaa(X, Y, Z) 18.38/5.65 U11_aaa(X, Y, Z, addx_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), one(Y), one(Z)) 18.38/5.65 U10_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), zero(Y), zero(Z)) 18.38/5.65 U3_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> add_out_aaa(X, Y, Z) 18.38/5.65 U37_aaa(R, S, RSS, add_out_aaa(S, zero(RS), RSS)) -> times_out_aaa(one(R), S, RSS) 18.38/5.65 U35_aaa(R, S, RS, times_out_aaa(R, S, RS)) -> times_out_aaa(zero(R), S, zero(RS)) 18.38/5.65 U36_aag(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aag(R, S, RSS, add_in_aag(S, zero(RS), RSS)) 18.38/5.65 add_in_aag(b, b, b) -> add_out_aag(b, b, b) 18.38/5.65 add_in_aag(X, b, X) -> U1_aag(X, binaryZ_in_g(X)) 18.38/5.65 binaryZ_in_g(zero(X)) -> U29_g(X, binaryZ_in_g(X)) 18.38/5.65 binaryZ_in_g(one(X)) -> U30_g(X, binary_in_g(X)) 18.38/5.65 binary_in_g(b) -> binary_out_g(b) 18.38/5.65 binary_in_g(zero(X)) -> U27_g(X, binaryZ_in_g(X)) 18.38/5.65 U27_g(X, binaryZ_out_g(X)) -> binary_out_g(zero(X)) 18.38/5.65 binary_in_g(one(X)) -> U28_g(X, binary_in_g(X)) 18.38/5.65 U28_g(X, binary_out_g(X)) -> binary_out_g(one(X)) 18.38/5.65 U30_g(X, binary_out_g(X)) -> binaryZ_out_g(one(X)) 18.38/5.65 U29_g(X, binaryZ_out_g(X)) -> binaryZ_out_g(zero(X)) 18.38/5.65 U1_aag(X, binaryZ_out_g(X)) -> add_out_aag(X, b, X) 18.38/5.65 add_in_aag(b, Y, Y) -> U2_aag(Y, binaryZ_in_g(Y)) 18.38/5.65 U2_aag(Y, binaryZ_out_g(Y)) -> add_out_aag(b, Y, Y) 18.38/5.65 add_in_aag(X, Y, Z) -> U3_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.65 addz_in_aag(zero(X), zero(Y), zero(Z)) -> U10_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.65 addz_in_aag(zero(X), one(Y), one(Z)) -> U11_aag(X, Y, Z, addx_in_aag(X, Y, Z)) 18.38/5.65 addx_in_aag(one(X), b, one(X)) -> U4_aag(X, binary_in_g(X)) 18.38/5.65 U4_aag(X, binary_out_g(X)) -> addx_out_aag(one(X), b, one(X)) 18.38/5.65 addx_in_aag(zero(X), b, zero(X)) -> U5_aag(X, binaryZ_in_g(X)) 18.38/5.65 U5_aag(X, binaryZ_out_g(X)) -> addx_out_aag(zero(X), b, zero(X)) 18.38/5.65 addx_in_aag(X, Y, Z) -> U6_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.65 addz_in_aag(one(X), zero(Y), one(Z)) -> U12_aag(X, Y, Z, addy_in_aag(X, Y, Z)) 18.38/5.65 addy_in_aag(b, one(Y), one(Y)) -> U7_aag(Y, binary_in_g(Y)) 18.38/5.65 U7_aag(Y, binary_out_g(Y)) -> addy_out_aag(b, one(Y), one(Y)) 18.38/5.65 addy_in_aag(b, zero(Y), zero(Y)) -> U8_aag(Y, binaryZ_in_g(Y)) 18.38/5.65 U8_aag(Y, binaryZ_out_g(Y)) -> addy_out_aag(b, zero(Y), zero(Y)) 18.38/5.65 addy_in_aag(X, Y, Z) -> U9_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.65 addz_in_aag(one(X), one(Y), zero(Z)) -> U13_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.38/5.65 addc_in_aag(b, b, one(b)) -> addc_out_aag(b, b, one(b)) 18.38/5.65 addc_in_aag(X, b, Z) -> U14_aag(X, Z, succZ_in_ag(X, Z)) 18.38/5.65 succZ_in_ag(zero(X), one(X)) -> U33_ag(X, binaryZ_in_g(X)) 18.38/5.65 U33_ag(X, binaryZ_out_g(X)) -> succZ_out_ag(zero(X), one(X)) 18.38/5.65 succZ_in_ag(one(X), zero(Z)) -> U34_ag(X, Z, succ_in_ag(X, Z)) 18.38/5.65 succ_in_ag(b, one(b)) -> succ_out_ag(b, one(b)) 18.38/5.65 succ_in_ag(zero(X), one(X)) -> U31_ag(X, binaryZ_in_g(X)) 18.38/5.65 U31_ag(X, binaryZ_out_g(X)) -> succ_out_ag(zero(X), one(X)) 18.38/5.65 succ_in_ag(one(X), zero(Z)) -> U32_ag(X, Z, succ_in_ag(X, Z)) 18.38/5.65 U32_ag(X, Z, succ_out_ag(X, Z)) -> succ_out_ag(one(X), zero(Z)) 18.38/5.65 U34_ag(X, Z, succ_out_ag(X, Z)) -> succZ_out_ag(one(X), zero(Z)) 18.38/5.65 U14_aag(X, Z, succZ_out_ag(X, Z)) -> addc_out_aag(X, b, Z) 18.38/5.65 addc_in_aag(b, Y, Z) -> U15_aag(Y, Z, succZ_in_ag(Y, Z)) 18.38/5.65 U15_aag(Y, Z, succZ_out_ag(Y, Z)) -> addc_out_aag(b, Y, Z) 18.38/5.65 addc_in_aag(X, Y, Z) -> U16_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.65 addC_in_aag(zero(X), zero(Y), one(Z)) -> U23_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.65 U23_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), zero(Y), one(Z)) 18.38/5.65 addC_in_aag(zero(X), one(Y), zero(Z)) -> U24_aag(X, Y, Z, addX_in_aag(X, Y, Z)) 18.38/5.65 addX_in_aag(zero(X), b, one(X)) -> U17_aag(X, binaryZ_in_g(X)) 18.38/5.65 U17_aag(X, binaryZ_out_g(X)) -> addX_out_aag(zero(X), b, one(X)) 18.38/5.65 addX_in_aag(one(X), b, zero(Z)) -> U18_aag(X, Z, succ_in_ag(X, Z)) 18.38/5.65 U18_aag(X, Z, succ_out_ag(X, Z)) -> addX_out_aag(one(X), b, zero(Z)) 18.38/5.65 addX_in_aag(X, Y, Z) -> U19_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.65 addC_in_aag(one(X), zero(Y), zero(Z)) -> U25_aag(X, Y, Z, addY_in_aag(X, Y, Z)) 18.38/5.65 addY_in_aag(b, zero(Y), one(Y)) -> U20_aag(Y, binaryZ_in_g(Y)) 18.38/5.65 U20_aag(Y, binaryZ_out_g(Y)) -> addY_out_aag(b, zero(Y), one(Y)) 18.38/5.65 addY_in_aag(b, one(Y), zero(Z)) -> U21_aag(Y, Z, succ_in_ag(Y, Z)) 18.38/5.65 U21_aag(Y, Z, succ_out_ag(Y, Z)) -> addY_out_aag(b, one(Y), zero(Z)) 18.38/5.65 addY_in_aag(X, Y, Z) -> U22_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.65 addC_in_aag(one(X), one(Y), one(Z)) -> U26_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.38/5.65 U26_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addC_out_aag(one(X), one(Y), one(Z)) 18.38/5.65 U22_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addY_out_aag(X, Y, Z) 18.38/5.65 U25_aag(X, Y, Z, addY_out_aag(X, Y, Z)) -> addC_out_aag(one(X), zero(Y), zero(Z)) 18.38/5.65 U19_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addX_out_aag(X, Y, Z) 18.38/5.65 U24_aag(X, Y, Z, addX_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), one(Y), zero(Z)) 18.38/5.65 U16_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addc_out_aag(X, Y, Z) 18.38/5.65 U13_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addz_out_aag(one(X), one(Y), zero(Z)) 18.38/5.65 U9_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addy_out_aag(X, Y, Z) 18.38/5.65 U12_aag(X, Y, Z, addy_out_aag(X, Y, Z)) -> addz_out_aag(one(X), zero(Y), one(Z)) 18.38/5.65 U6_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addx_out_aag(X, Y, Z) 18.38/5.65 U11_aag(X, Y, Z, addx_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), one(Y), one(Z)) 18.38/5.65 U10_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), zero(Y), zero(Z)) 18.38/5.65 U3_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> add_out_aag(X, Y, Z) 18.38/5.65 U37_aag(R, S, RSS, add_out_aag(S, zero(RS), RSS)) -> times_out_aag(one(R), S, RSS) 18.38/5.65 U35_aag(R, S, RS, times_out_aag(R, S, RS)) -> times_out_aag(zero(R), S, zero(RS)) 18.38/5.65 18.38/5.65 The argument filtering Pi contains the following mapping: 18.38/5.65 times_in_aag(x1, x2, x3) = times_in_aag(x3) 18.38/5.65 18.38/5.65 times_out_aag(x1, x2, x3) = times_out_aag(x1, x2, x3) 18.38/5.65 18.38/5.65 zero(x1) = zero(x1) 18.38/5.65 18.38/5.65 U35_aag(x1, x2, x3, x4) = U35_aag(x3, x4) 18.38/5.65 18.38/5.65 U36_aag(x1, x2, x3, x4) = U36_aag(x3, x4) 18.38/5.65 18.38/5.65 times_in_aaa(x1, x2, x3) = times_in_aaa 18.38/5.65 18.38/5.65 times_out_aaa(x1, x2, x3) = times_out_aaa(x1) 18.38/5.65 18.38/5.65 U35_aaa(x1, x2, x3, x4) = U35_aaa(x4) 18.38/5.65 18.38/5.65 U36_aaa(x1, x2, x3, x4) = U36_aaa(x4) 18.38/5.65 18.38/5.65 U37_aaa(x1, x2, x3, x4) = U37_aaa(x1, x4) 18.38/5.65 18.38/5.65 add_in_aaa(x1, x2, x3) = add_in_aaa 18.38/5.65 18.38/5.65 add_out_aaa(x1, x2, x3) = add_out_aaa(x1, x2, x3) 18.38/5.65 18.38/5.65 U1_aaa(x1, x2) = U1_aaa(x2) 18.38/5.65 18.38/5.65 binaryZ_in_a(x1) = binaryZ_in_a 18.38/5.65 18.38/5.65 U29_a(x1, x2) = U29_a(x2) 18.38/5.65 18.38/5.65 U30_a(x1, x2) = U30_a(x2) 18.38/5.65 18.38/5.65 binary_in_a(x1) = binary_in_a 18.38/5.65 18.38/5.65 binary_out_a(x1) = binary_out_a(x1) 18.38/5.65 18.38/5.65 U27_a(x1, x2) = U27_a(x2) 18.38/5.65 18.38/5.65 binaryZ_out_a(x1) = binaryZ_out_a(x1) 18.38/5.65 18.38/5.65 U28_a(x1, x2) = U28_a(x2) 18.38/5.65 18.38/5.65 U2_aaa(x1, x2) = U2_aaa(x2) 18.38/5.65 18.38/5.65 U3_aaa(x1, x2, x3, x4) = U3_aaa(x4) 18.38/5.65 18.38/5.65 addz_in_aaa(x1, x2, x3) = addz_in_aaa 18.38/5.65 18.38/5.65 U10_aaa(x1, x2, x3, x4) = U10_aaa(x4) 18.38/5.65 18.38/5.65 U11_aaa(x1, x2, x3, x4) = U11_aaa(x4) 18.38/5.65 18.38/5.65 addx_in_aaa(x1, x2, x3) = addx_in_aaa 18.38/5.65 18.38/5.65 U4_aaa(x1, x2) = U4_aaa(x2) 18.38/5.65 18.38/5.65 addx_out_aaa(x1, x2, x3) = addx_out_aaa(x1, x2, x3) 18.38/5.65 18.38/5.65 U5_aaa(x1, x2) = U5_aaa(x2) 18.38/5.65 18.38/5.65 U6_aaa(x1, x2, x3, x4) = U6_aaa(x4) 18.38/5.65 18.38/5.65 U12_aaa(x1, x2, x3, x4) = U12_aaa(x4) 18.38/5.65 18.38/5.65 addy_in_aaa(x1, x2, x3) = addy_in_aaa 18.38/5.65 18.38/5.65 U7_aaa(x1, x2) = U7_aaa(x2) 18.38/5.65 18.38/5.65 addy_out_aaa(x1, x2, x3) = addy_out_aaa(x1, x2, x3) 18.38/5.65 18.38/5.65 U8_aaa(x1, x2) = U8_aaa(x2) 18.38/5.65 18.38/5.65 U9_aaa(x1, x2, x3, x4) = U9_aaa(x4) 18.38/5.65 18.38/5.65 U13_aaa(x1, x2, x3, x4) = U13_aaa(x4) 18.38/5.65 18.38/5.65 addc_in_aaa(x1, x2, x3) = addc_in_aaa 18.38/5.65 18.38/5.65 addc_out_aaa(x1, x2, x3) = addc_out_aaa(x1, x2, x3) 18.38/5.65 18.38/5.65 U14_aaa(x1, x2, x3) = U14_aaa(x3) 18.38/5.65 18.38/5.65 succZ_in_aa(x1, x2) = succZ_in_aa 18.38/5.65 18.38/5.65 U33_aa(x1, x2) = U33_aa(x2) 18.38/5.65 18.38/5.65 succZ_out_aa(x1, x2) = succZ_out_aa(x1, x2) 18.38/5.65 18.38/5.65 U34_aa(x1, x2, x3) = U34_aa(x3) 18.38/5.65 18.38/5.65 succ_in_aa(x1, x2) = succ_in_aa 18.38/5.65 18.38/5.65 succ_out_aa(x1, x2) = succ_out_aa(x1, x2) 18.38/5.65 18.38/5.65 U31_aa(x1, x2) = U31_aa(x2) 18.38/5.65 18.38/5.65 U32_aa(x1, x2, x3) = U32_aa(x3) 18.38/5.65 18.38/5.65 U15_aaa(x1, x2, x3) = U15_aaa(x3) 18.38/5.65 18.38/5.65 U16_aaa(x1, x2, x3, x4) = U16_aaa(x4) 18.38/5.65 18.38/5.65 addC_in_aaa(x1, x2, x3) = addC_in_aaa 18.38/5.65 18.38/5.65 U23_aaa(x1, x2, x3, x4) = U23_aaa(x4) 18.38/5.65 18.38/5.65 addz_out_aaa(x1, x2, x3) = addz_out_aaa(x1, x2, x3) 18.38/5.65 18.38/5.65 addC_out_aaa(x1, x2, x3) = addC_out_aaa(x1, x2, x3) 18.38/5.65 18.38/5.65 U24_aaa(x1, x2, x3, x4) = U24_aaa(x4) 18.38/5.65 18.38/5.65 addX_in_aaa(x1, x2, x3) = addX_in_aaa 18.38/5.65 18.38/5.65 U17_aaa(x1, x2) = U17_aaa(x2) 18.38/5.65 18.38/5.65 addX_out_aaa(x1, x2, x3) = addX_out_aaa(x1, x2, x3) 18.38/5.65 18.38/5.65 U18_aaa(x1, x2, x3) = U18_aaa(x3) 18.38/5.65 18.38/5.65 U19_aaa(x1, x2, x3, x4) = U19_aaa(x4) 18.38/5.65 18.38/5.65 U25_aaa(x1, x2, x3, x4) = U25_aaa(x4) 18.38/5.65 18.38/5.65 addY_in_aaa(x1, x2, x3) = addY_in_aaa 18.38/5.65 18.38/5.65 U20_aaa(x1, x2) = U20_aaa(x2) 18.38/5.65 18.38/5.65 addY_out_aaa(x1, x2, x3) = addY_out_aaa(x1, x2, x3) 18.38/5.65 18.38/5.65 U21_aaa(x1, x2, x3) = U21_aaa(x3) 18.38/5.65 18.38/5.65 U22_aaa(x1, x2, x3, x4) = U22_aaa(x4) 18.38/5.65 18.38/5.65 U26_aaa(x1, x2, x3, x4) = U26_aaa(x4) 18.38/5.65 18.38/5.65 U37_aag(x1, x2, x3, x4) = U37_aag(x1, x3, x4) 18.38/5.65 18.38/5.65 add_in_aag(x1, x2, x3) = add_in_aag(x3) 18.38/5.65 18.38/5.65 b = b 18.38/5.65 18.38/5.65 add_out_aag(x1, x2, x3) = add_out_aag(x1, x2, x3) 18.38/5.65 18.38/5.65 U1_aag(x1, x2) = U1_aag(x1, x2) 18.38/5.65 18.38/5.65 binaryZ_in_g(x1) = binaryZ_in_g(x1) 18.38/5.65 18.38/5.65 U29_g(x1, x2) = U29_g(x1, x2) 18.38/5.65 18.38/5.65 one(x1) = one(x1) 18.38/5.65 18.38/5.65 U30_g(x1, x2) = U30_g(x1, x2) 18.38/5.65 18.38/5.65 binary_in_g(x1) = binary_in_g(x1) 18.38/5.65 18.38/5.65 binary_out_g(x1) = binary_out_g(x1) 18.38/5.65 18.38/5.65 U27_g(x1, x2) = U27_g(x1, x2) 18.38/5.65 18.38/5.65 binaryZ_out_g(x1) = binaryZ_out_g(x1) 18.38/5.65 18.38/5.65 U28_g(x1, x2) = U28_g(x1, x2) 18.38/5.65 18.38/5.65 U2_aag(x1, x2) = U2_aag(x1, x2) 18.38/5.65 18.38/5.65 U3_aag(x1, x2, x3, x4) = U3_aag(x3, x4) 18.38/5.65 18.38/5.65 addz_in_aag(x1, x2, x3) = addz_in_aag(x3) 18.38/5.65 18.38/5.65 U10_aag(x1, x2, x3, x4) = U10_aag(x3, x4) 18.38/5.65 18.38/5.65 U11_aag(x1, x2, x3, x4) = U11_aag(x3, x4) 18.38/5.65 18.38/5.65 addx_in_aag(x1, x2, x3) = addx_in_aag(x3) 18.38/5.65 18.38/5.65 U4_aag(x1, x2) = U4_aag(x1, x2) 18.38/5.65 18.38/5.65 addx_out_aag(x1, x2, x3) = addx_out_aag(x1, x2, x3) 18.38/5.65 18.38/5.65 U5_aag(x1, x2) = U5_aag(x1, x2) 18.38/5.65 18.38/5.65 U6_aag(x1, x2, x3, x4) = U6_aag(x3, x4) 18.38/5.65 18.38/5.65 U12_aag(x1, x2, x3, x4) = U12_aag(x3, x4) 18.38/5.65 18.38/5.65 addy_in_aag(x1, x2, x3) = addy_in_aag(x3) 18.38/5.65 18.38/5.65 U7_aag(x1, x2) = U7_aag(x1, x2) 18.38/5.65 18.38/5.65 addy_out_aag(x1, x2, x3) = addy_out_aag(x1, x2, x3) 18.38/5.65 18.38/5.65 U8_aag(x1, x2) = U8_aag(x1, x2) 18.38/5.65 18.38/5.65 U9_aag(x1, x2, x3, x4) = U9_aag(x3, x4) 18.38/5.65 18.38/5.65 U13_aag(x1, x2, x3, x4) = U13_aag(x3, x4) 18.38/5.65 18.38/5.65 addc_in_aag(x1, x2, x3) = addc_in_aag(x3) 18.38/5.65 18.38/5.65 addc_out_aag(x1, x2, x3) = addc_out_aag(x1, x2, x3) 18.38/5.65 18.38/5.65 U14_aag(x1, x2, x3) = U14_aag(x2, x3) 18.38/5.65 18.38/5.65 succZ_in_ag(x1, x2) = succZ_in_ag(x2) 18.38/5.65 18.38/5.65 U33_ag(x1, x2) = U33_ag(x1, x2) 18.38/5.65 18.38/5.65 succZ_out_ag(x1, x2) = succZ_out_ag(x1, x2) 18.38/5.65 18.38/5.65 U34_ag(x1, x2, x3) = U34_ag(x2, x3) 18.38/5.65 18.38/5.65 succ_in_ag(x1, x2) = succ_in_ag(x2) 18.38/5.65 18.38/5.65 succ_out_ag(x1, x2) = succ_out_ag(x1, x2) 18.38/5.65 18.38/5.65 U31_ag(x1, x2) = U31_ag(x1, x2) 18.38/5.65 18.38/5.65 U32_ag(x1, x2, x3) = U32_ag(x2, x3) 18.38/5.65 18.38/5.65 U15_aag(x1, x2, x3) = U15_aag(x2, x3) 18.38/5.65 18.38/5.65 U16_aag(x1, x2, x3, x4) = U16_aag(x3, x4) 18.38/5.65 18.38/5.65 addC_in_aag(x1, x2, x3) = addC_in_aag(x3) 18.38/5.65 18.38/5.65 U23_aag(x1, x2, x3, x4) = U23_aag(x3, x4) 18.38/5.65 18.38/5.65 addz_out_aag(x1, x2, x3) = addz_out_aag(x1, x2, x3) 18.38/5.65 18.38/5.65 addC_out_aag(x1, x2, x3) = addC_out_aag(x1, x2, x3) 18.38/5.65 18.38/5.65 U24_aag(x1, x2, x3, x4) = U24_aag(x3, x4) 18.38/5.65 18.38/5.65 addX_in_aag(x1, x2, x3) = addX_in_aag(x3) 18.38/5.65 18.38/5.65 U17_aag(x1, x2) = U17_aag(x1, x2) 18.38/5.65 18.38/5.65 addX_out_aag(x1, x2, x3) = addX_out_aag(x1, x2, x3) 18.38/5.65 18.38/5.65 U18_aag(x1, x2, x3) = U18_aag(x2, x3) 18.38/5.65 18.38/5.65 U19_aag(x1, x2, x3, x4) = U19_aag(x3, x4) 18.38/5.65 18.38/5.65 U25_aag(x1, x2, x3, x4) = U25_aag(x3, x4) 18.38/5.65 18.38/5.65 addY_in_aag(x1, x2, x3) = addY_in_aag(x3) 18.38/5.65 18.38/5.65 U20_aag(x1, x2) = U20_aag(x1, x2) 18.38/5.65 18.38/5.65 addY_out_aag(x1, x2, x3) = addY_out_aag(x1, x2, x3) 18.38/5.65 18.38/5.65 U21_aag(x1, x2, x3) = U21_aag(x2, x3) 18.38/5.65 18.38/5.65 U22_aag(x1, x2, x3, x4) = U22_aag(x3, x4) 18.38/5.65 18.38/5.65 U26_aag(x1, x2, x3, x4) = U26_aag(x3, x4) 18.38/5.65 18.38/5.65 TIMES_IN_AAG(x1, x2, x3) = TIMES_IN_AAG(x3) 18.38/5.65 18.38/5.65 18.38/5.65 We have to consider all (P,R,Pi)-chains 18.38/5.65 ---------------------------------------- 18.38/5.65 18.38/5.65 (47) UsableRulesProof (EQUIVALENT) 18.38/5.65 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 18.38/5.65 ---------------------------------------- 18.38/5.65 18.38/5.65 (48) 18.38/5.65 Obligation: 18.38/5.65 Pi DP problem: 18.38/5.65 The TRS P consists of the following rules: 18.38/5.65 18.38/5.65 TIMES_IN_AAG(zero(R), S, zero(RS)) -> TIMES_IN_AAG(R, S, RS) 18.38/5.65 18.38/5.65 R is empty. 18.38/5.65 The argument filtering Pi contains the following mapping: 18.38/5.65 zero(x1) = zero(x1) 18.38/5.65 18.38/5.65 TIMES_IN_AAG(x1, x2, x3) = TIMES_IN_AAG(x3) 18.38/5.65 18.38/5.65 18.38/5.65 We have to consider all (P,R,Pi)-chains 18.38/5.65 ---------------------------------------- 18.38/5.65 18.38/5.65 (49) PrologToPiTRSProof (SOUND) 18.38/5.65 We use the technique of [TOCL09]. With regard to the inferred argument filtering the predicates were used in the following modes: 18.38/5.65 18.38/5.65 times_in_3: (f,f,b) (f,f,f) 18.38/5.65 18.38/5.65 add_in_3: (f,f,f) (f,f,b) 18.38/5.65 18.38/5.65 binaryZ_in_1: (f) (b) 18.38/5.65 18.38/5.65 binary_in_1: (f) (b) 18.38/5.65 18.38/5.65 addz_in_3: (f,f,f) (f,f,b) 18.38/5.65 18.38/5.65 addx_in_3: (f,f,f) (f,f,b) 18.38/5.65 18.38/5.65 addy_in_3: (f,f,f) (f,f,b) 18.38/5.65 18.38/5.65 addc_in_3: (f,f,f) (f,f,b) 18.38/5.65 18.38/5.65 succZ_in_2: (f,f) (f,b) 18.38/5.65 18.38/5.65 succ_in_2: (f,f) (f,b) 18.38/5.65 18.38/5.65 addC_in_3: (f,f,f) (f,f,b) 18.38/5.65 18.38/5.65 addX_in_3: (f,f,f) (f,f,b) 18.38/5.65 18.38/5.65 addY_in_3: (f,f,f) (f,f,b) 18.38/5.65 18.38/5.65 Transforming Prolog into the following Term Rewriting System: 18.38/5.65 18.38/5.65 Pi-finite rewrite system: 18.38/5.65 The TRS R consists of the following rules: 18.38/5.65 18.38/5.65 times_in_aag(one(b), X, X) -> times_out_aag(one(b), X, X) 18.38/5.65 times_in_aag(zero(R), S, zero(RS)) -> U35_aag(R, S, RS, times_in_aag(R, S, RS)) 18.38/5.65 times_in_aag(one(R), S, RSS) -> U36_aag(R, S, RSS, times_in_aaa(R, S, RS)) 18.38/5.65 times_in_aaa(one(b), X, X) -> times_out_aaa(one(b), X, X) 18.38/5.65 times_in_aaa(zero(R), S, zero(RS)) -> U35_aaa(R, S, RS, times_in_aaa(R, S, RS)) 18.38/5.65 times_in_aaa(one(R), S, RSS) -> U36_aaa(R, S, RSS, times_in_aaa(R, S, RS)) 18.38/5.65 U36_aaa(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aaa(R, S, RSS, add_in_aaa(S, zero(RS), RSS)) 18.38/5.65 add_in_aaa(b, b, b) -> add_out_aaa(b, b, b) 18.38/5.65 add_in_aaa(X, b, X) -> U1_aaa(X, binaryZ_in_a(X)) 18.38/5.65 binaryZ_in_a(zero(X)) -> U29_a(X, binaryZ_in_a(X)) 18.38/5.65 binaryZ_in_a(one(X)) -> U30_a(X, binary_in_a(X)) 18.38/5.65 binary_in_a(b) -> binary_out_a(b) 18.38/5.65 binary_in_a(zero(X)) -> U27_a(X, binaryZ_in_a(X)) 18.38/5.65 U27_a(X, binaryZ_out_a(X)) -> binary_out_a(zero(X)) 18.38/5.65 binary_in_a(one(X)) -> U28_a(X, binary_in_a(X)) 18.38/5.65 U28_a(X, binary_out_a(X)) -> binary_out_a(one(X)) 18.38/5.65 U30_a(X, binary_out_a(X)) -> binaryZ_out_a(one(X)) 18.38/5.65 U29_a(X, binaryZ_out_a(X)) -> binaryZ_out_a(zero(X)) 18.38/5.65 U1_aaa(X, binaryZ_out_a(X)) -> add_out_aaa(X, b, X) 18.38/5.65 add_in_aaa(b, Y, Y) -> U2_aaa(Y, binaryZ_in_a(Y)) 18.38/5.65 U2_aaa(Y, binaryZ_out_a(Y)) -> add_out_aaa(b, Y, Y) 18.38/5.65 add_in_aaa(X, Y, Z) -> U3_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.65 addz_in_aaa(zero(X), zero(Y), zero(Z)) -> U10_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.65 addz_in_aaa(zero(X), one(Y), one(Z)) -> U11_aaa(X, Y, Z, addx_in_aaa(X, Y, Z)) 18.38/5.65 addx_in_aaa(one(X), b, one(X)) -> U4_aaa(X, binary_in_a(X)) 18.38/5.65 U4_aaa(X, binary_out_a(X)) -> addx_out_aaa(one(X), b, one(X)) 18.38/5.65 addx_in_aaa(zero(X), b, zero(X)) -> U5_aaa(X, binaryZ_in_a(X)) 18.38/5.65 U5_aaa(X, binaryZ_out_a(X)) -> addx_out_aaa(zero(X), b, zero(X)) 18.38/5.65 addx_in_aaa(X, Y, Z) -> U6_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.65 addz_in_aaa(one(X), zero(Y), one(Z)) -> U12_aaa(X, Y, Z, addy_in_aaa(X, Y, Z)) 18.38/5.65 addy_in_aaa(b, one(Y), one(Y)) -> U7_aaa(Y, binary_in_a(Y)) 18.38/5.65 U7_aaa(Y, binary_out_a(Y)) -> addy_out_aaa(b, one(Y), one(Y)) 18.38/5.65 addy_in_aaa(b, zero(Y), zero(Y)) -> U8_aaa(Y, binaryZ_in_a(Y)) 18.38/5.65 U8_aaa(Y, binaryZ_out_a(Y)) -> addy_out_aaa(b, zero(Y), zero(Y)) 18.38/5.65 addy_in_aaa(X, Y, Z) -> U9_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.65 addz_in_aaa(one(X), one(Y), zero(Z)) -> U13_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.38/5.65 addc_in_aaa(b, b, one(b)) -> addc_out_aaa(b, b, one(b)) 18.38/5.65 addc_in_aaa(X, b, Z) -> U14_aaa(X, Z, succZ_in_aa(X, Z)) 18.38/5.65 succZ_in_aa(zero(X), one(X)) -> U33_aa(X, binaryZ_in_a(X)) 18.38/5.65 U33_aa(X, binaryZ_out_a(X)) -> succZ_out_aa(zero(X), one(X)) 18.38/5.65 succZ_in_aa(one(X), zero(Z)) -> U34_aa(X, Z, succ_in_aa(X, Z)) 18.38/5.65 succ_in_aa(b, one(b)) -> succ_out_aa(b, one(b)) 18.38/5.65 succ_in_aa(zero(X), one(X)) -> U31_aa(X, binaryZ_in_a(X)) 18.38/5.65 U31_aa(X, binaryZ_out_a(X)) -> succ_out_aa(zero(X), one(X)) 18.38/5.65 succ_in_aa(one(X), zero(Z)) -> U32_aa(X, Z, succ_in_aa(X, Z)) 18.38/5.65 U32_aa(X, Z, succ_out_aa(X, Z)) -> succ_out_aa(one(X), zero(Z)) 18.38/5.65 U34_aa(X, Z, succ_out_aa(X, Z)) -> succZ_out_aa(one(X), zero(Z)) 18.38/5.65 U14_aaa(X, Z, succZ_out_aa(X, Z)) -> addc_out_aaa(X, b, Z) 18.38/5.65 addc_in_aaa(b, Y, Z) -> U15_aaa(Y, Z, succZ_in_aa(Y, Z)) 18.38/5.65 U15_aaa(Y, Z, succZ_out_aa(Y, Z)) -> addc_out_aaa(b, Y, Z) 18.38/5.65 addc_in_aaa(X, Y, Z) -> U16_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.65 addC_in_aaa(zero(X), zero(Y), one(Z)) -> U23_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.65 U23_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), zero(Y), one(Z)) 18.38/5.65 addC_in_aaa(zero(X), one(Y), zero(Z)) -> U24_aaa(X, Y, Z, addX_in_aaa(X, Y, Z)) 18.38/5.65 addX_in_aaa(zero(X), b, one(X)) -> U17_aaa(X, binaryZ_in_a(X)) 18.38/5.65 U17_aaa(X, binaryZ_out_a(X)) -> addX_out_aaa(zero(X), b, one(X)) 18.38/5.65 addX_in_aaa(one(X), b, zero(Z)) -> U18_aaa(X, Z, succ_in_aa(X, Z)) 18.38/5.65 U18_aaa(X, Z, succ_out_aa(X, Z)) -> addX_out_aaa(one(X), b, zero(Z)) 18.38/5.65 addX_in_aaa(X, Y, Z) -> U19_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.65 addC_in_aaa(one(X), zero(Y), zero(Z)) -> U25_aaa(X, Y, Z, addY_in_aaa(X, Y, Z)) 18.38/5.65 addY_in_aaa(b, zero(Y), one(Y)) -> U20_aaa(Y, binaryZ_in_a(Y)) 18.38/5.65 U20_aaa(Y, binaryZ_out_a(Y)) -> addY_out_aaa(b, zero(Y), one(Y)) 18.38/5.65 addY_in_aaa(b, one(Y), zero(Z)) -> U21_aaa(Y, Z, succ_in_aa(Y, Z)) 18.38/5.65 U21_aaa(Y, Z, succ_out_aa(Y, Z)) -> addY_out_aaa(b, one(Y), zero(Z)) 18.38/5.65 addY_in_aaa(X, Y, Z) -> U22_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.65 addC_in_aaa(one(X), one(Y), one(Z)) -> U26_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.38/5.65 U26_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), one(Y), one(Z)) 18.38/5.65 U22_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addY_out_aaa(X, Y, Z) 18.38/5.65 U25_aaa(X, Y, Z, addY_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), zero(Y), zero(Z)) 18.38/5.65 U19_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addX_out_aaa(X, Y, Z) 18.38/5.65 U24_aaa(X, Y, Z, addX_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), one(Y), zero(Z)) 18.38/5.65 U16_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addc_out_aaa(X, Y, Z) 18.38/5.65 U13_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), one(Y), zero(Z)) 18.38/5.65 U9_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addy_out_aaa(X, Y, Z) 18.38/5.65 U12_aaa(X, Y, Z, addy_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), zero(Y), one(Z)) 18.38/5.65 U6_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addx_out_aaa(X, Y, Z) 18.38/5.65 U11_aaa(X, Y, Z, addx_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), one(Y), one(Z)) 18.38/5.65 U10_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), zero(Y), zero(Z)) 18.38/5.65 U3_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> add_out_aaa(X, Y, Z) 18.38/5.65 U37_aaa(R, S, RSS, add_out_aaa(S, zero(RS), RSS)) -> times_out_aaa(one(R), S, RSS) 18.38/5.65 U35_aaa(R, S, RS, times_out_aaa(R, S, RS)) -> times_out_aaa(zero(R), S, zero(RS)) 18.38/5.65 U36_aag(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aag(R, S, RSS, add_in_aag(S, zero(RS), RSS)) 18.38/5.65 add_in_aag(b, b, b) -> add_out_aag(b, b, b) 18.38/5.65 add_in_aag(X, b, X) -> U1_aag(X, binaryZ_in_g(X)) 18.38/5.65 binaryZ_in_g(zero(X)) -> U29_g(X, binaryZ_in_g(X)) 18.38/5.65 binaryZ_in_g(one(X)) -> U30_g(X, binary_in_g(X)) 18.38/5.65 binary_in_g(b) -> binary_out_g(b) 18.38/5.65 binary_in_g(zero(X)) -> U27_g(X, binaryZ_in_g(X)) 18.38/5.65 U27_g(X, binaryZ_out_g(X)) -> binary_out_g(zero(X)) 18.38/5.65 binary_in_g(one(X)) -> U28_g(X, binary_in_g(X)) 18.38/5.65 U28_g(X, binary_out_g(X)) -> binary_out_g(one(X)) 18.38/5.65 U30_g(X, binary_out_g(X)) -> binaryZ_out_g(one(X)) 18.38/5.65 U29_g(X, binaryZ_out_g(X)) -> binaryZ_out_g(zero(X)) 18.38/5.65 U1_aag(X, binaryZ_out_g(X)) -> add_out_aag(X, b, X) 18.38/5.65 add_in_aag(b, Y, Y) -> U2_aag(Y, binaryZ_in_g(Y)) 18.38/5.65 U2_aag(Y, binaryZ_out_g(Y)) -> add_out_aag(b, Y, Y) 18.38/5.65 add_in_aag(X, Y, Z) -> U3_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.65 addz_in_aag(zero(X), zero(Y), zero(Z)) -> U10_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.65 addz_in_aag(zero(X), one(Y), one(Z)) -> U11_aag(X, Y, Z, addx_in_aag(X, Y, Z)) 18.38/5.65 addx_in_aag(one(X), b, one(X)) -> U4_aag(X, binary_in_g(X)) 18.38/5.65 U4_aag(X, binary_out_g(X)) -> addx_out_aag(one(X), b, one(X)) 18.38/5.65 addx_in_aag(zero(X), b, zero(X)) -> U5_aag(X, binaryZ_in_g(X)) 18.38/5.65 U5_aag(X, binaryZ_out_g(X)) -> addx_out_aag(zero(X), b, zero(X)) 18.38/5.65 addx_in_aag(X, Y, Z) -> U6_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.65 addz_in_aag(one(X), zero(Y), one(Z)) -> U12_aag(X, Y, Z, addy_in_aag(X, Y, Z)) 18.38/5.65 addy_in_aag(b, one(Y), one(Y)) -> U7_aag(Y, binary_in_g(Y)) 18.38/5.65 U7_aag(Y, binary_out_g(Y)) -> addy_out_aag(b, one(Y), one(Y)) 18.38/5.65 addy_in_aag(b, zero(Y), zero(Y)) -> U8_aag(Y, binaryZ_in_g(Y)) 18.38/5.65 U8_aag(Y, binaryZ_out_g(Y)) -> addy_out_aag(b, zero(Y), zero(Y)) 18.38/5.65 addy_in_aag(X, Y, Z) -> U9_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.65 addz_in_aag(one(X), one(Y), zero(Z)) -> U13_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.38/5.65 addc_in_aag(b, b, one(b)) -> addc_out_aag(b, b, one(b)) 18.38/5.65 addc_in_aag(X, b, Z) -> U14_aag(X, Z, succZ_in_ag(X, Z)) 18.38/5.65 succZ_in_ag(zero(X), one(X)) -> U33_ag(X, binaryZ_in_g(X)) 18.38/5.65 U33_ag(X, binaryZ_out_g(X)) -> succZ_out_ag(zero(X), one(X)) 18.38/5.65 succZ_in_ag(one(X), zero(Z)) -> U34_ag(X, Z, succ_in_ag(X, Z)) 18.38/5.65 succ_in_ag(b, one(b)) -> succ_out_ag(b, one(b)) 18.38/5.65 succ_in_ag(zero(X), one(X)) -> U31_ag(X, binaryZ_in_g(X)) 18.38/5.65 U31_ag(X, binaryZ_out_g(X)) -> succ_out_ag(zero(X), one(X)) 18.38/5.65 succ_in_ag(one(X), zero(Z)) -> U32_ag(X, Z, succ_in_ag(X, Z)) 18.38/5.65 U32_ag(X, Z, succ_out_ag(X, Z)) -> succ_out_ag(one(X), zero(Z)) 18.38/5.65 U34_ag(X, Z, succ_out_ag(X, Z)) -> succZ_out_ag(one(X), zero(Z)) 18.38/5.65 U14_aag(X, Z, succZ_out_ag(X, Z)) -> addc_out_aag(X, b, Z) 18.38/5.65 addc_in_aag(b, Y, Z) -> U15_aag(Y, Z, succZ_in_ag(Y, Z)) 18.38/5.65 U15_aag(Y, Z, succZ_out_ag(Y, Z)) -> addc_out_aag(b, Y, Z) 18.38/5.65 addc_in_aag(X, Y, Z) -> U16_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.65 addC_in_aag(zero(X), zero(Y), one(Z)) -> U23_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.65 U23_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), zero(Y), one(Z)) 18.38/5.65 addC_in_aag(zero(X), one(Y), zero(Z)) -> U24_aag(X, Y, Z, addX_in_aag(X, Y, Z)) 18.38/5.65 addX_in_aag(zero(X), b, one(X)) -> U17_aag(X, binaryZ_in_g(X)) 18.38/5.65 U17_aag(X, binaryZ_out_g(X)) -> addX_out_aag(zero(X), b, one(X)) 18.38/5.65 addX_in_aag(one(X), b, zero(Z)) -> U18_aag(X, Z, succ_in_ag(X, Z)) 18.38/5.65 U18_aag(X, Z, succ_out_ag(X, Z)) -> addX_out_aag(one(X), b, zero(Z)) 18.38/5.65 addX_in_aag(X, Y, Z) -> U19_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.65 addC_in_aag(one(X), zero(Y), zero(Z)) -> U25_aag(X, Y, Z, addY_in_aag(X, Y, Z)) 18.38/5.65 addY_in_aag(b, zero(Y), one(Y)) -> U20_aag(Y, binaryZ_in_g(Y)) 18.38/5.65 U20_aag(Y, binaryZ_out_g(Y)) -> addY_out_aag(b, zero(Y), one(Y)) 18.38/5.65 addY_in_aag(b, one(Y), zero(Z)) -> U21_aag(Y, Z, succ_in_ag(Y, Z)) 18.38/5.65 U21_aag(Y, Z, succ_out_ag(Y, Z)) -> addY_out_aag(b, one(Y), zero(Z)) 18.38/5.65 addY_in_aag(X, Y, Z) -> U22_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.65 addC_in_aag(one(X), one(Y), one(Z)) -> U26_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.38/5.65 U26_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addC_out_aag(one(X), one(Y), one(Z)) 18.38/5.65 U22_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addY_out_aag(X, Y, Z) 18.38/5.65 U25_aag(X, Y, Z, addY_out_aag(X, Y, Z)) -> addC_out_aag(one(X), zero(Y), zero(Z)) 18.38/5.65 U19_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addX_out_aag(X, Y, Z) 18.38/5.65 U24_aag(X, Y, Z, addX_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), one(Y), zero(Z)) 18.38/5.65 U16_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addc_out_aag(X, Y, Z) 18.38/5.65 U13_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addz_out_aag(one(X), one(Y), zero(Z)) 18.38/5.65 U9_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addy_out_aag(X, Y, Z) 18.38/5.65 U12_aag(X, Y, Z, addy_out_aag(X, Y, Z)) -> addz_out_aag(one(X), zero(Y), one(Z)) 18.38/5.65 U6_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addx_out_aag(X, Y, Z) 18.38/5.65 U11_aag(X, Y, Z, addx_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), one(Y), one(Z)) 18.38/5.65 U10_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), zero(Y), zero(Z)) 18.38/5.65 U3_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> add_out_aag(X, Y, Z) 18.38/5.65 U37_aag(R, S, RSS, add_out_aag(S, zero(RS), RSS)) -> times_out_aag(one(R), S, RSS) 18.38/5.65 U35_aag(R, S, RS, times_out_aag(R, S, RS)) -> times_out_aag(zero(R), S, zero(RS)) 18.38/5.65 18.38/5.65 The argument filtering Pi contains the following mapping: 18.38/5.65 times_in_aag(x1, x2, x3) = times_in_aag(x3) 18.38/5.65 18.38/5.65 times_out_aag(x1, x2, x3) = times_out_aag(x1, x2) 18.38/5.65 18.38/5.65 zero(x1) = zero(x1) 18.38/5.65 18.38/5.65 U35_aag(x1, x2, x3, x4) = U35_aag(x4) 18.38/5.65 18.38/5.65 U36_aag(x1, x2, x3, x4) = U36_aag(x3, x4) 18.38/5.65 18.38/5.65 times_in_aaa(x1, x2, x3) = times_in_aaa 18.38/5.65 18.38/5.65 times_out_aaa(x1, x2, x3) = times_out_aaa(x1) 18.38/5.65 18.38/5.65 U35_aaa(x1, x2, x3, x4) = U35_aaa(x4) 18.38/5.65 18.38/5.65 U36_aaa(x1, x2, x3, x4) = U36_aaa(x4) 18.38/5.65 18.38/5.65 U37_aaa(x1, x2, x3, x4) = U37_aaa(x1, x4) 18.38/5.65 18.38/5.65 add_in_aaa(x1, x2, x3) = add_in_aaa 18.38/5.65 18.38/5.65 add_out_aaa(x1, x2, x3) = add_out_aaa(x1, x2, x3) 18.38/5.65 18.38/5.65 U1_aaa(x1, x2) = U1_aaa(x2) 18.38/5.65 18.38/5.65 binaryZ_in_a(x1) = binaryZ_in_a 18.38/5.65 18.38/5.65 U29_a(x1, x2) = U29_a(x2) 18.38/5.65 18.38/5.65 U30_a(x1, x2) = U30_a(x2) 18.38/5.65 18.38/5.65 binary_in_a(x1) = binary_in_a 18.38/5.65 18.38/5.65 binary_out_a(x1) = binary_out_a(x1) 18.38/5.65 18.38/5.65 U27_a(x1, x2) = U27_a(x2) 18.38/5.65 18.38/5.65 binaryZ_out_a(x1) = binaryZ_out_a(x1) 18.38/5.65 18.38/5.65 U28_a(x1, x2) = U28_a(x2) 18.38/5.65 18.38/5.65 U2_aaa(x1, x2) = U2_aaa(x2) 18.38/5.65 18.38/5.65 U3_aaa(x1, x2, x3, x4) = U3_aaa(x4) 18.38/5.65 18.38/5.65 addz_in_aaa(x1, x2, x3) = addz_in_aaa 18.38/5.65 18.38/5.65 U10_aaa(x1, x2, x3, x4) = U10_aaa(x4) 18.38/5.65 18.38/5.65 U11_aaa(x1, x2, x3, x4) = U11_aaa(x4) 18.38/5.65 18.38/5.65 addx_in_aaa(x1, x2, x3) = addx_in_aaa 18.38/5.65 18.38/5.65 U4_aaa(x1, x2) = U4_aaa(x2) 18.38/5.65 18.38/5.65 addx_out_aaa(x1, x2, x3) = addx_out_aaa(x1, x2, x3) 18.38/5.65 18.38/5.65 U5_aaa(x1, x2) = U5_aaa(x2) 18.38/5.65 18.38/5.65 U6_aaa(x1, x2, x3, x4) = U6_aaa(x4) 18.38/5.65 18.38/5.65 U12_aaa(x1, x2, x3, x4) = U12_aaa(x4) 18.38/5.65 18.38/5.65 addy_in_aaa(x1, x2, x3) = addy_in_aaa 18.38/5.65 18.38/5.65 U7_aaa(x1, x2) = U7_aaa(x2) 18.38/5.65 18.38/5.65 addy_out_aaa(x1, x2, x3) = addy_out_aaa(x1, x2, x3) 18.38/5.65 18.38/5.65 U8_aaa(x1, x2) = U8_aaa(x2) 18.38/5.65 18.38/5.65 U9_aaa(x1, x2, x3, x4) = U9_aaa(x4) 18.38/5.65 18.38/5.65 U13_aaa(x1, x2, x3, x4) = U13_aaa(x4) 18.38/5.65 18.38/5.65 addc_in_aaa(x1, x2, x3) = addc_in_aaa 18.38/5.65 18.38/5.65 addc_out_aaa(x1, x2, x3) = addc_out_aaa(x1, x2, x3) 18.38/5.65 18.38/5.65 U14_aaa(x1, x2, x3) = U14_aaa(x3) 18.38/5.65 18.38/5.65 succZ_in_aa(x1, x2) = succZ_in_aa 18.38/5.65 18.38/5.65 U33_aa(x1, x2) = U33_aa(x2) 18.38/5.65 18.38/5.65 succZ_out_aa(x1, x2) = succZ_out_aa(x1, x2) 18.38/5.65 18.38/5.65 U34_aa(x1, x2, x3) = U34_aa(x3) 18.38/5.65 18.38/5.65 succ_in_aa(x1, x2) = succ_in_aa 18.38/5.65 18.38/5.65 succ_out_aa(x1, x2) = succ_out_aa(x1, x2) 18.38/5.65 18.38/5.65 U31_aa(x1, x2) = U31_aa(x2) 18.38/5.65 18.38/5.65 U32_aa(x1, x2, x3) = U32_aa(x3) 18.38/5.65 18.38/5.65 U15_aaa(x1, x2, x3) = U15_aaa(x3) 18.38/5.65 18.38/5.65 U16_aaa(x1, x2, x3, x4) = U16_aaa(x4) 18.38/5.65 18.38/5.65 addC_in_aaa(x1, x2, x3) = addC_in_aaa 18.38/5.65 18.38/5.65 U23_aaa(x1, x2, x3, x4) = U23_aaa(x4) 18.38/5.65 18.38/5.65 addz_out_aaa(x1, x2, x3) = addz_out_aaa(x1, x2, x3) 18.38/5.65 18.38/5.65 addC_out_aaa(x1, x2, x3) = addC_out_aaa(x1, x2, x3) 18.38/5.65 18.38/5.65 U24_aaa(x1, x2, x3, x4) = U24_aaa(x4) 18.38/5.65 18.38/5.65 addX_in_aaa(x1, x2, x3) = addX_in_aaa 18.38/5.65 18.38/5.65 U17_aaa(x1, x2) = U17_aaa(x2) 18.38/5.65 18.38/5.65 addX_out_aaa(x1, x2, x3) = addX_out_aaa(x1, x2, x3) 18.38/5.65 18.38/5.65 U18_aaa(x1, x2, x3) = U18_aaa(x3) 18.38/5.65 18.38/5.65 U19_aaa(x1, x2, x3, x4) = U19_aaa(x4) 18.38/5.65 18.38/5.65 U25_aaa(x1, x2, x3, x4) = U25_aaa(x4) 18.38/5.65 18.38/5.65 addY_in_aaa(x1, x2, x3) = addY_in_aaa 18.38/5.65 18.38/5.65 U20_aaa(x1, x2) = U20_aaa(x2) 18.38/5.65 18.38/5.65 addY_out_aaa(x1, x2, x3) = addY_out_aaa(x1, x2, x3) 18.38/5.65 18.38/5.65 U21_aaa(x1, x2, x3) = U21_aaa(x3) 18.38/5.65 18.38/5.65 U22_aaa(x1, x2, x3, x4) = U22_aaa(x4) 18.38/5.65 18.38/5.65 U26_aaa(x1, x2, x3, x4) = U26_aaa(x4) 18.38/5.65 18.38/5.65 U37_aag(x1, x2, x3, x4) = U37_aag(x1, x4) 18.38/5.65 18.38/5.65 add_in_aag(x1, x2, x3) = add_in_aag(x3) 18.38/5.65 18.38/5.65 b = b 18.38/5.65 18.38/5.65 add_out_aag(x1, x2, x3) = add_out_aag(x1, x2) 18.38/5.65 18.38/5.65 U1_aag(x1, x2) = U1_aag(x1, x2) 18.38/5.65 18.38/5.65 binaryZ_in_g(x1) = binaryZ_in_g(x1) 18.38/5.65 18.38/5.65 U29_g(x1, x2) = U29_g(x2) 18.38/5.65 18.38/5.65 one(x1) = one(x1) 18.38/5.65 18.38/5.65 U30_g(x1, x2) = U30_g(x2) 18.38/5.65 18.38/5.65 binary_in_g(x1) = binary_in_g(x1) 18.38/5.65 18.38/5.65 binary_out_g(x1) = binary_out_g 18.38/5.65 18.38/5.65 U27_g(x1, x2) = U27_g(x2) 18.38/5.65 18.38/5.65 binaryZ_out_g(x1) = binaryZ_out_g 18.38/5.65 18.38/5.65 U28_g(x1, x2) = U28_g(x2) 18.38/5.65 18.38/5.65 U2_aag(x1, x2) = U2_aag(x1, x2) 18.38/5.65 18.38/5.65 U3_aag(x1, x2, x3, x4) = U3_aag(x4) 18.38/5.65 18.38/5.65 addz_in_aag(x1, x2, x3) = addz_in_aag(x3) 18.38/5.65 18.38/5.65 U10_aag(x1, x2, x3, x4) = U10_aag(x4) 18.38/5.65 18.38/5.65 U11_aag(x1, x2, x3, x4) = U11_aag(x4) 18.38/5.65 18.38/5.65 addx_in_aag(x1, x2, x3) = addx_in_aag(x3) 18.38/5.65 18.38/5.65 U4_aag(x1, x2) = U4_aag(x1, x2) 18.38/5.65 18.38/5.65 addx_out_aag(x1, x2, x3) = addx_out_aag(x1, x2) 18.38/5.65 18.38/5.65 U5_aag(x1, x2) = U5_aag(x1, x2) 18.38/5.65 18.38/5.65 U6_aag(x1, x2, x3, x4) = U6_aag(x4) 18.38/5.65 18.38/5.65 U12_aag(x1, x2, x3, x4) = U12_aag(x4) 18.38/5.65 18.38/5.65 addy_in_aag(x1, x2, x3) = addy_in_aag(x3) 18.38/5.65 18.38/5.65 U7_aag(x1, x2) = U7_aag(x1, x2) 18.38/5.65 18.38/5.65 addy_out_aag(x1, x2, x3) = addy_out_aag(x1, x2) 18.38/5.65 18.38/5.65 U8_aag(x1, x2) = U8_aag(x1, x2) 18.38/5.65 18.38/5.65 U9_aag(x1, x2, x3, x4) = U9_aag(x4) 18.38/5.65 18.38/5.65 U13_aag(x1, x2, x3, x4) = U13_aag(x4) 18.38/5.65 18.38/5.65 addc_in_aag(x1, x2, x3) = addc_in_aag(x3) 18.38/5.65 18.38/5.65 addc_out_aag(x1, x2, x3) = addc_out_aag(x1, x2) 18.38/5.65 18.38/5.65 U14_aag(x1, x2, x3) = U14_aag(x3) 18.38/5.65 18.38/5.65 succZ_in_ag(x1, x2) = succZ_in_ag(x2) 18.38/5.65 18.38/5.65 U33_ag(x1, x2) = U33_ag(x1, x2) 18.38/5.65 18.38/5.65 succZ_out_ag(x1, x2) = succZ_out_ag(x1) 18.38/5.65 18.38/5.65 U34_ag(x1, x2, x3) = U34_ag(x3) 18.38/5.65 18.38/5.65 succ_in_ag(x1, x2) = succ_in_ag(x2) 18.38/5.65 18.38/5.65 succ_out_ag(x1, x2) = succ_out_ag(x1) 18.38/5.65 18.38/5.65 U31_ag(x1, x2) = U31_ag(x1, x2) 18.38/5.65 18.38/5.65 U32_ag(x1, x2, x3) = U32_ag(x3) 18.38/5.65 18.38/5.65 U15_aag(x1, x2, x3) = U15_aag(x3) 18.38/5.65 18.38/5.65 U16_aag(x1, x2, x3, x4) = U16_aag(x4) 18.38/5.65 18.38/5.65 addC_in_aag(x1, x2, x3) = addC_in_aag(x3) 18.38/5.65 18.38/5.65 U23_aag(x1, x2, x3, x4) = U23_aag(x4) 18.38/5.65 18.38/5.65 addz_out_aag(x1, x2, x3) = addz_out_aag(x1, x2) 18.38/5.65 18.38/5.65 addC_out_aag(x1, x2, x3) = addC_out_aag(x1, x2) 18.38/5.65 18.38/5.65 U24_aag(x1, x2, x3, x4) = U24_aag(x4) 18.38/5.65 18.38/5.65 addX_in_aag(x1, x2, x3) = addX_in_aag(x3) 18.38/5.65 18.38/5.65 U17_aag(x1, x2) = U17_aag(x1, x2) 18.38/5.65 18.38/5.65 addX_out_aag(x1, x2, x3) = addX_out_aag(x1, x2) 18.38/5.65 18.38/5.65 U18_aag(x1, x2, x3) = U18_aag(x3) 18.38/5.65 18.38/5.65 U19_aag(x1, x2, x3, x4) = U19_aag(x4) 18.38/5.65 18.38/5.65 U25_aag(x1, x2, x3, x4) = U25_aag(x4) 18.38/5.65 18.38/5.65 addY_in_aag(x1, x2, x3) = addY_in_aag(x3) 18.38/5.65 18.38/5.65 U20_aag(x1, x2) = U20_aag(x1, x2) 18.38/5.65 18.38/5.65 addY_out_aag(x1, x2, x3) = addY_out_aag(x1, x2) 18.38/5.65 18.38/5.65 U21_aag(x1, x2, x3) = U21_aag(x3) 18.38/5.65 18.38/5.65 U22_aag(x1, x2, x3, x4) = U22_aag(x4) 18.38/5.65 18.38/5.65 U26_aag(x1, x2, x3, x4) = U26_aag(x4) 18.38/5.65 18.38/5.65 18.38/5.65 18.38/5.65 18.38/5.65 18.38/5.65 Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog 18.38/5.65 18.38/5.65 18.38/5.65 18.38/5.65 ---------------------------------------- 18.38/5.65 18.38/5.65 (50) 18.38/5.65 Obligation: 18.38/5.65 Pi-finite rewrite system: 18.38/5.65 The TRS R consists of the following rules: 18.38/5.65 18.38/5.65 times_in_aag(one(b), X, X) -> times_out_aag(one(b), X, X) 18.38/5.65 times_in_aag(zero(R), S, zero(RS)) -> U35_aag(R, S, RS, times_in_aag(R, S, RS)) 18.38/5.65 times_in_aag(one(R), S, RSS) -> U36_aag(R, S, RSS, times_in_aaa(R, S, RS)) 18.38/5.65 times_in_aaa(one(b), X, X) -> times_out_aaa(one(b), X, X) 18.38/5.65 times_in_aaa(zero(R), S, zero(RS)) -> U35_aaa(R, S, RS, times_in_aaa(R, S, RS)) 18.38/5.65 times_in_aaa(one(R), S, RSS) -> U36_aaa(R, S, RSS, times_in_aaa(R, S, RS)) 18.38/5.65 U36_aaa(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aaa(R, S, RSS, add_in_aaa(S, zero(RS), RSS)) 18.38/5.65 add_in_aaa(b, b, b) -> add_out_aaa(b, b, b) 18.38/5.65 add_in_aaa(X, b, X) -> U1_aaa(X, binaryZ_in_a(X)) 18.38/5.65 binaryZ_in_a(zero(X)) -> U29_a(X, binaryZ_in_a(X)) 18.38/5.65 binaryZ_in_a(one(X)) -> U30_a(X, binary_in_a(X)) 18.38/5.65 binary_in_a(b) -> binary_out_a(b) 18.38/5.65 binary_in_a(zero(X)) -> U27_a(X, binaryZ_in_a(X)) 18.38/5.65 U27_a(X, binaryZ_out_a(X)) -> binary_out_a(zero(X)) 18.38/5.65 binary_in_a(one(X)) -> U28_a(X, binary_in_a(X)) 18.38/5.65 U28_a(X, binary_out_a(X)) -> binary_out_a(one(X)) 18.38/5.65 U30_a(X, binary_out_a(X)) -> binaryZ_out_a(one(X)) 18.38/5.65 U29_a(X, binaryZ_out_a(X)) -> binaryZ_out_a(zero(X)) 18.38/5.65 U1_aaa(X, binaryZ_out_a(X)) -> add_out_aaa(X, b, X) 18.38/5.65 add_in_aaa(b, Y, Y) -> U2_aaa(Y, binaryZ_in_a(Y)) 18.38/5.65 U2_aaa(Y, binaryZ_out_a(Y)) -> add_out_aaa(b, Y, Y) 18.38/5.65 add_in_aaa(X, Y, Z) -> U3_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.65 addz_in_aaa(zero(X), zero(Y), zero(Z)) -> U10_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.65 addz_in_aaa(zero(X), one(Y), one(Z)) -> U11_aaa(X, Y, Z, addx_in_aaa(X, Y, Z)) 18.38/5.65 addx_in_aaa(one(X), b, one(X)) -> U4_aaa(X, binary_in_a(X)) 18.38/5.65 U4_aaa(X, binary_out_a(X)) -> addx_out_aaa(one(X), b, one(X)) 18.38/5.65 addx_in_aaa(zero(X), b, zero(X)) -> U5_aaa(X, binaryZ_in_a(X)) 18.38/5.65 U5_aaa(X, binaryZ_out_a(X)) -> addx_out_aaa(zero(X), b, zero(X)) 18.38/5.65 addx_in_aaa(X, Y, Z) -> U6_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.65 addz_in_aaa(one(X), zero(Y), one(Z)) -> U12_aaa(X, Y, Z, addy_in_aaa(X, Y, Z)) 18.38/5.65 addy_in_aaa(b, one(Y), one(Y)) -> U7_aaa(Y, binary_in_a(Y)) 18.38/5.65 U7_aaa(Y, binary_out_a(Y)) -> addy_out_aaa(b, one(Y), one(Y)) 18.38/5.65 addy_in_aaa(b, zero(Y), zero(Y)) -> U8_aaa(Y, binaryZ_in_a(Y)) 18.38/5.65 U8_aaa(Y, binaryZ_out_a(Y)) -> addy_out_aaa(b, zero(Y), zero(Y)) 18.38/5.65 addy_in_aaa(X, Y, Z) -> U9_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.65 addz_in_aaa(one(X), one(Y), zero(Z)) -> U13_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.38/5.65 addc_in_aaa(b, b, one(b)) -> addc_out_aaa(b, b, one(b)) 18.38/5.65 addc_in_aaa(X, b, Z) -> U14_aaa(X, Z, succZ_in_aa(X, Z)) 18.38/5.65 succZ_in_aa(zero(X), one(X)) -> U33_aa(X, binaryZ_in_a(X)) 18.38/5.65 U33_aa(X, binaryZ_out_a(X)) -> succZ_out_aa(zero(X), one(X)) 18.38/5.65 succZ_in_aa(one(X), zero(Z)) -> U34_aa(X, Z, succ_in_aa(X, Z)) 18.38/5.65 succ_in_aa(b, one(b)) -> succ_out_aa(b, one(b)) 18.38/5.65 succ_in_aa(zero(X), one(X)) -> U31_aa(X, binaryZ_in_a(X)) 18.38/5.65 U31_aa(X, binaryZ_out_a(X)) -> succ_out_aa(zero(X), one(X)) 18.38/5.65 succ_in_aa(one(X), zero(Z)) -> U32_aa(X, Z, succ_in_aa(X, Z)) 18.38/5.65 U32_aa(X, Z, succ_out_aa(X, Z)) -> succ_out_aa(one(X), zero(Z)) 18.38/5.65 U34_aa(X, Z, succ_out_aa(X, Z)) -> succZ_out_aa(one(X), zero(Z)) 18.38/5.65 U14_aaa(X, Z, succZ_out_aa(X, Z)) -> addc_out_aaa(X, b, Z) 18.38/5.65 addc_in_aaa(b, Y, Z) -> U15_aaa(Y, Z, succZ_in_aa(Y, Z)) 18.38/5.65 U15_aaa(Y, Z, succZ_out_aa(Y, Z)) -> addc_out_aaa(b, Y, Z) 18.38/5.65 addc_in_aaa(X, Y, Z) -> U16_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.65 addC_in_aaa(zero(X), zero(Y), one(Z)) -> U23_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.65 U23_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), zero(Y), one(Z)) 18.38/5.65 addC_in_aaa(zero(X), one(Y), zero(Z)) -> U24_aaa(X, Y, Z, addX_in_aaa(X, Y, Z)) 18.38/5.65 addX_in_aaa(zero(X), b, one(X)) -> U17_aaa(X, binaryZ_in_a(X)) 18.38/5.65 U17_aaa(X, binaryZ_out_a(X)) -> addX_out_aaa(zero(X), b, one(X)) 18.38/5.65 addX_in_aaa(one(X), b, zero(Z)) -> U18_aaa(X, Z, succ_in_aa(X, Z)) 18.38/5.65 U18_aaa(X, Z, succ_out_aa(X, Z)) -> addX_out_aaa(one(X), b, zero(Z)) 18.38/5.65 addX_in_aaa(X, Y, Z) -> U19_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.65 addC_in_aaa(one(X), zero(Y), zero(Z)) -> U25_aaa(X, Y, Z, addY_in_aaa(X, Y, Z)) 18.38/5.65 addY_in_aaa(b, zero(Y), one(Y)) -> U20_aaa(Y, binaryZ_in_a(Y)) 18.38/5.65 U20_aaa(Y, binaryZ_out_a(Y)) -> addY_out_aaa(b, zero(Y), one(Y)) 18.38/5.65 addY_in_aaa(b, one(Y), zero(Z)) -> U21_aaa(Y, Z, succ_in_aa(Y, Z)) 18.38/5.65 U21_aaa(Y, Z, succ_out_aa(Y, Z)) -> addY_out_aaa(b, one(Y), zero(Z)) 18.38/5.65 addY_in_aaa(X, Y, Z) -> U22_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.65 addC_in_aaa(one(X), one(Y), one(Z)) -> U26_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.38/5.65 U26_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), one(Y), one(Z)) 18.38/5.65 U22_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addY_out_aaa(X, Y, Z) 18.38/5.65 U25_aaa(X, Y, Z, addY_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), zero(Y), zero(Z)) 18.38/5.65 U19_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addX_out_aaa(X, Y, Z) 18.38/5.65 U24_aaa(X, Y, Z, addX_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), one(Y), zero(Z)) 18.38/5.65 U16_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addc_out_aaa(X, Y, Z) 18.38/5.65 U13_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), one(Y), zero(Z)) 18.38/5.65 U9_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addy_out_aaa(X, Y, Z) 18.38/5.65 U12_aaa(X, Y, Z, addy_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), zero(Y), one(Z)) 18.38/5.65 U6_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addx_out_aaa(X, Y, Z) 18.38/5.65 U11_aaa(X, Y, Z, addx_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), one(Y), one(Z)) 18.38/5.65 U10_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), zero(Y), zero(Z)) 18.38/5.65 U3_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> add_out_aaa(X, Y, Z) 18.38/5.65 U37_aaa(R, S, RSS, add_out_aaa(S, zero(RS), RSS)) -> times_out_aaa(one(R), S, RSS) 18.38/5.65 U35_aaa(R, S, RS, times_out_aaa(R, S, RS)) -> times_out_aaa(zero(R), S, zero(RS)) 18.38/5.65 U36_aag(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aag(R, S, RSS, add_in_aag(S, zero(RS), RSS)) 18.38/5.65 add_in_aag(b, b, b) -> add_out_aag(b, b, b) 18.38/5.65 add_in_aag(X, b, X) -> U1_aag(X, binaryZ_in_g(X)) 18.38/5.65 binaryZ_in_g(zero(X)) -> U29_g(X, binaryZ_in_g(X)) 18.38/5.65 binaryZ_in_g(one(X)) -> U30_g(X, binary_in_g(X)) 18.38/5.65 binary_in_g(b) -> binary_out_g(b) 18.38/5.65 binary_in_g(zero(X)) -> U27_g(X, binaryZ_in_g(X)) 18.38/5.65 U27_g(X, binaryZ_out_g(X)) -> binary_out_g(zero(X)) 18.38/5.65 binary_in_g(one(X)) -> U28_g(X, binary_in_g(X)) 18.38/5.65 U28_g(X, binary_out_g(X)) -> binary_out_g(one(X)) 18.38/5.65 U30_g(X, binary_out_g(X)) -> binaryZ_out_g(one(X)) 18.38/5.65 U29_g(X, binaryZ_out_g(X)) -> binaryZ_out_g(zero(X)) 18.38/5.65 U1_aag(X, binaryZ_out_g(X)) -> add_out_aag(X, b, X) 18.38/5.65 add_in_aag(b, Y, Y) -> U2_aag(Y, binaryZ_in_g(Y)) 18.38/5.65 U2_aag(Y, binaryZ_out_g(Y)) -> add_out_aag(b, Y, Y) 18.38/5.65 add_in_aag(X, Y, Z) -> U3_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.65 addz_in_aag(zero(X), zero(Y), zero(Z)) -> U10_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.65 addz_in_aag(zero(X), one(Y), one(Z)) -> U11_aag(X, Y, Z, addx_in_aag(X, Y, Z)) 18.38/5.65 addx_in_aag(one(X), b, one(X)) -> U4_aag(X, binary_in_g(X)) 18.38/5.65 U4_aag(X, binary_out_g(X)) -> addx_out_aag(one(X), b, one(X)) 18.38/5.65 addx_in_aag(zero(X), b, zero(X)) -> U5_aag(X, binaryZ_in_g(X)) 18.38/5.65 U5_aag(X, binaryZ_out_g(X)) -> addx_out_aag(zero(X), b, zero(X)) 18.38/5.65 addx_in_aag(X, Y, Z) -> U6_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.65 addz_in_aag(one(X), zero(Y), one(Z)) -> U12_aag(X, Y, Z, addy_in_aag(X, Y, Z)) 18.38/5.65 addy_in_aag(b, one(Y), one(Y)) -> U7_aag(Y, binary_in_g(Y)) 18.38/5.65 U7_aag(Y, binary_out_g(Y)) -> addy_out_aag(b, one(Y), one(Y)) 18.38/5.65 addy_in_aag(b, zero(Y), zero(Y)) -> U8_aag(Y, binaryZ_in_g(Y)) 18.38/5.65 U8_aag(Y, binaryZ_out_g(Y)) -> addy_out_aag(b, zero(Y), zero(Y)) 18.38/5.65 addy_in_aag(X, Y, Z) -> U9_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.65 addz_in_aag(one(X), one(Y), zero(Z)) -> U13_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.38/5.65 addc_in_aag(b, b, one(b)) -> addc_out_aag(b, b, one(b)) 18.38/5.65 addc_in_aag(X, b, Z) -> U14_aag(X, Z, succZ_in_ag(X, Z)) 18.38/5.65 succZ_in_ag(zero(X), one(X)) -> U33_ag(X, binaryZ_in_g(X)) 18.38/5.65 U33_ag(X, binaryZ_out_g(X)) -> succZ_out_ag(zero(X), one(X)) 18.38/5.65 succZ_in_ag(one(X), zero(Z)) -> U34_ag(X, Z, succ_in_ag(X, Z)) 18.38/5.65 succ_in_ag(b, one(b)) -> succ_out_ag(b, one(b)) 18.38/5.65 succ_in_ag(zero(X), one(X)) -> U31_ag(X, binaryZ_in_g(X)) 18.38/5.65 U31_ag(X, binaryZ_out_g(X)) -> succ_out_ag(zero(X), one(X)) 18.38/5.65 succ_in_ag(one(X), zero(Z)) -> U32_ag(X, Z, succ_in_ag(X, Z)) 18.38/5.65 U32_ag(X, Z, succ_out_ag(X, Z)) -> succ_out_ag(one(X), zero(Z)) 18.38/5.65 U34_ag(X, Z, succ_out_ag(X, Z)) -> succZ_out_ag(one(X), zero(Z)) 18.38/5.65 U14_aag(X, Z, succZ_out_ag(X, Z)) -> addc_out_aag(X, b, Z) 18.38/5.65 addc_in_aag(b, Y, Z) -> U15_aag(Y, Z, succZ_in_ag(Y, Z)) 18.38/5.65 U15_aag(Y, Z, succZ_out_ag(Y, Z)) -> addc_out_aag(b, Y, Z) 18.38/5.65 addc_in_aag(X, Y, Z) -> U16_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.65 addC_in_aag(zero(X), zero(Y), one(Z)) -> U23_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.65 U23_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), zero(Y), one(Z)) 18.38/5.65 addC_in_aag(zero(X), one(Y), zero(Z)) -> U24_aag(X, Y, Z, addX_in_aag(X, Y, Z)) 18.38/5.65 addX_in_aag(zero(X), b, one(X)) -> U17_aag(X, binaryZ_in_g(X)) 18.38/5.65 U17_aag(X, binaryZ_out_g(X)) -> addX_out_aag(zero(X), b, one(X)) 18.38/5.65 addX_in_aag(one(X), b, zero(Z)) -> U18_aag(X, Z, succ_in_ag(X, Z)) 18.38/5.65 U18_aag(X, Z, succ_out_ag(X, Z)) -> addX_out_aag(one(X), b, zero(Z)) 18.38/5.65 addX_in_aag(X, Y, Z) -> U19_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.65 addC_in_aag(one(X), zero(Y), zero(Z)) -> U25_aag(X, Y, Z, addY_in_aag(X, Y, Z)) 18.38/5.65 addY_in_aag(b, zero(Y), one(Y)) -> U20_aag(Y, binaryZ_in_g(Y)) 18.38/5.65 U20_aag(Y, binaryZ_out_g(Y)) -> addY_out_aag(b, zero(Y), one(Y)) 18.38/5.65 addY_in_aag(b, one(Y), zero(Z)) -> U21_aag(Y, Z, succ_in_ag(Y, Z)) 18.38/5.65 U21_aag(Y, Z, succ_out_ag(Y, Z)) -> addY_out_aag(b, one(Y), zero(Z)) 18.38/5.65 addY_in_aag(X, Y, Z) -> U22_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.65 addC_in_aag(one(X), one(Y), one(Z)) -> U26_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.38/5.65 U26_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addC_out_aag(one(X), one(Y), one(Z)) 18.38/5.65 U22_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addY_out_aag(X, Y, Z) 18.38/5.65 U25_aag(X, Y, Z, addY_out_aag(X, Y, Z)) -> addC_out_aag(one(X), zero(Y), zero(Z)) 18.38/5.65 U19_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addX_out_aag(X, Y, Z) 18.38/5.65 U24_aag(X, Y, Z, addX_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), one(Y), zero(Z)) 18.38/5.65 U16_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addc_out_aag(X, Y, Z) 18.38/5.65 U13_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addz_out_aag(one(X), one(Y), zero(Z)) 18.38/5.65 U9_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addy_out_aag(X, Y, Z) 18.38/5.65 U12_aag(X, Y, Z, addy_out_aag(X, Y, Z)) -> addz_out_aag(one(X), zero(Y), one(Z)) 18.38/5.65 U6_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addx_out_aag(X, Y, Z) 18.38/5.65 U11_aag(X, Y, Z, addx_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), one(Y), one(Z)) 18.38/5.65 U10_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), zero(Y), zero(Z)) 18.38/5.65 U3_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> add_out_aag(X, Y, Z) 18.38/5.65 U37_aag(R, S, RSS, add_out_aag(S, zero(RS), RSS)) -> times_out_aag(one(R), S, RSS) 18.38/5.65 U35_aag(R, S, RS, times_out_aag(R, S, RS)) -> times_out_aag(zero(R), S, zero(RS)) 18.38/5.65 18.38/5.65 The argument filtering Pi contains the following mapping: 18.38/5.65 times_in_aag(x1, x2, x3) = times_in_aag(x3) 18.38/5.65 18.38/5.65 times_out_aag(x1, x2, x3) = times_out_aag(x1, x2) 18.38/5.65 18.38/5.65 zero(x1) = zero(x1) 18.38/5.65 18.38/5.65 U35_aag(x1, x2, x3, x4) = U35_aag(x4) 18.38/5.65 18.38/5.65 U36_aag(x1, x2, x3, x4) = U36_aag(x3, x4) 18.38/5.65 18.38/5.65 times_in_aaa(x1, x2, x3) = times_in_aaa 18.38/5.65 18.38/5.65 times_out_aaa(x1, x2, x3) = times_out_aaa(x1) 18.38/5.65 18.38/5.65 U35_aaa(x1, x2, x3, x4) = U35_aaa(x4) 18.38/5.65 18.38/5.65 U36_aaa(x1, x2, x3, x4) = U36_aaa(x4) 18.38/5.65 18.38/5.65 U37_aaa(x1, x2, x3, x4) = U37_aaa(x1, x4) 18.38/5.65 18.38/5.65 add_in_aaa(x1, x2, x3) = add_in_aaa 18.38/5.65 18.38/5.65 add_out_aaa(x1, x2, x3) = add_out_aaa(x1, x2, x3) 18.38/5.65 18.38/5.65 U1_aaa(x1, x2) = U1_aaa(x2) 18.38/5.65 18.38/5.65 binaryZ_in_a(x1) = binaryZ_in_a 18.38/5.65 18.38/5.65 U29_a(x1, x2) = U29_a(x2) 18.38/5.65 18.38/5.65 U30_a(x1, x2) = U30_a(x2) 18.38/5.65 18.38/5.65 binary_in_a(x1) = binary_in_a 18.38/5.65 18.38/5.65 binary_out_a(x1) = binary_out_a(x1) 18.38/5.65 18.38/5.65 U27_a(x1, x2) = U27_a(x2) 18.38/5.65 18.38/5.65 binaryZ_out_a(x1) = binaryZ_out_a(x1) 18.38/5.65 18.38/5.65 U28_a(x1, x2) = U28_a(x2) 18.38/5.65 18.38/5.65 U2_aaa(x1, x2) = U2_aaa(x2) 18.38/5.65 18.38/5.65 U3_aaa(x1, x2, x3, x4) = U3_aaa(x4) 18.38/5.65 18.38/5.65 addz_in_aaa(x1, x2, x3) = addz_in_aaa 18.38/5.65 18.38/5.65 U10_aaa(x1, x2, x3, x4) = U10_aaa(x4) 18.38/5.65 18.38/5.65 U11_aaa(x1, x2, x3, x4) = U11_aaa(x4) 18.38/5.65 18.38/5.65 addx_in_aaa(x1, x2, x3) = addx_in_aaa 18.38/5.65 18.38/5.65 U4_aaa(x1, x2) = U4_aaa(x2) 18.38/5.65 18.38/5.65 addx_out_aaa(x1, x2, x3) = addx_out_aaa(x1, x2, x3) 18.38/5.65 18.38/5.65 U5_aaa(x1, x2) = U5_aaa(x2) 18.38/5.65 18.38/5.65 U6_aaa(x1, x2, x3, x4) = U6_aaa(x4) 18.38/5.65 18.38/5.65 U12_aaa(x1, x2, x3, x4) = U12_aaa(x4) 18.38/5.65 18.38/5.65 addy_in_aaa(x1, x2, x3) = addy_in_aaa 18.38/5.65 18.38/5.65 U7_aaa(x1, x2) = U7_aaa(x2) 18.38/5.65 18.38/5.65 addy_out_aaa(x1, x2, x3) = addy_out_aaa(x1, x2, x3) 18.38/5.65 18.38/5.65 U8_aaa(x1, x2) = U8_aaa(x2) 18.38/5.65 18.38/5.65 U9_aaa(x1, x2, x3, x4) = U9_aaa(x4) 18.38/5.65 18.38/5.65 U13_aaa(x1, x2, x3, x4) = U13_aaa(x4) 18.38/5.65 18.38/5.65 addc_in_aaa(x1, x2, x3) = addc_in_aaa 18.38/5.65 18.38/5.65 addc_out_aaa(x1, x2, x3) = addc_out_aaa(x1, x2, x3) 18.38/5.65 18.38/5.65 U14_aaa(x1, x2, x3) = U14_aaa(x3) 18.38/5.65 18.38/5.65 succZ_in_aa(x1, x2) = succZ_in_aa 18.38/5.65 18.38/5.65 U33_aa(x1, x2) = U33_aa(x2) 18.38/5.65 18.38/5.65 succZ_out_aa(x1, x2) = succZ_out_aa(x1, x2) 18.38/5.65 18.38/5.65 U34_aa(x1, x2, x3) = U34_aa(x3) 18.38/5.65 18.38/5.65 succ_in_aa(x1, x2) = succ_in_aa 18.38/5.65 18.38/5.65 succ_out_aa(x1, x2) = succ_out_aa(x1, x2) 18.38/5.65 18.38/5.65 U31_aa(x1, x2) = U31_aa(x2) 18.38/5.65 18.38/5.65 U32_aa(x1, x2, x3) = U32_aa(x3) 18.38/5.65 18.38/5.65 U15_aaa(x1, x2, x3) = U15_aaa(x3) 18.38/5.65 18.38/5.65 U16_aaa(x1, x2, x3, x4) = U16_aaa(x4) 18.38/5.65 18.38/5.65 addC_in_aaa(x1, x2, x3) = addC_in_aaa 18.38/5.65 18.38/5.65 U23_aaa(x1, x2, x3, x4) = U23_aaa(x4) 18.38/5.65 18.38/5.65 addz_out_aaa(x1, x2, x3) = addz_out_aaa(x1, x2, x3) 18.38/5.65 18.38/5.65 addC_out_aaa(x1, x2, x3) = addC_out_aaa(x1, x2, x3) 18.38/5.65 18.38/5.65 U24_aaa(x1, x2, x3, x4) = U24_aaa(x4) 18.38/5.65 18.38/5.65 addX_in_aaa(x1, x2, x3) = addX_in_aaa 18.38/5.65 18.38/5.65 U17_aaa(x1, x2) = U17_aaa(x2) 18.38/5.65 18.38/5.65 addX_out_aaa(x1, x2, x3) = addX_out_aaa(x1, x2, x3) 18.38/5.65 18.38/5.65 U18_aaa(x1, x2, x3) = U18_aaa(x3) 18.38/5.65 18.38/5.65 U19_aaa(x1, x2, x3, x4) = U19_aaa(x4) 18.38/5.65 18.38/5.65 U25_aaa(x1, x2, x3, x4) = U25_aaa(x4) 18.38/5.65 18.38/5.65 addY_in_aaa(x1, x2, x3) = addY_in_aaa 18.38/5.65 18.38/5.65 U20_aaa(x1, x2) = U20_aaa(x2) 18.38/5.65 18.38/5.65 addY_out_aaa(x1, x2, x3) = addY_out_aaa(x1, x2, x3) 18.38/5.65 18.38/5.65 U21_aaa(x1, x2, x3) = U21_aaa(x3) 18.38/5.65 18.38/5.65 U22_aaa(x1, x2, x3, x4) = U22_aaa(x4) 18.38/5.65 18.38/5.65 U26_aaa(x1, x2, x3, x4) = U26_aaa(x4) 18.38/5.65 18.38/5.65 U37_aag(x1, x2, x3, x4) = U37_aag(x1, x4) 18.38/5.65 18.38/5.65 add_in_aag(x1, x2, x3) = add_in_aag(x3) 18.38/5.65 18.38/5.65 b = b 18.38/5.65 18.38/5.65 add_out_aag(x1, x2, x3) = add_out_aag(x1, x2) 18.38/5.65 18.38/5.65 U1_aag(x1, x2) = U1_aag(x1, x2) 18.38/5.65 18.38/5.65 binaryZ_in_g(x1) = binaryZ_in_g(x1) 18.38/5.65 18.38/5.65 U29_g(x1, x2) = U29_g(x2) 18.38/5.65 18.38/5.65 one(x1) = one(x1) 18.38/5.65 18.38/5.65 U30_g(x1, x2) = U30_g(x2) 18.38/5.65 18.38/5.65 binary_in_g(x1) = binary_in_g(x1) 18.38/5.65 18.38/5.65 binary_out_g(x1) = binary_out_g 18.38/5.65 18.38/5.65 U27_g(x1, x2) = U27_g(x2) 18.38/5.65 18.38/5.65 binaryZ_out_g(x1) = binaryZ_out_g 18.38/5.65 18.38/5.65 U28_g(x1, x2) = U28_g(x2) 18.38/5.65 18.38/5.65 U2_aag(x1, x2) = U2_aag(x1, x2) 18.38/5.65 18.38/5.65 U3_aag(x1, x2, x3, x4) = U3_aag(x4) 18.38/5.65 18.38/5.65 addz_in_aag(x1, x2, x3) = addz_in_aag(x3) 18.38/5.65 18.38/5.65 U10_aag(x1, x2, x3, x4) = U10_aag(x4) 18.38/5.65 18.38/5.65 U11_aag(x1, x2, x3, x4) = U11_aag(x4) 18.38/5.65 18.38/5.65 addx_in_aag(x1, x2, x3) = addx_in_aag(x3) 18.38/5.65 18.38/5.65 U4_aag(x1, x2) = U4_aag(x1, x2) 18.38/5.65 18.38/5.65 addx_out_aag(x1, x2, x3) = addx_out_aag(x1, x2) 18.38/5.65 18.38/5.65 U5_aag(x1, x2) = U5_aag(x1, x2) 18.38/5.65 18.38/5.65 U6_aag(x1, x2, x3, x4) = U6_aag(x4) 18.38/5.65 18.38/5.65 U12_aag(x1, x2, x3, x4) = U12_aag(x4) 18.38/5.65 18.38/5.65 addy_in_aag(x1, x2, x3) = addy_in_aag(x3) 18.38/5.65 18.38/5.65 U7_aag(x1, x2) = U7_aag(x1, x2) 18.38/5.65 18.38/5.65 addy_out_aag(x1, x2, x3) = addy_out_aag(x1, x2) 18.38/5.65 18.38/5.65 U8_aag(x1, x2) = U8_aag(x1, x2) 18.38/5.65 18.38/5.65 U9_aag(x1, x2, x3, x4) = U9_aag(x4) 18.38/5.65 18.38/5.65 U13_aag(x1, x2, x3, x4) = U13_aag(x4) 18.38/5.65 18.38/5.65 addc_in_aag(x1, x2, x3) = addc_in_aag(x3) 18.38/5.65 18.38/5.65 addc_out_aag(x1, x2, x3) = addc_out_aag(x1, x2) 18.38/5.65 18.38/5.65 U14_aag(x1, x2, x3) = U14_aag(x3) 18.38/5.65 18.38/5.65 succZ_in_ag(x1, x2) = succZ_in_ag(x2) 18.38/5.65 18.38/5.65 U33_ag(x1, x2) = U33_ag(x1, x2) 18.38/5.65 18.38/5.65 succZ_out_ag(x1, x2) = succZ_out_ag(x1) 18.38/5.65 18.38/5.65 U34_ag(x1, x2, x3) = U34_ag(x3) 18.38/5.65 18.38/5.65 succ_in_ag(x1, x2) = succ_in_ag(x2) 18.38/5.65 18.38/5.65 succ_out_ag(x1, x2) = succ_out_ag(x1) 18.38/5.65 18.38/5.65 U31_ag(x1, x2) = U31_ag(x1, x2) 18.38/5.65 18.38/5.65 U32_ag(x1, x2, x3) = U32_ag(x3) 18.38/5.65 18.38/5.65 U15_aag(x1, x2, x3) = U15_aag(x3) 18.38/5.65 18.38/5.65 U16_aag(x1, x2, x3, x4) = U16_aag(x4) 18.38/5.65 18.38/5.65 addC_in_aag(x1, x2, x3) = addC_in_aag(x3) 18.38/5.65 18.38/5.65 U23_aag(x1, x2, x3, x4) = U23_aag(x4) 18.38/5.65 18.38/5.65 addz_out_aag(x1, x2, x3) = addz_out_aag(x1, x2) 18.38/5.65 18.38/5.65 addC_out_aag(x1, x2, x3) = addC_out_aag(x1, x2) 18.38/5.65 18.38/5.65 U24_aag(x1, x2, x3, x4) = U24_aag(x4) 18.38/5.65 18.38/5.65 addX_in_aag(x1, x2, x3) = addX_in_aag(x3) 18.38/5.65 18.38/5.65 U17_aag(x1, x2) = U17_aag(x1, x2) 18.38/5.65 18.38/5.65 addX_out_aag(x1, x2, x3) = addX_out_aag(x1, x2) 18.38/5.65 18.38/5.65 U18_aag(x1, x2, x3) = U18_aag(x3) 18.38/5.65 18.38/5.65 U19_aag(x1, x2, x3, x4) = U19_aag(x4) 18.38/5.65 18.38/5.65 U25_aag(x1, x2, x3, x4) = U25_aag(x4) 18.38/5.65 18.38/5.65 addY_in_aag(x1, x2, x3) = addY_in_aag(x3) 18.38/5.65 18.38/5.65 U20_aag(x1, x2) = U20_aag(x1, x2) 18.38/5.65 18.38/5.65 addY_out_aag(x1, x2, x3) = addY_out_aag(x1, x2) 18.38/5.65 18.38/5.65 U21_aag(x1, x2, x3) = U21_aag(x3) 18.38/5.65 18.38/5.65 U22_aag(x1, x2, x3, x4) = U22_aag(x4) 18.38/5.65 18.38/5.65 U26_aag(x1, x2, x3, x4) = U26_aag(x4) 18.38/5.65 18.38/5.65 18.38/5.65 18.38/5.65 ---------------------------------------- 18.38/5.65 18.38/5.65 (51) DependencyPairsProof (EQUIVALENT) 18.38/5.65 Using Dependency Pairs [AG00,LOPSTR] we result in the following initial DP problem: 18.38/5.65 Pi DP problem: 18.38/5.65 The TRS P consists of the following rules: 18.38/5.65 18.38/5.65 TIMES_IN_AAG(zero(R), S, zero(RS)) -> U35_AAG(R, S, RS, times_in_aag(R, S, RS)) 18.38/5.65 TIMES_IN_AAG(zero(R), S, zero(RS)) -> TIMES_IN_AAG(R, S, RS) 18.38/5.65 TIMES_IN_AAG(one(R), S, RSS) -> U36_AAG(R, S, RSS, times_in_aaa(R, S, RS)) 18.38/5.65 TIMES_IN_AAG(one(R), S, RSS) -> TIMES_IN_AAA(R, S, RS) 18.38/5.65 TIMES_IN_AAA(zero(R), S, zero(RS)) -> U35_AAA(R, S, RS, times_in_aaa(R, S, RS)) 18.38/5.65 TIMES_IN_AAA(zero(R), S, zero(RS)) -> TIMES_IN_AAA(R, S, RS) 18.38/5.65 TIMES_IN_AAA(one(R), S, RSS) -> U36_AAA(R, S, RSS, times_in_aaa(R, S, RS)) 18.38/5.65 TIMES_IN_AAA(one(R), S, RSS) -> TIMES_IN_AAA(R, S, RS) 18.38/5.65 U36_AAA(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_AAA(R, S, RSS, add_in_aaa(S, zero(RS), RSS)) 18.38/5.65 U36_AAA(R, S, RSS, times_out_aaa(R, S, RS)) -> ADD_IN_AAA(S, zero(RS), RSS) 18.38/5.65 ADD_IN_AAA(X, b, X) -> U1_AAA(X, binaryZ_in_a(X)) 18.38/5.65 ADD_IN_AAA(X, b, X) -> BINARYZ_IN_A(X) 18.38/5.65 BINARYZ_IN_A(zero(X)) -> U29_A(X, binaryZ_in_a(X)) 18.38/5.65 BINARYZ_IN_A(zero(X)) -> BINARYZ_IN_A(X) 18.38/5.65 BINARYZ_IN_A(one(X)) -> U30_A(X, binary_in_a(X)) 18.38/5.65 BINARYZ_IN_A(one(X)) -> BINARY_IN_A(X) 18.38/5.65 BINARY_IN_A(zero(X)) -> U27_A(X, binaryZ_in_a(X)) 18.38/5.65 BINARY_IN_A(zero(X)) -> BINARYZ_IN_A(X) 18.38/5.65 BINARY_IN_A(one(X)) -> U28_A(X, binary_in_a(X)) 18.38/5.65 BINARY_IN_A(one(X)) -> BINARY_IN_A(X) 18.38/5.65 ADD_IN_AAA(b, Y, Y) -> U2_AAA(Y, binaryZ_in_a(Y)) 18.38/5.65 ADD_IN_AAA(b, Y, Y) -> BINARYZ_IN_A(Y) 18.38/5.65 ADD_IN_AAA(X, Y, Z) -> U3_AAA(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.65 ADD_IN_AAA(X, Y, Z) -> ADDZ_IN_AAA(X, Y, Z) 18.38/5.65 ADDZ_IN_AAA(zero(X), zero(Y), zero(Z)) -> U10_AAA(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.65 ADDZ_IN_AAA(zero(X), zero(Y), zero(Z)) -> ADDZ_IN_AAA(X, Y, Z) 18.38/5.65 ADDZ_IN_AAA(zero(X), one(Y), one(Z)) -> U11_AAA(X, Y, Z, addx_in_aaa(X, Y, Z)) 18.38/5.65 ADDZ_IN_AAA(zero(X), one(Y), one(Z)) -> ADDX_IN_AAA(X, Y, Z) 18.38/5.65 ADDX_IN_AAA(one(X), b, one(X)) -> U4_AAA(X, binary_in_a(X)) 18.38/5.65 ADDX_IN_AAA(one(X), b, one(X)) -> BINARY_IN_A(X) 18.38/5.65 ADDX_IN_AAA(zero(X), b, zero(X)) -> U5_AAA(X, binaryZ_in_a(X)) 18.38/5.65 ADDX_IN_AAA(zero(X), b, zero(X)) -> BINARYZ_IN_A(X) 18.38/5.65 ADDX_IN_AAA(X, Y, Z) -> U6_AAA(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.65 ADDX_IN_AAA(X, Y, Z) -> ADDZ_IN_AAA(X, Y, Z) 18.38/5.65 ADDZ_IN_AAA(one(X), zero(Y), one(Z)) -> U12_AAA(X, Y, Z, addy_in_aaa(X, Y, Z)) 18.38/5.65 ADDZ_IN_AAA(one(X), zero(Y), one(Z)) -> ADDY_IN_AAA(X, Y, Z) 18.38/5.65 ADDY_IN_AAA(b, one(Y), one(Y)) -> U7_AAA(Y, binary_in_a(Y)) 18.38/5.65 ADDY_IN_AAA(b, one(Y), one(Y)) -> BINARY_IN_A(Y) 18.38/5.65 ADDY_IN_AAA(b, zero(Y), zero(Y)) -> U8_AAA(Y, binaryZ_in_a(Y)) 18.38/5.65 ADDY_IN_AAA(b, zero(Y), zero(Y)) -> BINARYZ_IN_A(Y) 18.38/5.65 ADDY_IN_AAA(X, Y, Z) -> U9_AAA(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.65 ADDY_IN_AAA(X, Y, Z) -> ADDZ_IN_AAA(X, Y, Z) 18.38/5.65 ADDZ_IN_AAA(one(X), one(Y), zero(Z)) -> U13_AAA(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.38/5.65 ADDZ_IN_AAA(one(X), one(Y), zero(Z)) -> ADDC_IN_AAA(X, Y, Z) 18.38/5.65 ADDC_IN_AAA(X, b, Z) -> U14_AAA(X, Z, succZ_in_aa(X, Z)) 18.38/5.65 ADDC_IN_AAA(X, b, Z) -> SUCCZ_IN_AA(X, Z) 18.38/5.65 SUCCZ_IN_AA(zero(X), one(X)) -> U33_AA(X, binaryZ_in_a(X)) 18.38/5.65 SUCCZ_IN_AA(zero(X), one(X)) -> BINARYZ_IN_A(X) 18.38/5.65 SUCCZ_IN_AA(one(X), zero(Z)) -> U34_AA(X, Z, succ_in_aa(X, Z)) 18.38/5.65 SUCCZ_IN_AA(one(X), zero(Z)) -> SUCC_IN_AA(X, Z) 18.38/5.65 SUCC_IN_AA(zero(X), one(X)) -> U31_AA(X, binaryZ_in_a(X)) 18.38/5.65 SUCC_IN_AA(zero(X), one(X)) -> BINARYZ_IN_A(X) 18.38/5.65 SUCC_IN_AA(one(X), zero(Z)) -> U32_AA(X, Z, succ_in_aa(X, Z)) 18.38/5.65 SUCC_IN_AA(one(X), zero(Z)) -> SUCC_IN_AA(X, Z) 18.38/5.65 ADDC_IN_AAA(b, Y, Z) -> U15_AAA(Y, Z, succZ_in_aa(Y, Z)) 18.38/5.65 ADDC_IN_AAA(b, Y, Z) -> SUCCZ_IN_AA(Y, Z) 18.38/5.65 ADDC_IN_AAA(X, Y, Z) -> U16_AAA(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.65 ADDC_IN_AAA(X, Y, Z) -> ADDC_IN_AAA^1(X, Y, Z) 18.38/5.65 ADDC_IN_AAA^1(zero(X), zero(Y), one(Z)) -> U23_AAA(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.65 ADDC_IN_AAA^1(zero(X), zero(Y), one(Z)) -> ADDZ_IN_AAA(X, Y, Z) 18.38/5.65 ADDC_IN_AAA^1(zero(X), one(Y), zero(Z)) -> U24_AAA(X, Y, Z, addX_in_aaa(X, Y, Z)) 18.38/5.65 ADDC_IN_AAA^1(zero(X), one(Y), zero(Z)) -> ADDX_IN_AAA^1(X, Y, Z) 18.38/5.65 ADDX_IN_AAA^1(zero(X), b, one(X)) -> U17_AAA(X, binaryZ_in_a(X)) 18.38/5.65 ADDX_IN_AAA^1(zero(X), b, one(X)) -> BINARYZ_IN_A(X) 18.38/5.65 ADDX_IN_AAA^1(one(X), b, zero(Z)) -> U18_AAA(X, Z, succ_in_aa(X, Z)) 18.38/5.65 ADDX_IN_AAA^1(one(X), b, zero(Z)) -> SUCC_IN_AA(X, Z) 18.38/5.65 ADDX_IN_AAA^1(X, Y, Z) -> U19_AAA(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.65 ADDX_IN_AAA^1(X, Y, Z) -> ADDC_IN_AAA^1(X, Y, Z) 18.38/5.65 ADDC_IN_AAA^1(one(X), zero(Y), zero(Z)) -> U25_AAA(X, Y, Z, addY_in_aaa(X, Y, Z)) 18.38/5.65 ADDC_IN_AAA^1(one(X), zero(Y), zero(Z)) -> ADDY_IN_AAA^1(X, Y, Z) 18.38/5.65 ADDY_IN_AAA^1(b, zero(Y), one(Y)) -> U20_AAA(Y, binaryZ_in_a(Y)) 18.38/5.65 ADDY_IN_AAA^1(b, zero(Y), one(Y)) -> BINARYZ_IN_A(Y) 18.38/5.65 ADDY_IN_AAA^1(b, one(Y), zero(Z)) -> U21_AAA(Y, Z, succ_in_aa(Y, Z)) 18.38/5.65 ADDY_IN_AAA^1(b, one(Y), zero(Z)) -> SUCC_IN_AA(Y, Z) 18.38/5.65 ADDY_IN_AAA^1(X, Y, Z) -> U22_AAA(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.65 ADDY_IN_AAA^1(X, Y, Z) -> ADDC_IN_AAA^1(X, Y, Z) 18.38/5.65 ADDC_IN_AAA^1(one(X), one(Y), one(Z)) -> U26_AAA(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.38/5.65 ADDC_IN_AAA^1(one(X), one(Y), one(Z)) -> ADDC_IN_AAA(X, Y, Z) 18.38/5.65 U36_AAG(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_AAG(R, S, RSS, add_in_aag(S, zero(RS), RSS)) 18.38/5.65 U36_AAG(R, S, RSS, times_out_aaa(R, S, RS)) -> ADD_IN_AAG(S, zero(RS), RSS) 18.38/5.65 ADD_IN_AAG(X, b, X) -> U1_AAG(X, binaryZ_in_g(X)) 18.38/5.65 ADD_IN_AAG(X, b, X) -> BINARYZ_IN_G(X) 18.38/5.65 BINARYZ_IN_G(zero(X)) -> U29_G(X, binaryZ_in_g(X)) 18.38/5.65 BINARYZ_IN_G(zero(X)) -> BINARYZ_IN_G(X) 18.38/5.65 BINARYZ_IN_G(one(X)) -> U30_G(X, binary_in_g(X)) 18.38/5.65 BINARYZ_IN_G(one(X)) -> BINARY_IN_G(X) 18.38/5.65 BINARY_IN_G(zero(X)) -> U27_G(X, binaryZ_in_g(X)) 18.38/5.65 BINARY_IN_G(zero(X)) -> BINARYZ_IN_G(X) 18.38/5.65 BINARY_IN_G(one(X)) -> U28_G(X, binary_in_g(X)) 18.38/5.65 BINARY_IN_G(one(X)) -> BINARY_IN_G(X) 18.38/5.65 ADD_IN_AAG(b, Y, Y) -> U2_AAG(Y, binaryZ_in_g(Y)) 18.38/5.65 ADD_IN_AAG(b, Y, Y) -> BINARYZ_IN_G(Y) 18.38/5.65 ADD_IN_AAG(X, Y, Z) -> U3_AAG(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.65 ADD_IN_AAG(X, Y, Z) -> ADDZ_IN_AAG(X, Y, Z) 18.38/5.65 ADDZ_IN_AAG(zero(X), zero(Y), zero(Z)) -> U10_AAG(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.65 ADDZ_IN_AAG(zero(X), zero(Y), zero(Z)) -> ADDZ_IN_AAG(X, Y, Z) 18.38/5.65 ADDZ_IN_AAG(zero(X), one(Y), one(Z)) -> U11_AAG(X, Y, Z, addx_in_aag(X, Y, Z)) 18.38/5.65 ADDZ_IN_AAG(zero(X), one(Y), one(Z)) -> ADDX_IN_AAG(X, Y, Z) 18.38/5.65 ADDX_IN_AAG(one(X), b, one(X)) -> U4_AAG(X, binary_in_g(X)) 18.38/5.65 ADDX_IN_AAG(one(X), b, one(X)) -> BINARY_IN_G(X) 18.38/5.65 ADDX_IN_AAG(zero(X), b, zero(X)) -> U5_AAG(X, binaryZ_in_g(X)) 18.38/5.65 ADDX_IN_AAG(zero(X), b, zero(X)) -> BINARYZ_IN_G(X) 18.38/5.65 ADDX_IN_AAG(X, Y, Z) -> U6_AAG(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.65 ADDX_IN_AAG(X, Y, Z) -> ADDZ_IN_AAG(X, Y, Z) 18.38/5.65 ADDZ_IN_AAG(one(X), zero(Y), one(Z)) -> U12_AAG(X, Y, Z, addy_in_aag(X, Y, Z)) 18.38/5.65 ADDZ_IN_AAG(one(X), zero(Y), one(Z)) -> ADDY_IN_AAG(X, Y, Z) 18.38/5.65 ADDY_IN_AAG(b, one(Y), one(Y)) -> U7_AAG(Y, binary_in_g(Y)) 18.38/5.65 ADDY_IN_AAG(b, one(Y), one(Y)) -> BINARY_IN_G(Y) 18.38/5.65 ADDY_IN_AAG(b, zero(Y), zero(Y)) -> U8_AAG(Y, binaryZ_in_g(Y)) 18.38/5.65 ADDY_IN_AAG(b, zero(Y), zero(Y)) -> BINARYZ_IN_G(Y) 18.38/5.65 ADDY_IN_AAG(X, Y, Z) -> U9_AAG(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.65 ADDY_IN_AAG(X, Y, Z) -> ADDZ_IN_AAG(X, Y, Z) 18.38/5.65 ADDZ_IN_AAG(one(X), one(Y), zero(Z)) -> U13_AAG(X, Y, Z, addc_in_aag(X, Y, Z)) 18.38/5.65 ADDZ_IN_AAG(one(X), one(Y), zero(Z)) -> ADDC_IN_AAG(X, Y, Z) 18.38/5.65 ADDC_IN_AAG(X, b, Z) -> U14_AAG(X, Z, succZ_in_ag(X, Z)) 18.38/5.65 ADDC_IN_AAG(X, b, Z) -> SUCCZ_IN_AG(X, Z) 18.38/5.65 SUCCZ_IN_AG(zero(X), one(X)) -> U33_AG(X, binaryZ_in_g(X)) 18.38/5.65 SUCCZ_IN_AG(zero(X), one(X)) -> BINARYZ_IN_G(X) 18.38/5.65 SUCCZ_IN_AG(one(X), zero(Z)) -> U34_AG(X, Z, succ_in_ag(X, Z)) 18.38/5.65 SUCCZ_IN_AG(one(X), zero(Z)) -> SUCC_IN_AG(X, Z) 18.38/5.65 SUCC_IN_AG(zero(X), one(X)) -> U31_AG(X, binaryZ_in_g(X)) 18.38/5.65 SUCC_IN_AG(zero(X), one(X)) -> BINARYZ_IN_G(X) 18.38/5.65 SUCC_IN_AG(one(X), zero(Z)) -> U32_AG(X, Z, succ_in_ag(X, Z)) 18.38/5.65 SUCC_IN_AG(one(X), zero(Z)) -> SUCC_IN_AG(X, Z) 18.38/5.65 ADDC_IN_AAG(b, Y, Z) -> U15_AAG(Y, Z, succZ_in_ag(Y, Z)) 18.38/5.65 ADDC_IN_AAG(b, Y, Z) -> SUCCZ_IN_AG(Y, Z) 18.38/5.65 ADDC_IN_AAG(X, Y, Z) -> U16_AAG(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.65 ADDC_IN_AAG(X, Y, Z) -> ADDC_IN_AAG^1(X, Y, Z) 18.38/5.65 ADDC_IN_AAG^1(zero(X), zero(Y), one(Z)) -> U23_AAG(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.65 ADDC_IN_AAG^1(zero(X), zero(Y), one(Z)) -> ADDZ_IN_AAG(X, Y, Z) 18.38/5.65 ADDC_IN_AAG^1(zero(X), one(Y), zero(Z)) -> U24_AAG(X, Y, Z, addX_in_aag(X, Y, Z)) 18.38/5.65 ADDC_IN_AAG^1(zero(X), one(Y), zero(Z)) -> ADDX_IN_AAG^1(X, Y, Z) 18.38/5.65 ADDX_IN_AAG^1(zero(X), b, one(X)) -> U17_AAG(X, binaryZ_in_g(X)) 18.38/5.65 ADDX_IN_AAG^1(zero(X), b, one(X)) -> BINARYZ_IN_G(X) 18.38/5.65 ADDX_IN_AAG^1(one(X), b, zero(Z)) -> U18_AAG(X, Z, succ_in_ag(X, Z)) 18.38/5.65 ADDX_IN_AAG^1(one(X), b, zero(Z)) -> SUCC_IN_AG(X, Z) 18.38/5.65 ADDX_IN_AAG^1(X, Y, Z) -> U19_AAG(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.65 ADDX_IN_AAG^1(X, Y, Z) -> ADDC_IN_AAG^1(X, Y, Z) 18.38/5.65 ADDC_IN_AAG^1(one(X), zero(Y), zero(Z)) -> U25_AAG(X, Y, Z, addY_in_aag(X, Y, Z)) 18.38/5.65 ADDC_IN_AAG^1(one(X), zero(Y), zero(Z)) -> ADDY_IN_AAG^1(X, Y, Z) 18.38/5.65 ADDY_IN_AAG^1(b, zero(Y), one(Y)) -> U20_AAG(Y, binaryZ_in_g(Y)) 18.38/5.65 ADDY_IN_AAG^1(b, zero(Y), one(Y)) -> BINARYZ_IN_G(Y) 18.38/5.65 ADDY_IN_AAG^1(b, one(Y), zero(Z)) -> U21_AAG(Y, Z, succ_in_ag(Y, Z)) 18.38/5.65 ADDY_IN_AAG^1(b, one(Y), zero(Z)) -> SUCC_IN_AG(Y, Z) 18.38/5.65 ADDY_IN_AAG^1(X, Y, Z) -> U22_AAG(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.65 ADDY_IN_AAG^1(X, Y, Z) -> ADDC_IN_AAG^1(X, Y, Z) 18.38/5.65 ADDC_IN_AAG^1(one(X), one(Y), one(Z)) -> U26_AAG(X, Y, Z, addc_in_aag(X, Y, Z)) 18.38/5.65 ADDC_IN_AAG^1(one(X), one(Y), one(Z)) -> ADDC_IN_AAG(X, Y, Z) 18.38/5.65 18.38/5.65 The TRS R consists of the following rules: 18.38/5.65 18.38/5.65 times_in_aag(one(b), X, X) -> times_out_aag(one(b), X, X) 18.38/5.65 times_in_aag(zero(R), S, zero(RS)) -> U35_aag(R, S, RS, times_in_aag(R, S, RS)) 18.38/5.65 times_in_aag(one(R), S, RSS) -> U36_aag(R, S, RSS, times_in_aaa(R, S, RS)) 18.38/5.65 times_in_aaa(one(b), X, X) -> times_out_aaa(one(b), X, X) 18.38/5.65 times_in_aaa(zero(R), S, zero(RS)) -> U35_aaa(R, S, RS, times_in_aaa(R, S, RS)) 18.38/5.65 times_in_aaa(one(R), S, RSS) -> U36_aaa(R, S, RSS, times_in_aaa(R, S, RS)) 18.38/5.65 U36_aaa(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aaa(R, S, RSS, add_in_aaa(S, zero(RS), RSS)) 18.38/5.65 add_in_aaa(b, b, b) -> add_out_aaa(b, b, b) 18.38/5.65 add_in_aaa(X, b, X) -> U1_aaa(X, binaryZ_in_a(X)) 18.38/5.65 binaryZ_in_a(zero(X)) -> U29_a(X, binaryZ_in_a(X)) 18.38/5.65 binaryZ_in_a(one(X)) -> U30_a(X, binary_in_a(X)) 18.38/5.65 binary_in_a(b) -> binary_out_a(b) 18.38/5.65 binary_in_a(zero(X)) -> U27_a(X, binaryZ_in_a(X)) 18.38/5.65 U27_a(X, binaryZ_out_a(X)) -> binary_out_a(zero(X)) 18.38/5.65 binary_in_a(one(X)) -> U28_a(X, binary_in_a(X)) 18.38/5.65 U28_a(X, binary_out_a(X)) -> binary_out_a(one(X)) 18.38/5.65 U30_a(X, binary_out_a(X)) -> binaryZ_out_a(one(X)) 18.38/5.65 U29_a(X, binaryZ_out_a(X)) -> binaryZ_out_a(zero(X)) 18.38/5.65 U1_aaa(X, binaryZ_out_a(X)) -> add_out_aaa(X, b, X) 18.38/5.65 add_in_aaa(b, Y, Y) -> U2_aaa(Y, binaryZ_in_a(Y)) 18.38/5.65 U2_aaa(Y, binaryZ_out_a(Y)) -> add_out_aaa(b, Y, Y) 18.38/5.65 add_in_aaa(X, Y, Z) -> U3_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.65 addz_in_aaa(zero(X), zero(Y), zero(Z)) -> U10_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.65 addz_in_aaa(zero(X), one(Y), one(Z)) -> U11_aaa(X, Y, Z, addx_in_aaa(X, Y, Z)) 18.38/5.65 addx_in_aaa(one(X), b, one(X)) -> U4_aaa(X, binary_in_a(X)) 18.38/5.65 U4_aaa(X, binary_out_a(X)) -> addx_out_aaa(one(X), b, one(X)) 18.38/5.65 addx_in_aaa(zero(X), b, zero(X)) -> U5_aaa(X, binaryZ_in_a(X)) 18.38/5.65 U5_aaa(X, binaryZ_out_a(X)) -> addx_out_aaa(zero(X), b, zero(X)) 18.38/5.65 addx_in_aaa(X, Y, Z) -> U6_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.65 addz_in_aaa(one(X), zero(Y), one(Z)) -> U12_aaa(X, Y, Z, addy_in_aaa(X, Y, Z)) 18.38/5.65 addy_in_aaa(b, one(Y), one(Y)) -> U7_aaa(Y, binary_in_a(Y)) 18.38/5.65 U7_aaa(Y, binary_out_a(Y)) -> addy_out_aaa(b, one(Y), one(Y)) 18.38/5.65 addy_in_aaa(b, zero(Y), zero(Y)) -> U8_aaa(Y, binaryZ_in_a(Y)) 18.38/5.65 U8_aaa(Y, binaryZ_out_a(Y)) -> addy_out_aaa(b, zero(Y), zero(Y)) 18.38/5.65 addy_in_aaa(X, Y, Z) -> U9_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.65 addz_in_aaa(one(X), one(Y), zero(Z)) -> U13_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.38/5.65 addc_in_aaa(b, b, one(b)) -> addc_out_aaa(b, b, one(b)) 18.38/5.65 addc_in_aaa(X, b, Z) -> U14_aaa(X, Z, succZ_in_aa(X, Z)) 18.38/5.65 succZ_in_aa(zero(X), one(X)) -> U33_aa(X, binaryZ_in_a(X)) 18.38/5.65 U33_aa(X, binaryZ_out_a(X)) -> succZ_out_aa(zero(X), one(X)) 18.38/5.65 succZ_in_aa(one(X), zero(Z)) -> U34_aa(X, Z, succ_in_aa(X, Z)) 18.38/5.65 succ_in_aa(b, one(b)) -> succ_out_aa(b, one(b)) 18.38/5.65 succ_in_aa(zero(X), one(X)) -> U31_aa(X, binaryZ_in_a(X)) 18.38/5.65 U31_aa(X, binaryZ_out_a(X)) -> succ_out_aa(zero(X), one(X)) 18.38/5.65 succ_in_aa(one(X), zero(Z)) -> U32_aa(X, Z, succ_in_aa(X, Z)) 18.38/5.65 U32_aa(X, Z, succ_out_aa(X, Z)) -> succ_out_aa(one(X), zero(Z)) 18.38/5.65 U34_aa(X, Z, succ_out_aa(X, Z)) -> succZ_out_aa(one(X), zero(Z)) 18.38/5.65 U14_aaa(X, Z, succZ_out_aa(X, Z)) -> addc_out_aaa(X, b, Z) 18.38/5.65 addc_in_aaa(b, Y, Z) -> U15_aaa(Y, Z, succZ_in_aa(Y, Z)) 18.38/5.65 U15_aaa(Y, Z, succZ_out_aa(Y, Z)) -> addc_out_aaa(b, Y, Z) 18.38/5.65 addc_in_aaa(X, Y, Z) -> U16_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.65 addC_in_aaa(zero(X), zero(Y), one(Z)) -> U23_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.65 U23_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), zero(Y), one(Z)) 18.38/5.65 addC_in_aaa(zero(X), one(Y), zero(Z)) -> U24_aaa(X, Y, Z, addX_in_aaa(X, Y, Z)) 18.38/5.65 addX_in_aaa(zero(X), b, one(X)) -> U17_aaa(X, binaryZ_in_a(X)) 18.38/5.65 U17_aaa(X, binaryZ_out_a(X)) -> addX_out_aaa(zero(X), b, one(X)) 18.38/5.65 addX_in_aaa(one(X), b, zero(Z)) -> U18_aaa(X, Z, succ_in_aa(X, Z)) 18.38/5.65 U18_aaa(X, Z, succ_out_aa(X, Z)) -> addX_out_aaa(one(X), b, zero(Z)) 18.38/5.65 addX_in_aaa(X, Y, Z) -> U19_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.65 addC_in_aaa(one(X), zero(Y), zero(Z)) -> U25_aaa(X, Y, Z, addY_in_aaa(X, Y, Z)) 18.38/5.65 addY_in_aaa(b, zero(Y), one(Y)) -> U20_aaa(Y, binaryZ_in_a(Y)) 18.38/5.65 U20_aaa(Y, binaryZ_out_a(Y)) -> addY_out_aaa(b, zero(Y), one(Y)) 18.38/5.65 addY_in_aaa(b, one(Y), zero(Z)) -> U21_aaa(Y, Z, succ_in_aa(Y, Z)) 18.38/5.65 U21_aaa(Y, Z, succ_out_aa(Y, Z)) -> addY_out_aaa(b, one(Y), zero(Z)) 18.38/5.65 addY_in_aaa(X, Y, Z) -> U22_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.65 addC_in_aaa(one(X), one(Y), one(Z)) -> U26_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.38/5.65 U26_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), one(Y), one(Z)) 18.38/5.65 U22_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addY_out_aaa(X, Y, Z) 18.38/5.65 U25_aaa(X, Y, Z, addY_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), zero(Y), zero(Z)) 18.38/5.65 U19_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addX_out_aaa(X, Y, Z) 18.38/5.65 U24_aaa(X, Y, Z, addX_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), one(Y), zero(Z)) 18.38/5.65 U16_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addc_out_aaa(X, Y, Z) 18.38/5.65 U13_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), one(Y), zero(Z)) 18.38/5.65 U9_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addy_out_aaa(X, Y, Z) 18.38/5.65 U12_aaa(X, Y, Z, addy_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), zero(Y), one(Z)) 18.38/5.65 U6_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addx_out_aaa(X, Y, Z) 18.38/5.65 U11_aaa(X, Y, Z, addx_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), one(Y), one(Z)) 18.38/5.65 U10_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), zero(Y), zero(Z)) 18.38/5.65 U3_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> add_out_aaa(X, Y, Z) 18.38/5.65 U37_aaa(R, S, RSS, add_out_aaa(S, zero(RS), RSS)) -> times_out_aaa(one(R), S, RSS) 18.38/5.65 U35_aaa(R, S, RS, times_out_aaa(R, S, RS)) -> times_out_aaa(zero(R), S, zero(RS)) 18.38/5.65 U36_aag(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aag(R, S, RSS, add_in_aag(S, zero(RS), RSS)) 18.38/5.65 add_in_aag(b, b, b) -> add_out_aag(b, b, b) 18.38/5.65 add_in_aag(X, b, X) -> U1_aag(X, binaryZ_in_g(X)) 18.38/5.65 binaryZ_in_g(zero(X)) -> U29_g(X, binaryZ_in_g(X)) 18.38/5.65 binaryZ_in_g(one(X)) -> U30_g(X, binary_in_g(X)) 18.38/5.65 binary_in_g(b) -> binary_out_g(b) 18.38/5.65 binary_in_g(zero(X)) -> U27_g(X, binaryZ_in_g(X)) 18.38/5.65 U27_g(X, binaryZ_out_g(X)) -> binary_out_g(zero(X)) 18.38/5.65 binary_in_g(one(X)) -> U28_g(X, binary_in_g(X)) 18.38/5.65 U28_g(X, binary_out_g(X)) -> binary_out_g(one(X)) 18.38/5.65 U30_g(X, binary_out_g(X)) -> binaryZ_out_g(one(X)) 18.38/5.65 U29_g(X, binaryZ_out_g(X)) -> binaryZ_out_g(zero(X)) 18.38/5.65 U1_aag(X, binaryZ_out_g(X)) -> add_out_aag(X, b, X) 18.38/5.65 add_in_aag(b, Y, Y) -> U2_aag(Y, binaryZ_in_g(Y)) 18.38/5.65 U2_aag(Y, binaryZ_out_g(Y)) -> add_out_aag(b, Y, Y) 18.38/5.65 add_in_aag(X, Y, Z) -> U3_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.65 addz_in_aag(zero(X), zero(Y), zero(Z)) -> U10_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.65 addz_in_aag(zero(X), one(Y), one(Z)) -> U11_aag(X, Y, Z, addx_in_aag(X, Y, Z)) 18.38/5.65 addx_in_aag(one(X), b, one(X)) -> U4_aag(X, binary_in_g(X)) 18.38/5.65 U4_aag(X, binary_out_g(X)) -> addx_out_aag(one(X), b, one(X)) 18.38/5.65 addx_in_aag(zero(X), b, zero(X)) -> U5_aag(X, binaryZ_in_g(X)) 18.38/5.65 U5_aag(X, binaryZ_out_g(X)) -> addx_out_aag(zero(X), b, zero(X)) 18.38/5.65 addx_in_aag(X, Y, Z) -> U6_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.65 addz_in_aag(one(X), zero(Y), one(Z)) -> U12_aag(X, Y, Z, addy_in_aag(X, Y, Z)) 18.38/5.65 addy_in_aag(b, one(Y), one(Y)) -> U7_aag(Y, binary_in_g(Y)) 18.38/5.65 U7_aag(Y, binary_out_g(Y)) -> addy_out_aag(b, one(Y), one(Y)) 18.38/5.65 addy_in_aag(b, zero(Y), zero(Y)) -> U8_aag(Y, binaryZ_in_g(Y)) 18.38/5.65 U8_aag(Y, binaryZ_out_g(Y)) -> addy_out_aag(b, zero(Y), zero(Y)) 18.38/5.65 addy_in_aag(X, Y, Z) -> U9_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.65 addz_in_aag(one(X), one(Y), zero(Z)) -> U13_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.38/5.65 addc_in_aag(b, b, one(b)) -> addc_out_aag(b, b, one(b)) 18.38/5.65 addc_in_aag(X, b, Z) -> U14_aag(X, Z, succZ_in_ag(X, Z)) 18.38/5.65 succZ_in_ag(zero(X), one(X)) -> U33_ag(X, binaryZ_in_g(X)) 18.38/5.65 U33_ag(X, binaryZ_out_g(X)) -> succZ_out_ag(zero(X), one(X)) 18.38/5.65 succZ_in_ag(one(X), zero(Z)) -> U34_ag(X, Z, succ_in_ag(X, Z)) 18.38/5.65 succ_in_ag(b, one(b)) -> succ_out_ag(b, one(b)) 18.38/5.65 succ_in_ag(zero(X), one(X)) -> U31_ag(X, binaryZ_in_g(X)) 18.38/5.65 U31_ag(X, binaryZ_out_g(X)) -> succ_out_ag(zero(X), one(X)) 18.38/5.65 succ_in_ag(one(X), zero(Z)) -> U32_ag(X, Z, succ_in_ag(X, Z)) 18.38/5.65 U32_ag(X, Z, succ_out_ag(X, Z)) -> succ_out_ag(one(X), zero(Z)) 18.38/5.65 U34_ag(X, Z, succ_out_ag(X, Z)) -> succZ_out_ag(one(X), zero(Z)) 18.38/5.65 U14_aag(X, Z, succZ_out_ag(X, Z)) -> addc_out_aag(X, b, Z) 18.38/5.65 addc_in_aag(b, Y, Z) -> U15_aag(Y, Z, succZ_in_ag(Y, Z)) 18.38/5.65 U15_aag(Y, Z, succZ_out_ag(Y, Z)) -> addc_out_aag(b, Y, Z) 18.38/5.65 addc_in_aag(X, Y, Z) -> U16_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.65 addC_in_aag(zero(X), zero(Y), one(Z)) -> U23_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.65 U23_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), zero(Y), one(Z)) 18.38/5.65 addC_in_aag(zero(X), one(Y), zero(Z)) -> U24_aag(X, Y, Z, addX_in_aag(X, Y, Z)) 18.38/5.65 addX_in_aag(zero(X), b, one(X)) -> U17_aag(X, binaryZ_in_g(X)) 18.38/5.65 U17_aag(X, binaryZ_out_g(X)) -> addX_out_aag(zero(X), b, one(X)) 18.38/5.65 addX_in_aag(one(X), b, zero(Z)) -> U18_aag(X, Z, succ_in_ag(X, Z)) 18.38/5.66 U18_aag(X, Z, succ_out_ag(X, Z)) -> addX_out_aag(one(X), b, zero(Z)) 18.38/5.66 addX_in_aag(X, Y, Z) -> U19_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.66 addC_in_aag(one(X), zero(Y), zero(Z)) -> U25_aag(X, Y, Z, addY_in_aag(X, Y, Z)) 18.38/5.66 addY_in_aag(b, zero(Y), one(Y)) -> U20_aag(Y, binaryZ_in_g(Y)) 18.38/5.66 U20_aag(Y, binaryZ_out_g(Y)) -> addY_out_aag(b, zero(Y), one(Y)) 18.38/5.66 addY_in_aag(b, one(Y), zero(Z)) -> U21_aag(Y, Z, succ_in_ag(Y, Z)) 18.38/5.66 U21_aag(Y, Z, succ_out_ag(Y, Z)) -> addY_out_aag(b, one(Y), zero(Z)) 18.38/5.66 addY_in_aag(X, Y, Z) -> U22_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.66 addC_in_aag(one(X), one(Y), one(Z)) -> U26_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.38/5.66 U26_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addC_out_aag(one(X), one(Y), one(Z)) 18.38/5.66 U22_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addY_out_aag(X, Y, Z) 18.38/5.66 U25_aag(X, Y, Z, addY_out_aag(X, Y, Z)) -> addC_out_aag(one(X), zero(Y), zero(Z)) 18.38/5.66 U19_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addX_out_aag(X, Y, Z) 18.38/5.66 U24_aag(X, Y, Z, addX_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), one(Y), zero(Z)) 18.38/5.66 U16_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addc_out_aag(X, Y, Z) 18.38/5.66 U13_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addz_out_aag(one(X), one(Y), zero(Z)) 18.38/5.66 U9_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addy_out_aag(X, Y, Z) 18.38/5.66 U12_aag(X, Y, Z, addy_out_aag(X, Y, Z)) -> addz_out_aag(one(X), zero(Y), one(Z)) 18.38/5.66 U6_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addx_out_aag(X, Y, Z) 18.38/5.66 U11_aag(X, Y, Z, addx_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), one(Y), one(Z)) 18.38/5.66 U10_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), zero(Y), zero(Z)) 18.38/5.66 U3_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> add_out_aag(X, Y, Z) 18.38/5.66 U37_aag(R, S, RSS, add_out_aag(S, zero(RS), RSS)) -> times_out_aag(one(R), S, RSS) 18.38/5.66 U35_aag(R, S, RS, times_out_aag(R, S, RS)) -> times_out_aag(zero(R), S, zero(RS)) 18.38/5.66 18.38/5.66 The argument filtering Pi contains the following mapping: 18.38/5.66 times_in_aag(x1, x2, x3) = times_in_aag(x3) 18.38/5.66 18.38/5.66 times_out_aag(x1, x2, x3) = times_out_aag(x1, x2) 18.38/5.66 18.38/5.66 zero(x1) = zero(x1) 18.38/5.66 18.38/5.66 U35_aag(x1, x2, x3, x4) = U35_aag(x4) 18.38/5.66 18.38/5.66 U36_aag(x1, x2, x3, x4) = U36_aag(x3, x4) 18.38/5.66 18.38/5.66 times_in_aaa(x1, x2, x3) = times_in_aaa 18.38/5.66 18.38/5.66 times_out_aaa(x1, x2, x3) = times_out_aaa(x1) 18.38/5.66 18.38/5.66 U35_aaa(x1, x2, x3, x4) = U35_aaa(x4) 18.38/5.66 18.38/5.66 U36_aaa(x1, x2, x3, x4) = U36_aaa(x4) 18.38/5.66 18.38/5.66 U37_aaa(x1, x2, x3, x4) = U37_aaa(x1, x4) 18.38/5.66 18.38/5.66 add_in_aaa(x1, x2, x3) = add_in_aaa 18.38/5.66 18.38/5.66 add_out_aaa(x1, x2, x3) = add_out_aaa(x1, x2, x3) 18.38/5.66 18.38/5.66 U1_aaa(x1, x2) = U1_aaa(x2) 18.38/5.66 18.38/5.66 binaryZ_in_a(x1) = binaryZ_in_a 18.38/5.66 18.38/5.66 U29_a(x1, x2) = U29_a(x2) 18.38/5.66 18.38/5.66 U30_a(x1, x2) = U30_a(x2) 18.38/5.66 18.38/5.66 binary_in_a(x1) = binary_in_a 18.38/5.66 18.38/5.66 binary_out_a(x1) = binary_out_a(x1) 18.38/5.66 18.38/5.66 U27_a(x1, x2) = U27_a(x2) 18.38/5.66 18.38/5.66 binaryZ_out_a(x1) = binaryZ_out_a(x1) 18.38/5.66 18.38/5.66 U28_a(x1, x2) = U28_a(x2) 18.38/5.66 18.38/5.66 U2_aaa(x1, x2) = U2_aaa(x2) 18.38/5.66 18.38/5.66 U3_aaa(x1, x2, x3, x4) = U3_aaa(x4) 18.38/5.66 18.38/5.66 addz_in_aaa(x1, x2, x3) = addz_in_aaa 18.38/5.66 18.38/5.66 U10_aaa(x1, x2, x3, x4) = U10_aaa(x4) 18.38/5.66 18.38/5.66 U11_aaa(x1, x2, x3, x4) = U11_aaa(x4) 18.38/5.66 18.38/5.66 addx_in_aaa(x1, x2, x3) = addx_in_aaa 18.38/5.66 18.38/5.66 U4_aaa(x1, x2) = U4_aaa(x2) 18.38/5.66 18.38/5.66 addx_out_aaa(x1, x2, x3) = addx_out_aaa(x1, x2, x3) 18.38/5.66 18.38/5.66 U5_aaa(x1, x2) = U5_aaa(x2) 18.38/5.66 18.38/5.66 U6_aaa(x1, x2, x3, x4) = U6_aaa(x4) 18.38/5.66 18.38/5.66 U12_aaa(x1, x2, x3, x4) = U12_aaa(x4) 18.38/5.66 18.38/5.66 addy_in_aaa(x1, x2, x3) = addy_in_aaa 18.38/5.66 18.38/5.66 U7_aaa(x1, x2) = U7_aaa(x2) 18.38/5.66 18.38/5.66 addy_out_aaa(x1, x2, x3) = addy_out_aaa(x1, x2, x3) 18.38/5.66 18.38/5.66 U8_aaa(x1, x2) = U8_aaa(x2) 18.38/5.66 18.38/5.66 U9_aaa(x1, x2, x3, x4) = U9_aaa(x4) 18.38/5.66 18.38/5.66 U13_aaa(x1, x2, x3, x4) = U13_aaa(x4) 18.38/5.66 18.38/5.66 addc_in_aaa(x1, x2, x3) = addc_in_aaa 18.38/5.66 18.38/5.66 addc_out_aaa(x1, x2, x3) = addc_out_aaa(x1, x2, x3) 18.38/5.66 18.38/5.66 U14_aaa(x1, x2, x3) = U14_aaa(x3) 18.38/5.66 18.38/5.66 succZ_in_aa(x1, x2) = succZ_in_aa 18.38/5.66 18.38/5.66 U33_aa(x1, x2) = U33_aa(x2) 18.38/5.66 18.38/5.66 succZ_out_aa(x1, x2) = succZ_out_aa(x1, x2) 18.38/5.66 18.38/5.66 U34_aa(x1, x2, x3) = U34_aa(x3) 18.38/5.66 18.38/5.66 succ_in_aa(x1, x2) = succ_in_aa 18.38/5.66 18.38/5.66 succ_out_aa(x1, x2) = succ_out_aa(x1, x2) 18.38/5.66 18.38/5.66 U31_aa(x1, x2) = U31_aa(x2) 18.38/5.66 18.38/5.66 U32_aa(x1, x2, x3) = U32_aa(x3) 18.38/5.66 18.38/5.66 U15_aaa(x1, x2, x3) = U15_aaa(x3) 18.38/5.66 18.38/5.66 U16_aaa(x1, x2, x3, x4) = U16_aaa(x4) 18.38/5.66 18.38/5.66 addC_in_aaa(x1, x2, x3) = addC_in_aaa 18.38/5.66 18.38/5.66 U23_aaa(x1, x2, x3, x4) = U23_aaa(x4) 18.38/5.66 18.38/5.66 addz_out_aaa(x1, x2, x3) = addz_out_aaa(x1, x2, x3) 18.38/5.66 18.38/5.66 addC_out_aaa(x1, x2, x3) = addC_out_aaa(x1, x2, x3) 18.38/5.66 18.38/5.66 U24_aaa(x1, x2, x3, x4) = U24_aaa(x4) 18.38/5.66 18.38/5.66 addX_in_aaa(x1, x2, x3) = addX_in_aaa 18.38/5.66 18.38/5.66 U17_aaa(x1, x2) = U17_aaa(x2) 18.38/5.66 18.38/5.66 addX_out_aaa(x1, x2, x3) = addX_out_aaa(x1, x2, x3) 18.38/5.66 18.38/5.66 U18_aaa(x1, x2, x3) = U18_aaa(x3) 18.38/5.66 18.38/5.66 U19_aaa(x1, x2, x3, x4) = U19_aaa(x4) 18.38/5.66 18.38/5.66 U25_aaa(x1, x2, x3, x4) = U25_aaa(x4) 18.38/5.66 18.38/5.66 addY_in_aaa(x1, x2, x3) = addY_in_aaa 18.38/5.66 18.38/5.66 U20_aaa(x1, x2) = U20_aaa(x2) 18.38/5.66 18.38/5.66 addY_out_aaa(x1, x2, x3) = addY_out_aaa(x1, x2, x3) 18.38/5.66 18.38/5.66 U21_aaa(x1, x2, x3) = U21_aaa(x3) 18.38/5.66 18.38/5.66 U22_aaa(x1, x2, x3, x4) = U22_aaa(x4) 18.38/5.66 18.38/5.66 U26_aaa(x1, x2, x3, x4) = U26_aaa(x4) 18.38/5.66 18.38/5.66 U37_aag(x1, x2, x3, x4) = U37_aag(x1, x4) 18.38/5.66 18.38/5.66 add_in_aag(x1, x2, x3) = add_in_aag(x3) 18.38/5.66 18.38/5.66 b = b 18.38/5.66 18.38/5.66 add_out_aag(x1, x2, x3) = add_out_aag(x1, x2) 18.38/5.66 18.38/5.66 U1_aag(x1, x2) = U1_aag(x1, x2) 18.38/5.66 18.38/5.66 binaryZ_in_g(x1) = binaryZ_in_g(x1) 18.38/5.66 18.38/5.66 U29_g(x1, x2) = U29_g(x2) 18.38/5.66 18.38/5.66 one(x1) = one(x1) 18.38/5.66 18.38/5.66 U30_g(x1, x2) = U30_g(x2) 18.38/5.66 18.38/5.66 binary_in_g(x1) = binary_in_g(x1) 18.38/5.66 18.38/5.66 binary_out_g(x1) = binary_out_g 18.38/5.66 18.38/5.66 U27_g(x1, x2) = U27_g(x2) 18.38/5.66 18.38/5.66 binaryZ_out_g(x1) = binaryZ_out_g 18.38/5.66 18.38/5.66 U28_g(x1, x2) = U28_g(x2) 18.38/5.66 18.38/5.66 U2_aag(x1, x2) = U2_aag(x1, x2) 18.38/5.66 18.38/5.66 U3_aag(x1, x2, x3, x4) = U3_aag(x4) 18.38/5.66 18.38/5.66 addz_in_aag(x1, x2, x3) = addz_in_aag(x3) 18.38/5.66 18.38/5.66 U10_aag(x1, x2, x3, x4) = U10_aag(x4) 18.38/5.66 18.38/5.66 U11_aag(x1, x2, x3, x4) = U11_aag(x4) 18.38/5.66 18.38/5.66 addx_in_aag(x1, x2, x3) = addx_in_aag(x3) 18.38/5.66 18.38/5.66 U4_aag(x1, x2) = U4_aag(x1, x2) 18.38/5.66 18.38/5.66 addx_out_aag(x1, x2, x3) = addx_out_aag(x1, x2) 18.38/5.66 18.38/5.66 U5_aag(x1, x2) = U5_aag(x1, x2) 18.38/5.66 18.38/5.66 U6_aag(x1, x2, x3, x4) = U6_aag(x4) 18.38/5.66 18.38/5.66 U12_aag(x1, x2, x3, x4) = U12_aag(x4) 18.38/5.66 18.38/5.66 addy_in_aag(x1, x2, x3) = addy_in_aag(x3) 18.38/5.66 18.38/5.66 U7_aag(x1, x2) = U7_aag(x1, x2) 18.38/5.66 18.38/5.66 addy_out_aag(x1, x2, x3) = addy_out_aag(x1, x2) 18.38/5.66 18.38/5.66 U8_aag(x1, x2) = U8_aag(x1, x2) 18.38/5.66 18.38/5.66 U9_aag(x1, x2, x3, x4) = U9_aag(x4) 18.38/5.66 18.38/5.66 U13_aag(x1, x2, x3, x4) = U13_aag(x4) 18.38/5.66 18.38/5.66 addc_in_aag(x1, x2, x3) = addc_in_aag(x3) 18.38/5.66 18.38/5.66 addc_out_aag(x1, x2, x3) = addc_out_aag(x1, x2) 18.38/5.66 18.38/5.66 U14_aag(x1, x2, x3) = U14_aag(x3) 18.38/5.66 18.38/5.66 succZ_in_ag(x1, x2) = succZ_in_ag(x2) 18.38/5.66 18.38/5.66 U33_ag(x1, x2) = U33_ag(x1, x2) 18.38/5.66 18.38/5.66 succZ_out_ag(x1, x2) = succZ_out_ag(x1) 18.38/5.66 18.38/5.66 U34_ag(x1, x2, x3) = U34_ag(x3) 18.38/5.66 18.38/5.66 succ_in_ag(x1, x2) = succ_in_ag(x2) 18.38/5.66 18.38/5.66 succ_out_ag(x1, x2) = succ_out_ag(x1) 18.38/5.66 18.38/5.66 U31_ag(x1, x2) = U31_ag(x1, x2) 18.38/5.66 18.38/5.66 U32_ag(x1, x2, x3) = U32_ag(x3) 18.38/5.66 18.38/5.66 U15_aag(x1, x2, x3) = U15_aag(x3) 18.38/5.66 18.38/5.66 U16_aag(x1, x2, x3, x4) = U16_aag(x4) 18.38/5.66 18.38/5.66 addC_in_aag(x1, x2, x3) = addC_in_aag(x3) 18.38/5.66 18.38/5.66 U23_aag(x1, x2, x3, x4) = U23_aag(x4) 18.38/5.66 18.38/5.66 addz_out_aag(x1, x2, x3) = addz_out_aag(x1, x2) 18.38/5.66 18.38/5.66 addC_out_aag(x1, x2, x3) = addC_out_aag(x1, x2) 18.38/5.66 18.38/5.66 U24_aag(x1, x2, x3, x4) = U24_aag(x4) 18.38/5.66 18.38/5.66 addX_in_aag(x1, x2, x3) = addX_in_aag(x3) 18.38/5.66 18.38/5.66 U17_aag(x1, x2) = U17_aag(x1, x2) 18.38/5.66 18.38/5.66 addX_out_aag(x1, x2, x3) = addX_out_aag(x1, x2) 18.38/5.66 18.38/5.66 U18_aag(x1, x2, x3) = U18_aag(x3) 18.38/5.66 18.38/5.66 U19_aag(x1, x2, x3, x4) = U19_aag(x4) 18.38/5.66 18.38/5.66 U25_aag(x1, x2, x3, x4) = U25_aag(x4) 18.38/5.66 18.38/5.66 addY_in_aag(x1, x2, x3) = addY_in_aag(x3) 18.38/5.66 18.38/5.66 U20_aag(x1, x2) = U20_aag(x1, x2) 18.38/5.66 18.38/5.66 addY_out_aag(x1, x2, x3) = addY_out_aag(x1, x2) 18.38/5.66 18.38/5.66 U21_aag(x1, x2, x3) = U21_aag(x3) 18.38/5.66 18.38/5.66 U22_aag(x1, x2, x3, x4) = U22_aag(x4) 18.38/5.66 18.38/5.66 U26_aag(x1, x2, x3, x4) = U26_aag(x4) 18.38/5.66 18.38/5.66 TIMES_IN_AAG(x1, x2, x3) = TIMES_IN_AAG(x3) 18.38/5.66 18.38/5.66 U35_AAG(x1, x2, x3, x4) = U35_AAG(x4) 18.38/5.66 18.38/5.66 U36_AAG(x1, x2, x3, x4) = U36_AAG(x3, x4) 18.38/5.66 18.38/5.66 TIMES_IN_AAA(x1, x2, x3) = TIMES_IN_AAA 18.38/5.66 18.38/5.66 U35_AAA(x1, x2, x3, x4) = U35_AAA(x4) 18.38/5.66 18.38/5.66 U36_AAA(x1, x2, x3, x4) = U36_AAA(x4) 18.38/5.66 18.38/5.66 U37_AAA(x1, x2, x3, x4) = U37_AAA(x1, x4) 18.38/5.66 18.38/5.66 ADD_IN_AAA(x1, x2, x3) = ADD_IN_AAA 18.38/5.66 18.38/5.66 U1_AAA(x1, x2) = U1_AAA(x2) 18.38/5.66 18.38/5.66 BINARYZ_IN_A(x1) = BINARYZ_IN_A 18.38/5.66 18.38/5.66 U29_A(x1, x2) = U29_A(x2) 18.38/5.66 18.38/5.66 U30_A(x1, x2) = U30_A(x2) 18.38/5.66 18.38/5.66 BINARY_IN_A(x1) = BINARY_IN_A 18.38/5.66 18.38/5.66 U27_A(x1, x2) = U27_A(x2) 18.38/5.66 18.38/5.66 U28_A(x1, x2) = U28_A(x2) 18.38/5.66 18.38/5.66 U2_AAA(x1, x2) = U2_AAA(x2) 18.38/5.66 18.38/5.66 U3_AAA(x1, x2, x3, x4) = U3_AAA(x4) 18.38/5.66 18.38/5.66 ADDZ_IN_AAA(x1, x2, x3) = ADDZ_IN_AAA 18.38/5.66 18.38/5.66 U10_AAA(x1, x2, x3, x4) = U10_AAA(x4) 18.38/5.66 18.38/5.66 U11_AAA(x1, x2, x3, x4) = U11_AAA(x4) 18.38/5.66 18.38/5.66 ADDX_IN_AAA(x1, x2, x3) = ADDX_IN_AAA 18.38/5.66 18.38/5.66 U4_AAA(x1, x2) = U4_AAA(x2) 18.38/5.66 18.38/5.66 U5_AAA(x1, x2) = U5_AAA(x2) 18.38/5.66 18.38/5.66 U6_AAA(x1, x2, x3, x4) = U6_AAA(x4) 18.38/5.66 18.38/5.66 U12_AAA(x1, x2, x3, x4) = U12_AAA(x4) 18.38/5.66 18.38/5.66 ADDY_IN_AAA(x1, x2, x3) = ADDY_IN_AAA 18.38/5.66 18.38/5.66 U7_AAA(x1, x2) = U7_AAA(x2) 18.38/5.66 18.38/5.66 U8_AAA(x1, x2) = U8_AAA(x2) 18.38/5.66 18.38/5.66 U9_AAA(x1, x2, x3, x4) = U9_AAA(x4) 18.38/5.66 18.38/5.66 U13_AAA(x1, x2, x3, x4) = U13_AAA(x4) 18.38/5.66 18.38/5.66 ADDC_IN_AAA(x1, x2, x3) = ADDC_IN_AAA 18.38/5.66 18.38/5.66 U14_AAA(x1, x2, x3) = U14_AAA(x3) 18.38/5.66 18.38/5.66 SUCCZ_IN_AA(x1, x2) = SUCCZ_IN_AA 18.38/5.66 18.38/5.66 U33_AA(x1, x2) = U33_AA(x2) 18.38/5.66 18.38/5.66 U34_AA(x1, x2, x3) = U34_AA(x3) 18.38/5.66 18.38/5.66 SUCC_IN_AA(x1, x2) = SUCC_IN_AA 18.38/5.66 18.38/5.66 U31_AA(x1, x2) = U31_AA(x2) 18.38/5.66 18.38/5.66 U32_AA(x1, x2, x3) = U32_AA(x3) 18.38/5.66 18.38/5.66 U15_AAA(x1, x2, x3) = U15_AAA(x3) 18.38/5.66 18.38/5.66 U16_AAA(x1, x2, x3, x4) = U16_AAA(x4) 18.38/5.66 18.38/5.66 ADDC_IN_AAA^1(x1, x2, x3) = ADDC_IN_AAA^1 18.38/5.66 18.38/5.66 U23_AAA(x1, x2, x3, x4) = U23_AAA(x4) 18.38/5.66 18.38/5.66 U24_AAA(x1, x2, x3, x4) = U24_AAA(x4) 18.38/5.66 18.38/5.66 ADDX_IN_AAA^1(x1, x2, x3) = ADDX_IN_AAA^1 18.38/5.66 18.38/5.66 U17_AAA(x1, x2) = U17_AAA(x2) 18.38/5.66 18.38/5.66 U18_AAA(x1, x2, x3) = U18_AAA(x3) 18.38/5.66 18.38/5.66 U19_AAA(x1, x2, x3, x4) = U19_AAA(x4) 18.38/5.66 18.38/5.66 U25_AAA(x1, x2, x3, x4) = U25_AAA(x4) 18.38/5.66 18.38/5.66 ADDY_IN_AAA^1(x1, x2, x3) = ADDY_IN_AAA^1 18.38/5.66 18.38/5.66 U20_AAA(x1, x2) = U20_AAA(x2) 18.38/5.66 18.38/5.66 U21_AAA(x1, x2, x3) = U21_AAA(x3) 18.38/5.66 18.38/5.66 U22_AAA(x1, x2, x3, x4) = U22_AAA(x4) 18.38/5.66 18.38/5.66 U26_AAA(x1, x2, x3, x4) = U26_AAA(x4) 18.38/5.66 18.38/5.66 U37_AAG(x1, x2, x3, x4) = U37_AAG(x1, x4) 18.38/5.66 18.38/5.66 ADD_IN_AAG(x1, x2, x3) = ADD_IN_AAG(x3) 18.38/5.66 18.38/5.66 U1_AAG(x1, x2) = U1_AAG(x1, x2) 18.38/5.66 18.38/5.66 BINARYZ_IN_G(x1) = BINARYZ_IN_G(x1) 18.38/5.66 18.38/5.66 U29_G(x1, x2) = U29_G(x2) 18.38/5.66 18.38/5.66 U30_G(x1, x2) = U30_G(x2) 18.38/5.66 18.38/5.66 BINARY_IN_G(x1) = BINARY_IN_G(x1) 18.38/5.66 18.38/5.66 U27_G(x1, x2) = U27_G(x2) 18.38/5.66 18.38/5.66 U28_G(x1, x2) = U28_G(x2) 18.38/5.66 18.38/5.66 U2_AAG(x1, x2) = U2_AAG(x1, x2) 18.38/5.66 18.38/5.66 U3_AAG(x1, x2, x3, x4) = U3_AAG(x4) 18.38/5.66 18.38/5.66 ADDZ_IN_AAG(x1, x2, x3) = ADDZ_IN_AAG(x3) 18.38/5.66 18.38/5.66 U10_AAG(x1, x2, x3, x4) = U10_AAG(x4) 18.38/5.66 18.38/5.66 U11_AAG(x1, x2, x3, x4) = U11_AAG(x4) 18.38/5.66 18.38/5.66 ADDX_IN_AAG(x1, x2, x3) = ADDX_IN_AAG(x3) 18.38/5.66 18.38/5.66 U4_AAG(x1, x2) = U4_AAG(x1, x2) 18.38/5.66 18.38/5.66 U5_AAG(x1, x2) = U5_AAG(x1, x2) 18.38/5.66 18.38/5.66 U6_AAG(x1, x2, x3, x4) = U6_AAG(x4) 18.38/5.66 18.38/5.66 U12_AAG(x1, x2, x3, x4) = U12_AAG(x4) 18.38/5.66 18.38/5.66 ADDY_IN_AAG(x1, x2, x3) = ADDY_IN_AAG(x3) 18.38/5.66 18.38/5.66 U7_AAG(x1, x2) = U7_AAG(x1, x2) 18.38/5.66 18.38/5.66 U8_AAG(x1, x2) = U8_AAG(x1, x2) 18.38/5.66 18.38/5.66 U9_AAG(x1, x2, x3, x4) = U9_AAG(x4) 18.38/5.66 18.38/5.66 U13_AAG(x1, x2, x3, x4) = U13_AAG(x4) 18.38/5.66 18.38/5.66 ADDC_IN_AAG(x1, x2, x3) = ADDC_IN_AAG(x3) 18.38/5.66 18.38/5.66 U14_AAG(x1, x2, x3) = U14_AAG(x3) 18.38/5.66 18.38/5.66 SUCCZ_IN_AG(x1, x2) = SUCCZ_IN_AG(x2) 18.38/5.66 18.38/5.66 U33_AG(x1, x2) = U33_AG(x1, x2) 18.38/5.66 18.38/5.66 U34_AG(x1, x2, x3) = U34_AG(x3) 18.38/5.66 18.38/5.66 SUCC_IN_AG(x1, x2) = SUCC_IN_AG(x2) 18.38/5.66 18.38/5.66 U31_AG(x1, x2) = U31_AG(x1, x2) 18.38/5.66 18.38/5.66 U32_AG(x1, x2, x3) = U32_AG(x3) 18.38/5.66 18.38/5.66 U15_AAG(x1, x2, x3) = U15_AAG(x3) 18.38/5.66 18.38/5.66 U16_AAG(x1, x2, x3, x4) = U16_AAG(x4) 18.38/5.66 18.38/5.66 ADDC_IN_AAG^1(x1, x2, x3) = ADDC_IN_AAG^1(x3) 18.38/5.66 18.38/5.66 U23_AAG(x1, x2, x3, x4) = U23_AAG(x4) 18.38/5.66 18.38/5.66 U24_AAG(x1, x2, x3, x4) = U24_AAG(x4) 18.38/5.66 18.38/5.66 ADDX_IN_AAG^1(x1, x2, x3) = ADDX_IN_AAG^1(x3) 18.38/5.66 18.38/5.66 U17_AAG(x1, x2) = U17_AAG(x1, x2) 18.38/5.66 18.38/5.66 U18_AAG(x1, x2, x3) = U18_AAG(x3) 18.38/5.66 18.38/5.66 U19_AAG(x1, x2, x3, x4) = U19_AAG(x4) 18.38/5.66 18.38/5.66 U25_AAG(x1, x2, x3, x4) = U25_AAG(x4) 18.38/5.66 18.38/5.66 ADDY_IN_AAG^1(x1, x2, x3) = ADDY_IN_AAG^1(x3) 18.38/5.66 18.38/5.66 U20_AAG(x1, x2) = U20_AAG(x1, x2) 18.38/5.66 18.38/5.66 U21_AAG(x1, x2, x3) = U21_AAG(x3) 18.38/5.66 18.38/5.66 U22_AAG(x1, x2, x3, x4) = U22_AAG(x4) 18.38/5.66 18.38/5.66 U26_AAG(x1, x2, x3, x4) = U26_AAG(x4) 18.38/5.66 18.38/5.66 18.38/5.66 We have to consider all (P,R,Pi)-chains 18.38/5.66 ---------------------------------------- 18.38/5.66 18.38/5.66 (52) 18.38/5.66 Obligation: 18.38/5.66 Pi DP problem: 18.38/5.66 The TRS P consists of the following rules: 18.38/5.66 18.38/5.66 TIMES_IN_AAG(zero(R), S, zero(RS)) -> U35_AAG(R, S, RS, times_in_aag(R, S, RS)) 18.38/5.66 TIMES_IN_AAG(zero(R), S, zero(RS)) -> TIMES_IN_AAG(R, S, RS) 18.38/5.66 TIMES_IN_AAG(one(R), S, RSS) -> U36_AAG(R, S, RSS, times_in_aaa(R, S, RS)) 18.38/5.66 TIMES_IN_AAG(one(R), S, RSS) -> TIMES_IN_AAA(R, S, RS) 18.38/5.66 TIMES_IN_AAA(zero(R), S, zero(RS)) -> U35_AAA(R, S, RS, times_in_aaa(R, S, RS)) 18.38/5.66 TIMES_IN_AAA(zero(R), S, zero(RS)) -> TIMES_IN_AAA(R, S, RS) 18.38/5.66 TIMES_IN_AAA(one(R), S, RSS) -> U36_AAA(R, S, RSS, times_in_aaa(R, S, RS)) 18.38/5.66 TIMES_IN_AAA(one(R), S, RSS) -> TIMES_IN_AAA(R, S, RS) 18.38/5.66 U36_AAA(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_AAA(R, S, RSS, add_in_aaa(S, zero(RS), RSS)) 18.38/5.66 U36_AAA(R, S, RSS, times_out_aaa(R, S, RS)) -> ADD_IN_AAA(S, zero(RS), RSS) 18.38/5.66 ADD_IN_AAA(X, b, X) -> U1_AAA(X, binaryZ_in_a(X)) 18.38/5.66 ADD_IN_AAA(X, b, X) -> BINARYZ_IN_A(X) 18.38/5.66 BINARYZ_IN_A(zero(X)) -> U29_A(X, binaryZ_in_a(X)) 18.38/5.66 BINARYZ_IN_A(zero(X)) -> BINARYZ_IN_A(X) 18.38/5.66 BINARYZ_IN_A(one(X)) -> U30_A(X, binary_in_a(X)) 18.38/5.66 BINARYZ_IN_A(one(X)) -> BINARY_IN_A(X) 18.38/5.66 BINARY_IN_A(zero(X)) -> U27_A(X, binaryZ_in_a(X)) 18.38/5.66 BINARY_IN_A(zero(X)) -> BINARYZ_IN_A(X) 18.38/5.66 BINARY_IN_A(one(X)) -> U28_A(X, binary_in_a(X)) 18.38/5.66 BINARY_IN_A(one(X)) -> BINARY_IN_A(X) 18.38/5.66 ADD_IN_AAA(b, Y, Y) -> U2_AAA(Y, binaryZ_in_a(Y)) 18.38/5.66 ADD_IN_AAA(b, Y, Y) -> BINARYZ_IN_A(Y) 18.38/5.66 ADD_IN_AAA(X, Y, Z) -> U3_AAA(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.66 ADD_IN_AAA(X, Y, Z) -> ADDZ_IN_AAA(X, Y, Z) 18.38/5.66 ADDZ_IN_AAA(zero(X), zero(Y), zero(Z)) -> U10_AAA(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.66 ADDZ_IN_AAA(zero(X), zero(Y), zero(Z)) -> ADDZ_IN_AAA(X, Y, Z) 18.38/5.66 ADDZ_IN_AAA(zero(X), one(Y), one(Z)) -> U11_AAA(X, Y, Z, addx_in_aaa(X, Y, Z)) 18.38/5.66 ADDZ_IN_AAA(zero(X), one(Y), one(Z)) -> ADDX_IN_AAA(X, Y, Z) 18.38/5.66 ADDX_IN_AAA(one(X), b, one(X)) -> U4_AAA(X, binary_in_a(X)) 18.38/5.66 ADDX_IN_AAA(one(X), b, one(X)) -> BINARY_IN_A(X) 18.38/5.66 ADDX_IN_AAA(zero(X), b, zero(X)) -> U5_AAA(X, binaryZ_in_a(X)) 18.38/5.66 ADDX_IN_AAA(zero(X), b, zero(X)) -> BINARYZ_IN_A(X) 18.38/5.66 ADDX_IN_AAA(X, Y, Z) -> U6_AAA(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.66 ADDX_IN_AAA(X, Y, Z) -> ADDZ_IN_AAA(X, Y, Z) 18.38/5.66 ADDZ_IN_AAA(one(X), zero(Y), one(Z)) -> U12_AAA(X, Y, Z, addy_in_aaa(X, Y, Z)) 18.38/5.66 ADDZ_IN_AAA(one(X), zero(Y), one(Z)) -> ADDY_IN_AAA(X, Y, Z) 18.38/5.66 ADDY_IN_AAA(b, one(Y), one(Y)) -> U7_AAA(Y, binary_in_a(Y)) 18.38/5.66 ADDY_IN_AAA(b, one(Y), one(Y)) -> BINARY_IN_A(Y) 18.38/5.66 ADDY_IN_AAA(b, zero(Y), zero(Y)) -> U8_AAA(Y, binaryZ_in_a(Y)) 18.38/5.66 ADDY_IN_AAA(b, zero(Y), zero(Y)) -> BINARYZ_IN_A(Y) 18.38/5.66 ADDY_IN_AAA(X, Y, Z) -> U9_AAA(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.66 ADDY_IN_AAA(X, Y, Z) -> ADDZ_IN_AAA(X, Y, Z) 18.38/5.66 ADDZ_IN_AAA(one(X), one(Y), zero(Z)) -> U13_AAA(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.38/5.66 ADDZ_IN_AAA(one(X), one(Y), zero(Z)) -> ADDC_IN_AAA(X, Y, Z) 18.38/5.66 ADDC_IN_AAA(X, b, Z) -> U14_AAA(X, Z, succZ_in_aa(X, Z)) 18.38/5.66 ADDC_IN_AAA(X, b, Z) -> SUCCZ_IN_AA(X, Z) 18.38/5.66 SUCCZ_IN_AA(zero(X), one(X)) -> U33_AA(X, binaryZ_in_a(X)) 18.38/5.66 SUCCZ_IN_AA(zero(X), one(X)) -> BINARYZ_IN_A(X) 18.38/5.66 SUCCZ_IN_AA(one(X), zero(Z)) -> U34_AA(X, Z, succ_in_aa(X, Z)) 18.38/5.66 SUCCZ_IN_AA(one(X), zero(Z)) -> SUCC_IN_AA(X, Z) 18.38/5.66 SUCC_IN_AA(zero(X), one(X)) -> U31_AA(X, binaryZ_in_a(X)) 18.38/5.66 SUCC_IN_AA(zero(X), one(X)) -> BINARYZ_IN_A(X) 18.38/5.66 SUCC_IN_AA(one(X), zero(Z)) -> U32_AA(X, Z, succ_in_aa(X, Z)) 18.38/5.66 SUCC_IN_AA(one(X), zero(Z)) -> SUCC_IN_AA(X, Z) 18.38/5.66 ADDC_IN_AAA(b, Y, Z) -> U15_AAA(Y, Z, succZ_in_aa(Y, Z)) 18.38/5.66 ADDC_IN_AAA(b, Y, Z) -> SUCCZ_IN_AA(Y, Z) 18.38/5.66 ADDC_IN_AAA(X, Y, Z) -> U16_AAA(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.66 ADDC_IN_AAA(X, Y, Z) -> ADDC_IN_AAA^1(X, Y, Z) 18.38/5.66 ADDC_IN_AAA^1(zero(X), zero(Y), one(Z)) -> U23_AAA(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.66 ADDC_IN_AAA^1(zero(X), zero(Y), one(Z)) -> ADDZ_IN_AAA(X, Y, Z) 18.38/5.66 ADDC_IN_AAA^1(zero(X), one(Y), zero(Z)) -> U24_AAA(X, Y, Z, addX_in_aaa(X, Y, Z)) 18.38/5.66 ADDC_IN_AAA^1(zero(X), one(Y), zero(Z)) -> ADDX_IN_AAA^1(X, Y, Z) 18.38/5.66 ADDX_IN_AAA^1(zero(X), b, one(X)) -> U17_AAA(X, binaryZ_in_a(X)) 18.38/5.66 ADDX_IN_AAA^1(zero(X), b, one(X)) -> BINARYZ_IN_A(X) 18.38/5.66 ADDX_IN_AAA^1(one(X), b, zero(Z)) -> U18_AAA(X, Z, succ_in_aa(X, Z)) 18.38/5.66 ADDX_IN_AAA^1(one(X), b, zero(Z)) -> SUCC_IN_AA(X, Z) 18.38/5.66 ADDX_IN_AAA^1(X, Y, Z) -> U19_AAA(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.66 ADDX_IN_AAA^1(X, Y, Z) -> ADDC_IN_AAA^1(X, Y, Z) 18.38/5.66 ADDC_IN_AAA^1(one(X), zero(Y), zero(Z)) -> U25_AAA(X, Y, Z, addY_in_aaa(X, Y, Z)) 18.38/5.66 ADDC_IN_AAA^1(one(X), zero(Y), zero(Z)) -> ADDY_IN_AAA^1(X, Y, Z) 18.38/5.66 ADDY_IN_AAA^1(b, zero(Y), one(Y)) -> U20_AAA(Y, binaryZ_in_a(Y)) 18.38/5.66 ADDY_IN_AAA^1(b, zero(Y), one(Y)) -> BINARYZ_IN_A(Y) 18.38/5.66 ADDY_IN_AAA^1(b, one(Y), zero(Z)) -> U21_AAA(Y, Z, succ_in_aa(Y, Z)) 18.38/5.66 ADDY_IN_AAA^1(b, one(Y), zero(Z)) -> SUCC_IN_AA(Y, Z) 18.38/5.66 ADDY_IN_AAA^1(X, Y, Z) -> U22_AAA(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.66 ADDY_IN_AAA^1(X, Y, Z) -> ADDC_IN_AAA^1(X, Y, Z) 18.38/5.66 ADDC_IN_AAA^1(one(X), one(Y), one(Z)) -> U26_AAA(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.38/5.66 ADDC_IN_AAA^1(one(X), one(Y), one(Z)) -> ADDC_IN_AAA(X, Y, Z) 18.38/5.66 U36_AAG(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_AAG(R, S, RSS, add_in_aag(S, zero(RS), RSS)) 18.38/5.66 U36_AAG(R, S, RSS, times_out_aaa(R, S, RS)) -> ADD_IN_AAG(S, zero(RS), RSS) 18.38/5.66 ADD_IN_AAG(X, b, X) -> U1_AAG(X, binaryZ_in_g(X)) 18.38/5.66 ADD_IN_AAG(X, b, X) -> BINARYZ_IN_G(X) 18.38/5.66 BINARYZ_IN_G(zero(X)) -> U29_G(X, binaryZ_in_g(X)) 18.38/5.66 BINARYZ_IN_G(zero(X)) -> BINARYZ_IN_G(X) 18.38/5.66 BINARYZ_IN_G(one(X)) -> U30_G(X, binary_in_g(X)) 18.38/5.66 BINARYZ_IN_G(one(X)) -> BINARY_IN_G(X) 18.38/5.66 BINARY_IN_G(zero(X)) -> U27_G(X, binaryZ_in_g(X)) 18.38/5.66 BINARY_IN_G(zero(X)) -> BINARYZ_IN_G(X) 18.38/5.66 BINARY_IN_G(one(X)) -> U28_G(X, binary_in_g(X)) 18.38/5.66 BINARY_IN_G(one(X)) -> BINARY_IN_G(X) 18.38/5.66 ADD_IN_AAG(b, Y, Y) -> U2_AAG(Y, binaryZ_in_g(Y)) 18.38/5.66 ADD_IN_AAG(b, Y, Y) -> BINARYZ_IN_G(Y) 18.38/5.66 ADD_IN_AAG(X, Y, Z) -> U3_AAG(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.66 ADD_IN_AAG(X, Y, Z) -> ADDZ_IN_AAG(X, Y, Z) 18.38/5.66 ADDZ_IN_AAG(zero(X), zero(Y), zero(Z)) -> U10_AAG(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.66 ADDZ_IN_AAG(zero(X), zero(Y), zero(Z)) -> ADDZ_IN_AAG(X, Y, Z) 18.38/5.66 ADDZ_IN_AAG(zero(X), one(Y), one(Z)) -> U11_AAG(X, Y, Z, addx_in_aag(X, Y, Z)) 18.38/5.66 ADDZ_IN_AAG(zero(X), one(Y), one(Z)) -> ADDX_IN_AAG(X, Y, Z) 18.38/5.66 ADDX_IN_AAG(one(X), b, one(X)) -> U4_AAG(X, binary_in_g(X)) 18.38/5.66 ADDX_IN_AAG(one(X), b, one(X)) -> BINARY_IN_G(X) 18.38/5.66 ADDX_IN_AAG(zero(X), b, zero(X)) -> U5_AAG(X, binaryZ_in_g(X)) 18.38/5.66 ADDX_IN_AAG(zero(X), b, zero(X)) -> BINARYZ_IN_G(X) 18.38/5.66 ADDX_IN_AAG(X, Y, Z) -> U6_AAG(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.66 ADDX_IN_AAG(X, Y, Z) -> ADDZ_IN_AAG(X, Y, Z) 18.38/5.66 ADDZ_IN_AAG(one(X), zero(Y), one(Z)) -> U12_AAG(X, Y, Z, addy_in_aag(X, Y, Z)) 18.38/5.66 ADDZ_IN_AAG(one(X), zero(Y), one(Z)) -> ADDY_IN_AAG(X, Y, Z) 18.38/5.66 ADDY_IN_AAG(b, one(Y), one(Y)) -> U7_AAG(Y, binary_in_g(Y)) 18.38/5.66 ADDY_IN_AAG(b, one(Y), one(Y)) -> BINARY_IN_G(Y) 18.38/5.66 ADDY_IN_AAG(b, zero(Y), zero(Y)) -> U8_AAG(Y, binaryZ_in_g(Y)) 18.38/5.66 ADDY_IN_AAG(b, zero(Y), zero(Y)) -> BINARYZ_IN_G(Y) 18.38/5.66 ADDY_IN_AAG(X, Y, Z) -> U9_AAG(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.66 ADDY_IN_AAG(X, Y, Z) -> ADDZ_IN_AAG(X, Y, Z) 18.38/5.66 ADDZ_IN_AAG(one(X), one(Y), zero(Z)) -> U13_AAG(X, Y, Z, addc_in_aag(X, Y, Z)) 18.38/5.66 ADDZ_IN_AAG(one(X), one(Y), zero(Z)) -> ADDC_IN_AAG(X, Y, Z) 18.38/5.66 ADDC_IN_AAG(X, b, Z) -> U14_AAG(X, Z, succZ_in_ag(X, Z)) 18.38/5.66 ADDC_IN_AAG(X, b, Z) -> SUCCZ_IN_AG(X, Z) 18.38/5.66 SUCCZ_IN_AG(zero(X), one(X)) -> U33_AG(X, binaryZ_in_g(X)) 18.38/5.66 SUCCZ_IN_AG(zero(X), one(X)) -> BINARYZ_IN_G(X) 18.38/5.66 SUCCZ_IN_AG(one(X), zero(Z)) -> U34_AG(X, Z, succ_in_ag(X, Z)) 18.38/5.66 SUCCZ_IN_AG(one(X), zero(Z)) -> SUCC_IN_AG(X, Z) 18.38/5.66 SUCC_IN_AG(zero(X), one(X)) -> U31_AG(X, binaryZ_in_g(X)) 18.38/5.66 SUCC_IN_AG(zero(X), one(X)) -> BINARYZ_IN_G(X) 18.38/5.66 SUCC_IN_AG(one(X), zero(Z)) -> U32_AG(X, Z, succ_in_ag(X, Z)) 18.38/5.66 SUCC_IN_AG(one(X), zero(Z)) -> SUCC_IN_AG(X, Z) 18.38/5.66 ADDC_IN_AAG(b, Y, Z) -> U15_AAG(Y, Z, succZ_in_ag(Y, Z)) 18.38/5.66 ADDC_IN_AAG(b, Y, Z) -> SUCCZ_IN_AG(Y, Z) 18.38/5.66 ADDC_IN_AAG(X, Y, Z) -> U16_AAG(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.66 ADDC_IN_AAG(X, Y, Z) -> ADDC_IN_AAG^1(X, Y, Z) 18.38/5.66 ADDC_IN_AAG^1(zero(X), zero(Y), one(Z)) -> U23_AAG(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.66 ADDC_IN_AAG^1(zero(X), zero(Y), one(Z)) -> ADDZ_IN_AAG(X, Y, Z) 18.38/5.66 ADDC_IN_AAG^1(zero(X), one(Y), zero(Z)) -> U24_AAG(X, Y, Z, addX_in_aag(X, Y, Z)) 18.38/5.66 ADDC_IN_AAG^1(zero(X), one(Y), zero(Z)) -> ADDX_IN_AAG^1(X, Y, Z) 18.38/5.66 ADDX_IN_AAG^1(zero(X), b, one(X)) -> U17_AAG(X, binaryZ_in_g(X)) 18.38/5.66 ADDX_IN_AAG^1(zero(X), b, one(X)) -> BINARYZ_IN_G(X) 18.38/5.66 ADDX_IN_AAG^1(one(X), b, zero(Z)) -> U18_AAG(X, Z, succ_in_ag(X, Z)) 18.38/5.66 ADDX_IN_AAG^1(one(X), b, zero(Z)) -> SUCC_IN_AG(X, Z) 18.38/5.66 ADDX_IN_AAG^1(X, Y, Z) -> U19_AAG(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.66 ADDX_IN_AAG^1(X, Y, Z) -> ADDC_IN_AAG^1(X, Y, Z) 18.38/5.66 ADDC_IN_AAG^1(one(X), zero(Y), zero(Z)) -> U25_AAG(X, Y, Z, addY_in_aag(X, Y, Z)) 18.38/5.66 ADDC_IN_AAG^1(one(X), zero(Y), zero(Z)) -> ADDY_IN_AAG^1(X, Y, Z) 18.38/5.66 ADDY_IN_AAG^1(b, zero(Y), one(Y)) -> U20_AAG(Y, binaryZ_in_g(Y)) 18.38/5.66 ADDY_IN_AAG^1(b, zero(Y), one(Y)) -> BINARYZ_IN_G(Y) 18.38/5.66 ADDY_IN_AAG^1(b, one(Y), zero(Z)) -> U21_AAG(Y, Z, succ_in_ag(Y, Z)) 18.38/5.66 ADDY_IN_AAG^1(b, one(Y), zero(Z)) -> SUCC_IN_AG(Y, Z) 18.38/5.66 ADDY_IN_AAG^1(X, Y, Z) -> U22_AAG(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.66 ADDY_IN_AAG^1(X, Y, Z) -> ADDC_IN_AAG^1(X, Y, Z) 18.38/5.66 ADDC_IN_AAG^1(one(X), one(Y), one(Z)) -> U26_AAG(X, Y, Z, addc_in_aag(X, Y, Z)) 18.38/5.66 ADDC_IN_AAG^1(one(X), one(Y), one(Z)) -> ADDC_IN_AAG(X, Y, Z) 18.38/5.66 18.38/5.66 The TRS R consists of the following rules: 18.38/5.66 18.38/5.66 times_in_aag(one(b), X, X) -> times_out_aag(one(b), X, X) 18.38/5.66 times_in_aag(zero(R), S, zero(RS)) -> U35_aag(R, S, RS, times_in_aag(R, S, RS)) 18.38/5.66 times_in_aag(one(R), S, RSS) -> U36_aag(R, S, RSS, times_in_aaa(R, S, RS)) 18.38/5.66 times_in_aaa(one(b), X, X) -> times_out_aaa(one(b), X, X) 18.38/5.66 times_in_aaa(zero(R), S, zero(RS)) -> U35_aaa(R, S, RS, times_in_aaa(R, S, RS)) 18.38/5.66 times_in_aaa(one(R), S, RSS) -> U36_aaa(R, S, RSS, times_in_aaa(R, S, RS)) 18.38/5.66 U36_aaa(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aaa(R, S, RSS, add_in_aaa(S, zero(RS), RSS)) 18.38/5.66 add_in_aaa(b, b, b) -> add_out_aaa(b, b, b) 18.38/5.66 add_in_aaa(X, b, X) -> U1_aaa(X, binaryZ_in_a(X)) 18.38/5.66 binaryZ_in_a(zero(X)) -> U29_a(X, binaryZ_in_a(X)) 18.38/5.66 binaryZ_in_a(one(X)) -> U30_a(X, binary_in_a(X)) 18.38/5.66 binary_in_a(b) -> binary_out_a(b) 18.38/5.66 binary_in_a(zero(X)) -> U27_a(X, binaryZ_in_a(X)) 18.38/5.66 U27_a(X, binaryZ_out_a(X)) -> binary_out_a(zero(X)) 18.38/5.66 binary_in_a(one(X)) -> U28_a(X, binary_in_a(X)) 18.38/5.66 U28_a(X, binary_out_a(X)) -> binary_out_a(one(X)) 18.38/5.66 U30_a(X, binary_out_a(X)) -> binaryZ_out_a(one(X)) 18.38/5.66 U29_a(X, binaryZ_out_a(X)) -> binaryZ_out_a(zero(X)) 18.38/5.66 U1_aaa(X, binaryZ_out_a(X)) -> add_out_aaa(X, b, X) 18.38/5.66 add_in_aaa(b, Y, Y) -> U2_aaa(Y, binaryZ_in_a(Y)) 18.38/5.66 U2_aaa(Y, binaryZ_out_a(Y)) -> add_out_aaa(b, Y, Y) 18.38/5.66 add_in_aaa(X, Y, Z) -> U3_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.66 addz_in_aaa(zero(X), zero(Y), zero(Z)) -> U10_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.66 addz_in_aaa(zero(X), one(Y), one(Z)) -> U11_aaa(X, Y, Z, addx_in_aaa(X, Y, Z)) 18.38/5.66 addx_in_aaa(one(X), b, one(X)) -> U4_aaa(X, binary_in_a(X)) 18.38/5.66 U4_aaa(X, binary_out_a(X)) -> addx_out_aaa(one(X), b, one(X)) 18.38/5.66 addx_in_aaa(zero(X), b, zero(X)) -> U5_aaa(X, binaryZ_in_a(X)) 18.38/5.66 U5_aaa(X, binaryZ_out_a(X)) -> addx_out_aaa(zero(X), b, zero(X)) 18.38/5.66 addx_in_aaa(X, Y, Z) -> U6_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.66 addz_in_aaa(one(X), zero(Y), one(Z)) -> U12_aaa(X, Y, Z, addy_in_aaa(X, Y, Z)) 18.38/5.66 addy_in_aaa(b, one(Y), one(Y)) -> U7_aaa(Y, binary_in_a(Y)) 18.38/5.66 U7_aaa(Y, binary_out_a(Y)) -> addy_out_aaa(b, one(Y), one(Y)) 18.38/5.66 addy_in_aaa(b, zero(Y), zero(Y)) -> U8_aaa(Y, binaryZ_in_a(Y)) 18.38/5.66 U8_aaa(Y, binaryZ_out_a(Y)) -> addy_out_aaa(b, zero(Y), zero(Y)) 18.38/5.66 addy_in_aaa(X, Y, Z) -> U9_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.66 addz_in_aaa(one(X), one(Y), zero(Z)) -> U13_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.38/5.66 addc_in_aaa(b, b, one(b)) -> addc_out_aaa(b, b, one(b)) 18.38/5.66 addc_in_aaa(X, b, Z) -> U14_aaa(X, Z, succZ_in_aa(X, Z)) 18.38/5.66 succZ_in_aa(zero(X), one(X)) -> U33_aa(X, binaryZ_in_a(X)) 18.38/5.66 U33_aa(X, binaryZ_out_a(X)) -> succZ_out_aa(zero(X), one(X)) 18.38/5.66 succZ_in_aa(one(X), zero(Z)) -> U34_aa(X, Z, succ_in_aa(X, Z)) 18.38/5.66 succ_in_aa(b, one(b)) -> succ_out_aa(b, one(b)) 18.38/5.66 succ_in_aa(zero(X), one(X)) -> U31_aa(X, binaryZ_in_a(X)) 18.38/5.66 U31_aa(X, binaryZ_out_a(X)) -> succ_out_aa(zero(X), one(X)) 18.38/5.66 succ_in_aa(one(X), zero(Z)) -> U32_aa(X, Z, succ_in_aa(X, Z)) 18.38/5.66 U32_aa(X, Z, succ_out_aa(X, Z)) -> succ_out_aa(one(X), zero(Z)) 18.38/5.66 U34_aa(X, Z, succ_out_aa(X, Z)) -> succZ_out_aa(one(X), zero(Z)) 18.38/5.66 U14_aaa(X, Z, succZ_out_aa(X, Z)) -> addc_out_aaa(X, b, Z) 18.38/5.66 addc_in_aaa(b, Y, Z) -> U15_aaa(Y, Z, succZ_in_aa(Y, Z)) 18.38/5.66 U15_aaa(Y, Z, succZ_out_aa(Y, Z)) -> addc_out_aaa(b, Y, Z) 18.38/5.66 addc_in_aaa(X, Y, Z) -> U16_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.66 addC_in_aaa(zero(X), zero(Y), one(Z)) -> U23_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.66 U23_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), zero(Y), one(Z)) 18.38/5.66 addC_in_aaa(zero(X), one(Y), zero(Z)) -> U24_aaa(X, Y, Z, addX_in_aaa(X, Y, Z)) 18.38/5.66 addX_in_aaa(zero(X), b, one(X)) -> U17_aaa(X, binaryZ_in_a(X)) 18.38/5.66 U17_aaa(X, binaryZ_out_a(X)) -> addX_out_aaa(zero(X), b, one(X)) 18.38/5.66 addX_in_aaa(one(X), b, zero(Z)) -> U18_aaa(X, Z, succ_in_aa(X, Z)) 18.38/5.66 U18_aaa(X, Z, succ_out_aa(X, Z)) -> addX_out_aaa(one(X), b, zero(Z)) 18.38/5.66 addX_in_aaa(X, Y, Z) -> U19_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.66 addC_in_aaa(one(X), zero(Y), zero(Z)) -> U25_aaa(X, Y, Z, addY_in_aaa(X, Y, Z)) 18.38/5.66 addY_in_aaa(b, zero(Y), one(Y)) -> U20_aaa(Y, binaryZ_in_a(Y)) 18.38/5.66 U20_aaa(Y, binaryZ_out_a(Y)) -> addY_out_aaa(b, zero(Y), one(Y)) 18.38/5.66 addY_in_aaa(b, one(Y), zero(Z)) -> U21_aaa(Y, Z, succ_in_aa(Y, Z)) 18.38/5.66 U21_aaa(Y, Z, succ_out_aa(Y, Z)) -> addY_out_aaa(b, one(Y), zero(Z)) 18.38/5.66 addY_in_aaa(X, Y, Z) -> U22_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.66 addC_in_aaa(one(X), one(Y), one(Z)) -> U26_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.38/5.66 U26_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), one(Y), one(Z)) 18.38/5.66 U22_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addY_out_aaa(X, Y, Z) 18.38/5.66 U25_aaa(X, Y, Z, addY_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), zero(Y), zero(Z)) 18.38/5.66 U19_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addX_out_aaa(X, Y, Z) 18.38/5.66 U24_aaa(X, Y, Z, addX_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), one(Y), zero(Z)) 18.38/5.66 U16_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addc_out_aaa(X, Y, Z) 18.38/5.66 U13_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), one(Y), zero(Z)) 18.38/5.66 U9_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addy_out_aaa(X, Y, Z) 18.38/5.66 U12_aaa(X, Y, Z, addy_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), zero(Y), one(Z)) 18.38/5.66 U6_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addx_out_aaa(X, Y, Z) 18.38/5.66 U11_aaa(X, Y, Z, addx_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), one(Y), one(Z)) 18.38/5.66 U10_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), zero(Y), zero(Z)) 18.38/5.66 U3_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> add_out_aaa(X, Y, Z) 18.38/5.66 U37_aaa(R, S, RSS, add_out_aaa(S, zero(RS), RSS)) -> times_out_aaa(one(R), S, RSS) 18.38/5.66 U35_aaa(R, S, RS, times_out_aaa(R, S, RS)) -> times_out_aaa(zero(R), S, zero(RS)) 18.38/5.66 U36_aag(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aag(R, S, RSS, add_in_aag(S, zero(RS), RSS)) 18.38/5.66 add_in_aag(b, b, b) -> add_out_aag(b, b, b) 18.38/5.66 add_in_aag(X, b, X) -> U1_aag(X, binaryZ_in_g(X)) 18.38/5.66 binaryZ_in_g(zero(X)) -> U29_g(X, binaryZ_in_g(X)) 18.38/5.66 binaryZ_in_g(one(X)) -> U30_g(X, binary_in_g(X)) 18.38/5.66 binary_in_g(b) -> binary_out_g(b) 18.38/5.66 binary_in_g(zero(X)) -> U27_g(X, binaryZ_in_g(X)) 18.38/5.66 U27_g(X, binaryZ_out_g(X)) -> binary_out_g(zero(X)) 18.38/5.66 binary_in_g(one(X)) -> U28_g(X, binary_in_g(X)) 18.38/5.66 U28_g(X, binary_out_g(X)) -> binary_out_g(one(X)) 18.38/5.66 U30_g(X, binary_out_g(X)) -> binaryZ_out_g(one(X)) 18.38/5.66 U29_g(X, binaryZ_out_g(X)) -> binaryZ_out_g(zero(X)) 18.38/5.66 U1_aag(X, binaryZ_out_g(X)) -> add_out_aag(X, b, X) 18.38/5.66 add_in_aag(b, Y, Y) -> U2_aag(Y, binaryZ_in_g(Y)) 18.38/5.66 U2_aag(Y, binaryZ_out_g(Y)) -> add_out_aag(b, Y, Y) 18.38/5.66 add_in_aag(X, Y, Z) -> U3_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.66 addz_in_aag(zero(X), zero(Y), zero(Z)) -> U10_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.66 addz_in_aag(zero(X), one(Y), one(Z)) -> U11_aag(X, Y, Z, addx_in_aag(X, Y, Z)) 18.38/5.66 addx_in_aag(one(X), b, one(X)) -> U4_aag(X, binary_in_g(X)) 18.38/5.66 U4_aag(X, binary_out_g(X)) -> addx_out_aag(one(X), b, one(X)) 18.38/5.66 addx_in_aag(zero(X), b, zero(X)) -> U5_aag(X, binaryZ_in_g(X)) 18.38/5.66 U5_aag(X, binaryZ_out_g(X)) -> addx_out_aag(zero(X), b, zero(X)) 18.38/5.66 addx_in_aag(X, Y, Z) -> U6_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.66 addz_in_aag(one(X), zero(Y), one(Z)) -> U12_aag(X, Y, Z, addy_in_aag(X, Y, Z)) 18.38/5.66 addy_in_aag(b, one(Y), one(Y)) -> U7_aag(Y, binary_in_g(Y)) 18.38/5.66 U7_aag(Y, binary_out_g(Y)) -> addy_out_aag(b, one(Y), one(Y)) 18.38/5.66 addy_in_aag(b, zero(Y), zero(Y)) -> U8_aag(Y, binaryZ_in_g(Y)) 18.38/5.66 U8_aag(Y, binaryZ_out_g(Y)) -> addy_out_aag(b, zero(Y), zero(Y)) 18.38/5.66 addy_in_aag(X, Y, Z) -> U9_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.66 addz_in_aag(one(X), one(Y), zero(Z)) -> U13_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.38/5.66 addc_in_aag(b, b, one(b)) -> addc_out_aag(b, b, one(b)) 18.38/5.66 addc_in_aag(X, b, Z) -> U14_aag(X, Z, succZ_in_ag(X, Z)) 18.38/5.66 succZ_in_ag(zero(X), one(X)) -> U33_ag(X, binaryZ_in_g(X)) 18.38/5.66 U33_ag(X, binaryZ_out_g(X)) -> succZ_out_ag(zero(X), one(X)) 18.38/5.66 succZ_in_ag(one(X), zero(Z)) -> U34_ag(X, Z, succ_in_ag(X, Z)) 18.38/5.66 succ_in_ag(b, one(b)) -> succ_out_ag(b, one(b)) 18.38/5.66 succ_in_ag(zero(X), one(X)) -> U31_ag(X, binaryZ_in_g(X)) 18.38/5.66 U31_ag(X, binaryZ_out_g(X)) -> succ_out_ag(zero(X), one(X)) 18.38/5.66 succ_in_ag(one(X), zero(Z)) -> U32_ag(X, Z, succ_in_ag(X, Z)) 18.38/5.66 U32_ag(X, Z, succ_out_ag(X, Z)) -> succ_out_ag(one(X), zero(Z)) 18.38/5.66 U34_ag(X, Z, succ_out_ag(X, Z)) -> succZ_out_ag(one(X), zero(Z)) 18.38/5.66 U14_aag(X, Z, succZ_out_ag(X, Z)) -> addc_out_aag(X, b, Z) 18.38/5.66 addc_in_aag(b, Y, Z) -> U15_aag(Y, Z, succZ_in_ag(Y, Z)) 18.38/5.66 U15_aag(Y, Z, succZ_out_ag(Y, Z)) -> addc_out_aag(b, Y, Z) 18.38/5.66 addc_in_aag(X, Y, Z) -> U16_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.66 addC_in_aag(zero(X), zero(Y), one(Z)) -> U23_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.66 U23_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), zero(Y), one(Z)) 18.38/5.66 addC_in_aag(zero(X), one(Y), zero(Z)) -> U24_aag(X, Y, Z, addX_in_aag(X, Y, Z)) 18.38/5.66 addX_in_aag(zero(X), b, one(X)) -> U17_aag(X, binaryZ_in_g(X)) 18.38/5.66 U17_aag(X, binaryZ_out_g(X)) -> addX_out_aag(zero(X), b, one(X)) 18.38/5.66 addX_in_aag(one(X), b, zero(Z)) -> U18_aag(X, Z, succ_in_ag(X, Z)) 18.38/5.66 U18_aag(X, Z, succ_out_ag(X, Z)) -> addX_out_aag(one(X), b, zero(Z)) 18.38/5.66 addX_in_aag(X, Y, Z) -> U19_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.66 addC_in_aag(one(X), zero(Y), zero(Z)) -> U25_aag(X, Y, Z, addY_in_aag(X, Y, Z)) 18.38/5.66 addY_in_aag(b, zero(Y), one(Y)) -> U20_aag(Y, binaryZ_in_g(Y)) 18.38/5.66 U20_aag(Y, binaryZ_out_g(Y)) -> addY_out_aag(b, zero(Y), one(Y)) 18.38/5.66 addY_in_aag(b, one(Y), zero(Z)) -> U21_aag(Y, Z, succ_in_ag(Y, Z)) 18.38/5.66 U21_aag(Y, Z, succ_out_ag(Y, Z)) -> addY_out_aag(b, one(Y), zero(Z)) 18.38/5.66 addY_in_aag(X, Y, Z) -> U22_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.66 addC_in_aag(one(X), one(Y), one(Z)) -> U26_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.38/5.66 U26_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addC_out_aag(one(X), one(Y), one(Z)) 18.38/5.66 U22_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addY_out_aag(X, Y, Z) 18.38/5.66 U25_aag(X, Y, Z, addY_out_aag(X, Y, Z)) -> addC_out_aag(one(X), zero(Y), zero(Z)) 18.38/5.66 U19_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addX_out_aag(X, Y, Z) 18.38/5.66 U24_aag(X, Y, Z, addX_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), one(Y), zero(Z)) 18.38/5.66 U16_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addc_out_aag(X, Y, Z) 18.38/5.66 U13_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addz_out_aag(one(X), one(Y), zero(Z)) 18.38/5.66 U9_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addy_out_aag(X, Y, Z) 18.38/5.66 U12_aag(X, Y, Z, addy_out_aag(X, Y, Z)) -> addz_out_aag(one(X), zero(Y), one(Z)) 18.38/5.66 U6_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addx_out_aag(X, Y, Z) 18.38/5.66 U11_aag(X, Y, Z, addx_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), one(Y), one(Z)) 18.38/5.66 U10_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), zero(Y), zero(Z)) 18.38/5.66 U3_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> add_out_aag(X, Y, Z) 18.38/5.66 U37_aag(R, S, RSS, add_out_aag(S, zero(RS), RSS)) -> times_out_aag(one(R), S, RSS) 18.38/5.66 U35_aag(R, S, RS, times_out_aag(R, S, RS)) -> times_out_aag(zero(R), S, zero(RS)) 18.38/5.66 18.38/5.66 The argument filtering Pi contains the following mapping: 18.38/5.66 times_in_aag(x1, x2, x3) = times_in_aag(x3) 18.38/5.66 18.38/5.66 times_out_aag(x1, x2, x3) = times_out_aag(x1, x2) 18.38/5.66 18.38/5.66 zero(x1) = zero(x1) 18.38/5.66 18.38/5.66 U35_aag(x1, x2, x3, x4) = U35_aag(x4) 18.38/5.66 18.38/5.66 U36_aag(x1, x2, x3, x4) = U36_aag(x3, x4) 18.38/5.66 18.38/5.66 times_in_aaa(x1, x2, x3) = times_in_aaa 18.38/5.66 18.38/5.66 times_out_aaa(x1, x2, x3) = times_out_aaa(x1) 18.38/5.66 18.38/5.66 U35_aaa(x1, x2, x3, x4) = U35_aaa(x4) 18.38/5.66 18.38/5.66 U36_aaa(x1, x2, x3, x4) = U36_aaa(x4) 18.38/5.66 18.38/5.66 U37_aaa(x1, x2, x3, x4) = U37_aaa(x1, x4) 18.38/5.66 18.38/5.66 add_in_aaa(x1, x2, x3) = add_in_aaa 18.38/5.66 18.38/5.66 add_out_aaa(x1, x2, x3) = add_out_aaa(x1, x2, x3) 18.38/5.66 18.38/5.66 U1_aaa(x1, x2) = U1_aaa(x2) 18.38/5.66 18.38/5.66 binaryZ_in_a(x1) = binaryZ_in_a 18.38/5.66 18.38/5.66 U29_a(x1, x2) = U29_a(x2) 18.38/5.66 18.38/5.66 U30_a(x1, x2) = U30_a(x2) 18.38/5.66 18.38/5.66 binary_in_a(x1) = binary_in_a 18.38/5.66 18.38/5.66 binary_out_a(x1) = binary_out_a(x1) 18.38/5.66 18.38/5.66 U27_a(x1, x2) = U27_a(x2) 18.38/5.66 18.38/5.66 binaryZ_out_a(x1) = binaryZ_out_a(x1) 18.38/5.66 18.38/5.66 U28_a(x1, x2) = U28_a(x2) 18.38/5.66 18.38/5.66 U2_aaa(x1, x2) = U2_aaa(x2) 18.38/5.66 18.38/5.66 U3_aaa(x1, x2, x3, x4) = U3_aaa(x4) 18.38/5.66 18.38/5.66 addz_in_aaa(x1, x2, x3) = addz_in_aaa 18.38/5.66 18.38/5.66 U10_aaa(x1, x2, x3, x4) = U10_aaa(x4) 18.38/5.66 18.38/5.66 U11_aaa(x1, x2, x3, x4) = U11_aaa(x4) 18.38/5.66 18.38/5.66 addx_in_aaa(x1, x2, x3) = addx_in_aaa 18.38/5.66 18.38/5.66 U4_aaa(x1, x2) = U4_aaa(x2) 18.38/5.66 18.38/5.66 addx_out_aaa(x1, x2, x3) = addx_out_aaa(x1, x2, x3) 18.38/5.66 18.38/5.66 U5_aaa(x1, x2) = U5_aaa(x2) 18.38/5.66 18.38/5.66 U6_aaa(x1, x2, x3, x4) = U6_aaa(x4) 18.38/5.66 18.38/5.66 U12_aaa(x1, x2, x3, x4) = U12_aaa(x4) 18.38/5.66 18.38/5.66 addy_in_aaa(x1, x2, x3) = addy_in_aaa 18.38/5.66 18.38/5.66 U7_aaa(x1, x2) = U7_aaa(x2) 18.38/5.66 18.38/5.66 addy_out_aaa(x1, x2, x3) = addy_out_aaa(x1, x2, x3) 18.38/5.66 18.38/5.66 U8_aaa(x1, x2) = U8_aaa(x2) 18.38/5.66 18.38/5.66 U9_aaa(x1, x2, x3, x4) = U9_aaa(x4) 18.38/5.66 18.38/5.66 U13_aaa(x1, x2, x3, x4) = U13_aaa(x4) 18.38/5.66 18.38/5.66 addc_in_aaa(x1, x2, x3) = addc_in_aaa 18.38/5.66 18.38/5.66 addc_out_aaa(x1, x2, x3) = addc_out_aaa(x1, x2, x3) 18.38/5.66 18.38/5.66 U14_aaa(x1, x2, x3) = U14_aaa(x3) 18.38/5.66 18.38/5.66 succZ_in_aa(x1, x2) = succZ_in_aa 18.38/5.66 18.38/5.66 U33_aa(x1, x2) = U33_aa(x2) 18.38/5.66 18.38/5.66 succZ_out_aa(x1, x2) = succZ_out_aa(x1, x2) 18.38/5.66 18.38/5.66 U34_aa(x1, x2, x3) = U34_aa(x3) 18.38/5.66 18.38/5.66 succ_in_aa(x1, x2) = succ_in_aa 18.38/5.66 18.38/5.66 succ_out_aa(x1, x2) = succ_out_aa(x1, x2) 18.38/5.66 18.38/5.66 U31_aa(x1, x2) = U31_aa(x2) 18.38/5.66 18.38/5.66 U32_aa(x1, x2, x3) = U32_aa(x3) 18.38/5.66 18.38/5.66 U15_aaa(x1, x2, x3) = U15_aaa(x3) 18.38/5.66 18.38/5.66 U16_aaa(x1, x2, x3, x4) = U16_aaa(x4) 18.38/5.66 18.38/5.66 addC_in_aaa(x1, x2, x3) = addC_in_aaa 18.38/5.66 18.38/5.66 U23_aaa(x1, x2, x3, x4) = U23_aaa(x4) 18.38/5.66 18.38/5.66 addz_out_aaa(x1, x2, x3) = addz_out_aaa(x1, x2, x3) 18.38/5.66 18.38/5.66 addC_out_aaa(x1, x2, x3) = addC_out_aaa(x1, x2, x3) 18.38/5.66 18.38/5.66 U24_aaa(x1, x2, x3, x4) = U24_aaa(x4) 18.38/5.66 18.38/5.66 addX_in_aaa(x1, x2, x3) = addX_in_aaa 18.38/5.66 18.38/5.66 U17_aaa(x1, x2) = U17_aaa(x2) 18.38/5.66 18.38/5.66 addX_out_aaa(x1, x2, x3) = addX_out_aaa(x1, x2, x3) 18.38/5.66 18.38/5.66 U18_aaa(x1, x2, x3) = U18_aaa(x3) 18.38/5.66 18.38/5.66 U19_aaa(x1, x2, x3, x4) = U19_aaa(x4) 18.38/5.66 18.38/5.66 U25_aaa(x1, x2, x3, x4) = U25_aaa(x4) 18.38/5.66 18.38/5.66 addY_in_aaa(x1, x2, x3) = addY_in_aaa 18.38/5.66 18.38/5.66 U20_aaa(x1, x2) = U20_aaa(x2) 18.38/5.66 18.38/5.66 addY_out_aaa(x1, x2, x3) = addY_out_aaa(x1, x2, x3) 18.38/5.66 18.38/5.66 U21_aaa(x1, x2, x3) = U21_aaa(x3) 18.38/5.66 18.38/5.66 U22_aaa(x1, x2, x3, x4) = U22_aaa(x4) 18.38/5.66 18.38/5.66 U26_aaa(x1, x2, x3, x4) = U26_aaa(x4) 18.38/5.66 18.38/5.66 U37_aag(x1, x2, x3, x4) = U37_aag(x1, x4) 18.38/5.66 18.38/5.66 add_in_aag(x1, x2, x3) = add_in_aag(x3) 18.38/5.66 18.38/5.66 b = b 18.38/5.66 18.38/5.66 add_out_aag(x1, x2, x3) = add_out_aag(x1, x2) 18.38/5.66 18.38/5.66 U1_aag(x1, x2) = U1_aag(x1, x2) 18.38/5.66 18.38/5.66 binaryZ_in_g(x1) = binaryZ_in_g(x1) 18.38/5.66 18.38/5.66 U29_g(x1, x2) = U29_g(x2) 18.38/5.66 18.38/5.66 one(x1) = one(x1) 18.38/5.66 18.38/5.66 U30_g(x1, x2) = U30_g(x2) 18.38/5.66 18.38/5.66 binary_in_g(x1) = binary_in_g(x1) 18.38/5.66 18.38/5.66 binary_out_g(x1) = binary_out_g 18.38/5.66 18.38/5.66 U27_g(x1, x2) = U27_g(x2) 18.38/5.66 18.38/5.66 binaryZ_out_g(x1) = binaryZ_out_g 18.38/5.66 18.38/5.66 U28_g(x1, x2) = U28_g(x2) 18.38/5.66 18.38/5.66 U2_aag(x1, x2) = U2_aag(x1, x2) 18.38/5.66 18.38/5.66 U3_aag(x1, x2, x3, x4) = U3_aag(x4) 18.38/5.66 18.38/5.66 addz_in_aag(x1, x2, x3) = addz_in_aag(x3) 18.38/5.66 18.38/5.66 U10_aag(x1, x2, x3, x4) = U10_aag(x4) 18.38/5.66 18.38/5.66 U11_aag(x1, x2, x3, x4) = U11_aag(x4) 18.38/5.66 18.38/5.66 addx_in_aag(x1, x2, x3) = addx_in_aag(x3) 18.38/5.66 18.38/5.66 U4_aag(x1, x2) = U4_aag(x1, x2) 18.38/5.66 18.38/5.66 addx_out_aag(x1, x2, x3) = addx_out_aag(x1, x2) 18.38/5.66 18.38/5.66 U5_aag(x1, x2) = U5_aag(x1, x2) 18.38/5.66 18.38/5.66 U6_aag(x1, x2, x3, x4) = U6_aag(x4) 18.38/5.66 18.38/5.66 U12_aag(x1, x2, x3, x4) = U12_aag(x4) 18.38/5.66 18.38/5.66 addy_in_aag(x1, x2, x3) = addy_in_aag(x3) 18.38/5.66 18.38/5.66 U7_aag(x1, x2) = U7_aag(x1, x2) 18.38/5.66 18.38/5.66 addy_out_aag(x1, x2, x3) = addy_out_aag(x1, x2) 18.38/5.66 18.38/5.66 U8_aag(x1, x2) = U8_aag(x1, x2) 18.38/5.66 18.38/5.66 U9_aag(x1, x2, x3, x4) = U9_aag(x4) 18.38/5.66 18.38/5.66 U13_aag(x1, x2, x3, x4) = U13_aag(x4) 18.38/5.66 18.38/5.66 addc_in_aag(x1, x2, x3) = addc_in_aag(x3) 18.38/5.66 18.38/5.66 addc_out_aag(x1, x2, x3) = addc_out_aag(x1, x2) 18.38/5.66 18.38/5.66 U14_aag(x1, x2, x3) = U14_aag(x3) 18.38/5.66 18.38/5.66 succZ_in_ag(x1, x2) = succZ_in_ag(x2) 18.38/5.66 18.38/5.66 U33_ag(x1, x2) = U33_ag(x1, x2) 18.38/5.66 18.38/5.66 succZ_out_ag(x1, x2) = succZ_out_ag(x1) 18.38/5.66 18.38/5.66 U34_ag(x1, x2, x3) = U34_ag(x3) 18.38/5.66 18.38/5.66 succ_in_ag(x1, x2) = succ_in_ag(x2) 18.38/5.66 18.38/5.66 succ_out_ag(x1, x2) = succ_out_ag(x1) 18.38/5.66 18.38/5.66 U31_ag(x1, x2) = U31_ag(x1, x2) 18.38/5.66 18.38/5.66 U32_ag(x1, x2, x3) = U32_ag(x3) 18.38/5.66 18.38/5.66 U15_aag(x1, x2, x3) = U15_aag(x3) 18.38/5.66 18.38/5.66 U16_aag(x1, x2, x3, x4) = U16_aag(x4) 18.38/5.66 18.38/5.66 addC_in_aag(x1, x2, x3) = addC_in_aag(x3) 18.38/5.66 18.38/5.66 U23_aag(x1, x2, x3, x4) = U23_aag(x4) 18.38/5.66 18.38/5.66 addz_out_aag(x1, x2, x3) = addz_out_aag(x1, x2) 18.38/5.66 18.38/5.66 addC_out_aag(x1, x2, x3) = addC_out_aag(x1, x2) 18.38/5.66 18.38/5.66 U24_aag(x1, x2, x3, x4) = U24_aag(x4) 18.38/5.66 18.38/5.66 addX_in_aag(x1, x2, x3) = addX_in_aag(x3) 18.38/5.66 18.38/5.66 U17_aag(x1, x2) = U17_aag(x1, x2) 18.38/5.66 18.38/5.66 addX_out_aag(x1, x2, x3) = addX_out_aag(x1, x2) 18.38/5.66 18.38/5.66 U18_aag(x1, x2, x3) = U18_aag(x3) 18.38/5.66 18.38/5.66 U19_aag(x1, x2, x3, x4) = U19_aag(x4) 18.38/5.66 18.38/5.66 U25_aag(x1, x2, x3, x4) = U25_aag(x4) 18.38/5.66 18.38/5.66 addY_in_aag(x1, x2, x3) = addY_in_aag(x3) 18.38/5.66 18.38/5.66 U20_aag(x1, x2) = U20_aag(x1, x2) 18.38/5.66 18.38/5.66 addY_out_aag(x1, x2, x3) = addY_out_aag(x1, x2) 18.38/5.66 18.38/5.66 U21_aag(x1, x2, x3) = U21_aag(x3) 18.38/5.66 18.38/5.66 U22_aag(x1, x2, x3, x4) = U22_aag(x4) 18.38/5.66 18.38/5.66 U26_aag(x1, x2, x3, x4) = U26_aag(x4) 18.38/5.66 18.38/5.66 TIMES_IN_AAG(x1, x2, x3) = TIMES_IN_AAG(x3) 18.38/5.66 18.38/5.66 U35_AAG(x1, x2, x3, x4) = U35_AAG(x4) 18.38/5.66 18.38/5.66 U36_AAG(x1, x2, x3, x4) = U36_AAG(x3, x4) 18.38/5.66 18.38/5.66 TIMES_IN_AAA(x1, x2, x3) = TIMES_IN_AAA 18.38/5.66 18.38/5.66 U35_AAA(x1, x2, x3, x4) = U35_AAA(x4) 18.38/5.66 18.38/5.66 U36_AAA(x1, x2, x3, x4) = U36_AAA(x4) 18.38/5.66 18.38/5.66 U37_AAA(x1, x2, x3, x4) = U37_AAA(x1, x4) 18.38/5.66 18.38/5.66 ADD_IN_AAA(x1, x2, x3) = ADD_IN_AAA 18.38/5.66 18.38/5.66 U1_AAA(x1, x2) = U1_AAA(x2) 18.38/5.66 18.38/5.66 BINARYZ_IN_A(x1) = BINARYZ_IN_A 18.38/5.66 18.38/5.66 U29_A(x1, x2) = U29_A(x2) 18.38/5.66 18.38/5.66 U30_A(x1, x2) = U30_A(x2) 18.38/5.66 18.38/5.66 BINARY_IN_A(x1) = BINARY_IN_A 18.38/5.66 18.38/5.66 U27_A(x1, x2) = U27_A'(x2) 18.38/5.66 18.38/5.66 U28_A(x1, x2) = U28_A(x2) 18.38/5.66 18.38/5.66 U2_AAA(x1, x2) = U2_AAA(x2) 18.38/5.66 18.38/5.66 U3_AAA(x1, x2, x3, x4) = U3_AAA(x4) 18.38/5.66 18.38/5.66 ADDZ_IN_AAA(x1, x2, x3) = ADDZ_IN_AAA 18.38/5.66 18.38/5.66 U10_AAA(x1, x2, x3, x4) = U10_AAA(x4) 18.38/5.66 18.38/5.66 U11_AAA(x1, x2, x3, x4) = U11_AAA(x4) 18.38/5.66 18.38/5.66 ADDX_IN_AAA(x1, x2, x3) = ADDX_IN_AAA 18.38/5.66 18.38/5.66 U4_AAA(x1, x2) = U4_AAA(x2) 18.38/5.66 18.38/5.66 U5_AAA(x1, x2) = U5_AAA(x2) 18.38/5.66 18.38/5.66 U6_AAA(x1, x2, x3, x4) = U6_AAA(x4) 18.38/5.66 18.38/5.66 U12_AAA(x1, x2, x3, x4) = U12_AAA(x4) 18.38/5.66 18.38/5.66 ADDY_IN_AAA(x1, x2, x3) = ADDY_IN_AAA 18.38/5.66 18.38/5.66 U7_AAA(x1, x2) = U7_AAA(x2) 18.38/5.66 18.38/5.66 U8_AAA(x1, x2) = U8_AAA(x2) 18.38/5.66 18.38/5.66 U9_AAA(x1, x2, x3, x4) = U9_AAA(x4) 18.38/5.66 18.38/5.66 U13_AAA(x1, x2, x3, x4) = U13_AAA(x4) 18.38/5.66 18.38/5.66 ADDC_IN_AAA(x1, x2, x3) = ADDC_IN_AAA 18.38/5.66 18.38/5.66 U14_AAA(x1, x2, x3) = U14_AAA(x3) 18.38/5.66 18.38/5.66 SUCCZ_IN_AA(x1, x2) = SUCCZ_IN_AA 18.38/5.66 18.38/5.66 U33_AA(x1, x2) = U33_AA(x2) 18.38/5.66 18.38/5.66 U34_AA(x1, x2, x3) = U34_AA(x3) 18.38/5.66 18.38/5.66 SUCC_IN_AA(x1, x2) = SUCC_IN_AA 18.38/5.66 18.38/5.66 U31_AA(x1, x2) = U31_AA(x2) 18.38/5.66 18.38/5.66 U32_AA(x1, x2, x3) = U32_AA(x3) 18.38/5.66 18.38/5.66 U15_AAA(x1, x2, x3) = U15_AAA(x3) 18.38/5.66 18.38/5.66 U16_AAA(x1, x2, x3, x4) = U16_AAA(x4) 18.38/5.66 18.38/5.66 ADDC_IN_AAA^1(x1, x2, x3) = ADDC_IN_AAA^1 18.38/5.66 18.38/5.66 U23_AAA(x1, x2, x3, x4) = U23_AAA(x4) 18.38/5.66 18.38/5.66 U24_AAA(x1, x2, x3, x4) = U24_AAA(x4) 18.38/5.66 18.38/5.66 ADDX_IN_AAA^1(x1, x2, x3) = ADDX_IN_AAA^1 18.38/5.66 18.38/5.66 U17_AAA(x1, x2) = U17_AAA(x2) 18.38/5.66 18.38/5.66 U18_AAA(x1, x2, x3) = U18_AAA(x3) 18.38/5.66 18.38/5.66 U19_AAA(x1, x2, x3, x4) = U19_AAA(x4) 18.38/5.66 18.38/5.66 U25_AAA(x1, x2, x3, x4) = U25_AAA(x4) 18.38/5.66 18.38/5.66 ADDY_IN_AAA^1(x1, x2, x3) = ADDY_IN_AAA^1 18.38/5.66 18.38/5.66 U20_AAA(x1, x2) = U20_AAA(x2) 18.38/5.66 18.38/5.66 U21_AAA(x1, x2, x3) = U21_AAA(x3) 18.38/5.66 18.38/5.66 U22_AAA(x1, x2, x3, x4) = U22_AAA(x4) 18.38/5.66 18.38/5.66 U26_AAA(x1, x2, x3, x4) = U26_AAA(x4) 18.38/5.66 18.38/5.66 U37_AAG(x1, x2, x3, x4) = U37_AAG(x1, x4) 18.38/5.66 18.38/5.66 ADD_IN_AAG(x1, x2, x3) = ADD_IN_AAG(x3) 18.38/5.66 18.38/5.66 U1_AAG(x1, x2) = U1_AAG(x1, x2) 18.38/5.66 18.38/5.66 BINARYZ_IN_G(x1) = BINARYZ_IN_G(x1) 18.38/5.66 18.38/5.66 U29_G(x1, x2) = U29_G(x2) 18.38/5.66 18.38/5.66 U30_G(x1, x2) = U30_G(x2) 18.38/5.66 18.38/5.66 BINARY_IN_G(x1) = BINARY_IN_G(x1) 18.38/5.66 18.38/5.66 U27_G(x1, x2) = U27_G(x2) 18.38/5.66 18.38/5.66 U28_G(x1, x2) = U28_G(x2) 18.38/5.66 18.38/5.66 U2_AAG(x1, x2) = U2_AAG(x1, x2) 18.38/5.66 18.38/5.66 U3_AAG(x1, x2, x3, x4) = U3_AAG(x4) 18.38/5.66 18.38/5.66 ADDZ_IN_AAG(x1, x2, x3) = ADDZ_IN_AAG(x3) 18.38/5.66 18.38/5.66 U10_AAG(x1, x2, x3, x4) = U10_AAG(x4) 18.38/5.66 18.38/5.66 U11_AAG(x1, x2, x3, x4) = U11_AAG(x4) 18.38/5.66 18.38/5.66 ADDX_IN_AAG(x1, x2, x3) = ADDX_IN_AAG(x3) 18.38/5.66 18.38/5.66 U4_AAG(x1, x2) = U4_AAG(x1, x2) 18.38/5.66 18.38/5.66 U5_AAG(x1, x2) = U5_AAG(x1, x2) 18.38/5.66 18.38/5.66 U6_AAG(x1, x2, x3, x4) = U6_AAG(x4) 18.38/5.66 18.38/5.66 U12_AAG(x1, x2, x3, x4) = U12_AAG(x4) 18.38/5.66 18.38/5.66 ADDY_IN_AAG(x1, x2, x3) = ADDY_IN_AAG(x3) 18.38/5.66 18.38/5.66 U7_AAG(x1, x2) = U7_AAG(x1, x2) 18.38/5.66 18.38/5.66 U8_AAG(x1, x2) = U8_AAG(x1, x2) 18.38/5.66 18.38/5.66 U9_AAG(x1, x2, x3, x4) = U9_AAG(x4) 18.38/5.66 18.38/5.66 U13_AAG(x1, x2, x3, x4) = U13_AAG(x4) 18.38/5.66 18.38/5.66 ADDC_IN_AAG(x1, x2, x3) = ADDC_IN_AAG(x3) 18.38/5.66 18.38/5.66 U14_AAG(x1, x2, x3) = U14_AAG(x3) 18.38/5.66 18.38/5.66 SUCCZ_IN_AG(x1, x2) = SUCCZ_IN_AG(x2) 18.38/5.66 18.38/5.66 U33_AG(x1, x2) = U33_AG(x1, x2) 18.38/5.66 18.38/5.66 U34_AG(x1, x2, x3) = U34_AG(x3) 18.38/5.66 18.38/5.66 SUCC_IN_AG(x1, x2) = SUCC_IN_AG(x2) 18.38/5.66 18.38/5.66 U31_AG(x1, x2) = U31_AG(x1, x2) 18.38/5.66 18.38/5.66 U32_AG(x1, x2, x3) = U32_AG(x3) 18.38/5.66 18.38/5.66 U15_AAG(x1, x2, x3) = U15_AAG(x3) 18.38/5.66 18.38/5.66 U16_AAG(x1, x2, x3, x4) = U16_AAG(x4) 18.38/5.66 18.38/5.66 ADDC_IN_AAG^1(x1, x2, x3) = ADDC_IN_AAG^1(x3) 18.38/5.66 18.38/5.66 U23_AAG(x1, x2, x3, x4) = U23_AAG(x4) 18.38/5.66 18.38/5.66 U24_AAG(x1, x2, x3, x4) = U24_AAG(x4) 18.38/5.66 18.38/5.66 ADDX_IN_AAG^1(x1, x2, x3) = ADDX_IN_AAG^1(x3) 18.38/5.66 18.38/5.66 U17_AAG(x1, x2) = U17_AAG(x1, x2) 18.38/5.66 18.38/5.66 U18_AAG(x1, x2, x3) = U18_AAG(x3) 18.38/5.66 18.38/5.66 U19_AAG(x1, x2, x3, x4) = U19_AAG(x4) 18.38/5.66 18.38/5.66 U25_AAG(x1, x2, x3, x4) = U25_AAG(x4) 18.38/5.66 18.38/5.66 ADDY_IN_AAG^1(x1, x2, x3) = ADDY_IN_AAG^1(x3) 18.38/5.66 18.38/5.66 U20_AAG(x1, x2) = U20_AAG(x1, x2) 18.38/5.66 18.38/5.66 U21_AAG(x1, x2, x3) = U21_AAG(x3) 18.38/5.66 18.38/5.66 U22_AAG(x1, x2, x3, x4) = U22_AAG(x4) 18.38/5.66 18.38/5.66 U26_AAG(x1, x2, x3, x4) = U26_AAG(x4) 18.38/5.66 18.38/5.66 18.38/5.66 We have to consider all (P,R,Pi)-chains 18.38/5.66 ---------------------------------------- 18.38/5.66 18.38/5.66 (53) DependencyGraphProof (EQUIVALENT) 18.38/5.66 The approximation of the Dependency Graph [LOPSTR] contains 8 SCCs with 109 less nodes. 18.38/5.66 ---------------------------------------- 18.38/5.66 18.38/5.66 (54) 18.38/5.66 Complex Obligation (AND) 18.38/5.66 18.38/5.66 ---------------------------------------- 18.38/5.66 18.38/5.66 (55) 18.38/5.66 Obligation: 18.38/5.66 Pi DP problem: 18.38/5.66 The TRS P consists of the following rules: 18.38/5.66 18.38/5.66 BINARYZ_IN_G(one(X)) -> BINARY_IN_G(X) 18.38/5.66 BINARY_IN_G(zero(X)) -> BINARYZ_IN_G(X) 18.38/5.66 BINARYZ_IN_G(zero(X)) -> BINARYZ_IN_G(X) 18.38/5.66 BINARY_IN_G(one(X)) -> BINARY_IN_G(X) 18.38/5.66 18.38/5.66 The TRS R consists of the following rules: 18.38/5.66 18.38/5.66 times_in_aag(one(b), X, X) -> times_out_aag(one(b), X, X) 18.38/5.66 times_in_aag(zero(R), S, zero(RS)) -> U35_aag(R, S, RS, times_in_aag(R, S, RS)) 18.38/5.66 times_in_aag(one(R), S, RSS) -> U36_aag(R, S, RSS, times_in_aaa(R, S, RS)) 18.38/5.66 times_in_aaa(one(b), X, X) -> times_out_aaa(one(b), X, X) 18.38/5.66 times_in_aaa(zero(R), S, zero(RS)) -> U35_aaa(R, S, RS, times_in_aaa(R, S, RS)) 18.38/5.66 times_in_aaa(one(R), S, RSS) -> U36_aaa(R, S, RSS, times_in_aaa(R, S, RS)) 18.38/5.66 U36_aaa(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aaa(R, S, RSS, add_in_aaa(S, zero(RS), RSS)) 18.38/5.66 add_in_aaa(b, b, b) -> add_out_aaa(b, b, b) 18.38/5.66 add_in_aaa(X, b, X) -> U1_aaa(X, binaryZ_in_a(X)) 18.38/5.66 binaryZ_in_a(zero(X)) -> U29_a(X, binaryZ_in_a(X)) 18.38/5.66 binaryZ_in_a(one(X)) -> U30_a(X, binary_in_a(X)) 18.38/5.66 binary_in_a(b) -> binary_out_a(b) 18.38/5.66 binary_in_a(zero(X)) -> U27_a(X, binaryZ_in_a(X)) 18.38/5.66 U27_a(X, binaryZ_out_a(X)) -> binary_out_a(zero(X)) 18.38/5.66 binary_in_a(one(X)) -> U28_a(X, binary_in_a(X)) 18.38/5.66 U28_a(X, binary_out_a(X)) -> binary_out_a(one(X)) 18.38/5.66 U30_a(X, binary_out_a(X)) -> binaryZ_out_a(one(X)) 18.38/5.66 U29_a(X, binaryZ_out_a(X)) -> binaryZ_out_a(zero(X)) 18.38/5.66 U1_aaa(X, binaryZ_out_a(X)) -> add_out_aaa(X, b, X) 18.38/5.66 add_in_aaa(b, Y, Y) -> U2_aaa(Y, binaryZ_in_a(Y)) 18.38/5.66 U2_aaa(Y, binaryZ_out_a(Y)) -> add_out_aaa(b, Y, Y) 18.38/5.66 add_in_aaa(X, Y, Z) -> U3_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.66 addz_in_aaa(zero(X), zero(Y), zero(Z)) -> U10_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.66 addz_in_aaa(zero(X), one(Y), one(Z)) -> U11_aaa(X, Y, Z, addx_in_aaa(X, Y, Z)) 18.38/5.66 addx_in_aaa(one(X), b, one(X)) -> U4_aaa(X, binary_in_a(X)) 18.38/5.66 U4_aaa(X, binary_out_a(X)) -> addx_out_aaa(one(X), b, one(X)) 18.38/5.66 addx_in_aaa(zero(X), b, zero(X)) -> U5_aaa(X, binaryZ_in_a(X)) 18.38/5.66 U5_aaa(X, binaryZ_out_a(X)) -> addx_out_aaa(zero(X), b, zero(X)) 18.38/5.66 addx_in_aaa(X, Y, Z) -> U6_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.66 addz_in_aaa(one(X), zero(Y), one(Z)) -> U12_aaa(X, Y, Z, addy_in_aaa(X, Y, Z)) 18.38/5.66 addy_in_aaa(b, one(Y), one(Y)) -> U7_aaa(Y, binary_in_a(Y)) 18.38/5.66 U7_aaa(Y, binary_out_a(Y)) -> addy_out_aaa(b, one(Y), one(Y)) 18.38/5.66 addy_in_aaa(b, zero(Y), zero(Y)) -> U8_aaa(Y, binaryZ_in_a(Y)) 18.38/5.66 U8_aaa(Y, binaryZ_out_a(Y)) -> addy_out_aaa(b, zero(Y), zero(Y)) 18.38/5.66 addy_in_aaa(X, Y, Z) -> U9_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.66 addz_in_aaa(one(X), one(Y), zero(Z)) -> U13_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.38/5.66 addc_in_aaa(b, b, one(b)) -> addc_out_aaa(b, b, one(b)) 18.38/5.66 addc_in_aaa(X, b, Z) -> U14_aaa(X, Z, succZ_in_aa(X, Z)) 18.38/5.66 succZ_in_aa(zero(X), one(X)) -> U33_aa(X, binaryZ_in_a(X)) 18.38/5.66 U33_aa(X, binaryZ_out_a(X)) -> succZ_out_aa(zero(X), one(X)) 18.38/5.66 succZ_in_aa(one(X), zero(Z)) -> U34_aa(X, Z, succ_in_aa(X, Z)) 18.38/5.66 succ_in_aa(b, one(b)) -> succ_out_aa(b, one(b)) 18.38/5.66 succ_in_aa(zero(X), one(X)) -> U31_aa(X, binaryZ_in_a(X)) 18.38/5.66 U31_aa(X, binaryZ_out_a(X)) -> succ_out_aa(zero(X), one(X)) 18.38/5.66 succ_in_aa(one(X), zero(Z)) -> U32_aa(X, Z, succ_in_aa(X, Z)) 18.38/5.66 U32_aa(X, Z, succ_out_aa(X, Z)) -> succ_out_aa(one(X), zero(Z)) 18.38/5.66 U34_aa(X, Z, succ_out_aa(X, Z)) -> succZ_out_aa(one(X), zero(Z)) 18.38/5.66 U14_aaa(X, Z, succZ_out_aa(X, Z)) -> addc_out_aaa(X, b, Z) 18.38/5.66 addc_in_aaa(b, Y, Z) -> U15_aaa(Y, Z, succZ_in_aa(Y, Z)) 18.38/5.66 U15_aaa(Y, Z, succZ_out_aa(Y, Z)) -> addc_out_aaa(b, Y, Z) 18.38/5.66 addc_in_aaa(X, Y, Z) -> U16_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.66 addC_in_aaa(zero(X), zero(Y), one(Z)) -> U23_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.66 U23_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), zero(Y), one(Z)) 18.38/5.66 addC_in_aaa(zero(X), one(Y), zero(Z)) -> U24_aaa(X, Y, Z, addX_in_aaa(X, Y, Z)) 18.38/5.66 addX_in_aaa(zero(X), b, one(X)) -> U17_aaa(X, binaryZ_in_a(X)) 18.38/5.66 U17_aaa(X, binaryZ_out_a(X)) -> addX_out_aaa(zero(X), b, one(X)) 18.38/5.66 addX_in_aaa(one(X), b, zero(Z)) -> U18_aaa(X, Z, succ_in_aa(X, Z)) 18.38/5.66 U18_aaa(X, Z, succ_out_aa(X, Z)) -> addX_out_aaa(one(X), b, zero(Z)) 18.38/5.66 addX_in_aaa(X, Y, Z) -> U19_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.66 addC_in_aaa(one(X), zero(Y), zero(Z)) -> U25_aaa(X, Y, Z, addY_in_aaa(X, Y, Z)) 18.38/5.66 addY_in_aaa(b, zero(Y), one(Y)) -> U20_aaa(Y, binaryZ_in_a(Y)) 18.38/5.66 U20_aaa(Y, binaryZ_out_a(Y)) -> addY_out_aaa(b, zero(Y), one(Y)) 18.38/5.66 addY_in_aaa(b, one(Y), zero(Z)) -> U21_aaa(Y, Z, succ_in_aa(Y, Z)) 18.38/5.66 U21_aaa(Y, Z, succ_out_aa(Y, Z)) -> addY_out_aaa(b, one(Y), zero(Z)) 18.38/5.66 addY_in_aaa(X, Y, Z) -> U22_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.66 addC_in_aaa(one(X), one(Y), one(Z)) -> U26_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.38/5.66 U26_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), one(Y), one(Z)) 18.38/5.66 U22_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addY_out_aaa(X, Y, Z) 18.38/5.66 U25_aaa(X, Y, Z, addY_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), zero(Y), zero(Z)) 18.38/5.66 U19_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addX_out_aaa(X, Y, Z) 18.38/5.66 U24_aaa(X, Y, Z, addX_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), one(Y), zero(Z)) 18.38/5.66 U16_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addc_out_aaa(X, Y, Z) 18.38/5.66 U13_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), one(Y), zero(Z)) 18.38/5.66 U9_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addy_out_aaa(X, Y, Z) 18.38/5.66 U12_aaa(X, Y, Z, addy_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), zero(Y), one(Z)) 18.38/5.66 U6_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addx_out_aaa(X, Y, Z) 18.38/5.66 U11_aaa(X, Y, Z, addx_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), one(Y), one(Z)) 18.38/5.66 U10_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), zero(Y), zero(Z)) 18.38/5.66 U3_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> add_out_aaa(X, Y, Z) 18.38/5.66 U37_aaa(R, S, RSS, add_out_aaa(S, zero(RS), RSS)) -> times_out_aaa(one(R), S, RSS) 18.38/5.66 U35_aaa(R, S, RS, times_out_aaa(R, S, RS)) -> times_out_aaa(zero(R), S, zero(RS)) 18.38/5.66 U36_aag(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aag(R, S, RSS, add_in_aag(S, zero(RS), RSS)) 18.38/5.66 add_in_aag(b, b, b) -> add_out_aag(b, b, b) 18.38/5.66 add_in_aag(X, b, X) -> U1_aag(X, binaryZ_in_g(X)) 18.38/5.66 binaryZ_in_g(zero(X)) -> U29_g(X, binaryZ_in_g(X)) 18.38/5.66 binaryZ_in_g(one(X)) -> U30_g(X, binary_in_g(X)) 18.38/5.66 binary_in_g(b) -> binary_out_g(b) 18.38/5.66 binary_in_g(zero(X)) -> U27_g(X, binaryZ_in_g(X)) 18.38/5.66 U27_g(X, binaryZ_out_g(X)) -> binary_out_g(zero(X)) 18.38/5.66 binary_in_g(one(X)) -> U28_g(X, binary_in_g(X)) 18.38/5.66 U28_g(X, binary_out_g(X)) -> binary_out_g(one(X)) 18.38/5.66 U30_g(X, binary_out_g(X)) -> binaryZ_out_g(one(X)) 18.38/5.66 U29_g(X, binaryZ_out_g(X)) -> binaryZ_out_g(zero(X)) 18.38/5.66 U1_aag(X, binaryZ_out_g(X)) -> add_out_aag(X, b, X) 18.38/5.66 add_in_aag(b, Y, Y) -> U2_aag(Y, binaryZ_in_g(Y)) 18.38/5.66 U2_aag(Y, binaryZ_out_g(Y)) -> add_out_aag(b, Y, Y) 18.38/5.66 add_in_aag(X, Y, Z) -> U3_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.66 addz_in_aag(zero(X), zero(Y), zero(Z)) -> U10_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.66 addz_in_aag(zero(X), one(Y), one(Z)) -> U11_aag(X, Y, Z, addx_in_aag(X, Y, Z)) 18.38/5.66 addx_in_aag(one(X), b, one(X)) -> U4_aag(X, binary_in_g(X)) 18.38/5.66 U4_aag(X, binary_out_g(X)) -> addx_out_aag(one(X), b, one(X)) 18.38/5.66 addx_in_aag(zero(X), b, zero(X)) -> U5_aag(X, binaryZ_in_g(X)) 18.38/5.66 U5_aag(X, binaryZ_out_g(X)) -> addx_out_aag(zero(X), b, zero(X)) 18.38/5.66 addx_in_aag(X, Y, Z) -> U6_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.66 addz_in_aag(one(X), zero(Y), one(Z)) -> U12_aag(X, Y, Z, addy_in_aag(X, Y, Z)) 18.38/5.66 addy_in_aag(b, one(Y), one(Y)) -> U7_aag(Y, binary_in_g(Y)) 18.38/5.66 U7_aag(Y, binary_out_g(Y)) -> addy_out_aag(b, one(Y), one(Y)) 18.38/5.66 addy_in_aag(b, zero(Y), zero(Y)) -> U8_aag(Y, binaryZ_in_g(Y)) 18.38/5.66 U8_aag(Y, binaryZ_out_g(Y)) -> addy_out_aag(b, zero(Y), zero(Y)) 18.38/5.66 addy_in_aag(X, Y, Z) -> U9_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.66 addz_in_aag(one(X), one(Y), zero(Z)) -> U13_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.38/5.66 addc_in_aag(b, b, one(b)) -> addc_out_aag(b, b, one(b)) 18.38/5.66 addc_in_aag(X, b, Z) -> U14_aag(X, Z, succZ_in_ag(X, Z)) 18.38/5.66 succZ_in_ag(zero(X), one(X)) -> U33_ag(X, binaryZ_in_g(X)) 18.38/5.66 U33_ag(X, binaryZ_out_g(X)) -> succZ_out_ag(zero(X), one(X)) 18.38/5.66 succZ_in_ag(one(X), zero(Z)) -> U34_ag(X, Z, succ_in_ag(X, Z)) 18.38/5.66 succ_in_ag(b, one(b)) -> succ_out_ag(b, one(b)) 18.38/5.66 succ_in_ag(zero(X), one(X)) -> U31_ag(X, binaryZ_in_g(X)) 18.38/5.66 U31_ag(X, binaryZ_out_g(X)) -> succ_out_ag(zero(X), one(X)) 18.38/5.66 succ_in_ag(one(X), zero(Z)) -> U32_ag(X, Z, succ_in_ag(X, Z)) 18.38/5.66 U32_ag(X, Z, succ_out_ag(X, Z)) -> succ_out_ag(one(X), zero(Z)) 18.38/5.66 U34_ag(X, Z, succ_out_ag(X, Z)) -> succZ_out_ag(one(X), zero(Z)) 18.38/5.66 U14_aag(X, Z, succZ_out_ag(X, Z)) -> addc_out_aag(X, b, Z) 18.38/5.66 addc_in_aag(b, Y, Z) -> U15_aag(Y, Z, succZ_in_ag(Y, Z)) 18.38/5.66 U15_aag(Y, Z, succZ_out_ag(Y, Z)) -> addc_out_aag(b, Y, Z) 18.38/5.66 addc_in_aag(X, Y, Z) -> U16_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.66 addC_in_aag(zero(X), zero(Y), one(Z)) -> U23_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.66 U23_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), zero(Y), one(Z)) 18.38/5.66 addC_in_aag(zero(X), one(Y), zero(Z)) -> U24_aag(X, Y, Z, addX_in_aag(X, Y, Z)) 18.38/5.66 addX_in_aag(zero(X), b, one(X)) -> U17_aag(X, binaryZ_in_g(X)) 18.38/5.66 U17_aag(X, binaryZ_out_g(X)) -> addX_out_aag(zero(X), b, one(X)) 18.38/5.66 addX_in_aag(one(X), b, zero(Z)) -> U18_aag(X, Z, succ_in_ag(X, Z)) 18.38/5.66 U18_aag(X, Z, succ_out_ag(X, Z)) -> addX_out_aag(one(X), b, zero(Z)) 18.38/5.66 addX_in_aag(X, Y, Z) -> U19_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.66 addC_in_aag(one(X), zero(Y), zero(Z)) -> U25_aag(X, Y, Z, addY_in_aag(X, Y, Z)) 18.38/5.66 addY_in_aag(b, zero(Y), one(Y)) -> U20_aag(Y, binaryZ_in_g(Y)) 18.38/5.66 U20_aag(Y, binaryZ_out_g(Y)) -> addY_out_aag(b, zero(Y), one(Y)) 18.38/5.66 addY_in_aag(b, one(Y), zero(Z)) -> U21_aag(Y, Z, succ_in_ag(Y, Z)) 18.38/5.66 U21_aag(Y, Z, succ_out_ag(Y, Z)) -> addY_out_aag(b, one(Y), zero(Z)) 18.38/5.66 addY_in_aag(X, Y, Z) -> U22_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.66 addC_in_aag(one(X), one(Y), one(Z)) -> U26_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.38/5.66 U26_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addC_out_aag(one(X), one(Y), one(Z)) 18.38/5.66 U22_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addY_out_aag(X, Y, Z) 18.38/5.66 U25_aag(X, Y, Z, addY_out_aag(X, Y, Z)) -> addC_out_aag(one(X), zero(Y), zero(Z)) 18.38/5.66 U19_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addX_out_aag(X, Y, Z) 18.38/5.66 U24_aag(X, Y, Z, addX_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), one(Y), zero(Z)) 18.38/5.66 U16_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addc_out_aag(X, Y, Z) 18.38/5.66 U13_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addz_out_aag(one(X), one(Y), zero(Z)) 18.38/5.66 U9_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addy_out_aag(X, Y, Z) 18.38/5.66 U12_aag(X, Y, Z, addy_out_aag(X, Y, Z)) -> addz_out_aag(one(X), zero(Y), one(Z)) 18.38/5.66 U6_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addx_out_aag(X, Y, Z) 18.38/5.66 U11_aag(X, Y, Z, addx_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), one(Y), one(Z)) 18.38/5.66 U10_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), zero(Y), zero(Z)) 18.38/5.66 U3_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> add_out_aag(X, Y, Z) 18.38/5.66 U37_aag(R, S, RSS, add_out_aag(S, zero(RS), RSS)) -> times_out_aag(one(R), S, RSS) 18.38/5.66 U35_aag(R, S, RS, times_out_aag(R, S, RS)) -> times_out_aag(zero(R), S, zero(RS)) 18.38/5.66 18.38/5.66 The argument filtering Pi contains the following mapping: 18.38/5.66 times_in_aag(x1, x2, x3) = times_in_aag(x3) 18.38/5.66 18.38/5.66 times_out_aag(x1, x2, x3) = times_out_aag(x1, x2) 18.38/5.66 18.38/5.66 zero(x1) = zero(x1) 18.38/5.66 18.38/5.66 U35_aag(x1, x2, x3, x4) = U35_aag(x4) 18.38/5.66 18.38/5.66 U36_aag(x1, x2, x3, x4) = U36_aag(x3, x4) 18.38/5.66 18.38/5.66 times_in_aaa(x1, x2, x3) = times_in_aaa 18.38/5.66 18.38/5.66 times_out_aaa(x1, x2, x3) = times_out_aaa(x1) 18.38/5.66 18.38/5.66 U35_aaa(x1, x2, x3, x4) = U35_aaa(x4) 18.38/5.66 18.38/5.66 U36_aaa(x1, x2, x3, x4) = U36_aaa(x4) 18.38/5.66 18.38/5.66 U37_aaa(x1, x2, x3, x4) = U37_aaa(x1, x4) 18.38/5.66 18.38/5.66 add_in_aaa(x1, x2, x3) = add_in_aaa 18.38/5.66 18.38/5.66 add_out_aaa(x1, x2, x3) = add_out_aaa(x1, x2, x3) 18.38/5.66 18.38/5.66 U1_aaa(x1, x2) = U1_aaa(x2) 18.38/5.66 18.38/5.66 binaryZ_in_a(x1) = binaryZ_in_a 18.38/5.66 18.38/5.66 U29_a(x1, x2) = U29_a(x2) 18.38/5.66 18.38/5.66 U30_a(x1, x2) = U30_a(x2) 18.38/5.66 18.38/5.66 binary_in_a(x1) = binary_in_a 18.38/5.66 18.38/5.66 binary_out_a(x1) = binary_out_a(x1) 18.38/5.66 18.38/5.66 U27_a(x1, x2) = U27_a(x2) 18.38/5.66 18.38/5.66 binaryZ_out_a(x1) = binaryZ_out_a(x1) 18.38/5.66 18.38/5.66 U28_a(x1, x2) = U28_a(x2) 18.38/5.66 18.38/5.66 U2_aaa(x1, x2) = U2_aaa(x2) 18.38/5.66 18.38/5.66 U3_aaa(x1, x2, x3, x4) = U3_aaa(x4) 18.38/5.66 18.38/5.66 addz_in_aaa(x1, x2, x3) = addz_in_aaa 18.38/5.66 18.38/5.66 U10_aaa(x1, x2, x3, x4) = U10_aaa(x4) 18.38/5.66 18.38/5.66 U11_aaa(x1, x2, x3, x4) = U11_aaa(x4) 18.38/5.66 18.38/5.66 addx_in_aaa(x1, x2, x3) = addx_in_aaa 18.38/5.66 18.38/5.66 U4_aaa(x1, x2) = U4_aaa(x2) 18.38/5.66 18.38/5.66 addx_out_aaa(x1, x2, x3) = addx_out_aaa(x1, x2, x3) 18.38/5.66 18.38/5.66 U5_aaa(x1, x2) = U5_aaa(x2) 18.38/5.66 18.38/5.66 U6_aaa(x1, x2, x3, x4) = U6_aaa(x4) 18.38/5.66 18.38/5.66 U12_aaa(x1, x2, x3, x4) = U12_aaa(x4) 18.38/5.66 18.38/5.66 addy_in_aaa(x1, x2, x3) = addy_in_aaa 18.38/5.66 18.38/5.66 U7_aaa(x1, x2) = U7_aaa(x2) 18.38/5.66 18.38/5.66 addy_out_aaa(x1, x2, x3) = addy_out_aaa(x1, x2, x3) 18.38/5.66 18.38/5.66 U8_aaa(x1, x2) = U8_aaa(x2) 18.38/5.66 18.38/5.66 U9_aaa(x1, x2, x3, x4) = U9_aaa(x4) 18.38/5.66 18.38/5.66 U13_aaa(x1, x2, x3, x4) = U13_aaa(x4) 18.38/5.66 18.38/5.66 addc_in_aaa(x1, x2, x3) = addc_in_aaa 18.38/5.66 18.38/5.66 addc_out_aaa(x1, x2, x3) = addc_out_aaa(x1, x2, x3) 18.38/5.66 18.38/5.66 U14_aaa(x1, x2, x3) = U14_aaa(x3) 18.38/5.66 18.38/5.66 succZ_in_aa(x1, x2) = succZ_in_aa 18.38/5.66 18.38/5.66 U33_aa(x1, x2) = U33_aa(x2) 18.38/5.66 18.38/5.66 succZ_out_aa(x1, x2) = succZ_out_aa(x1, x2) 18.38/5.66 18.38/5.66 U34_aa(x1, x2, x3) = U34_aa(x3) 18.38/5.66 18.38/5.66 succ_in_aa(x1, x2) = succ_in_aa 18.38/5.66 18.38/5.66 succ_out_aa(x1, x2) = succ_out_aa(x1, x2) 18.38/5.66 18.38/5.66 U31_aa(x1, x2) = U31_aa(x2) 18.38/5.66 18.38/5.66 U32_aa(x1, x2, x3) = U32_aa(x3) 18.38/5.66 18.38/5.66 U15_aaa(x1, x2, x3) = U15_aaa(x3) 18.38/5.66 18.38/5.66 U16_aaa(x1, x2, x3, x4) = U16_aaa(x4) 18.38/5.66 18.38/5.66 addC_in_aaa(x1, x2, x3) = addC_in_aaa 18.38/5.66 18.38/5.66 U23_aaa(x1, x2, x3, x4) = U23_aaa(x4) 18.38/5.66 18.38/5.66 addz_out_aaa(x1, x2, x3) = addz_out_aaa(x1, x2, x3) 18.38/5.66 18.38/5.66 addC_out_aaa(x1, x2, x3) = addC_out_aaa(x1, x2, x3) 18.38/5.66 18.38/5.66 U24_aaa(x1, x2, x3, x4) = U24_aaa(x4) 18.38/5.66 18.38/5.66 addX_in_aaa(x1, x2, x3) = addX_in_aaa 18.38/5.66 18.38/5.66 U17_aaa(x1, x2) = U17_aaa(x2) 18.38/5.66 18.38/5.66 addX_out_aaa(x1, x2, x3) = addX_out_aaa(x1, x2, x3) 18.38/5.66 18.38/5.66 U18_aaa(x1, x2, x3) = U18_aaa(x3) 18.38/5.66 18.38/5.66 U19_aaa(x1, x2, x3, x4) = U19_aaa(x4) 18.38/5.66 18.38/5.66 U25_aaa(x1, x2, x3, x4) = U25_aaa(x4) 18.38/5.66 18.38/5.66 addY_in_aaa(x1, x2, x3) = addY_in_aaa 18.38/5.66 18.38/5.66 U20_aaa(x1, x2) = U20_aaa(x2) 18.38/5.66 18.38/5.66 addY_out_aaa(x1, x2, x3) = addY_out_aaa(x1, x2, x3) 18.38/5.66 18.38/5.66 U21_aaa(x1, x2, x3) = U21_aaa(x3) 18.38/5.66 18.38/5.66 U22_aaa(x1, x2, x3, x4) = U22_aaa(x4) 18.38/5.66 18.38/5.66 U26_aaa(x1, x2, x3, x4) = U26_aaa(x4) 18.38/5.66 18.38/5.66 U37_aag(x1, x2, x3, x4) = U37_aag(x1, x4) 18.38/5.66 18.38/5.66 add_in_aag(x1, x2, x3) = add_in_aag(x3) 18.38/5.66 18.38/5.66 b = b 18.38/5.66 18.38/5.66 add_out_aag(x1, x2, x3) = add_out_aag(x1, x2) 18.38/5.66 18.38/5.66 U1_aag(x1, x2) = U1_aag(x1, x2) 18.38/5.66 18.38/5.66 binaryZ_in_g(x1) = binaryZ_in_g(x1) 18.38/5.66 18.38/5.66 U29_g(x1, x2) = U29_g(x2) 18.38/5.66 18.38/5.66 one(x1) = one(x1) 18.38/5.66 18.38/5.66 U30_g(x1, x2) = U30_g(x2) 18.38/5.66 18.38/5.66 binary_in_g(x1) = binary_in_g(x1) 18.38/5.66 18.38/5.66 binary_out_g(x1) = binary_out_g 18.38/5.66 18.38/5.66 U27_g(x1, x2) = U27_g(x2) 18.38/5.66 18.38/5.66 binaryZ_out_g(x1) = binaryZ_out_g 18.38/5.66 18.38/5.66 U28_g(x1, x2) = U28_g(x2) 18.38/5.66 18.38/5.66 U2_aag(x1, x2) = U2_aag(x1, x2) 18.38/5.66 18.38/5.66 U3_aag(x1, x2, x3, x4) = U3_aag(x4) 18.38/5.66 18.38/5.66 addz_in_aag(x1, x2, x3) = addz_in_aag(x3) 18.38/5.66 18.38/5.66 U10_aag(x1, x2, x3, x4) = U10_aag(x4) 18.38/5.66 18.38/5.66 U11_aag(x1, x2, x3, x4) = U11_aag(x4) 18.38/5.66 18.38/5.66 addx_in_aag(x1, x2, x3) = addx_in_aag(x3) 18.38/5.66 18.38/5.66 U4_aag(x1, x2) = U4_aag(x1, x2) 18.38/5.66 18.38/5.66 addx_out_aag(x1, x2, x3) = addx_out_aag(x1, x2) 18.38/5.66 18.38/5.66 U5_aag(x1, x2) = U5_aag(x1, x2) 18.38/5.66 18.38/5.66 U6_aag(x1, x2, x3, x4) = U6_aag(x4) 18.38/5.66 18.38/5.66 U12_aag(x1, x2, x3, x4) = U12_aag(x4) 18.38/5.66 18.38/5.66 addy_in_aag(x1, x2, x3) = addy_in_aag(x3) 18.38/5.66 18.38/5.66 U7_aag(x1, x2) = U7_aag(x1, x2) 18.38/5.66 18.38/5.66 addy_out_aag(x1, x2, x3) = addy_out_aag(x1, x2) 18.38/5.66 18.38/5.66 U8_aag(x1, x2) = U8_aag(x1, x2) 18.38/5.66 18.38/5.66 U9_aag(x1, x2, x3, x4) = U9_aag(x4) 18.38/5.66 18.38/5.66 U13_aag(x1, x2, x3, x4) = U13_aag(x4) 18.38/5.66 18.38/5.66 addc_in_aag(x1, x2, x3) = addc_in_aag(x3) 18.38/5.66 18.38/5.66 addc_out_aag(x1, x2, x3) = addc_out_aag(x1, x2) 18.38/5.66 18.38/5.66 U14_aag(x1, x2, x3) = U14_aag(x3) 18.38/5.66 18.38/5.66 succZ_in_ag(x1, x2) = succZ_in_ag(x2) 18.38/5.66 18.38/5.66 U33_ag(x1, x2) = U33_ag(x1, x2) 18.38/5.66 18.38/5.66 succZ_out_ag(x1, x2) = succZ_out_ag(x1) 18.38/5.66 18.38/5.66 U34_ag(x1, x2, x3) = U34_ag(x3) 18.38/5.66 18.38/5.66 succ_in_ag(x1, x2) = succ_in_ag(x2) 18.38/5.66 18.38/5.66 succ_out_ag(x1, x2) = succ_out_ag(x1) 18.38/5.66 18.38/5.66 U31_ag(x1, x2) = U31_ag(x1, x2) 18.38/5.66 18.38/5.66 U32_ag(x1, x2, x3) = U32_ag(x3) 18.38/5.66 18.38/5.66 U15_aag(x1, x2, x3) = U15_aag(x3) 18.38/5.66 18.38/5.66 U16_aag(x1, x2, x3, x4) = U16_aag(x4) 18.38/5.66 18.38/5.66 addC_in_aag(x1, x2, x3) = addC_in_aag(x3) 18.38/5.66 18.38/5.66 U23_aag(x1, x2, x3, x4) = U23_aag(x4) 18.38/5.66 18.38/5.66 addz_out_aag(x1, x2, x3) = addz_out_aag(x1, x2) 18.38/5.66 18.38/5.66 addC_out_aag(x1, x2, x3) = addC_out_aag(x1, x2) 18.38/5.66 18.38/5.66 U24_aag(x1, x2, x3, x4) = U24_aag(x4) 18.38/5.66 18.38/5.66 addX_in_aag(x1, x2, x3) = addX_in_aag(x3) 18.38/5.66 18.38/5.66 U17_aag(x1, x2) = U17_aag(x1, x2) 18.38/5.66 18.38/5.66 addX_out_aag(x1, x2, x3) = addX_out_aag(x1, x2) 18.38/5.66 18.38/5.66 U18_aag(x1, x2, x3) = U18_aag(x3) 18.38/5.66 18.38/5.66 U19_aag(x1, x2, x3, x4) = U19_aag(x4) 18.38/5.66 18.38/5.66 U25_aag(x1, x2, x3, x4) = U25_aag(x4) 18.38/5.66 18.38/5.66 addY_in_aag(x1, x2, x3) = addY_in_aag(x3) 18.38/5.66 18.38/5.66 U20_aag(x1, x2) = U20_aag(x1, x2) 18.38/5.66 18.38/5.66 addY_out_aag(x1, x2, x3) = addY_out_aag(x1, x2) 18.38/5.66 18.38/5.66 U21_aag(x1, x2, x3) = U21_aag(x3) 18.38/5.66 18.38/5.66 U22_aag(x1, x2, x3, x4) = U22_aag(x4) 18.38/5.66 18.38/5.66 U26_aag(x1, x2, x3, x4) = U26_aag(x4) 18.38/5.66 18.38/5.66 BINARYZ_IN_G(x1) = BINARYZ_IN_G(x1) 18.38/5.66 18.38/5.66 BINARY_IN_G(x1) = BINARY_IN_G(x1) 18.38/5.66 18.38/5.66 18.38/5.66 We have to consider all (P,R,Pi)-chains 18.38/5.66 ---------------------------------------- 18.38/5.66 18.38/5.66 (56) UsableRulesProof (EQUIVALENT) 18.38/5.66 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 18.38/5.66 ---------------------------------------- 18.38/5.66 18.38/5.66 (57) 18.38/5.66 Obligation: 18.38/5.66 Pi DP problem: 18.38/5.66 The TRS P consists of the following rules: 18.38/5.66 18.38/5.66 BINARYZ_IN_G(one(X)) -> BINARY_IN_G(X) 18.38/5.66 BINARY_IN_G(zero(X)) -> BINARYZ_IN_G(X) 18.38/5.66 BINARYZ_IN_G(zero(X)) -> BINARYZ_IN_G(X) 18.38/5.66 BINARY_IN_G(one(X)) -> BINARY_IN_G(X) 18.38/5.66 18.38/5.66 R is empty. 18.38/5.66 Pi is empty. 18.38/5.66 We have to consider all (P,R,Pi)-chains 18.38/5.66 ---------------------------------------- 18.38/5.66 18.38/5.66 (58) PiDPToQDPProof (EQUIVALENT) 18.38/5.66 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 18.38/5.66 ---------------------------------------- 18.38/5.66 18.38/5.66 (59) 18.38/5.66 Obligation: 18.38/5.66 Q DP problem: 18.38/5.66 The TRS P consists of the following rules: 18.38/5.66 18.38/5.66 BINARYZ_IN_G(one(X)) -> BINARY_IN_G(X) 18.38/5.66 BINARY_IN_G(zero(X)) -> BINARYZ_IN_G(X) 18.38/5.66 BINARYZ_IN_G(zero(X)) -> BINARYZ_IN_G(X) 18.38/5.66 BINARY_IN_G(one(X)) -> BINARY_IN_G(X) 18.38/5.66 18.38/5.66 R is empty. 18.38/5.66 Q is empty. 18.38/5.66 We have to consider all (P,Q,R)-chains. 18.38/5.66 ---------------------------------------- 18.38/5.66 18.38/5.66 (60) QDPSizeChangeProof (EQUIVALENT) 18.38/5.66 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 18.38/5.66 18.38/5.66 From the DPs we obtained the following set of size-change graphs: 18.38/5.66 *BINARY_IN_G(zero(X)) -> BINARYZ_IN_G(X) 18.38/5.66 The graph contains the following edges 1 > 1 18.38/5.66 18.38/5.66 18.38/5.66 *BINARY_IN_G(one(X)) -> BINARY_IN_G(X) 18.38/5.66 The graph contains the following edges 1 > 1 18.38/5.66 18.38/5.66 18.38/5.66 *BINARYZ_IN_G(zero(X)) -> BINARYZ_IN_G(X) 18.38/5.66 The graph contains the following edges 1 > 1 18.38/5.66 18.38/5.66 18.38/5.66 *BINARYZ_IN_G(one(X)) -> BINARY_IN_G(X) 18.38/5.66 The graph contains the following edges 1 > 1 18.38/5.66 18.38/5.66 18.38/5.66 ---------------------------------------- 18.38/5.66 18.38/5.66 (61) 18.38/5.66 YES 18.38/5.66 18.38/5.66 ---------------------------------------- 18.38/5.66 18.38/5.66 (62) 18.38/5.66 Obligation: 18.38/5.66 Pi DP problem: 18.38/5.66 The TRS P consists of the following rules: 18.38/5.66 18.38/5.66 SUCC_IN_AG(one(X), zero(Z)) -> SUCC_IN_AG(X, Z) 18.38/5.66 18.38/5.66 The TRS R consists of the following rules: 18.38/5.66 18.38/5.66 times_in_aag(one(b), X, X) -> times_out_aag(one(b), X, X) 18.38/5.66 times_in_aag(zero(R), S, zero(RS)) -> U35_aag(R, S, RS, times_in_aag(R, S, RS)) 18.38/5.66 times_in_aag(one(R), S, RSS) -> U36_aag(R, S, RSS, times_in_aaa(R, S, RS)) 18.38/5.66 times_in_aaa(one(b), X, X) -> times_out_aaa(one(b), X, X) 18.38/5.66 times_in_aaa(zero(R), S, zero(RS)) -> U35_aaa(R, S, RS, times_in_aaa(R, S, RS)) 18.38/5.66 times_in_aaa(one(R), S, RSS) -> U36_aaa(R, S, RSS, times_in_aaa(R, S, RS)) 18.38/5.66 U36_aaa(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aaa(R, S, RSS, add_in_aaa(S, zero(RS), RSS)) 18.38/5.66 add_in_aaa(b, b, b) -> add_out_aaa(b, b, b) 18.38/5.66 add_in_aaa(X, b, X) -> U1_aaa(X, binaryZ_in_a(X)) 18.38/5.66 binaryZ_in_a(zero(X)) -> U29_a(X, binaryZ_in_a(X)) 18.38/5.66 binaryZ_in_a(one(X)) -> U30_a(X, binary_in_a(X)) 18.38/5.66 binary_in_a(b) -> binary_out_a(b) 18.38/5.66 binary_in_a(zero(X)) -> U27_a(X, binaryZ_in_a(X)) 18.38/5.66 U27_a(X, binaryZ_out_a(X)) -> binary_out_a(zero(X)) 18.38/5.66 binary_in_a(one(X)) -> U28_a(X, binary_in_a(X)) 18.38/5.66 U28_a(X, binary_out_a(X)) -> binary_out_a(one(X)) 18.38/5.66 U30_a(X, binary_out_a(X)) -> binaryZ_out_a(one(X)) 18.38/5.66 U29_a(X, binaryZ_out_a(X)) -> binaryZ_out_a(zero(X)) 18.38/5.66 U1_aaa(X, binaryZ_out_a(X)) -> add_out_aaa(X, b, X) 18.38/5.66 add_in_aaa(b, Y, Y) -> U2_aaa(Y, binaryZ_in_a(Y)) 18.38/5.66 U2_aaa(Y, binaryZ_out_a(Y)) -> add_out_aaa(b, Y, Y) 18.38/5.66 add_in_aaa(X, Y, Z) -> U3_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.66 addz_in_aaa(zero(X), zero(Y), zero(Z)) -> U10_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.66 addz_in_aaa(zero(X), one(Y), one(Z)) -> U11_aaa(X, Y, Z, addx_in_aaa(X, Y, Z)) 18.38/5.66 addx_in_aaa(one(X), b, one(X)) -> U4_aaa(X, binary_in_a(X)) 18.38/5.66 U4_aaa(X, binary_out_a(X)) -> addx_out_aaa(one(X), b, one(X)) 18.38/5.66 addx_in_aaa(zero(X), b, zero(X)) -> U5_aaa(X, binaryZ_in_a(X)) 18.38/5.66 U5_aaa(X, binaryZ_out_a(X)) -> addx_out_aaa(zero(X), b, zero(X)) 18.38/5.66 addx_in_aaa(X, Y, Z) -> U6_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.66 addz_in_aaa(one(X), zero(Y), one(Z)) -> U12_aaa(X, Y, Z, addy_in_aaa(X, Y, Z)) 18.38/5.66 addy_in_aaa(b, one(Y), one(Y)) -> U7_aaa(Y, binary_in_a(Y)) 18.38/5.66 U7_aaa(Y, binary_out_a(Y)) -> addy_out_aaa(b, one(Y), one(Y)) 18.38/5.66 addy_in_aaa(b, zero(Y), zero(Y)) -> U8_aaa(Y, binaryZ_in_a(Y)) 18.38/5.66 U8_aaa(Y, binaryZ_out_a(Y)) -> addy_out_aaa(b, zero(Y), zero(Y)) 18.38/5.66 addy_in_aaa(X, Y, Z) -> U9_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.66 addz_in_aaa(one(X), one(Y), zero(Z)) -> U13_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.38/5.66 addc_in_aaa(b, b, one(b)) -> addc_out_aaa(b, b, one(b)) 18.38/5.66 addc_in_aaa(X, b, Z) -> U14_aaa(X, Z, succZ_in_aa(X, Z)) 18.38/5.66 succZ_in_aa(zero(X), one(X)) -> U33_aa(X, binaryZ_in_a(X)) 18.38/5.66 U33_aa(X, binaryZ_out_a(X)) -> succZ_out_aa(zero(X), one(X)) 18.38/5.66 succZ_in_aa(one(X), zero(Z)) -> U34_aa(X, Z, succ_in_aa(X, Z)) 18.38/5.66 succ_in_aa(b, one(b)) -> succ_out_aa(b, one(b)) 18.38/5.66 succ_in_aa(zero(X), one(X)) -> U31_aa(X, binaryZ_in_a(X)) 18.38/5.66 U31_aa(X, binaryZ_out_a(X)) -> succ_out_aa(zero(X), one(X)) 18.38/5.66 succ_in_aa(one(X), zero(Z)) -> U32_aa(X, Z, succ_in_aa(X, Z)) 18.38/5.66 U32_aa(X, Z, succ_out_aa(X, Z)) -> succ_out_aa(one(X), zero(Z)) 18.38/5.66 U34_aa(X, Z, succ_out_aa(X, Z)) -> succZ_out_aa(one(X), zero(Z)) 18.38/5.66 U14_aaa(X, Z, succZ_out_aa(X, Z)) -> addc_out_aaa(X, b, Z) 18.38/5.66 addc_in_aaa(b, Y, Z) -> U15_aaa(Y, Z, succZ_in_aa(Y, Z)) 18.38/5.66 U15_aaa(Y, Z, succZ_out_aa(Y, Z)) -> addc_out_aaa(b, Y, Z) 18.38/5.66 addc_in_aaa(X, Y, Z) -> U16_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.66 addC_in_aaa(zero(X), zero(Y), one(Z)) -> U23_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.38/5.66 U23_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), zero(Y), one(Z)) 18.38/5.66 addC_in_aaa(zero(X), one(Y), zero(Z)) -> U24_aaa(X, Y, Z, addX_in_aaa(X, Y, Z)) 18.38/5.66 addX_in_aaa(zero(X), b, one(X)) -> U17_aaa(X, binaryZ_in_a(X)) 18.38/5.66 U17_aaa(X, binaryZ_out_a(X)) -> addX_out_aaa(zero(X), b, one(X)) 18.38/5.66 addX_in_aaa(one(X), b, zero(Z)) -> U18_aaa(X, Z, succ_in_aa(X, Z)) 18.38/5.66 U18_aaa(X, Z, succ_out_aa(X, Z)) -> addX_out_aaa(one(X), b, zero(Z)) 18.38/5.66 addX_in_aaa(X, Y, Z) -> U19_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.66 addC_in_aaa(one(X), zero(Y), zero(Z)) -> U25_aaa(X, Y, Z, addY_in_aaa(X, Y, Z)) 18.38/5.66 addY_in_aaa(b, zero(Y), one(Y)) -> U20_aaa(Y, binaryZ_in_a(Y)) 18.38/5.66 U20_aaa(Y, binaryZ_out_a(Y)) -> addY_out_aaa(b, zero(Y), one(Y)) 18.38/5.66 addY_in_aaa(b, one(Y), zero(Z)) -> U21_aaa(Y, Z, succ_in_aa(Y, Z)) 18.38/5.66 U21_aaa(Y, Z, succ_out_aa(Y, Z)) -> addY_out_aaa(b, one(Y), zero(Z)) 18.38/5.66 addY_in_aaa(X, Y, Z) -> U22_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.38/5.66 addC_in_aaa(one(X), one(Y), one(Z)) -> U26_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.38/5.66 U26_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), one(Y), one(Z)) 18.38/5.66 U22_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addY_out_aaa(X, Y, Z) 18.38/5.66 U25_aaa(X, Y, Z, addY_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), zero(Y), zero(Z)) 18.38/5.66 U19_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addX_out_aaa(X, Y, Z) 18.38/5.66 U24_aaa(X, Y, Z, addX_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), one(Y), zero(Z)) 18.38/5.66 U16_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addc_out_aaa(X, Y, Z) 18.38/5.66 U13_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), one(Y), zero(Z)) 18.38/5.66 U9_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addy_out_aaa(X, Y, Z) 18.38/5.66 U12_aaa(X, Y, Z, addy_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), zero(Y), one(Z)) 18.38/5.66 U6_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addx_out_aaa(X, Y, Z) 18.38/5.66 U11_aaa(X, Y, Z, addx_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), one(Y), one(Z)) 18.38/5.66 U10_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), zero(Y), zero(Z)) 18.38/5.66 U3_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> add_out_aaa(X, Y, Z) 18.38/5.66 U37_aaa(R, S, RSS, add_out_aaa(S, zero(RS), RSS)) -> times_out_aaa(one(R), S, RSS) 18.38/5.66 U35_aaa(R, S, RS, times_out_aaa(R, S, RS)) -> times_out_aaa(zero(R), S, zero(RS)) 18.38/5.66 U36_aag(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aag(R, S, RSS, add_in_aag(S, zero(RS), RSS)) 18.38/5.66 add_in_aag(b, b, b) -> add_out_aag(b, b, b) 18.38/5.66 add_in_aag(X, b, X) -> U1_aag(X, binaryZ_in_g(X)) 18.38/5.66 binaryZ_in_g(zero(X)) -> U29_g(X, binaryZ_in_g(X)) 18.38/5.66 binaryZ_in_g(one(X)) -> U30_g(X, binary_in_g(X)) 18.38/5.66 binary_in_g(b) -> binary_out_g(b) 18.38/5.66 binary_in_g(zero(X)) -> U27_g(X, binaryZ_in_g(X)) 18.38/5.66 U27_g(X, binaryZ_out_g(X)) -> binary_out_g(zero(X)) 18.38/5.66 binary_in_g(one(X)) -> U28_g(X, binary_in_g(X)) 18.38/5.66 U28_g(X, binary_out_g(X)) -> binary_out_g(one(X)) 18.38/5.66 U30_g(X, binary_out_g(X)) -> binaryZ_out_g(one(X)) 18.38/5.66 U29_g(X, binaryZ_out_g(X)) -> binaryZ_out_g(zero(X)) 18.38/5.66 U1_aag(X, binaryZ_out_g(X)) -> add_out_aag(X, b, X) 18.38/5.66 add_in_aag(b, Y, Y) -> U2_aag(Y, binaryZ_in_g(Y)) 18.38/5.66 U2_aag(Y, binaryZ_out_g(Y)) -> add_out_aag(b, Y, Y) 18.38/5.66 add_in_aag(X, Y, Z) -> U3_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.66 addz_in_aag(zero(X), zero(Y), zero(Z)) -> U10_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.66 addz_in_aag(zero(X), one(Y), one(Z)) -> U11_aag(X, Y, Z, addx_in_aag(X, Y, Z)) 18.38/5.66 addx_in_aag(one(X), b, one(X)) -> U4_aag(X, binary_in_g(X)) 18.38/5.66 U4_aag(X, binary_out_g(X)) -> addx_out_aag(one(X), b, one(X)) 18.38/5.66 addx_in_aag(zero(X), b, zero(X)) -> U5_aag(X, binaryZ_in_g(X)) 18.38/5.66 U5_aag(X, binaryZ_out_g(X)) -> addx_out_aag(zero(X), b, zero(X)) 18.38/5.66 addx_in_aag(X, Y, Z) -> U6_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.66 addz_in_aag(one(X), zero(Y), one(Z)) -> U12_aag(X, Y, Z, addy_in_aag(X, Y, Z)) 18.38/5.66 addy_in_aag(b, one(Y), one(Y)) -> U7_aag(Y, binary_in_g(Y)) 18.38/5.66 U7_aag(Y, binary_out_g(Y)) -> addy_out_aag(b, one(Y), one(Y)) 18.38/5.66 addy_in_aag(b, zero(Y), zero(Y)) -> U8_aag(Y, binaryZ_in_g(Y)) 18.38/5.66 U8_aag(Y, binaryZ_out_g(Y)) -> addy_out_aag(b, zero(Y), zero(Y)) 18.38/5.66 addy_in_aag(X, Y, Z) -> U9_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.66 addz_in_aag(one(X), one(Y), zero(Z)) -> U13_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.38/5.66 addc_in_aag(b, b, one(b)) -> addc_out_aag(b, b, one(b)) 18.38/5.66 addc_in_aag(X, b, Z) -> U14_aag(X, Z, succZ_in_ag(X, Z)) 18.38/5.66 succZ_in_ag(zero(X), one(X)) -> U33_ag(X, binaryZ_in_g(X)) 18.38/5.66 U33_ag(X, binaryZ_out_g(X)) -> succZ_out_ag(zero(X), one(X)) 18.38/5.66 succZ_in_ag(one(X), zero(Z)) -> U34_ag(X, Z, succ_in_ag(X, Z)) 18.38/5.66 succ_in_ag(b, one(b)) -> succ_out_ag(b, one(b)) 18.38/5.66 succ_in_ag(zero(X), one(X)) -> U31_ag(X, binaryZ_in_g(X)) 18.38/5.66 U31_ag(X, binaryZ_out_g(X)) -> succ_out_ag(zero(X), one(X)) 18.38/5.66 succ_in_ag(one(X), zero(Z)) -> U32_ag(X, Z, succ_in_ag(X, Z)) 18.38/5.66 U32_ag(X, Z, succ_out_ag(X, Z)) -> succ_out_ag(one(X), zero(Z)) 18.38/5.66 U34_ag(X, Z, succ_out_ag(X, Z)) -> succZ_out_ag(one(X), zero(Z)) 18.38/5.66 U14_aag(X, Z, succZ_out_ag(X, Z)) -> addc_out_aag(X, b, Z) 18.38/5.66 addc_in_aag(b, Y, Z) -> U15_aag(Y, Z, succZ_in_ag(Y, Z)) 18.38/5.66 U15_aag(Y, Z, succZ_out_ag(Y, Z)) -> addc_out_aag(b, Y, Z) 18.38/5.66 addc_in_aag(X, Y, Z) -> U16_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.66 addC_in_aag(zero(X), zero(Y), one(Z)) -> U23_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.38/5.66 U23_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), zero(Y), one(Z)) 18.38/5.66 addC_in_aag(zero(X), one(Y), zero(Z)) -> U24_aag(X, Y, Z, addX_in_aag(X, Y, Z)) 18.38/5.66 addX_in_aag(zero(X), b, one(X)) -> U17_aag(X, binaryZ_in_g(X)) 18.38/5.66 U17_aag(X, binaryZ_out_g(X)) -> addX_out_aag(zero(X), b, one(X)) 18.38/5.66 addX_in_aag(one(X), b, zero(Z)) -> U18_aag(X, Z, succ_in_ag(X, Z)) 18.38/5.66 U18_aag(X, Z, succ_out_ag(X, Z)) -> addX_out_aag(one(X), b, zero(Z)) 18.38/5.66 addX_in_aag(X, Y, Z) -> U19_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.66 addC_in_aag(one(X), zero(Y), zero(Z)) -> U25_aag(X, Y, Z, addY_in_aag(X, Y, Z)) 18.38/5.66 addY_in_aag(b, zero(Y), one(Y)) -> U20_aag(Y, binaryZ_in_g(Y)) 18.38/5.66 U20_aag(Y, binaryZ_out_g(Y)) -> addY_out_aag(b, zero(Y), one(Y)) 18.38/5.66 addY_in_aag(b, one(Y), zero(Z)) -> U21_aag(Y, Z, succ_in_ag(Y, Z)) 18.38/5.66 U21_aag(Y, Z, succ_out_ag(Y, Z)) -> addY_out_aag(b, one(Y), zero(Z)) 18.38/5.66 addY_in_aag(X, Y, Z) -> U22_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.38/5.66 addC_in_aag(one(X), one(Y), one(Z)) -> U26_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.38/5.66 U26_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addC_out_aag(one(X), one(Y), one(Z)) 18.38/5.66 U22_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addY_out_aag(X, Y, Z) 18.38/5.66 U25_aag(X, Y, Z, addY_out_aag(X, Y, Z)) -> addC_out_aag(one(X), zero(Y), zero(Z)) 18.38/5.66 U19_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addX_out_aag(X, Y, Z) 18.38/5.66 U24_aag(X, Y, Z, addX_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), one(Y), zero(Z)) 18.38/5.66 U16_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addc_out_aag(X, Y, Z) 18.38/5.66 U13_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addz_out_aag(one(X), one(Y), zero(Z)) 18.38/5.66 U9_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addy_out_aag(X, Y, Z) 18.38/5.66 U12_aag(X, Y, Z, addy_out_aag(X, Y, Z)) -> addz_out_aag(one(X), zero(Y), one(Z)) 18.38/5.66 U6_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addx_out_aag(X, Y, Z) 18.38/5.66 U11_aag(X, Y, Z, addx_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), one(Y), one(Z)) 18.38/5.66 U10_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), zero(Y), zero(Z)) 18.38/5.66 U3_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> add_out_aag(X, Y, Z) 18.38/5.66 U37_aag(R, S, RSS, add_out_aag(S, zero(RS), RSS)) -> times_out_aag(one(R), S, RSS) 18.38/5.66 U35_aag(R, S, RS, times_out_aag(R, S, RS)) -> times_out_aag(zero(R), S, zero(RS)) 18.38/5.66 18.38/5.66 The argument filtering Pi contains the following mapping: 18.38/5.66 times_in_aag(x1, x2, x3) = times_in_aag(x3) 18.38/5.66 18.38/5.66 times_out_aag(x1, x2, x3) = times_out_aag(x1, x2) 18.38/5.66 18.38/5.66 zero(x1) = zero(x1) 18.38/5.66 18.38/5.66 U35_aag(x1, x2, x3, x4) = U35_aag(x4) 18.38/5.66 18.38/5.66 U36_aag(x1, x2, x3, x4) = U36_aag(x3, x4) 18.38/5.66 18.38/5.66 times_in_aaa(x1, x2, x3) = times_in_aaa 18.38/5.66 18.38/5.66 times_out_aaa(x1, x2, x3) = times_out_aaa(x1) 18.38/5.66 18.38/5.66 U35_aaa(x1, x2, x3, x4) = U35_aaa(x4) 18.38/5.66 18.38/5.66 U36_aaa(x1, x2, x3, x4) = U36_aaa(x4) 18.38/5.66 18.38/5.66 U37_aaa(x1, x2, x3, x4) = U37_aaa(x1, x4) 18.38/5.66 18.38/5.66 add_in_aaa(x1, x2, x3) = add_in_aaa 18.38/5.66 18.38/5.66 add_out_aaa(x1, x2, x3) = add_out_aaa(x1, x2, x3) 18.38/5.66 18.38/5.66 U1_aaa(x1, x2) = U1_aaa(x2) 18.38/5.66 18.38/5.66 binaryZ_in_a(x1) = binaryZ_in_a 18.38/5.66 18.38/5.66 U29_a(x1, x2) = U29_a(x2) 18.38/5.66 18.38/5.66 U30_a(x1, x2) = U30_a(x2) 18.38/5.66 18.38/5.66 binary_in_a(x1) = binary_in_a 18.38/5.66 18.38/5.66 binary_out_a(x1) = binary_out_a(x1) 18.38/5.66 18.38/5.66 U27_a(x1, x2) = U27_a(x2) 18.38/5.66 18.38/5.66 binaryZ_out_a(x1) = binaryZ_out_a(x1) 18.38/5.66 18.38/5.66 U28_a(x1, x2) = U28_a(x2) 18.38/5.66 18.38/5.66 U2_aaa(x1, x2) = U2_aaa(x2) 18.38/5.66 18.38/5.66 U3_aaa(x1, x2, x3, x4) = U3_aaa(x4) 18.38/5.66 18.38/5.66 addz_in_aaa(x1, x2, x3) = addz_in_aaa 18.38/5.66 18.38/5.66 U10_aaa(x1, x2, x3, x4) = U10_aaa(x4) 18.38/5.66 18.38/5.66 U11_aaa(x1, x2, x3, x4) = U11_aaa(x4) 18.38/5.66 18.38/5.66 addx_in_aaa(x1, x2, x3) = addx_in_aaa 18.38/5.66 18.38/5.66 U4_aaa(x1, x2) = U4_aaa(x2) 18.38/5.66 18.38/5.66 addx_out_aaa(x1, x2, x3) = addx_out_aaa(x1, x2, x3) 18.38/5.66 18.38/5.66 U5_aaa(x1, x2) = U5_aaa(x2) 18.38/5.66 18.38/5.66 U6_aaa(x1, x2, x3, x4) = U6_aaa(x4) 18.38/5.66 18.38/5.66 U12_aaa(x1, x2, x3, x4) = U12_aaa(x4) 18.38/5.66 18.38/5.66 addy_in_aaa(x1, x2, x3) = addy_in_aaa 18.38/5.66 18.38/5.66 U7_aaa(x1, x2) = U7_aaa(x2) 18.38/5.66 18.38/5.66 addy_out_aaa(x1, x2, x3) = addy_out_aaa(x1, x2, x3) 18.38/5.66 18.38/5.66 U8_aaa(x1, x2) = U8_aaa(x2) 18.38/5.66 18.38/5.66 U9_aaa(x1, x2, x3, x4) = U9_aaa(x4) 18.38/5.66 18.38/5.66 U13_aaa(x1, x2, x3, x4) = U13_aaa(x4) 18.38/5.66 18.38/5.66 addc_in_aaa(x1, x2, x3) = addc_in_aaa 18.38/5.66 18.38/5.66 addc_out_aaa(x1, x2, x3) = addc_out_aaa(x1, x2, x3) 18.38/5.66 18.38/5.66 U14_aaa(x1, x2, x3) = U14_aaa(x3) 18.38/5.66 18.38/5.66 succZ_in_aa(x1, x2) = succZ_in_aa 18.38/5.66 18.38/5.66 U33_aa(x1, x2) = U33_aa(x2) 18.38/5.66 18.38/5.66 succZ_out_aa(x1, x2) = succZ_out_aa(x1, x2) 18.48/5.67 18.48/5.67 U34_aa(x1, x2, x3) = U34_aa(x3) 18.48/5.67 18.48/5.67 succ_in_aa(x1, x2) = succ_in_aa 18.48/5.67 18.48/5.67 succ_out_aa(x1, x2) = succ_out_aa(x1, x2) 18.48/5.67 18.48/5.67 U31_aa(x1, x2) = U31_aa(x2) 18.48/5.67 18.48/5.67 U32_aa(x1, x2, x3) = U32_aa(x3) 18.48/5.67 18.48/5.67 U15_aaa(x1, x2, x3) = U15_aaa(x3) 18.48/5.67 18.48/5.67 U16_aaa(x1, x2, x3, x4) = U16_aaa(x4) 18.48/5.67 18.48/5.67 addC_in_aaa(x1, x2, x3) = addC_in_aaa 18.48/5.67 18.48/5.67 U23_aaa(x1, x2, x3, x4) = U23_aaa(x4) 18.48/5.67 18.48/5.67 addz_out_aaa(x1, x2, x3) = addz_out_aaa(x1, x2, x3) 18.48/5.67 18.48/5.67 addC_out_aaa(x1, x2, x3) = addC_out_aaa(x1, x2, x3) 18.48/5.67 18.48/5.67 U24_aaa(x1, x2, x3, x4) = U24_aaa(x4) 18.48/5.67 18.48/5.67 addX_in_aaa(x1, x2, x3) = addX_in_aaa 18.48/5.67 18.48/5.67 U17_aaa(x1, x2) = U17_aaa(x2) 18.48/5.67 18.48/5.67 addX_out_aaa(x1, x2, x3) = addX_out_aaa(x1, x2, x3) 18.48/5.67 18.48/5.67 U18_aaa(x1, x2, x3) = U18_aaa(x3) 18.48/5.67 18.48/5.67 U19_aaa(x1, x2, x3, x4) = U19_aaa(x4) 18.48/5.67 18.48/5.67 U25_aaa(x1, x2, x3, x4) = U25_aaa(x4) 18.48/5.67 18.48/5.67 addY_in_aaa(x1, x2, x3) = addY_in_aaa 18.48/5.67 18.48/5.67 U20_aaa(x1, x2) = U20_aaa(x2) 18.48/5.67 18.48/5.67 addY_out_aaa(x1, x2, x3) = addY_out_aaa(x1, x2, x3) 18.48/5.67 18.48/5.67 U21_aaa(x1, x2, x3) = U21_aaa(x3) 18.48/5.67 18.48/5.67 U22_aaa(x1, x2, x3, x4) = U22_aaa(x4) 18.48/5.67 18.48/5.67 U26_aaa(x1, x2, x3, x4) = U26_aaa(x4) 18.48/5.67 18.48/5.67 U37_aag(x1, x2, x3, x4) = U37_aag(x1, x4) 18.48/5.67 18.48/5.67 add_in_aag(x1, x2, x3) = add_in_aag(x3) 18.48/5.67 18.48/5.67 b = b 18.48/5.67 18.48/5.67 add_out_aag(x1, x2, x3) = add_out_aag(x1, x2) 18.48/5.67 18.48/5.67 U1_aag(x1, x2) = U1_aag(x1, x2) 18.48/5.67 18.48/5.67 binaryZ_in_g(x1) = binaryZ_in_g(x1) 18.48/5.67 18.48/5.67 U29_g(x1, x2) = U29_g(x2) 18.48/5.67 18.48/5.67 one(x1) = one(x1) 18.48/5.67 18.48/5.67 U30_g(x1, x2) = U30_g(x2) 18.48/5.67 18.48/5.67 binary_in_g(x1) = binary_in_g(x1) 18.48/5.67 18.48/5.67 binary_out_g(x1) = binary_out_g 18.48/5.67 18.48/5.67 U27_g(x1, x2) = U27_g(x2) 18.48/5.67 18.48/5.67 binaryZ_out_g(x1) = binaryZ_out_g 18.48/5.67 18.48/5.67 U28_g(x1, x2) = U28_g(x2) 18.48/5.67 18.48/5.67 U2_aag(x1, x2) = U2_aag(x1, x2) 18.48/5.67 18.48/5.67 U3_aag(x1, x2, x3, x4) = U3_aag(x4) 18.48/5.67 18.48/5.67 addz_in_aag(x1, x2, x3) = addz_in_aag(x3) 18.48/5.67 18.48/5.67 U10_aag(x1, x2, x3, x4) = U10_aag(x4) 18.48/5.67 18.48/5.67 U11_aag(x1, x2, x3, x4) = U11_aag(x4) 18.48/5.67 18.48/5.67 addx_in_aag(x1, x2, x3) = addx_in_aag(x3) 18.48/5.67 18.48/5.67 U4_aag(x1, x2) = U4_aag(x1, x2) 18.48/5.67 18.48/5.67 addx_out_aag(x1, x2, x3) = addx_out_aag(x1, x2) 18.48/5.67 18.48/5.67 U5_aag(x1, x2) = U5_aag(x1, x2) 18.48/5.67 18.48/5.67 U6_aag(x1, x2, x3, x4) = U6_aag(x4) 18.48/5.67 18.48/5.67 U12_aag(x1, x2, x3, x4) = U12_aag(x4) 18.48/5.67 18.48/5.67 addy_in_aag(x1, x2, x3) = addy_in_aag(x3) 18.48/5.67 18.48/5.67 U7_aag(x1, x2) = U7_aag(x1, x2) 18.48/5.67 18.48/5.67 addy_out_aag(x1, x2, x3) = addy_out_aag(x1, x2) 18.48/5.67 18.48/5.67 U8_aag(x1, x2) = U8_aag(x1, x2) 18.48/5.67 18.48/5.67 U9_aag(x1, x2, x3, x4) = U9_aag(x4) 18.48/5.67 18.48/5.67 U13_aag(x1, x2, x3, x4) = U13_aag(x4) 18.48/5.67 18.48/5.67 addc_in_aag(x1, x2, x3) = addc_in_aag(x3) 18.48/5.67 18.48/5.67 addc_out_aag(x1, x2, x3) = addc_out_aag(x1, x2) 18.48/5.67 18.48/5.67 U14_aag(x1, x2, x3) = U14_aag(x3) 18.48/5.67 18.48/5.67 succZ_in_ag(x1, x2) = succZ_in_ag(x2) 18.48/5.67 18.48/5.67 U33_ag(x1, x2) = U33_ag(x1, x2) 18.48/5.67 18.48/5.67 succZ_out_ag(x1, x2) = succZ_out_ag(x1) 18.48/5.67 18.48/5.67 U34_ag(x1, x2, x3) = U34_ag(x3) 18.48/5.67 18.48/5.67 succ_in_ag(x1, x2) = succ_in_ag(x2) 18.48/5.67 18.48/5.67 succ_out_ag(x1, x2) = succ_out_ag(x1) 18.48/5.67 18.48/5.67 U31_ag(x1, x2) = U31_ag(x1, x2) 18.48/5.67 18.48/5.67 U32_ag(x1, x2, x3) = U32_ag(x3) 18.48/5.67 18.48/5.67 U15_aag(x1, x2, x3) = U15_aag(x3) 18.48/5.67 18.48/5.67 U16_aag(x1, x2, x3, x4) = U16_aag(x4) 18.48/5.67 18.48/5.67 addC_in_aag(x1, x2, x3) = addC_in_aag(x3) 18.48/5.67 18.48/5.67 U23_aag(x1, x2, x3, x4) = U23_aag(x4) 18.48/5.67 18.48/5.67 addz_out_aag(x1, x2, x3) = addz_out_aag(x1, x2) 18.48/5.67 18.48/5.67 addC_out_aag(x1, x2, x3) = addC_out_aag(x1, x2) 18.48/5.67 18.48/5.67 U24_aag(x1, x2, x3, x4) = U24_aag(x4) 18.48/5.67 18.48/5.67 addX_in_aag(x1, x2, x3) = addX_in_aag(x3) 18.48/5.67 18.48/5.67 U17_aag(x1, x2) = U17_aag(x1, x2) 18.48/5.67 18.48/5.67 addX_out_aag(x1, x2, x3) = addX_out_aag(x1, x2) 18.48/5.67 18.48/5.67 U18_aag(x1, x2, x3) = U18_aag(x3) 18.48/5.67 18.48/5.67 U19_aag(x1, x2, x3, x4) = U19_aag(x4) 18.48/5.67 18.48/5.67 U25_aag(x1, x2, x3, x4) = U25_aag(x4) 18.48/5.67 18.48/5.67 addY_in_aag(x1, x2, x3) = addY_in_aag(x3) 18.48/5.67 18.48/5.67 U20_aag(x1, x2) = U20_aag(x1, x2) 18.48/5.67 18.48/5.67 addY_out_aag(x1, x2, x3) = addY_out_aag(x1, x2) 18.48/5.67 18.48/5.67 U21_aag(x1, x2, x3) = U21_aag(x3) 18.48/5.67 18.48/5.67 U22_aag(x1, x2, x3, x4) = U22_aag(x4) 18.48/5.67 18.48/5.67 U26_aag(x1, x2, x3, x4) = U26_aag(x4) 18.48/5.67 18.48/5.67 SUCC_IN_AG(x1, x2) = SUCC_IN_AG(x2) 18.48/5.67 18.48/5.67 18.48/5.67 We have to consider all (P,R,Pi)-chains 18.48/5.67 ---------------------------------------- 18.48/5.67 18.48/5.67 (63) UsableRulesProof (EQUIVALENT) 18.48/5.67 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 18.48/5.67 ---------------------------------------- 18.48/5.67 18.48/5.67 (64) 18.48/5.67 Obligation: 18.48/5.67 Pi DP problem: 18.48/5.67 The TRS P consists of the following rules: 18.48/5.67 18.48/5.67 SUCC_IN_AG(one(X), zero(Z)) -> SUCC_IN_AG(X, Z) 18.48/5.67 18.48/5.67 R is empty. 18.48/5.67 The argument filtering Pi contains the following mapping: 18.48/5.67 zero(x1) = zero(x1) 18.48/5.67 18.48/5.67 one(x1) = one(x1) 18.48/5.67 18.48/5.67 SUCC_IN_AG(x1, x2) = SUCC_IN_AG(x2) 18.48/5.67 18.48/5.67 18.48/5.67 We have to consider all (P,R,Pi)-chains 18.48/5.67 ---------------------------------------- 18.48/5.67 18.48/5.67 (65) PiDPToQDPProof (SOUND) 18.48/5.67 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 18.48/5.67 ---------------------------------------- 18.48/5.67 18.48/5.67 (66) 18.48/5.67 Obligation: 18.48/5.67 Q DP problem: 18.48/5.67 The TRS P consists of the following rules: 18.48/5.67 18.48/5.67 SUCC_IN_AG(zero(Z)) -> SUCC_IN_AG(Z) 18.48/5.67 18.48/5.67 R is empty. 18.48/5.67 Q is empty. 18.48/5.67 We have to consider all (P,Q,R)-chains. 18.48/5.67 ---------------------------------------- 18.48/5.67 18.48/5.67 (67) QDPSizeChangeProof (EQUIVALENT) 18.48/5.67 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 18.48/5.67 18.48/5.67 From the DPs we obtained the following set of size-change graphs: 18.48/5.67 *SUCC_IN_AG(zero(Z)) -> SUCC_IN_AG(Z) 18.48/5.67 The graph contains the following edges 1 > 1 18.48/5.67 18.48/5.67 18.48/5.67 ---------------------------------------- 18.48/5.67 18.48/5.67 (68) 18.48/5.67 YES 18.48/5.67 18.48/5.67 ---------------------------------------- 18.48/5.67 18.48/5.67 (69) 18.48/5.67 Obligation: 18.48/5.67 Pi DP problem: 18.48/5.67 The TRS P consists of the following rules: 18.48/5.67 18.48/5.67 ADDX_IN_AAG(X, Y, Z) -> ADDZ_IN_AAG(X, Y, Z) 18.48/5.67 ADDZ_IN_AAG(zero(X), zero(Y), zero(Z)) -> ADDZ_IN_AAG(X, Y, Z) 18.48/5.67 ADDZ_IN_AAG(zero(X), one(Y), one(Z)) -> ADDX_IN_AAG(X, Y, Z) 18.48/5.67 ADDZ_IN_AAG(one(X), zero(Y), one(Z)) -> ADDY_IN_AAG(X, Y, Z) 18.48/5.67 ADDY_IN_AAG(X, Y, Z) -> ADDZ_IN_AAG(X, Y, Z) 18.48/5.67 ADDZ_IN_AAG(one(X), one(Y), zero(Z)) -> ADDC_IN_AAG(X, Y, Z) 18.48/5.67 ADDC_IN_AAG(X, Y, Z) -> ADDC_IN_AAG^1(X, Y, Z) 18.48/5.67 ADDC_IN_AAG^1(zero(X), zero(Y), one(Z)) -> ADDZ_IN_AAG(X, Y, Z) 18.48/5.67 ADDC_IN_AAG^1(zero(X), one(Y), zero(Z)) -> ADDX_IN_AAG^1(X, Y, Z) 18.48/5.67 ADDX_IN_AAG^1(X, Y, Z) -> ADDC_IN_AAG^1(X, Y, Z) 18.48/5.67 ADDC_IN_AAG^1(one(X), zero(Y), zero(Z)) -> ADDY_IN_AAG^1(X, Y, Z) 18.48/5.67 ADDY_IN_AAG^1(X, Y, Z) -> ADDC_IN_AAG^1(X, Y, Z) 18.48/5.67 ADDC_IN_AAG^1(one(X), one(Y), one(Z)) -> ADDC_IN_AAG(X, Y, Z) 18.48/5.67 18.48/5.67 The TRS R consists of the following rules: 18.48/5.67 18.48/5.67 times_in_aag(one(b), X, X) -> times_out_aag(one(b), X, X) 18.48/5.67 times_in_aag(zero(R), S, zero(RS)) -> U35_aag(R, S, RS, times_in_aag(R, S, RS)) 18.48/5.67 times_in_aag(one(R), S, RSS) -> U36_aag(R, S, RSS, times_in_aaa(R, S, RS)) 18.48/5.67 times_in_aaa(one(b), X, X) -> times_out_aaa(one(b), X, X) 18.48/5.67 times_in_aaa(zero(R), S, zero(RS)) -> U35_aaa(R, S, RS, times_in_aaa(R, S, RS)) 18.48/5.67 times_in_aaa(one(R), S, RSS) -> U36_aaa(R, S, RSS, times_in_aaa(R, S, RS)) 18.48/5.67 U36_aaa(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aaa(R, S, RSS, add_in_aaa(S, zero(RS), RSS)) 18.48/5.67 add_in_aaa(b, b, b) -> add_out_aaa(b, b, b) 18.48/5.67 add_in_aaa(X, b, X) -> U1_aaa(X, binaryZ_in_a(X)) 18.48/5.67 binaryZ_in_a(zero(X)) -> U29_a(X, binaryZ_in_a(X)) 18.48/5.67 binaryZ_in_a(one(X)) -> U30_a(X, binary_in_a(X)) 18.48/5.67 binary_in_a(b) -> binary_out_a(b) 18.48/5.67 binary_in_a(zero(X)) -> U27_a(X, binaryZ_in_a(X)) 18.48/5.67 U27_a(X, binaryZ_out_a(X)) -> binary_out_a(zero(X)) 18.48/5.67 binary_in_a(one(X)) -> U28_a(X, binary_in_a(X)) 18.48/5.67 U28_a(X, binary_out_a(X)) -> binary_out_a(one(X)) 18.48/5.67 U30_a(X, binary_out_a(X)) -> binaryZ_out_a(one(X)) 18.48/5.67 U29_a(X, binaryZ_out_a(X)) -> binaryZ_out_a(zero(X)) 18.48/5.67 U1_aaa(X, binaryZ_out_a(X)) -> add_out_aaa(X, b, X) 18.48/5.67 add_in_aaa(b, Y, Y) -> U2_aaa(Y, binaryZ_in_a(Y)) 18.48/5.67 U2_aaa(Y, binaryZ_out_a(Y)) -> add_out_aaa(b, Y, Y) 18.48/5.67 add_in_aaa(X, Y, Z) -> U3_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.48/5.67 addz_in_aaa(zero(X), zero(Y), zero(Z)) -> U10_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.48/5.67 addz_in_aaa(zero(X), one(Y), one(Z)) -> U11_aaa(X, Y, Z, addx_in_aaa(X, Y, Z)) 18.48/5.67 addx_in_aaa(one(X), b, one(X)) -> U4_aaa(X, binary_in_a(X)) 18.48/5.67 U4_aaa(X, binary_out_a(X)) -> addx_out_aaa(one(X), b, one(X)) 18.48/5.67 addx_in_aaa(zero(X), b, zero(X)) -> U5_aaa(X, binaryZ_in_a(X)) 18.48/5.67 U5_aaa(X, binaryZ_out_a(X)) -> addx_out_aaa(zero(X), b, zero(X)) 18.48/5.67 addx_in_aaa(X, Y, Z) -> U6_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.48/5.67 addz_in_aaa(one(X), zero(Y), one(Z)) -> U12_aaa(X, Y, Z, addy_in_aaa(X, Y, Z)) 18.48/5.67 addy_in_aaa(b, one(Y), one(Y)) -> U7_aaa(Y, binary_in_a(Y)) 18.48/5.67 U7_aaa(Y, binary_out_a(Y)) -> addy_out_aaa(b, one(Y), one(Y)) 18.48/5.67 addy_in_aaa(b, zero(Y), zero(Y)) -> U8_aaa(Y, binaryZ_in_a(Y)) 18.48/5.67 U8_aaa(Y, binaryZ_out_a(Y)) -> addy_out_aaa(b, zero(Y), zero(Y)) 18.48/5.67 addy_in_aaa(X, Y, Z) -> U9_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.48/5.67 addz_in_aaa(one(X), one(Y), zero(Z)) -> U13_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.48/5.67 addc_in_aaa(b, b, one(b)) -> addc_out_aaa(b, b, one(b)) 18.48/5.67 addc_in_aaa(X, b, Z) -> U14_aaa(X, Z, succZ_in_aa(X, Z)) 18.48/5.67 succZ_in_aa(zero(X), one(X)) -> U33_aa(X, binaryZ_in_a(X)) 18.48/5.67 U33_aa(X, binaryZ_out_a(X)) -> succZ_out_aa(zero(X), one(X)) 18.48/5.67 succZ_in_aa(one(X), zero(Z)) -> U34_aa(X, Z, succ_in_aa(X, Z)) 18.48/5.67 succ_in_aa(b, one(b)) -> succ_out_aa(b, one(b)) 18.48/5.67 succ_in_aa(zero(X), one(X)) -> U31_aa(X, binaryZ_in_a(X)) 18.48/5.67 U31_aa(X, binaryZ_out_a(X)) -> succ_out_aa(zero(X), one(X)) 18.48/5.67 succ_in_aa(one(X), zero(Z)) -> U32_aa(X, Z, succ_in_aa(X, Z)) 18.48/5.67 U32_aa(X, Z, succ_out_aa(X, Z)) -> succ_out_aa(one(X), zero(Z)) 18.48/5.67 U34_aa(X, Z, succ_out_aa(X, Z)) -> succZ_out_aa(one(X), zero(Z)) 18.48/5.67 U14_aaa(X, Z, succZ_out_aa(X, Z)) -> addc_out_aaa(X, b, Z) 18.48/5.67 addc_in_aaa(b, Y, Z) -> U15_aaa(Y, Z, succZ_in_aa(Y, Z)) 18.48/5.67 U15_aaa(Y, Z, succZ_out_aa(Y, Z)) -> addc_out_aaa(b, Y, Z) 18.48/5.67 addc_in_aaa(X, Y, Z) -> U16_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.48/5.67 addC_in_aaa(zero(X), zero(Y), one(Z)) -> U23_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.48/5.67 U23_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), zero(Y), one(Z)) 18.48/5.68 addC_in_aaa(zero(X), one(Y), zero(Z)) -> U24_aaa(X, Y, Z, addX_in_aaa(X, Y, Z)) 18.48/5.68 addX_in_aaa(zero(X), b, one(X)) -> U17_aaa(X, binaryZ_in_a(X)) 18.48/5.68 U17_aaa(X, binaryZ_out_a(X)) -> addX_out_aaa(zero(X), b, one(X)) 18.48/5.68 addX_in_aaa(one(X), b, zero(Z)) -> U18_aaa(X, Z, succ_in_aa(X, Z)) 18.48/5.68 U18_aaa(X, Z, succ_out_aa(X, Z)) -> addX_out_aaa(one(X), b, zero(Z)) 18.48/5.68 addX_in_aaa(X, Y, Z) -> U19_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.48/5.68 addC_in_aaa(one(X), zero(Y), zero(Z)) -> U25_aaa(X, Y, Z, addY_in_aaa(X, Y, Z)) 18.48/5.68 addY_in_aaa(b, zero(Y), one(Y)) -> U20_aaa(Y, binaryZ_in_a(Y)) 18.48/5.68 U20_aaa(Y, binaryZ_out_a(Y)) -> addY_out_aaa(b, zero(Y), one(Y)) 18.48/5.68 addY_in_aaa(b, one(Y), zero(Z)) -> U21_aaa(Y, Z, succ_in_aa(Y, Z)) 18.48/5.68 U21_aaa(Y, Z, succ_out_aa(Y, Z)) -> addY_out_aaa(b, one(Y), zero(Z)) 18.48/5.68 addY_in_aaa(X, Y, Z) -> U22_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.48/5.68 addC_in_aaa(one(X), one(Y), one(Z)) -> U26_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.48/5.68 U26_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), one(Y), one(Z)) 18.48/5.68 U22_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addY_out_aaa(X, Y, Z) 18.48/5.68 U25_aaa(X, Y, Z, addY_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), zero(Y), zero(Z)) 18.48/5.68 U19_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addX_out_aaa(X, Y, Z) 18.48/5.68 U24_aaa(X, Y, Z, addX_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), one(Y), zero(Z)) 18.48/5.68 U16_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addc_out_aaa(X, Y, Z) 18.48/5.68 U13_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), one(Y), zero(Z)) 18.48/5.68 U9_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addy_out_aaa(X, Y, Z) 18.48/5.68 U12_aaa(X, Y, Z, addy_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), zero(Y), one(Z)) 18.48/5.68 U6_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addx_out_aaa(X, Y, Z) 18.48/5.68 U11_aaa(X, Y, Z, addx_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), one(Y), one(Z)) 18.48/5.68 U10_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), zero(Y), zero(Z)) 18.48/5.68 U3_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> add_out_aaa(X, Y, Z) 18.48/5.68 U37_aaa(R, S, RSS, add_out_aaa(S, zero(RS), RSS)) -> times_out_aaa(one(R), S, RSS) 18.48/5.68 U35_aaa(R, S, RS, times_out_aaa(R, S, RS)) -> times_out_aaa(zero(R), S, zero(RS)) 18.48/5.68 U36_aag(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aag(R, S, RSS, add_in_aag(S, zero(RS), RSS)) 18.48/5.68 add_in_aag(b, b, b) -> add_out_aag(b, b, b) 18.48/5.68 add_in_aag(X, b, X) -> U1_aag(X, binaryZ_in_g(X)) 18.48/5.68 binaryZ_in_g(zero(X)) -> U29_g(X, binaryZ_in_g(X)) 18.48/5.68 binaryZ_in_g(one(X)) -> U30_g(X, binary_in_g(X)) 18.48/5.68 binary_in_g(b) -> binary_out_g(b) 18.48/5.68 binary_in_g(zero(X)) -> U27_g(X, binaryZ_in_g(X)) 18.48/5.68 U27_g(X, binaryZ_out_g(X)) -> binary_out_g(zero(X)) 18.48/5.68 binary_in_g(one(X)) -> U28_g(X, binary_in_g(X)) 18.48/5.68 U28_g(X, binary_out_g(X)) -> binary_out_g(one(X)) 18.48/5.68 U30_g(X, binary_out_g(X)) -> binaryZ_out_g(one(X)) 18.48/5.68 U29_g(X, binaryZ_out_g(X)) -> binaryZ_out_g(zero(X)) 18.48/5.68 U1_aag(X, binaryZ_out_g(X)) -> add_out_aag(X, b, X) 18.48/5.68 add_in_aag(b, Y, Y) -> U2_aag(Y, binaryZ_in_g(Y)) 18.48/5.68 U2_aag(Y, binaryZ_out_g(Y)) -> add_out_aag(b, Y, Y) 18.48/5.68 add_in_aag(X, Y, Z) -> U3_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.48/5.68 addz_in_aag(zero(X), zero(Y), zero(Z)) -> U10_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.48/5.68 addz_in_aag(zero(X), one(Y), one(Z)) -> U11_aag(X, Y, Z, addx_in_aag(X, Y, Z)) 18.48/5.68 addx_in_aag(one(X), b, one(X)) -> U4_aag(X, binary_in_g(X)) 18.48/5.68 U4_aag(X, binary_out_g(X)) -> addx_out_aag(one(X), b, one(X)) 18.48/5.68 addx_in_aag(zero(X), b, zero(X)) -> U5_aag(X, binaryZ_in_g(X)) 18.48/5.68 U5_aag(X, binaryZ_out_g(X)) -> addx_out_aag(zero(X), b, zero(X)) 18.48/5.68 addx_in_aag(X, Y, Z) -> U6_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.48/5.68 addz_in_aag(one(X), zero(Y), one(Z)) -> U12_aag(X, Y, Z, addy_in_aag(X, Y, Z)) 18.48/5.68 addy_in_aag(b, one(Y), one(Y)) -> U7_aag(Y, binary_in_g(Y)) 18.48/5.68 U7_aag(Y, binary_out_g(Y)) -> addy_out_aag(b, one(Y), one(Y)) 18.48/5.68 addy_in_aag(b, zero(Y), zero(Y)) -> U8_aag(Y, binaryZ_in_g(Y)) 18.48/5.68 U8_aag(Y, binaryZ_out_g(Y)) -> addy_out_aag(b, zero(Y), zero(Y)) 18.48/5.68 addy_in_aag(X, Y, Z) -> U9_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.48/5.68 addz_in_aag(one(X), one(Y), zero(Z)) -> U13_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.48/5.68 addc_in_aag(b, b, one(b)) -> addc_out_aag(b, b, one(b)) 18.48/5.68 addc_in_aag(X, b, Z) -> U14_aag(X, Z, succZ_in_ag(X, Z)) 18.48/5.68 succZ_in_ag(zero(X), one(X)) -> U33_ag(X, binaryZ_in_g(X)) 18.48/5.68 U33_ag(X, binaryZ_out_g(X)) -> succZ_out_ag(zero(X), one(X)) 18.48/5.68 succZ_in_ag(one(X), zero(Z)) -> U34_ag(X, Z, succ_in_ag(X, Z)) 18.48/5.68 succ_in_ag(b, one(b)) -> succ_out_ag(b, one(b)) 18.48/5.68 succ_in_ag(zero(X), one(X)) -> U31_ag(X, binaryZ_in_g(X)) 18.48/5.68 U31_ag(X, binaryZ_out_g(X)) -> succ_out_ag(zero(X), one(X)) 18.48/5.68 succ_in_ag(one(X), zero(Z)) -> U32_ag(X, Z, succ_in_ag(X, Z)) 18.48/5.68 U32_ag(X, Z, succ_out_ag(X, Z)) -> succ_out_ag(one(X), zero(Z)) 18.48/5.68 U34_ag(X, Z, succ_out_ag(X, Z)) -> succZ_out_ag(one(X), zero(Z)) 18.48/5.68 U14_aag(X, Z, succZ_out_ag(X, Z)) -> addc_out_aag(X, b, Z) 18.48/5.68 addc_in_aag(b, Y, Z) -> U15_aag(Y, Z, succZ_in_ag(Y, Z)) 18.48/5.68 U15_aag(Y, Z, succZ_out_ag(Y, Z)) -> addc_out_aag(b, Y, Z) 18.48/5.68 addc_in_aag(X, Y, Z) -> U16_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.48/5.68 addC_in_aag(zero(X), zero(Y), one(Z)) -> U23_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.48/5.68 U23_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), zero(Y), one(Z)) 18.48/5.68 addC_in_aag(zero(X), one(Y), zero(Z)) -> U24_aag(X, Y, Z, addX_in_aag(X, Y, Z)) 18.48/5.68 addX_in_aag(zero(X), b, one(X)) -> U17_aag(X, binaryZ_in_g(X)) 18.48/5.68 U17_aag(X, binaryZ_out_g(X)) -> addX_out_aag(zero(X), b, one(X)) 18.48/5.68 addX_in_aag(one(X), b, zero(Z)) -> U18_aag(X, Z, succ_in_ag(X, Z)) 18.48/5.68 U18_aag(X, Z, succ_out_ag(X, Z)) -> addX_out_aag(one(X), b, zero(Z)) 18.48/5.68 addX_in_aag(X, Y, Z) -> U19_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.48/5.68 addC_in_aag(one(X), zero(Y), zero(Z)) -> U25_aag(X, Y, Z, addY_in_aag(X, Y, Z)) 18.48/5.68 addY_in_aag(b, zero(Y), one(Y)) -> U20_aag(Y, binaryZ_in_g(Y)) 18.48/5.68 U20_aag(Y, binaryZ_out_g(Y)) -> addY_out_aag(b, zero(Y), one(Y)) 18.48/5.68 addY_in_aag(b, one(Y), zero(Z)) -> U21_aag(Y, Z, succ_in_ag(Y, Z)) 18.48/5.68 U21_aag(Y, Z, succ_out_ag(Y, Z)) -> addY_out_aag(b, one(Y), zero(Z)) 18.48/5.68 addY_in_aag(X, Y, Z) -> U22_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.48/5.68 addC_in_aag(one(X), one(Y), one(Z)) -> U26_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.48/5.68 U26_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addC_out_aag(one(X), one(Y), one(Z)) 18.48/5.68 U22_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addY_out_aag(X, Y, Z) 18.48/5.68 U25_aag(X, Y, Z, addY_out_aag(X, Y, Z)) -> addC_out_aag(one(X), zero(Y), zero(Z)) 18.48/5.68 U19_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addX_out_aag(X, Y, Z) 18.48/5.68 U24_aag(X, Y, Z, addX_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), one(Y), zero(Z)) 18.48/5.68 U16_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addc_out_aag(X, Y, Z) 18.48/5.68 U13_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addz_out_aag(one(X), one(Y), zero(Z)) 18.48/5.68 U9_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addy_out_aag(X, Y, Z) 18.48/5.68 U12_aag(X, Y, Z, addy_out_aag(X, Y, Z)) -> addz_out_aag(one(X), zero(Y), one(Z)) 18.48/5.68 U6_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addx_out_aag(X, Y, Z) 18.48/5.68 U11_aag(X, Y, Z, addx_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), one(Y), one(Z)) 18.48/5.68 U10_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), zero(Y), zero(Z)) 18.48/5.68 U3_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> add_out_aag(X, Y, Z) 18.48/5.68 U37_aag(R, S, RSS, add_out_aag(S, zero(RS), RSS)) -> times_out_aag(one(R), S, RSS) 18.48/5.68 U35_aag(R, S, RS, times_out_aag(R, S, RS)) -> times_out_aag(zero(R), S, zero(RS)) 18.48/5.68 18.48/5.68 The argument filtering Pi contains the following mapping: 18.48/5.68 times_in_aag(x1, x2, x3) = times_in_aag(x3) 18.48/5.68 18.48/5.68 times_out_aag(x1, x2, x3) = times_out_aag(x1, x2) 18.48/5.68 18.48/5.68 zero(x1) = zero(x1) 18.48/5.68 18.48/5.68 U35_aag(x1, x2, x3, x4) = U35_aag(x4) 18.48/5.68 18.48/5.68 U36_aag(x1, x2, x3, x4) = U36_aag(x3, x4) 18.48/5.68 18.48/5.68 times_in_aaa(x1, x2, x3) = times_in_aaa 18.48/5.68 18.48/5.68 times_out_aaa(x1, x2, x3) = times_out_aaa(x1) 18.48/5.68 18.48/5.68 U35_aaa(x1, x2, x3, x4) = U35_aaa(x4) 18.48/5.68 18.48/5.68 U36_aaa(x1, x2, x3, x4) = U36_aaa(x4) 18.48/5.68 18.48/5.68 U37_aaa(x1, x2, x3, x4) = U37_aaa(x1, x4) 18.48/5.68 18.48/5.68 add_in_aaa(x1, x2, x3) = add_in_aaa 18.48/5.68 18.48/5.68 add_out_aaa(x1, x2, x3) = add_out_aaa(x1, x2, x3) 18.48/5.68 18.48/5.68 U1_aaa(x1, x2) = U1_aaa(x2) 18.48/5.68 18.48/5.68 binaryZ_in_a(x1) = binaryZ_in_a 18.48/5.68 18.48/5.68 U29_a(x1, x2) = U29_a(x2) 18.48/5.68 18.48/5.68 U30_a(x1, x2) = U30_a(x2) 18.48/5.68 18.48/5.68 binary_in_a(x1) = binary_in_a 18.48/5.68 18.48/5.68 binary_out_a(x1) = binary_out_a(x1) 18.48/5.68 18.48/5.68 U27_a(x1, x2) = U27_a(x2) 18.48/5.68 18.48/5.68 binaryZ_out_a(x1) = binaryZ_out_a(x1) 18.48/5.68 18.48/5.68 U28_a(x1, x2) = U28_a(x2) 18.48/5.68 18.48/5.68 U2_aaa(x1, x2) = U2_aaa(x2) 18.48/5.68 18.48/5.68 U3_aaa(x1, x2, x3, x4) = U3_aaa(x4) 18.48/5.68 18.48/5.68 addz_in_aaa(x1, x2, x3) = addz_in_aaa 18.48/5.68 18.48/5.68 U10_aaa(x1, x2, x3, x4) = U10_aaa(x4) 18.48/5.68 18.48/5.68 U11_aaa(x1, x2, x3, x4) = U11_aaa(x4) 18.48/5.68 18.48/5.68 addx_in_aaa(x1, x2, x3) = addx_in_aaa 18.48/5.68 18.48/5.68 U4_aaa(x1, x2) = U4_aaa(x2) 18.48/5.68 18.48/5.68 addx_out_aaa(x1, x2, x3) = addx_out_aaa(x1, x2, x3) 18.48/5.68 18.48/5.68 U5_aaa(x1, x2) = U5_aaa(x2) 18.48/5.68 18.48/5.68 U6_aaa(x1, x2, x3, x4) = U6_aaa(x4) 18.48/5.68 18.48/5.68 U12_aaa(x1, x2, x3, x4) = U12_aaa(x4) 18.48/5.68 18.48/5.68 addy_in_aaa(x1, x2, x3) = addy_in_aaa 18.48/5.68 18.48/5.68 U7_aaa(x1, x2) = U7_aaa(x2) 18.48/5.68 18.48/5.68 addy_out_aaa(x1, x2, x3) = addy_out_aaa(x1, x2, x3) 18.48/5.68 18.48/5.68 U8_aaa(x1, x2) = U8_aaa(x2) 18.48/5.68 18.48/5.68 U9_aaa(x1, x2, x3, x4) = U9_aaa(x4) 18.48/5.68 18.48/5.68 U13_aaa(x1, x2, x3, x4) = U13_aaa(x4) 18.48/5.68 18.48/5.68 addc_in_aaa(x1, x2, x3) = addc_in_aaa 18.48/5.68 18.48/5.68 addc_out_aaa(x1, x2, x3) = addc_out_aaa(x1, x2, x3) 18.48/5.68 18.48/5.68 U14_aaa(x1, x2, x3) = U14_aaa(x3) 18.48/5.68 18.48/5.68 succZ_in_aa(x1, x2) = succZ_in_aa 18.48/5.68 18.48/5.68 U33_aa(x1, x2) = U33_aa(x2) 18.48/5.68 18.48/5.68 succZ_out_aa(x1, x2) = succZ_out_aa(x1, x2) 18.48/5.68 18.48/5.68 U34_aa(x1, x2, x3) = U34_aa(x3) 18.48/5.68 18.48/5.68 succ_in_aa(x1, x2) = succ_in_aa 18.48/5.68 18.48/5.68 succ_out_aa(x1, x2) = succ_out_aa(x1, x2) 18.48/5.68 18.48/5.68 U31_aa(x1, x2) = U31_aa(x2) 18.48/5.68 18.48/5.68 U32_aa(x1, x2, x3) = U32_aa(x3) 18.48/5.68 18.48/5.68 U15_aaa(x1, x2, x3) = U15_aaa(x3) 18.48/5.68 18.48/5.68 U16_aaa(x1, x2, x3, x4) = U16_aaa(x4) 18.48/5.68 18.48/5.68 addC_in_aaa(x1, x2, x3) = addC_in_aaa 18.48/5.68 18.48/5.68 U23_aaa(x1, x2, x3, x4) = U23_aaa(x4) 18.48/5.68 18.48/5.68 addz_out_aaa(x1, x2, x3) = addz_out_aaa(x1, x2, x3) 18.48/5.68 18.48/5.68 addC_out_aaa(x1, x2, x3) = addC_out_aaa(x1, x2, x3) 18.48/5.68 18.48/5.68 U24_aaa(x1, x2, x3, x4) = U24_aaa(x4) 18.48/5.68 18.48/5.68 addX_in_aaa(x1, x2, x3) = addX_in_aaa 18.48/5.68 18.48/5.68 U17_aaa(x1, x2) = U17_aaa(x2) 18.48/5.68 18.48/5.68 addX_out_aaa(x1, x2, x3) = addX_out_aaa(x1, x2, x3) 18.48/5.68 18.48/5.68 U18_aaa(x1, x2, x3) = U18_aaa(x3) 18.48/5.68 18.48/5.68 U19_aaa(x1, x2, x3, x4) = U19_aaa(x4) 18.48/5.68 18.48/5.68 U25_aaa(x1, x2, x3, x4) = U25_aaa(x4) 18.48/5.68 18.48/5.68 addY_in_aaa(x1, x2, x3) = addY_in_aaa 18.48/5.68 18.48/5.68 U20_aaa(x1, x2) = U20_aaa(x2) 18.48/5.68 18.48/5.68 addY_out_aaa(x1, x2, x3) = addY_out_aaa(x1, x2, x3) 18.48/5.68 18.48/5.68 U21_aaa(x1, x2, x3) = U21_aaa(x3) 18.48/5.68 18.48/5.68 U22_aaa(x1, x2, x3, x4) = U22_aaa(x4) 18.48/5.68 18.48/5.68 U26_aaa(x1, x2, x3, x4) = U26_aaa(x4) 18.48/5.68 18.48/5.68 U37_aag(x1, x2, x3, x4) = U37_aag(x1, x4) 18.48/5.68 18.48/5.68 add_in_aag(x1, x2, x3) = add_in_aag(x3) 18.48/5.68 18.48/5.68 b = b 18.48/5.68 18.48/5.68 add_out_aag(x1, x2, x3) = add_out_aag(x1, x2) 18.48/5.68 18.48/5.68 U1_aag(x1, x2) = U1_aag(x1, x2) 18.48/5.68 18.48/5.68 binaryZ_in_g(x1) = binaryZ_in_g(x1) 18.48/5.68 18.48/5.68 U29_g(x1, x2) = U29_g(x2) 18.48/5.68 18.48/5.68 one(x1) = one(x1) 18.48/5.68 18.48/5.68 U30_g(x1, x2) = U30_g(x2) 18.48/5.68 18.48/5.68 binary_in_g(x1) = binary_in_g(x1) 18.48/5.68 18.48/5.68 binary_out_g(x1) = binary_out_g 18.48/5.68 18.48/5.68 U27_g(x1, x2) = U27_g(x2) 18.48/5.68 18.48/5.68 binaryZ_out_g(x1) = binaryZ_out_g 18.48/5.68 18.48/5.68 U28_g(x1, x2) = U28_g(x2) 18.48/5.68 18.48/5.68 U2_aag(x1, x2) = U2_aag(x1, x2) 18.48/5.68 18.48/5.68 U3_aag(x1, x2, x3, x4) = U3_aag(x4) 18.48/5.68 18.48/5.68 addz_in_aag(x1, x2, x3) = addz_in_aag(x3) 18.48/5.68 18.48/5.68 U10_aag(x1, x2, x3, x4) = U10_aag(x4) 18.48/5.68 18.48/5.68 U11_aag(x1, x2, x3, x4) = U11_aag(x4) 18.48/5.68 18.48/5.68 addx_in_aag(x1, x2, x3) = addx_in_aag(x3) 18.48/5.68 18.48/5.68 U4_aag(x1, x2) = U4_aag(x1, x2) 18.48/5.68 18.48/5.68 addx_out_aag(x1, x2, x3) = addx_out_aag(x1, x2) 18.48/5.68 18.48/5.68 U5_aag(x1, x2) = U5_aag(x1, x2) 18.48/5.68 18.48/5.68 U6_aag(x1, x2, x3, x4) = U6_aag(x4) 18.48/5.68 18.48/5.68 U12_aag(x1, x2, x3, x4) = U12_aag(x4) 18.48/5.68 18.48/5.68 addy_in_aag(x1, x2, x3) = addy_in_aag(x3) 18.48/5.68 18.48/5.68 U7_aag(x1, x2) = U7_aag(x1, x2) 18.48/5.68 18.48/5.68 addy_out_aag(x1, x2, x3) = addy_out_aag(x1, x2) 18.48/5.68 18.48/5.68 U8_aag(x1, x2) = U8_aag(x1, x2) 18.48/5.68 18.48/5.68 U9_aag(x1, x2, x3, x4) = U9_aag(x4) 18.48/5.68 18.48/5.68 U13_aag(x1, x2, x3, x4) = U13_aag(x4) 18.48/5.68 18.48/5.68 addc_in_aag(x1, x2, x3) = addc_in_aag(x3) 18.48/5.68 18.48/5.68 addc_out_aag(x1, x2, x3) = addc_out_aag(x1, x2) 18.48/5.68 18.48/5.68 U14_aag(x1, x2, x3) = U14_aag(x3) 18.48/5.68 18.48/5.68 succZ_in_ag(x1, x2) = succZ_in_ag(x2) 18.48/5.68 18.48/5.68 U33_ag(x1, x2) = U33_ag(x1, x2) 18.48/5.68 18.48/5.68 succZ_out_ag(x1, x2) = succZ_out_ag(x1) 18.48/5.68 18.48/5.68 U34_ag(x1, x2, x3) = U34_ag(x3) 18.48/5.68 18.48/5.68 succ_in_ag(x1, x2) = succ_in_ag(x2) 18.48/5.68 18.48/5.68 succ_out_ag(x1, x2) = succ_out_ag(x1) 18.48/5.68 18.48/5.68 U31_ag(x1, x2) = U31_ag(x1, x2) 18.48/5.68 18.48/5.68 U32_ag(x1, x2, x3) = U32_ag(x3) 18.48/5.68 18.48/5.68 U15_aag(x1, x2, x3) = U15_aag(x3) 18.48/5.68 18.48/5.68 U16_aag(x1, x2, x3, x4) = U16_aag(x4) 18.48/5.68 18.48/5.68 addC_in_aag(x1, x2, x3) = addC_in_aag(x3) 18.48/5.68 18.48/5.68 U23_aag(x1, x2, x3, x4) = U23_aag(x4) 18.48/5.68 18.48/5.68 addz_out_aag(x1, x2, x3) = addz_out_aag(x1, x2) 18.48/5.68 18.48/5.68 addC_out_aag(x1, x2, x3) = addC_out_aag(x1, x2) 18.48/5.68 18.48/5.68 U24_aag(x1, x2, x3, x4) = U24_aag(x4) 18.48/5.68 18.48/5.68 addX_in_aag(x1, x2, x3) = addX_in_aag(x3) 18.48/5.68 18.48/5.68 U17_aag(x1, x2) = U17_aag(x1, x2) 18.48/5.68 18.48/5.68 addX_out_aag(x1, x2, x3) = addX_out_aag(x1, x2) 18.48/5.68 18.48/5.68 U18_aag(x1, x2, x3) = U18_aag(x3) 18.48/5.68 18.48/5.68 U19_aag(x1, x2, x3, x4) = U19_aag(x4) 18.48/5.68 18.48/5.68 U25_aag(x1, x2, x3, x4) = U25_aag(x4) 18.48/5.68 18.48/5.68 addY_in_aag(x1, x2, x3) = addY_in_aag(x3) 18.48/5.68 18.48/5.68 U20_aag(x1, x2) = U20_aag(x1, x2) 18.48/5.68 18.48/5.68 addY_out_aag(x1, x2, x3) = addY_out_aag(x1, x2) 18.48/5.68 18.48/5.68 U21_aag(x1, x2, x3) = U21_aag(x3) 18.48/5.68 18.48/5.68 U22_aag(x1, x2, x3, x4) = U22_aag(x4) 18.48/5.68 18.48/5.68 U26_aag(x1, x2, x3, x4) = U26_aag(x4) 18.48/5.68 18.48/5.68 ADDZ_IN_AAG(x1, x2, x3) = ADDZ_IN_AAG(x3) 18.48/5.68 18.48/5.68 ADDX_IN_AAG(x1, x2, x3) = ADDX_IN_AAG(x3) 18.48/5.68 18.48/5.68 ADDY_IN_AAG(x1, x2, x3) = ADDY_IN_AAG(x3) 18.48/5.68 18.48/5.68 ADDC_IN_AAG(x1, x2, x3) = ADDC_IN_AAG(x3) 18.48/5.68 18.48/5.68 ADDC_IN_AAG^1(x1, x2, x3) = ADDC_IN_AAG^1(x3) 18.48/5.68 18.48/5.68 ADDX_IN_AAG^1(x1, x2, x3) = ADDX_IN_AAG^1(x3) 18.48/5.68 18.48/5.68 ADDY_IN_AAG^1(x1, x2, x3) = ADDY_IN_AAG^1(x3) 18.48/5.68 18.48/5.68 18.48/5.68 We have to consider all (P,R,Pi)-chains 18.48/5.68 ---------------------------------------- 18.48/5.68 18.48/5.68 (70) UsableRulesProof (EQUIVALENT) 18.48/5.68 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 18.48/5.68 ---------------------------------------- 18.48/5.68 18.48/5.68 (71) 18.48/5.68 Obligation: 18.48/5.68 Pi DP problem: 18.48/5.68 The TRS P consists of the following rules: 18.48/5.68 18.48/5.68 ADDX_IN_AAG(X, Y, Z) -> ADDZ_IN_AAG(X, Y, Z) 18.48/5.68 ADDZ_IN_AAG(zero(X), zero(Y), zero(Z)) -> ADDZ_IN_AAG(X, Y, Z) 18.48/5.68 ADDZ_IN_AAG(zero(X), one(Y), one(Z)) -> ADDX_IN_AAG(X, Y, Z) 18.48/5.68 ADDZ_IN_AAG(one(X), zero(Y), one(Z)) -> ADDY_IN_AAG(X, Y, Z) 18.48/5.68 ADDY_IN_AAG(X, Y, Z) -> ADDZ_IN_AAG(X, Y, Z) 18.48/5.68 ADDZ_IN_AAG(one(X), one(Y), zero(Z)) -> ADDC_IN_AAG(X, Y, Z) 18.48/5.68 ADDC_IN_AAG(X, Y, Z) -> ADDC_IN_AAG^1(X, Y, Z) 18.48/5.68 ADDC_IN_AAG^1(zero(X), zero(Y), one(Z)) -> ADDZ_IN_AAG(X, Y, Z) 18.48/5.68 ADDC_IN_AAG^1(zero(X), one(Y), zero(Z)) -> ADDX_IN_AAG^1(X, Y, Z) 18.48/5.68 ADDX_IN_AAG^1(X, Y, Z) -> ADDC_IN_AAG^1(X, Y, Z) 18.48/5.68 ADDC_IN_AAG^1(one(X), zero(Y), zero(Z)) -> ADDY_IN_AAG^1(X, Y, Z) 18.48/5.68 ADDY_IN_AAG^1(X, Y, Z) -> ADDC_IN_AAG^1(X, Y, Z) 18.48/5.68 ADDC_IN_AAG^1(one(X), one(Y), one(Z)) -> ADDC_IN_AAG(X, Y, Z) 18.48/5.68 18.48/5.68 R is empty. 18.48/5.68 The argument filtering Pi contains the following mapping: 18.48/5.68 zero(x1) = zero(x1) 18.48/5.68 18.48/5.68 one(x1) = one(x1) 18.48/5.68 18.48/5.68 ADDZ_IN_AAG(x1, x2, x3) = ADDZ_IN_AAG(x3) 18.48/5.68 18.48/5.68 ADDX_IN_AAG(x1, x2, x3) = ADDX_IN_AAG(x3) 18.48/5.68 18.48/5.68 ADDY_IN_AAG(x1, x2, x3) = ADDY_IN_AAG(x3) 18.48/5.68 18.48/5.68 ADDC_IN_AAG(x1, x2, x3) = ADDC_IN_AAG(x3) 18.48/5.68 18.48/5.68 ADDC_IN_AAG^1(x1, x2, x3) = ADDC_IN_AAG^1(x3) 18.48/5.68 18.48/5.68 ADDX_IN_AAG^1(x1, x2, x3) = ADDX_IN_AAG^1(x3) 18.48/5.68 18.48/5.68 ADDY_IN_AAG^1(x1, x2, x3) = ADDY_IN_AAG^1(x3) 18.48/5.68 18.48/5.68 18.48/5.68 We have to consider all (P,R,Pi)-chains 18.48/5.68 ---------------------------------------- 18.48/5.68 18.48/5.68 (72) PiDPToQDPProof (SOUND) 18.48/5.68 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 18.48/5.68 ---------------------------------------- 18.48/5.68 18.48/5.68 (73) 18.48/5.68 Obligation: 18.48/5.68 Q DP problem: 18.48/5.68 The TRS P consists of the following rules: 18.48/5.68 18.48/5.68 ADDX_IN_AAG(Z) -> ADDZ_IN_AAG(Z) 18.48/5.68 ADDZ_IN_AAG(zero(Z)) -> ADDZ_IN_AAG(Z) 18.48/5.68 ADDZ_IN_AAG(one(Z)) -> ADDX_IN_AAG(Z) 18.48/5.68 ADDZ_IN_AAG(one(Z)) -> ADDY_IN_AAG(Z) 18.48/5.68 ADDY_IN_AAG(Z) -> ADDZ_IN_AAG(Z) 18.48/5.68 ADDZ_IN_AAG(zero(Z)) -> ADDC_IN_AAG(Z) 18.48/5.68 ADDC_IN_AAG(Z) -> ADDC_IN_AAG^1(Z) 18.48/5.68 ADDC_IN_AAG^1(one(Z)) -> ADDZ_IN_AAG(Z) 18.48/5.68 ADDC_IN_AAG^1(zero(Z)) -> ADDX_IN_AAG^1(Z) 18.48/5.68 ADDX_IN_AAG^1(Z) -> ADDC_IN_AAG^1(Z) 18.48/5.68 ADDC_IN_AAG^1(zero(Z)) -> ADDY_IN_AAG^1(Z) 18.48/5.68 ADDY_IN_AAG^1(Z) -> ADDC_IN_AAG^1(Z) 18.48/5.68 ADDC_IN_AAG^1(one(Z)) -> ADDC_IN_AAG(Z) 18.48/5.68 18.48/5.68 R is empty. 18.48/5.68 Q is empty. 18.48/5.68 We have to consider all (P,Q,R)-chains. 18.48/5.68 ---------------------------------------- 18.48/5.68 18.48/5.68 (74) QDPSizeChangeProof (EQUIVALENT) 18.48/5.68 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 18.48/5.68 18.48/5.68 From the DPs we obtained the following set of size-change graphs: 18.48/5.68 *ADDZ_IN_AAG(one(Z)) -> ADDX_IN_AAG(Z) 18.48/5.68 The graph contains the following edges 1 > 1 18.48/5.68 18.48/5.68 18.48/5.68 *ADDZ_IN_AAG(zero(Z)) -> ADDZ_IN_AAG(Z) 18.48/5.68 The graph contains the following edges 1 > 1 18.48/5.68 18.48/5.68 18.48/5.68 *ADDX_IN_AAG(Z) -> ADDZ_IN_AAG(Z) 18.48/5.68 The graph contains the following edges 1 >= 1 18.48/5.68 18.48/5.68 18.48/5.68 *ADDY_IN_AAG(Z) -> ADDZ_IN_AAG(Z) 18.48/5.68 The graph contains the following edges 1 >= 1 18.48/5.68 18.48/5.68 18.48/5.68 *ADDC_IN_AAG^1(one(Z)) -> ADDZ_IN_AAG(Z) 18.48/5.68 The graph contains the following edges 1 > 1 18.48/5.68 18.48/5.68 18.48/5.68 *ADDZ_IN_AAG(one(Z)) -> ADDY_IN_AAG(Z) 18.48/5.68 The graph contains the following edges 1 > 1 18.48/5.68 18.48/5.68 18.48/5.68 *ADDZ_IN_AAG(zero(Z)) -> ADDC_IN_AAG(Z) 18.48/5.68 The graph contains the following edges 1 > 1 18.48/5.68 18.48/5.68 18.48/5.68 *ADDC_IN_AAG(Z) -> ADDC_IN_AAG^1(Z) 18.48/5.68 The graph contains the following edges 1 >= 1 18.48/5.68 18.48/5.68 18.48/5.68 *ADDC_IN_AAG^1(one(Z)) -> ADDC_IN_AAG(Z) 18.48/5.68 The graph contains the following edges 1 > 1 18.48/5.68 18.48/5.68 18.48/5.68 *ADDX_IN_AAG^1(Z) -> ADDC_IN_AAG^1(Z) 18.48/5.68 The graph contains the following edges 1 >= 1 18.48/5.68 18.48/5.68 18.48/5.68 *ADDY_IN_AAG^1(Z) -> ADDC_IN_AAG^1(Z) 18.48/5.68 The graph contains the following edges 1 >= 1 18.48/5.68 18.48/5.68 18.48/5.68 *ADDC_IN_AAG^1(zero(Z)) -> ADDX_IN_AAG^1(Z) 18.48/5.68 The graph contains the following edges 1 > 1 18.48/5.68 18.48/5.68 18.48/5.68 *ADDC_IN_AAG^1(zero(Z)) -> ADDY_IN_AAG^1(Z) 18.48/5.68 The graph contains the following edges 1 > 1 18.48/5.68 18.48/5.68 18.48/5.68 ---------------------------------------- 18.48/5.68 18.48/5.68 (75) 18.48/5.68 YES 18.48/5.68 18.48/5.68 ---------------------------------------- 18.48/5.68 18.48/5.68 (76) 18.48/5.68 Obligation: 18.48/5.68 Pi DP problem: 18.48/5.68 The TRS P consists of the following rules: 18.48/5.68 18.48/5.68 BINARYZ_IN_A(one(X)) -> BINARY_IN_A(X) 18.48/5.68 BINARY_IN_A(zero(X)) -> BINARYZ_IN_A(X) 18.48/5.68 BINARYZ_IN_A(zero(X)) -> BINARYZ_IN_A(X) 18.48/5.68 BINARY_IN_A(one(X)) -> BINARY_IN_A(X) 18.48/5.68 18.48/5.68 The TRS R consists of the following rules: 18.48/5.68 18.48/5.68 times_in_aag(one(b), X, X) -> times_out_aag(one(b), X, X) 18.48/5.68 times_in_aag(zero(R), S, zero(RS)) -> U35_aag(R, S, RS, times_in_aag(R, S, RS)) 18.48/5.68 times_in_aag(one(R), S, RSS) -> U36_aag(R, S, RSS, times_in_aaa(R, S, RS)) 18.48/5.68 times_in_aaa(one(b), X, X) -> times_out_aaa(one(b), X, X) 18.48/5.68 times_in_aaa(zero(R), S, zero(RS)) -> U35_aaa(R, S, RS, times_in_aaa(R, S, RS)) 18.48/5.68 times_in_aaa(one(R), S, RSS) -> U36_aaa(R, S, RSS, times_in_aaa(R, S, RS)) 18.48/5.68 U36_aaa(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aaa(R, S, RSS, add_in_aaa(S, zero(RS), RSS)) 18.48/5.68 add_in_aaa(b, b, b) -> add_out_aaa(b, b, b) 18.48/5.68 add_in_aaa(X, b, X) -> U1_aaa(X, binaryZ_in_a(X)) 18.48/5.68 binaryZ_in_a(zero(X)) -> U29_a(X, binaryZ_in_a(X)) 18.48/5.68 binaryZ_in_a(one(X)) -> U30_a(X, binary_in_a(X)) 18.48/5.68 binary_in_a(b) -> binary_out_a(b) 18.48/5.68 binary_in_a(zero(X)) -> U27_a(X, binaryZ_in_a(X)) 18.48/5.68 U27_a(X, binaryZ_out_a(X)) -> binary_out_a(zero(X)) 18.48/5.68 binary_in_a(one(X)) -> U28_a(X, binary_in_a(X)) 18.48/5.68 U28_a(X, binary_out_a(X)) -> binary_out_a(one(X)) 18.48/5.68 U30_a(X, binary_out_a(X)) -> binaryZ_out_a(one(X)) 18.48/5.68 U29_a(X, binaryZ_out_a(X)) -> binaryZ_out_a(zero(X)) 18.48/5.68 U1_aaa(X, binaryZ_out_a(X)) -> add_out_aaa(X, b, X) 18.48/5.68 add_in_aaa(b, Y, Y) -> U2_aaa(Y, binaryZ_in_a(Y)) 18.48/5.68 U2_aaa(Y, binaryZ_out_a(Y)) -> add_out_aaa(b, Y, Y) 18.48/5.68 add_in_aaa(X, Y, Z) -> U3_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.48/5.68 addz_in_aaa(zero(X), zero(Y), zero(Z)) -> U10_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.48/5.68 addz_in_aaa(zero(X), one(Y), one(Z)) -> U11_aaa(X, Y, Z, addx_in_aaa(X, Y, Z)) 18.48/5.68 addx_in_aaa(one(X), b, one(X)) -> U4_aaa(X, binary_in_a(X)) 18.48/5.68 U4_aaa(X, binary_out_a(X)) -> addx_out_aaa(one(X), b, one(X)) 18.48/5.68 addx_in_aaa(zero(X), b, zero(X)) -> U5_aaa(X, binaryZ_in_a(X)) 18.48/5.68 U5_aaa(X, binaryZ_out_a(X)) -> addx_out_aaa(zero(X), b, zero(X)) 18.48/5.68 addx_in_aaa(X, Y, Z) -> U6_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.48/5.68 addz_in_aaa(one(X), zero(Y), one(Z)) -> U12_aaa(X, Y, Z, addy_in_aaa(X, Y, Z)) 18.48/5.68 addy_in_aaa(b, one(Y), one(Y)) -> U7_aaa(Y, binary_in_a(Y)) 18.48/5.68 U7_aaa(Y, binary_out_a(Y)) -> addy_out_aaa(b, one(Y), one(Y)) 18.48/5.68 addy_in_aaa(b, zero(Y), zero(Y)) -> U8_aaa(Y, binaryZ_in_a(Y)) 18.48/5.68 U8_aaa(Y, binaryZ_out_a(Y)) -> addy_out_aaa(b, zero(Y), zero(Y)) 18.48/5.68 addy_in_aaa(X, Y, Z) -> U9_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.48/5.68 addz_in_aaa(one(X), one(Y), zero(Z)) -> U13_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.48/5.68 addc_in_aaa(b, b, one(b)) -> addc_out_aaa(b, b, one(b)) 18.48/5.68 addc_in_aaa(X, b, Z) -> U14_aaa(X, Z, succZ_in_aa(X, Z)) 18.48/5.68 succZ_in_aa(zero(X), one(X)) -> U33_aa(X, binaryZ_in_a(X)) 18.48/5.68 U33_aa(X, binaryZ_out_a(X)) -> succZ_out_aa(zero(X), one(X)) 18.48/5.68 succZ_in_aa(one(X), zero(Z)) -> U34_aa(X, Z, succ_in_aa(X, Z)) 18.48/5.68 succ_in_aa(b, one(b)) -> succ_out_aa(b, one(b)) 18.48/5.68 succ_in_aa(zero(X), one(X)) -> U31_aa(X, binaryZ_in_a(X)) 18.48/5.68 U31_aa(X, binaryZ_out_a(X)) -> succ_out_aa(zero(X), one(X)) 18.48/5.68 succ_in_aa(one(X), zero(Z)) -> U32_aa(X, Z, succ_in_aa(X, Z)) 18.48/5.68 U32_aa(X, Z, succ_out_aa(X, Z)) -> succ_out_aa(one(X), zero(Z)) 18.48/5.68 U34_aa(X, Z, succ_out_aa(X, Z)) -> succZ_out_aa(one(X), zero(Z)) 18.48/5.68 U14_aaa(X, Z, succZ_out_aa(X, Z)) -> addc_out_aaa(X, b, Z) 18.48/5.68 addc_in_aaa(b, Y, Z) -> U15_aaa(Y, Z, succZ_in_aa(Y, Z)) 18.48/5.68 U15_aaa(Y, Z, succZ_out_aa(Y, Z)) -> addc_out_aaa(b, Y, Z) 18.48/5.68 addc_in_aaa(X, Y, Z) -> U16_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.48/5.68 addC_in_aaa(zero(X), zero(Y), one(Z)) -> U23_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.48/5.68 U23_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), zero(Y), one(Z)) 18.48/5.68 addC_in_aaa(zero(X), one(Y), zero(Z)) -> U24_aaa(X, Y, Z, addX_in_aaa(X, Y, Z)) 18.48/5.68 addX_in_aaa(zero(X), b, one(X)) -> U17_aaa(X, binaryZ_in_a(X)) 18.48/5.68 U17_aaa(X, binaryZ_out_a(X)) -> addX_out_aaa(zero(X), b, one(X)) 18.48/5.68 addX_in_aaa(one(X), b, zero(Z)) -> U18_aaa(X, Z, succ_in_aa(X, Z)) 18.48/5.68 U18_aaa(X, Z, succ_out_aa(X, Z)) -> addX_out_aaa(one(X), b, zero(Z)) 18.48/5.68 addX_in_aaa(X, Y, Z) -> U19_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.48/5.68 addC_in_aaa(one(X), zero(Y), zero(Z)) -> U25_aaa(X, Y, Z, addY_in_aaa(X, Y, Z)) 18.48/5.68 addY_in_aaa(b, zero(Y), one(Y)) -> U20_aaa(Y, binaryZ_in_a(Y)) 18.48/5.68 U20_aaa(Y, binaryZ_out_a(Y)) -> addY_out_aaa(b, zero(Y), one(Y)) 18.48/5.68 addY_in_aaa(b, one(Y), zero(Z)) -> U21_aaa(Y, Z, succ_in_aa(Y, Z)) 18.48/5.68 U21_aaa(Y, Z, succ_out_aa(Y, Z)) -> addY_out_aaa(b, one(Y), zero(Z)) 18.48/5.68 addY_in_aaa(X, Y, Z) -> U22_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.48/5.68 addC_in_aaa(one(X), one(Y), one(Z)) -> U26_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.48/5.68 U26_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), one(Y), one(Z)) 18.48/5.68 U22_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addY_out_aaa(X, Y, Z) 18.48/5.68 U25_aaa(X, Y, Z, addY_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), zero(Y), zero(Z)) 18.48/5.68 U19_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addX_out_aaa(X, Y, Z) 18.48/5.68 U24_aaa(X, Y, Z, addX_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), one(Y), zero(Z)) 18.48/5.68 U16_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addc_out_aaa(X, Y, Z) 18.48/5.68 U13_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), one(Y), zero(Z)) 18.48/5.68 U9_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addy_out_aaa(X, Y, Z) 18.48/5.68 U12_aaa(X, Y, Z, addy_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), zero(Y), one(Z)) 18.48/5.68 U6_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addx_out_aaa(X, Y, Z) 18.48/5.68 U11_aaa(X, Y, Z, addx_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), one(Y), one(Z)) 18.48/5.68 U10_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), zero(Y), zero(Z)) 18.48/5.68 U3_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> add_out_aaa(X, Y, Z) 18.48/5.68 U37_aaa(R, S, RSS, add_out_aaa(S, zero(RS), RSS)) -> times_out_aaa(one(R), S, RSS) 18.48/5.68 U35_aaa(R, S, RS, times_out_aaa(R, S, RS)) -> times_out_aaa(zero(R), S, zero(RS)) 18.48/5.68 U36_aag(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aag(R, S, RSS, add_in_aag(S, zero(RS), RSS)) 18.48/5.68 add_in_aag(b, b, b) -> add_out_aag(b, b, b) 18.48/5.68 add_in_aag(X, b, X) -> U1_aag(X, binaryZ_in_g(X)) 18.48/5.68 binaryZ_in_g(zero(X)) -> U29_g(X, binaryZ_in_g(X)) 18.48/5.68 binaryZ_in_g(one(X)) -> U30_g(X, binary_in_g(X)) 18.48/5.68 binary_in_g(b) -> binary_out_g(b) 18.48/5.68 binary_in_g(zero(X)) -> U27_g(X, binaryZ_in_g(X)) 18.48/5.68 U27_g(X, binaryZ_out_g(X)) -> binary_out_g(zero(X)) 18.48/5.68 binary_in_g(one(X)) -> U28_g(X, binary_in_g(X)) 18.48/5.68 U28_g(X, binary_out_g(X)) -> binary_out_g(one(X)) 18.48/5.68 U30_g(X, binary_out_g(X)) -> binaryZ_out_g(one(X)) 18.48/5.68 U29_g(X, binaryZ_out_g(X)) -> binaryZ_out_g(zero(X)) 18.48/5.68 U1_aag(X, binaryZ_out_g(X)) -> add_out_aag(X, b, X) 18.48/5.68 add_in_aag(b, Y, Y) -> U2_aag(Y, binaryZ_in_g(Y)) 18.48/5.68 U2_aag(Y, binaryZ_out_g(Y)) -> add_out_aag(b, Y, Y) 18.48/5.68 add_in_aag(X, Y, Z) -> U3_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.48/5.68 addz_in_aag(zero(X), zero(Y), zero(Z)) -> U10_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.48/5.68 addz_in_aag(zero(X), one(Y), one(Z)) -> U11_aag(X, Y, Z, addx_in_aag(X, Y, Z)) 18.48/5.68 addx_in_aag(one(X), b, one(X)) -> U4_aag(X, binary_in_g(X)) 18.48/5.68 U4_aag(X, binary_out_g(X)) -> addx_out_aag(one(X), b, one(X)) 18.48/5.68 addx_in_aag(zero(X), b, zero(X)) -> U5_aag(X, binaryZ_in_g(X)) 18.48/5.68 U5_aag(X, binaryZ_out_g(X)) -> addx_out_aag(zero(X), b, zero(X)) 18.48/5.68 addx_in_aag(X, Y, Z) -> U6_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.48/5.68 addz_in_aag(one(X), zero(Y), one(Z)) -> U12_aag(X, Y, Z, addy_in_aag(X, Y, Z)) 18.48/5.68 addy_in_aag(b, one(Y), one(Y)) -> U7_aag(Y, binary_in_g(Y)) 18.48/5.68 U7_aag(Y, binary_out_g(Y)) -> addy_out_aag(b, one(Y), one(Y)) 18.48/5.68 addy_in_aag(b, zero(Y), zero(Y)) -> U8_aag(Y, binaryZ_in_g(Y)) 18.48/5.68 U8_aag(Y, binaryZ_out_g(Y)) -> addy_out_aag(b, zero(Y), zero(Y)) 18.48/5.68 addy_in_aag(X, Y, Z) -> U9_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.48/5.68 addz_in_aag(one(X), one(Y), zero(Z)) -> U13_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.48/5.68 addc_in_aag(b, b, one(b)) -> addc_out_aag(b, b, one(b)) 18.48/5.68 addc_in_aag(X, b, Z) -> U14_aag(X, Z, succZ_in_ag(X, Z)) 18.48/5.68 succZ_in_ag(zero(X), one(X)) -> U33_ag(X, binaryZ_in_g(X)) 18.48/5.68 U33_ag(X, binaryZ_out_g(X)) -> succZ_out_ag(zero(X), one(X)) 18.48/5.68 succZ_in_ag(one(X), zero(Z)) -> U34_ag(X, Z, succ_in_ag(X, Z)) 18.48/5.68 succ_in_ag(b, one(b)) -> succ_out_ag(b, one(b)) 18.48/5.68 succ_in_ag(zero(X), one(X)) -> U31_ag(X, binaryZ_in_g(X)) 18.48/5.68 U31_ag(X, binaryZ_out_g(X)) -> succ_out_ag(zero(X), one(X)) 18.48/5.68 succ_in_ag(one(X), zero(Z)) -> U32_ag(X, Z, succ_in_ag(X, Z)) 18.48/5.68 U32_ag(X, Z, succ_out_ag(X, Z)) -> succ_out_ag(one(X), zero(Z)) 18.48/5.68 U34_ag(X, Z, succ_out_ag(X, Z)) -> succZ_out_ag(one(X), zero(Z)) 18.48/5.68 U14_aag(X, Z, succZ_out_ag(X, Z)) -> addc_out_aag(X, b, Z) 18.48/5.68 addc_in_aag(b, Y, Z) -> U15_aag(Y, Z, succZ_in_ag(Y, Z)) 18.48/5.68 U15_aag(Y, Z, succZ_out_ag(Y, Z)) -> addc_out_aag(b, Y, Z) 18.48/5.68 addc_in_aag(X, Y, Z) -> U16_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.48/5.68 addC_in_aag(zero(X), zero(Y), one(Z)) -> U23_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.48/5.68 U23_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), zero(Y), one(Z)) 18.48/5.68 addC_in_aag(zero(X), one(Y), zero(Z)) -> U24_aag(X, Y, Z, addX_in_aag(X, Y, Z)) 18.48/5.68 addX_in_aag(zero(X), b, one(X)) -> U17_aag(X, binaryZ_in_g(X)) 18.48/5.68 U17_aag(X, binaryZ_out_g(X)) -> addX_out_aag(zero(X), b, one(X)) 18.48/5.68 addX_in_aag(one(X), b, zero(Z)) -> U18_aag(X, Z, succ_in_ag(X, Z)) 18.48/5.68 U18_aag(X, Z, succ_out_ag(X, Z)) -> addX_out_aag(one(X), b, zero(Z)) 18.48/5.68 addX_in_aag(X, Y, Z) -> U19_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.48/5.68 addC_in_aag(one(X), zero(Y), zero(Z)) -> U25_aag(X, Y, Z, addY_in_aag(X, Y, Z)) 18.48/5.68 addY_in_aag(b, zero(Y), one(Y)) -> U20_aag(Y, binaryZ_in_g(Y)) 18.48/5.68 U20_aag(Y, binaryZ_out_g(Y)) -> addY_out_aag(b, zero(Y), one(Y)) 18.48/5.68 addY_in_aag(b, one(Y), zero(Z)) -> U21_aag(Y, Z, succ_in_ag(Y, Z)) 18.48/5.68 U21_aag(Y, Z, succ_out_ag(Y, Z)) -> addY_out_aag(b, one(Y), zero(Z)) 18.48/5.68 addY_in_aag(X, Y, Z) -> U22_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.48/5.68 addC_in_aag(one(X), one(Y), one(Z)) -> U26_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.48/5.68 U26_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addC_out_aag(one(X), one(Y), one(Z)) 18.48/5.68 U22_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addY_out_aag(X, Y, Z) 18.48/5.68 U25_aag(X, Y, Z, addY_out_aag(X, Y, Z)) -> addC_out_aag(one(X), zero(Y), zero(Z)) 18.48/5.68 U19_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addX_out_aag(X, Y, Z) 18.48/5.68 U24_aag(X, Y, Z, addX_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), one(Y), zero(Z)) 18.48/5.68 U16_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addc_out_aag(X, Y, Z) 18.48/5.68 U13_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addz_out_aag(one(X), one(Y), zero(Z)) 18.48/5.68 U9_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addy_out_aag(X, Y, Z) 18.48/5.68 U12_aag(X, Y, Z, addy_out_aag(X, Y, Z)) -> addz_out_aag(one(X), zero(Y), one(Z)) 18.48/5.68 U6_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addx_out_aag(X, Y, Z) 18.48/5.68 U11_aag(X, Y, Z, addx_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), one(Y), one(Z)) 18.48/5.68 U10_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), zero(Y), zero(Z)) 18.48/5.68 U3_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> add_out_aag(X, Y, Z) 18.48/5.68 U37_aag(R, S, RSS, add_out_aag(S, zero(RS), RSS)) -> times_out_aag(one(R), S, RSS) 18.48/5.68 U35_aag(R, S, RS, times_out_aag(R, S, RS)) -> times_out_aag(zero(R), S, zero(RS)) 18.48/5.68 18.48/5.68 The argument filtering Pi contains the following mapping: 18.48/5.68 times_in_aag(x1, x2, x3) = times_in_aag(x3) 18.48/5.68 18.48/5.68 times_out_aag(x1, x2, x3) = times_out_aag(x1, x2) 18.48/5.68 18.48/5.68 zero(x1) = zero(x1) 18.48/5.68 18.48/5.68 U35_aag(x1, x2, x3, x4) = U35_aag(x4) 18.48/5.68 18.48/5.68 U36_aag(x1, x2, x3, x4) = U36_aag(x3, x4) 18.48/5.68 18.48/5.68 times_in_aaa(x1, x2, x3) = times_in_aaa 18.48/5.68 18.48/5.68 times_out_aaa(x1, x2, x3) = times_out_aaa(x1) 18.48/5.68 18.48/5.68 U35_aaa(x1, x2, x3, x4) = U35_aaa(x4) 18.48/5.68 18.48/5.68 U36_aaa(x1, x2, x3, x4) = U36_aaa(x4) 18.48/5.68 18.48/5.68 U37_aaa(x1, x2, x3, x4) = U37_aaa(x1, x4) 18.48/5.68 18.48/5.68 add_in_aaa(x1, x2, x3) = add_in_aaa 18.48/5.68 18.48/5.68 add_out_aaa(x1, x2, x3) = add_out_aaa(x1, x2, x3) 18.48/5.68 18.48/5.68 U1_aaa(x1, x2) = U1_aaa(x2) 18.48/5.68 18.48/5.68 binaryZ_in_a(x1) = binaryZ_in_a 18.48/5.68 18.48/5.68 U29_a(x1, x2) = U29_a(x2) 18.48/5.68 18.48/5.68 U30_a(x1, x2) = U30_a(x2) 18.48/5.68 18.48/5.68 binary_in_a(x1) = binary_in_a 18.48/5.68 18.48/5.68 binary_out_a(x1) = binary_out_a(x1) 18.48/5.68 18.48/5.68 U27_a(x1, x2) = U27_a(x2) 18.48/5.68 18.48/5.68 binaryZ_out_a(x1) = binaryZ_out_a(x1) 18.48/5.68 18.48/5.68 U28_a(x1, x2) = U28_a(x2) 18.48/5.68 18.48/5.68 U2_aaa(x1, x2) = U2_aaa(x2) 18.48/5.68 18.48/5.68 U3_aaa(x1, x2, x3, x4) = U3_aaa(x4) 18.48/5.68 18.48/5.68 addz_in_aaa(x1, x2, x3) = addz_in_aaa 18.48/5.68 18.48/5.68 U10_aaa(x1, x2, x3, x4) = U10_aaa(x4) 18.48/5.68 18.48/5.68 U11_aaa(x1, x2, x3, x4) = U11_aaa(x4) 18.48/5.68 18.48/5.68 addx_in_aaa(x1, x2, x3) = addx_in_aaa 18.48/5.68 18.48/5.68 U4_aaa(x1, x2) = U4_aaa(x2) 18.48/5.68 18.48/5.68 addx_out_aaa(x1, x2, x3) = addx_out_aaa(x1, x2, x3) 18.48/5.68 18.48/5.68 U5_aaa(x1, x2) = U5_aaa(x2) 18.48/5.68 18.48/5.68 U6_aaa(x1, x2, x3, x4) = U6_aaa(x4) 18.48/5.68 18.48/5.68 U12_aaa(x1, x2, x3, x4) = U12_aaa(x4) 18.48/5.68 18.48/5.68 addy_in_aaa(x1, x2, x3) = addy_in_aaa 18.48/5.68 18.48/5.68 U7_aaa(x1, x2) = U7_aaa(x2) 18.48/5.68 18.48/5.68 addy_out_aaa(x1, x2, x3) = addy_out_aaa(x1, x2, x3) 18.48/5.68 18.48/5.68 U8_aaa(x1, x2) = U8_aaa(x2) 18.48/5.68 18.48/5.68 U9_aaa(x1, x2, x3, x4) = U9_aaa(x4) 18.48/5.68 18.48/5.68 U13_aaa(x1, x2, x3, x4) = U13_aaa(x4) 18.48/5.68 18.48/5.68 addc_in_aaa(x1, x2, x3) = addc_in_aaa 18.48/5.68 18.48/5.68 addc_out_aaa(x1, x2, x3) = addc_out_aaa(x1, x2, x3) 18.48/5.68 18.48/5.68 U14_aaa(x1, x2, x3) = U14_aaa(x3) 18.48/5.68 18.48/5.68 succZ_in_aa(x1, x2) = succZ_in_aa 18.48/5.68 18.48/5.68 U33_aa(x1, x2) = U33_aa(x2) 18.48/5.68 18.48/5.68 succZ_out_aa(x1, x2) = succZ_out_aa(x1, x2) 18.48/5.68 18.48/5.68 U34_aa(x1, x2, x3) = U34_aa(x3) 18.48/5.68 18.48/5.68 succ_in_aa(x1, x2) = succ_in_aa 18.48/5.68 18.48/5.68 succ_out_aa(x1, x2) = succ_out_aa(x1, x2) 18.48/5.68 18.48/5.68 U31_aa(x1, x2) = U31_aa(x2) 18.48/5.68 18.48/5.68 U32_aa(x1, x2, x3) = U32_aa(x3) 18.48/5.68 18.48/5.68 U15_aaa(x1, x2, x3) = U15_aaa(x3) 18.48/5.68 18.48/5.68 U16_aaa(x1, x2, x3, x4) = U16_aaa(x4) 18.48/5.68 18.48/5.68 addC_in_aaa(x1, x2, x3) = addC_in_aaa 18.48/5.68 18.48/5.68 U23_aaa(x1, x2, x3, x4) = U23_aaa(x4) 18.48/5.68 18.48/5.68 addz_out_aaa(x1, x2, x3) = addz_out_aaa(x1, x2, x3) 18.48/5.68 18.48/5.68 addC_out_aaa(x1, x2, x3) = addC_out_aaa(x1, x2, x3) 18.48/5.68 18.48/5.68 U24_aaa(x1, x2, x3, x4) = U24_aaa(x4) 18.48/5.68 18.48/5.68 addX_in_aaa(x1, x2, x3) = addX_in_aaa 18.48/5.68 18.48/5.68 U17_aaa(x1, x2) = U17_aaa(x2) 18.48/5.68 18.48/5.68 addX_out_aaa(x1, x2, x3) = addX_out_aaa(x1, x2, x3) 18.48/5.68 18.48/5.68 U18_aaa(x1, x2, x3) = U18_aaa(x3) 18.48/5.68 18.48/5.68 U19_aaa(x1, x2, x3, x4) = U19_aaa(x4) 18.48/5.68 18.48/5.68 U25_aaa(x1, x2, x3, x4) = U25_aaa(x4) 18.48/5.68 18.48/5.68 addY_in_aaa(x1, x2, x3) = addY_in_aaa 18.48/5.68 18.48/5.68 U20_aaa(x1, x2) = U20_aaa(x2) 18.48/5.68 18.48/5.68 addY_out_aaa(x1, x2, x3) = addY_out_aaa(x1, x2, x3) 18.48/5.68 18.48/5.68 U21_aaa(x1, x2, x3) = U21_aaa(x3) 18.48/5.68 18.48/5.68 U22_aaa(x1, x2, x3, x4) = U22_aaa(x4) 18.48/5.68 18.48/5.68 U26_aaa(x1, x2, x3, x4) = U26_aaa(x4) 18.48/5.68 18.48/5.68 U37_aag(x1, x2, x3, x4) = U37_aag(x1, x4) 18.48/5.68 18.48/5.68 add_in_aag(x1, x2, x3) = add_in_aag(x3) 18.48/5.68 18.48/5.68 b = b 18.48/5.68 18.48/5.68 add_out_aag(x1, x2, x3) = add_out_aag(x1, x2) 18.48/5.68 18.48/5.68 U1_aag(x1, x2) = U1_aag(x1, x2) 18.48/5.68 18.48/5.68 binaryZ_in_g(x1) = binaryZ_in_g(x1) 18.48/5.68 18.48/5.68 U29_g(x1, x2) = U29_g(x2) 18.48/5.68 18.48/5.68 one(x1) = one(x1) 18.48/5.68 18.48/5.68 U30_g(x1, x2) = U30_g(x2) 18.48/5.68 18.48/5.68 binary_in_g(x1) = binary_in_g(x1) 18.48/5.68 18.48/5.68 binary_out_g(x1) = binary_out_g 18.48/5.68 18.48/5.68 U27_g(x1, x2) = U27_g(x2) 18.48/5.68 18.48/5.68 binaryZ_out_g(x1) = binaryZ_out_g 18.48/5.68 18.48/5.68 U28_g(x1, x2) = U28_g(x2) 18.48/5.68 18.48/5.68 U2_aag(x1, x2) = U2_aag(x1, x2) 18.48/5.68 18.48/5.68 U3_aag(x1, x2, x3, x4) = U3_aag(x4) 18.48/5.68 18.48/5.68 addz_in_aag(x1, x2, x3) = addz_in_aag(x3) 18.48/5.68 18.48/5.68 U10_aag(x1, x2, x3, x4) = U10_aag(x4) 18.48/5.68 18.48/5.68 U11_aag(x1, x2, x3, x4) = U11_aag(x4) 18.48/5.68 18.48/5.68 addx_in_aag(x1, x2, x3) = addx_in_aag(x3) 18.48/5.68 18.48/5.68 U4_aag(x1, x2) = U4_aag(x1, x2) 18.48/5.68 18.48/5.68 addx_out_aag(x1, x2, x3) = addx_out_aag(x1, x2) 18.48/5.68 18.48/5.68 U5_aag(x1, x2) = U5_aag(x1, x2) 18.48/5.68 18.48/5.68 U6_aag(x1, x2, x3, x4) = U6_aag(x4) 18.48/5.68 18.48/5.68 U12_aag(x1, x2, x3, x4) = U12_aag(x4) 18.48/5.68 18.48/5.68 addy_in_aag(x1, x2, x3) = addy_in_aag(x3) 18.48/5.68 18.48/5.68 U7_aag(x1, x2) = U7_aag(x1, x2) 18.48/5.68 18.48/5.68 addy_out_aag(x1, x2, x3) = addy_out_aag(x1, x2) 18.48/5.68 18.48/5.68 U8_aag(x1, x2) = U8_aag(x1, x2) 18.48/5.68 18.48/5.68 U9_aag(x1, x2, x3, x4) = U9_aag(x4) 18.48/5.68 18.48/5.68 U13_aag(x1, x2, x3, x4) = U13_aag(x4) 18.48/5.68 18.48/5.68 addc_in_aag(x1, x2, x3) = addc_in_aag(x3) 18.48/5.68 18.48/5.68 addc_out_aag(x1, x2, x3) = addc_out_aag(x1, x2) 18.48/5.68 18.48/5.68 U14_aag(x1, x2, x3) = U14_aag(x3) 18.48/5.68 18.48/5.68 succZ_in_ag(x1, x2) = succZ_in_ag(x2) 18.48/5.68 18.48/5.68 U33_ag(x1, x2) = U33_ag(x1, x2) 18.48/5.68 18.48/5.68 succZ_out_ag(x1, x2) = succZ_out_ag(x1) 18.48/5.68 18.48/5.68 U34_ag(x1, x2, x3) = U34_ag(x3) 18.48/5.68 18.48/5.68 succ_in_ag(x1, x2) = succ_in_ag(x2) 18.48/5.68 18.48/5.68 succ_out_ag(x1, x2) = succ_out_ag(x1) 18.48/5.68 18.48/5.68 U31_ag(x1, x2) = U31_ag(x1, x2) 18.48/5.68 18.48/5.68 U32_ag(x1, x2, x3) = U32_ag(x3) 18.48/5.68 18.48/5.68 U15_aag(x1, x2, x3) = U15_aag(x3) 18.48/5.68 18.48/5.68 U16_aag(x1, x2, x3, x4) = U16_aag(x4) 18.48/5.68 18.48/5.68 addC_in_aag(x1, x2, x3) = addC_in_aag(x3) 18.48/5.68 18.48/5.68 U23_aag(x1, x2, x3, x4) = U23_aag(x4) 18.48/5.68 18.48/5.68 addz_out_aag(x1, x2, x3) = addz_out_aag(x1, x2) 18.48/5.68 18.48/5.68 addC_out_aag(x1, x2, x3) = addC_out_aag(x1, x2) 18.48/5.68 18.48/5.68 U24_aag(x1, x2, x3, x4) = U24_aag(x4) 18.48/5.68 18.48/5.68 addX_in_aag(x1, x2, x3) = addX_in_aag(x3) 18.48/5.68 18.48/5.68 U17_aag(x1, x2) = U17_aag(x1, x2) 18.48/5.68 18.48/5.68 addX_out_aag(x1, x2, x3) = addX_out_aag(x1, x2) 18.48/5.68 18.48/5.68 U18_aag(x1, x2, x3) = U18_aag(x3) 18.48/5.68 18.48/5.68 U19_aag(x1, x2, x3, x4) = U19_aag(x4) 18.48/5.68 18.48/5.68 U25_aag(x1, x2, x3, x4) = U25_aag(x4) 18.48/5.68 18.48/5.68 addY_in_aag(x1, x2, x3) = addY_in_aag(x3) 18.48/5.68 18.48/5.68 U20_aag(x1, x2) = U20_aag(x1, x2) 18.48/5.68 18.48/5.68 addY_out_aag(x1, x2, x3) = addY_out_aag(x1, x2) 18.48/5.68 18.48/5.68 U21_aag(x1, x2, x3) = U21_aag(x3) 18.48/5.69 18.48/5.69 U22_aag(x1, x2, x3, x4) = U22_aag(x4) 18.48/5.69 18.48/5.69 U26_aag(x1, x2, x3, x4) = U26_aag(x4) 18.48/5.69 18.48/5.69 BINARYZ_IN_A(x1) = BINARYZ_IN_A 18.48/5.69 18.48/5.69 BINARY_IN_A(x1) = BINARY_IN_A 18.48/5.69 18.48/5.69 18.48/5.69 We have to consider all (P,R,Pi)-chains 18.48/5.69 ---------------------------------------- 18.48/5.69 18.48/5.69 (77) UsableRulesProof (EQUIVALENT) 18.48/5.69 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 18.48/5.69 ---------------------------------------- 18.48/5.69 18.48/5.69 (78) 18.48/5.69 Obligation: 18.48/5.69 Pi DP problem: 18.48/5.69 The TRS P consists of the following rules: 18.48/5.69 18.48/5.69 BINARYZ_IN_A(one(X)) -> BINARY_IN_A(X) 18.48/5.69 BINARY_IN_A(zero(X)) -> BINARYZ_IN_A(X) 18.48/5.69 BINARYZ_IN_A(zero(X)) -> BINARYZ_IN_A(X) 18.48/5.69 BINARY_IN_A(one(X)) -> BINARY_IN_A(X) 18.48/5.69 18.48/5.69 R is empty. 18.48/5.69 The argument filtering Pi contains the following mapping: 18.48/5.69 zero(x1) = zero(x1) 18.48/5.69 18.48/5.69 one(x1) = one(x1) 18.48/5.69 18.48/5.69 BINARYZ_IN_A(x1) = BINARYZ_IN_A 18.48/5.69 18.48/5.69 BINARY_IN_A(x1) = BINARY_IN_A 18.48/5.69 18.48/5.69 18.48/5.69 We have to consider all (P,R,Pi)-chains 18.48/5.69 ---------------------------------------- 18.48/5.69 18.48/5.69 (79) PiDPToQDPProof (SOUND) 18.48/5.69 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 18.48/5.69 ---------------------------------------- 18.48/5.69 18.48/5.69 (80) 18.48/5.69 Obligation: 18.48/5.69 Q DP problem: 18.48/5.69 The TRS P consists of the following rules: 18.48/5.69 18.48/5.69 BINARYZ_IN_A -> BINARY_IN_A 18.48/5.69 BINARY_IN_A -> BINARYZ_IN_A 18.48/5.69 BINARYZ_IN_A -> BINARYZ_IN_A 18.48/5.69 BINARY_IN_A -> BINARY_IN_A 18.48/5.69 18.48/5.69 R is empty. 18.48/5.69 Q is empty. 18.48/5.69 We have to consider all (P,Q,R)-chains. 18.48/5.69 ---------------------------------------- 18.48/5.69 18.48/5.69 (81) NonTerminationLoopProof (COMPLETE) 18.48/5.69 We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. 18.48/5.69 Found a loop by semiunifying a rule from P directly. 18.48/5.69 18.48/5.69 s = BINARYZ_IN_A evaluates to t =BINARYZ_IN_A 18.48/5.69 18.48/5.69 Thus s starts an infinite chain as s semiunifies with t with the following substitutions: 18.48/5.69 * Matcher: [ ] 18.48/5.69 * Semiunifier: [ ] 18.48/5.69 18.48/5.69 -------------------------------------------------------------------------------- 18.48/5.69 Rewriting sequence 18.48/5.69 18.48/5.69 The DP semiunifies directly so there is only one rewrite step from BINARYZ_IN_A to BINARYZ_IN_A. 18.48/5.69 18.48/5.69 18.48/5.69 18.48/5.69 18.48/5.69 ---------------------------------------- 18.48/5.69 18.48/5.69 (82) 18.48/5.69 NO 18.48/5.69 18.48/5.69 ---------------------------------------- 18.48/5.69 18.48/5.69 (83) 18.48/5.69 Obligation: 18.48/5.69 Pi DP problem: 18.48/5.69 The TRS P consists of the following rules: 18.48/5.69 18.48/5.69 SUCC_IN_AA(one(X), zero(Z)) -> SUCC_IN_AA(X, Z) 18.48/5.69 18.48/5.69 The TRS R consists of the following rules: 18.48/5.69 18.48/5.69 times_in_aag(one(b), X, X) -> times_out_aag(one(b), X, X) 18.48/5.69 times_in_aag(zero(R), S, zero(RS)) -> U35_aag(R, S, RS, times_in_aag(R, S, RS)) 18.48/5.69 times_in_aag(one(R), S, RSS) -> U36_aag(R, S, RSS, times_in_aaa(R, S, RS)) 18.48/5.69 times_in_aaa(one(b), X, X) -> times_out_aaa(one(b), X, X) 18.48/5.69 times_in_aaa(zero(R), S, zero(RS)) -> U35_aaa(R, S, RS, times_in_aaa(R, S, RS)) 18.48/5.69 times_in_aaa(one(R), S, RSS) -> U36_aaa(R, S, RSS, times_in_aaa(R, S, RS)) 18.48/5.69 U36_aaa(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aaa(R, S, RSS, add_in_aaa(S, zero(RS), RSS)) 18.48/5.69 add_in_aaa(b, b, b) -> add_out_aaa(b, b, b) 18.48/5.69 add_in_aaa(X, b, X) -> U1_aaa(X, binaryZ_in_a(X)) 18.48/5.69 binaryZ_in_a(zero(X)) -> U29_a(X, binaryZ_in_a(X)) 18.48/5.69 binaryZ_in_a(one(X)) -> U30_a(X, binary_in_a(X)) 18.48/5.69 binary_in_a(b) -> binary_out_a(b) 18.48/5.69 binary_in_a(zero(X)) -> U27_a(X, binaryZ_in_a(X)) 18.48/5.69 U27_a(X, binaryZ_out_a(X)) -> binary_out_a(zero(X)) 18.48/5.69 binary_in_a(one(X)) -> U28_a(X, binary_in_a(X)) 18.48/5.69 U28_a(X, binary_out_a(X)) -> binary_out_a(one(X)) 18.48/5.69 U30_a(X, binary_out_a(X)) -> binaryZ_out_a(one(X)) 18.48/5.69 U29_a(X, binaryZ_out_a(X)) -> binaryZ_out_a(zero(X)) 18.48/5.69 U1_aaa(X, binaryZ_out_a(X)) -> add_out_aaa(X, b, X) 18.48/5.69 add_in_aaa(b, Y, Y) -> U2_aaa(Y, binaryZ_in_a(Y)) 18.48/5.69 U2_aaa(Y, binaryZ_out_a(Y)) -> add_out_aaa(b, Y, Y) 18.48/5.69 add_in_aaa(X, Y, Z) -> U3_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.48/5.69 addz_in_aaa(zero(X), zero(Y), zero(Z)) -> U10_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.48/5.69 addz_in_aaa(zero(X), one(Y), one(Z)) -> U11_aaa(X, Y, Z, addx_in_aaa(X, Y, Z)) 18.48/5.69 addx_in_aaa(one(X), b, one(X)) -> U4_aaa(X, binary_in_a(X)) 18.48/5.69 U4_aaa(X, binary_out_a(X)) -> addx_out_aaa(one(X), b, one(X)) 18.48/5.69 addx_in_aaa(zero(X), b, zero(X)) -> U5_aaa(X, binaryZ_in_a(X)) 18.48/5.69 U5_aaa(X, binaryZ_out_a(X)) -> addx_out_aaa(zero(X), b, zero(X)) 18.48/5.69 addx_in_aaa(X, Y, Z) -> U6_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.48/5.69 addz_in_aaa(one(X), zero(Y), one(Z)) -> U12_aaa(X, Y, Z, addy_in_aaa(X, Y, Z)) 18.48/5.69 addy_in_aaa(b, one(Y), one(Y)) -> U7_aaa(Y, binary_in_a(Y)) 18.48/5.69 U7_aaa(Y, binary_out_a(Y)) -> addy_out_aaa(b, one(Y), one(Y)) 18.48/5.69 addy_in_aaa(b, zero(Y), zero(Y)) -> U8_aaa(Y, binaryZ_in_a(Y)) 18.48/5.69 U8_aaa(Y, binaryZ_out_a(Y)) -> addy_out_aaa(b, zero(Y), zero(Y)) 18.48/5.69 addy_in_aaa(X, Y, Z) -> U9_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.48/5.69 addz_in_aaa(one(X), one(Y), zero(Z)) -> U13_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.48/5.69 addc_in_aaa(b, b, one(b)) -> addc_out_aaa(b, b, one(b)) 18.48/5.69 addc_in_aaa(X, b, Z) -> U14_aaa(X, Z, succZ_in_aa(X, Z)) 18.48/5.69 succZ_in_aa(zero(X), one(X)) -> U33_aa(X, binaryZ_in_a(X)) 18.48/5.69 U33_aa(X, binaryZ_out_a(X)) -> succZ_out_aa(zero(X), one(X)) 18.48/5.69 succZ_in_aa(one(X), zero(Z)) -> U34_aa(X, Z, succ_in_aa(X, Z)) 18.48/5.69 succ_in_aa(b, one(b)) -> succ_out_aa(b, one(b)) 18.48/5.69 succ_in_aa(zero(X), one(X)) -> U31_aa(X, binaryZ_in_a(X)) 18.48/5.69 U31_aa(X, binaryZ_out_a(X)) -> succ_out_aa(zero(X), one(X)) 18.48/5.69 succ_in_aa(one(X), zero(Z)) -> U32_aa(X, Z, succ_in_aa(X, Z)) 18.48/5.69 U32_aa(X, Z, succ_out_aa(X, Z)) -> succ_out_aa(one(X), zero(Z)) 18.48/5.69 U34_aa(X, Z, succ_out_aa(X, Z)) -> succZ_out_aa(one(X), zero(Z)) 18.48/5.69 U14_aaa(X, Z, succZ_out_aa(X, Z)) -> addc_out_aaa(X, b, Z) 18.48/5.69 addc_in_aaa(b, Y, Z) -> U15_aaa(Y, Z, succZ_in_aa(Y, Z)) 18.48/5.69 U15_aaa(Y, Z, succZ_out_aa(Y, Z)) -> addc_out_aaa(b, Y, Z) 18.48/5.69 addc_in_aaa(X, Y, Z) -> U16_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.48/5.69 addC_in_aaa(zero(X), zero(Y), one(Z)) -> U23_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.48/5.69 U23_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), zero(Y), one(Z)) 18.48/5.69 addC_in_aaa(zero(X), one(Y), zero(Z)) -> U24_aaa(X, Y, Z, addX_in_aaa(X, Y, Z)) 18.48/5.69 addX_in_aaa(zero(X), b, one(X)) -> U17_aaa(X, binaryZ_in_a(X)) 18.48/5.69 U17_aaa(X, binaryZ_out_a(X)) -> addX_out_aaa(zero(X), b, one(X)) 18.48/5.69 addX_in_aaa(one(X), b, zero(Z)) -> U18_aaa(X, Z, succ_in_aa(X, Z)) 18.48/5.69 U18_aaa(X, Z, succ_out_aa(X, Z)) -> addX_out_aaa(one(X), b, zero(Z)) 18.48/5.69 addX_in_aaa(X, Y, Z) -> U19_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.48/5.69 addC_in_aaa(one(X), zero(Y), zero(Z)) -> U25_aaa(X, Y, Z, addY_in_aaa(X, Y, Z)) 18.48/5.69 addY_in_aaa(b, zero(Y), one(Y)) -> U20_aaa(Y, binaryZ_in_a(Y)) 18.48/5.69 U20_aaa(Y, binaryZ_out_a(Y)) -> addY_out_aaa(b, zero(Y), one(Y)) 18.48/5.69 addY_in_aaa(b, one(Y), zero(Z)) -> U21_aaa(Y, Z, succ_in_aa(Y, Z)) 18.48/5.69 U21_aaa(Y, Z, succ_out_aa(Y, Z)) -> addY_out_aaa(b, one(Y), zero(Z)) 18.48/5.69 addY_in_aaa(X, Y, Z) -> U22_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.48/5.69 addC_in_aaa(one(X), one(Y), one(Z)) -> U26_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.48/5.69 U26_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), one(Y), one(Z)) 18.48/5.69 U22_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addY_out_aaa(X, Y, Z) 18.48/5.69 U25_aaa(X, Y, Z, addY_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), zero(Y), zero(Z)) 18.48/5.69 U19_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addX_out_aaa(X, Y, Z) 18.48/5.69 U24_aaa(X, Y, Z, addX_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), one(Y), zero(Z)) 18.48/5.69 U16_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addc_out_aaa(X, Y, Z) 18.48/5.69 U13_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), one(Y), zero(Z)) 18.48/5.69 U9_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addy_out_aaa(X, Y, Z) 18.48/5.69 U12_aaa(X, Y, Z, addy_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), zero(Y), one(Z)) 18.48/5.69 U6_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addx_out_aaa(X, Y, Z) 18.48/5.69 U11_aaa(X, Y, Z, addx_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), one(Y), one(Z)) 18.48/5.69 U10_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), zero(Y), zero(Z)) 18.48/5.69 U3_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> add_out_aaa(X, Y, Z) 18.48/5.69 U37_aaa(R, S, RSS, add_out_aaa(S, zero(RS), RSS)) -> times_out_aaa(one(R), S, RSS) 18.48/5.69 U35_aaa(R, S, RS, times_out_aaa(R, S, RS)) -> times_out_aaa(zero(R), S, zero(RS)) 18.48/5.69 U36_aag(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aag(R, S, RSS, add_in_aag(S, zero(RS), RSS)) 18.48/5.69 add_in_aag(b, b, b) -> add_out_aag(b, b, b) 18.48/5.69 add_in_aag(X, b, X) -> U1_aag(X, binaryZ_in_g(X)) 18.48/5.69 binaryZ_in_g(zero(X)) -> U29_g(X, binaryZ_in_g(X)) 18.48/5.69 binaryZ_in_g(one(X)) -> U30_g(X, binary_in_g(X)) 18.48/5.69 binary_in_g(b) -> binary_out_g(b) 18.48/5.69 binary_in_g(zero(X)) -> U27_g(X, binaryZ_in_g(X)) 18.48/5.69 U27_g(X, binaryZ_out_g(X)) -> binary_out_g(zero(X)) 18.48/5.69 binary_in_g(one(X)) -> U28_g(X, binary_in_g(X)) 18.48/5.69 U28_g(X, binary_out_g(X)) -> binary_out_g(one(X)) 18.48/5.69 U30_g(X, binary_out_g(X)) -> binaryZ_out_g(one(X)) 18.48/5.69 U29_g(X, binaryZ_out_g(X)) -> binaryZ_out_g(zero(X)) 18.48/5.69 U1_aag(X, binaryZ_out_g(X)) -> add_out_aag(X, b, X) 18.48/5.69 add_in_aag(b, Y, Y) -> U2_aag(Y, binaryZ_in_g(Y)) 18.48/5.69 U2_aag(Y, binaryZ_out_g(Y)) -> add_out_aag(b, Y, Y) 18.48/5.69 add_in_aag(X, Y, Z) -> U3_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.48/5.69 addz_in_aag(zero(X), zero(Y), zero(Z)) -> U10_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.48/5.69 addz_in_aag(zero(X), one(Y), one(Z)) -> U11_aag(X, Y, Z, addx_in_aag(X, Y, Z)) 18.48/5.69 addx_in_aag(one(X), b, one(X)) -> U4_aag(X, binary_in_g(X)) 18.48/5.69 U4_aag(X, binary_out_g(X)) -> addx_out_aag(one(X), b, one(X)) 18.48/5.69 addx_in_aag(zero(X), b, zero(X)) -> U5_aag(X, binaryZ_in_g(X)) 18.48/5.69 U5_aag(X, binaryZ_out_g(X)) -> addx_out_aag(zero(X), b, zero(X)) 18.48/5.69 addx_in_aag(X, Y, Z) -> U6_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.48/5.69 addz_in_aag(one(X), zero(Y), one(Z)) -> U12_aag(X, Y, Z, addy_in_aag(X, Y, Z)) 18.48/5.69 addy_in_aag(b, one(Y), one(Y)) -> U7_aag(Y, binary_in_g(Y)) 18.48/5.69 U7_aag(Y, binary_out_g(Y)) -> addy_out_aag(b, one(Y), one(Y)) 18.48/5.69 addy_in_aag(b, zero(Y), zero(Y)) -> U8_aag(Y, binaryZ_in_g(Y)) 18.48/5.69 U8_aag(Y, binaryZ_out_g(Y)) -> addy_out_aag(b, zero(Y), zero(Y)) 18.48/5.69 addy_in_aag(X, Y, Z) -> U9_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.48/5.69 addz_in_aag(one(X), one(Y), zero(Z)) -> U13_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.48/5.69 addc_in_aag(b, b, one(b)) -> addc_out_aag(b, b, one(b)) 18.48/5.69 addc_in_aag(X, b, Z) -> U14_aag(X, Z, succZ_in_ag(X, Z)) 18.48/5.69 succZ_in_ag(zero(X), one(X)) -> U33_ag(X, binaryZ_in_g(X)) 18.48/5.69 U33_ag(X, binaryZ_out_g(X)) -> succZ_out_ag(zero(X), one(X)) 18.48/5.69 succZ_in_ag(one(X), zero(Z)) -> U34_ag(X, Z, succ_in_ag(X, Z)) 18.48/5.69 succ_in_ag(b, one(b)) -> succ_out_ag(b, one(b)) 18.48/5.69 succ_in_ag(zero(X), one(X)) -> U31_ag(X, binaryZ_in_g(X)) 18.48/5.69 U31_ag(X, binaryZ_out_g(X)) -> succ_out_ag(zero(X), one(X)) 18.48/5.69 succ_in_ag(one(X), zero(Z)) -> U32_ag(X, Z, succ_in_ag(X, Z)) 18.48/5.69 U32_ag(X, Z, succ_out_ag(X, Z)) -> succ_out_ag(one(X), zero(Z)) 18.48/5.69 U34_ag(X, Z, succ_out_ag(X, Z)) -> succZ_out_ag(one(X), zero(Z)) 18.48/5.69 U14_aag(X, Z, succZ_out_ag(X, Z)) -> addc_out_aag(X, b, Z) 18.48/5.69 addc_in_aag(b, Y, Z) -> U15_aag(Y, Z, succZ_in_ag(Y, Z)) 18.48/5.69 U15_aag(Y, Z, succZ_out_ag(Y, Z)) -> addc_out_aag(b, Y, Z) 18.48/5.69 addc_in_aag(X, Y, Z) -> U16_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.48/5.69 addC_in_aag(zero(X), zero(Y), one(Z)) -> U23_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.48/5.69 U23_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), zero(Y), one(Z)) 18.48/5.69 addC_in_aag(zero(X), one(Y), zero(Z)) -> U24_aag(X, Y, Z, addX_in_aag(X, Y, Z)) 18.48/5.69 addX_in_aag(zero(X), b, one(X)) -> U17_aag(X, binaryZ_in_g(X)) 18.48/5.69 U17_aag(X, binaryZ_out_g(X)) -> addX_out_aag(zero(X), b, one(X)) 18.48/5.69 addX_in_aag(one(X), b, zero(Z)) -> U18_aag(X, Z, succ_in_ag(X, Z)) 18.48/5.69 U18_aag(X, Z, succ_out_ag(X, Z)) -> addX_out_aag(one(X), b, zero(Z)) 18.48/5.69 addX_in_aag(X, Y, Z) -> U19_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.48/5.69 addC_in_aag(one(X), zero(Y), zero(Z)) -> U25_aag(X, Y, Z, addY_in_aag(X, Y, Z)) 18.48/5.69 addY_in_aag(b, zero(Y), one(Y)) -> U20_aag(Y, binaryZ_in_g(Y)) 18.48/5.69 U20_aag(Y, binaryZ_out_g(Y)) -> addY_out_aag(b, zero(Y), one(Y)) 18.48/5.69 addY_in_aag(b, one(Y), zero(Z)) -> U21_aag(Y, Z, succ_in_ag(Y, Z)) 18.48/5.69 U21_aag(Y, Z, succ_out_ag(Y, Z)) -> addY_out_aag(b, one(Y), zero(Z)) 18.48/5.69 addY_in_aag(X, Y, Z) -> U22_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.48/5.69 addC_in_aag(one(X), one(Y), one(Z)) -> U26_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.48/5.69 U26_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addC_out_aag(one(X), one(Y), one(Z)) 18.48/5.69 U22_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addY_out_aag(X, Y, Z) 18.48/5.69 U25_aag(X, Y, Z, addY_out_aag(X, Y, Z)) -> addC_out_aag(one(X), zero(Y), zero(Z)) 18.48/5.69 U19_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addX_out_aag(X, Y, Z) 18.48/5.69 U24_aag(X, Y, Z, addX_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), one(Y), zero(Z)) 18.48/5.69 U16_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addc_out_aag(X, Y, Z) 18.48/5.69 U13_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addz_out_aag(one(X), one(Y), zero(Z)) 18.48/5.69 U9_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addy_out_aag(X, Y, Z) 18.48/5.69 U12_aag(X, Y, Z, addy_out_aag(X, Y, Z)) -> addz_out_aag(one(X), zero(Y), one(Z)) 18.48/5.69 U6_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addx_out_aag(X, Y, Z) 18.48/5.69 U11_aag(X, Y, Z, addx_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), one(Y), one(Z)) 18.48/5.69 U10_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), zero(Y), zero(Z)) 18.48/5.69 U3_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> add_out_aag(X, Y, Z) 18.48/5.69 U37_aag(R, S, RSS, add_out_aag(S, zero(RS), RSS)) -> times_out_aag(one(R), S, RSS) 18.48/5.69 U35_aag(R, S, RS, times_out_aag(R, S, RS)) -> times_out_aag(zero(R), S, zero(RS)) 18.48/5.69 18.48/5.69 The argument filtering Pi contains the following mapping: 18.48/5.69 times_in_aag(x1, x2, x3) = times_in_aag(x3) 18.48/5.69 18.48/5.69 times_out_aag(x1, x2, x3) = times_out_aag(x1, x2) 18.48/5.69 18.48/5.69 zero(x1) = zero(x1) 18.48/5.69 18.48/5.69 U35_aag(x1, x2, x3, x4) = U35_aag(x4) 18.48/5.69 18.48/5.69 U36_aag(x1, x2, x3, x4) = U36_aag(x3, x4) 18.48/5.69 18.48/5.69 times_in_aaa(x1, x2, x3) = times_in_aaa 18.48/5.69 18.48/5.69 times_out_aaa(x1, x2, x3) = times_out_aaa(x1) 18.48/5.69 18.48/5.69 U35_aaa(x1, x2, x3, x4) = U35_aaa(x4) 18.48/5.69 18.48/5.69 U36_aaa(x1, x2, x3, x4) = U36_aaa(x4) 18.48/5.69 18.48/5.69 U37_aaa(x1, x2, x3, x4) = U37_aaa(x1, x4) 18.48/5.69 18.48/5.69 add_in_aaa(x1, x2, x3) = add_in_aaa 18.48/5.69 18.48/5.69 add_out_aaa(x1, x2, x3) = add_out_aaa(x1, x2, x3) 18.48/5.69 18.48/5.69 U1_aaa(x1, x2) = U1_aaa(x2) 18.48/5.69 18.48/5.69 binaryZ_in_a(x1) = binaryZ_in_a 18.48/5.69 18.48/5.69 U29_a(x1, x2) = U29_a(x2) 18.48/5.69 18.48/5.69 U30_a(x1, x2) = U30_a(x2) 18.48/5.69 18.48/5.69 binary_in_a(x1) = binary_in_a 18.48/5.69 18.48/5.69 binary_out_a(x1) = binary_out_a(x1) 18.48/5.69 18.48/5.69 U27_a(x1, x2) = U27_a(x2) 18.48/5.69 18.48/5.69 binaryZ_out_a(x1) = binaryZ_out_a(x1) 18.48/5.69 18.48/5.69 U28_a(x1, x2) = U28_a(x2) 18.48/5.69 18.48/5.69 U2_aaa(x1, x2) = U2_aaa(x2) 18.48/5.69 18.48/5.69 U3_aaa(x1, x2, x3, x4) = U3_aaa(x4) 18.48/5.69 18.48/5.69 addz_in_aaa(x1, x2, x3) = addz_in_aaa 18.48/5.69 18.48/5.69 U10_aaa(x1, x2, x3, x4) = U10_aaa(x4) 18.48/5.69 18.48/5.69 U11_aaa(x1, x2, x3, x4) = U11_aaa(x4) 18.48/5.69 18.48/5.69 addx_in_aaa(x1, x2, x3) = addx_in_aaa 18.48/5.69 18.48/5.69 U4_aaa(x1, x2) = U4_aaa(x2) 18.48/5.69 18.48/5.69 addx_out_aaa(x1, x2, x3) = addx_out_aaa(x1, x2, x3) 18.48/5.69 18.48/5.69 U5_aaa(x1, x2) = U5_aaa(x2) 18.48/5.69 18.48/5.69 U6_aaa(x1, x2, x3, x4) = U6_aaa(x4) 18.48/5.69 18.48/5.69 U12_aaa(x1, x2, x3, x4) = U12_aaa(x4) 18.48/5.69 18.48/5.69 addy_in_aaa(x1, x2, x3) = addy_in_aaa 18.48/5.69 18.48/5.69 U7_aaa(x1, x2) = U7_aaa(x2) 18.48/5.69 18.48/5.69 addy_out_aaa(x1, x2, x3) = addy_out_aaa(x1, x2, x3) 18.48/5.69 18.48/5.69 U8_aaa(x1, x2) = U8_aaa(x2) 18.48/5.69 18.48/5.69 U9_aaa(x1, x2, x3, x4) = U9_aaa(x4) 18.48/5.69 18.48/5.69 U13_aaa(x1, x2, x3, x4) = U13_aaa(x4) 18.48/5.69 18.48/5.69 addc_in_aaa(x1, x2, x3) = addc_in_aaa 18.48/5.69 18.48/5.69 addc_out_aaa(x1, x2, x3) = addc_out_aaa(x1, x2, x3) 18.48/5.69 18.48/5.69 U14_aaa(x1, x2, x3) = U14_aaa(x3) 18.48/5.69 18.48/5.69 succZ_in_aa(x1, x2) = succZ_in_aa 18.48/5.69 18.48/5.69 U33_aa(x1, x2) = U33_aa(x2) 18.48/5.69 18.48/5.69 succZ_out_aa(x1, x2) = succZ_out_aa(x1, x2) 18.48/5.69 18.48/5.69 U34_aa(x1, x2, x3) = U34_aa(x3) 18.48/5.69 18.48/5.69 succ_in_aa(x1, x2) = succ_in_aa 18.48/5.69 18.48/5.69 succ_out_aa(x1, x2) = succ_out_aa(x1, x2) 18.48/5.69 18.48/5.69 U31_aa(x1, x2) = U31_aa(x2) 18.48/5.69 18.48/5.69 U32_aa(x1, x2, x3) = U32_aa(x3) 18.48/5.69 18.48/5.69 U15_aaa(x1, x2, x3) = U15_aaa(x3) 18.48/5.69 18.48/5.69 U16_aaa(x1, x2, x3, x4) = U16_aaa(x4) 18.48/5.69 18.48/5.69 addC_in_aaa(x1, x2, x3) = addC_in_aaa 18.48/5.69 18.48/5.69 U23_aaa(x1, x2, x3, x4) = U23_aaa(x4) 18.48/5.69 18.48/5.69 addz_out_aaa(x1, x2, x3) = addz_out_aaa(x1, x2, x3) 18.48/5.69 18.48/5.69 addC_out_aaa(x1, x2, x3) = addC_out_aaa(x1, x2, x3) 18.48/5.69 18.48/5.69 U24_aaa(x1, x2, x3, x4) = U24_aaa(x4) 18.48/5.69 18.48/5.69 addX_in_aaa(x1, x2, x3) = addX_in_aaa 18.48/5.69 18.48/5.69 U17_aaa(x1, x2) = U17_aaa(x2) 18.48/5.69 18.48/5.69 addX_out_aaa(x1, x2, x3) = addX_out_aaa(x1, x2, x3) 18.48/5.69 18.48/5.69 U18_aaa(x1, x2, x3) = U18_aaa(x3) 18.48/5.69 18.48/5.69 U19_aaa(x1, x2, x3, x4) = U19_aaa(x4) 18.48/5.69 18.48/5.69 U25_aaa(x1, x2, x3, x4) = U25_aaa(x4) 18.48/5.69 18.48/5.69 addY_in_aaa(x1, x2, x3) = addY_in_aaa 18.48/5.69 18.48/5.69 U20_aaa(x1, x2) = U20_aaa(x2) 18.48/5.69 18.48/5.69 addY_out_aaa(x1, x2, x3) = addY_out_aaa(x1, x2, x3) 18.48/5.69 18.48/5.69 U21_aaa(x1, x2, x3) = U21_aaa(x3) 18.48/5.69 18.48/5.69 U22_aaa(x1, x2, x3, x4) = U22_aaa(x4) 18.48/5.69 18.48/5.69 U26_aaa(x1, x2, x3, x4) = U26_aaa(x4) 18.48/5.69 18.48/5.69 U37_aag(x1, x2, x3, x4) = U37_aag(x1, x4) 18.48/5.69 18.48/5.69 add_in_aag(x1, x2, x3) = add_in_aag(x3) 18.48/5.69 18.48/5.69 b = b 18.48/5.69 18.48/5.69 add_out_aag(x1, x2, x3) = add_out_aag(x1, x2) 18.48/5.69 18.48/5.69 U1_aag(x1, x2) = U1_aag(x1, x2) 18.48/5.69 18.48/5.69 binaryZ_in_g(x1) = binaryZ_in_g(x1) 18.48/5.69 18.48/5.69 U29_g(x1, x2) = U29_g(x2) 18.48/5.69 18.48/5.69 one(x1) = one(x1) 18.48/5.69 18.48/5.69 U30_g(x1, x2) = U30_g(x2) 18.48/5.69 18.48/5.69 binary_in_g(x1) = binary_in_g(x1) 18.48/5.69 18.48/5.69 binary_out_g(x1) = binary_out_g 18.48/5.69 18.48/5.69 U27_g(x1, x2) = U27_g(x2) 18.48/5.69 18.48/5.69 binaryZ_out_g(x1) = binaryZ_out_g 18.48/5.69 18.48/5.69 U28_g(x1, x2) = U28_g(x2) 18.48/5.69 18.48/5.69 U2_aag(x1, x2) = U2_aag(x1, x2) 18.48/5.69 18.48/5.69 U3_aag(x1, x2, x3, x4) = U3_aag(x4) 18.48/5.69 18.48/5.69 addz_in_aag(x1, x2, x3) = addz_in_aag(x3) 18.48/5.69 18.48/5.69 U10_aag(x1, x2, x3, x4) = U10_aag(x4) 18.48/5.69 18.48/5.69 U11_aag(x1, x2, x3, x4) = U11_aag(x4) 18.48/5.69 18.48/5.69 addx_in_aag(x1, x2, x3) = addx_in_aag(x3) 18.48/5.69 18.48/5.69 U4_aag(x1, x2) = U4_aag(x1, x2) 18.48/5.69 18.48/5.69 addx_out_aag(x1, x2, x3) = addx_out_aag(x1, x2) 18.48/5.69 18.48/5.69 U5_aag(x1, x2) = U5_aag(x1, x2) 18.48/5.69 18.48/5.69 U6_aag(x1, x2, x3, x4) = U6_aag(x4) 18.48/5.69 18.48/5.69 U12_aag(x1, x2, x3, x4) = U12_aag(x4) 18.48/5.69 18.48/5.69 addy_in_aag(x1, x2, x3) = addy_in_aag(x3) 18.48/5.69 18.48/5.69 U7_aag(x1, x2) = U7_aag(x1, x2) 18.48/5.69 18.48/5.69 addy_out_aag(x1, x2, x3) = addy_out_aag(x1, x2) 18.48/5.69 18.48/5.69 U8_aag(x1, x2) = U8_aag(x1, x2) 18.48/5.69 18.48/5.69 U9_aag(x1, x2, x3, x4) = U9_aag(x4) 18.48/5.69 18.48/5.69 U13_aag(x1, x2, x3, x4) = U13_aag(x4) 18.48/5.69 18.48/5.69 addc_in_aag(x1, x2, x3) = addc_in_aag(x3) 18.48/5.69 18.48/5.69 addc_out_aag(x1, x2, x3) = addc_out_aag(x1, x2) 18.48/5.69 18.48/5.69 U14_aag(x1, x2, x3) = U14_aag(x3) 18.48/5.69 18.48/5.69 succZ_in_ag(x1, x2) = succZ_in_ag(x2) 18.48/5.69 18.48/5.69 U33_ag(x1, x2) = U33_ag(x1, x2) 18.48/5.69 18.48/5.69 succZ_out_ag(x1, x2) = succZ_out_ag(x1) 18.48/5.69 18.48/5.69 U34_ag(x1, x2, x3) = U34_ag(x3) 18.48/5.69 18.48/5.69 succ_in_ag(x1, x2) = succ_in_ag(x2) 18.48/5.69 18.48/5.69 succ_out_ag(x1, x2) = succ_out_ag(x1) 18.48/5.69 18.48/5.69 U31_ag(x1, x2) = U31_ag(x1, x2) 18.48/5.69 18.48/5.69 U32_ag(x1, x2, x3) = U32_ag(x3) 18.48/5.69 18.48/5.69 U15_aag(x1, x2, x3) = U15_aag(x3) 18.48/5.69 18.48/5.69 U16_aag(x1, x2, x3, x4) = U16_aag(x4) 18.48/5.69 18.48/5.69 addC_in_aag(x1, x2, x3) = addC_in_aag(x3) 18.48/5.69 18.48/5.69 U23_aag(x1, x2, x3, x4) = U23_aag(x4) 18.48/5.69 18.48/5.69 addz_out_aag(x1, x2, x3) = addz_out_aag(x1, x2) 18.48/5.69 18.48/5.69 addC_out_aag(x1, x2, x3) = addC_out_aag(x1, x2) 18.48/5.69 18.48/5.69 U24_aag(x1, x2, x3, x4) = U24_aag(x4) 18.48/5.69 18.48/5.69 addX_in_aag(x1, x2, x3) = addX_in_aag(x3) 18.48/5.69 18.48/5.69 U17_aag(x1, x2) = U17_aag(x1, x2) 18.48/5.69 18.48/5.69 addX_out_aag(x1, x2, x3) = addX_out_aag(x1, x2) 18.48/5.69 18.48/5.69 U18_aag(x1, x2, x3) = U18_aag(x3) 18.48/5.69 18.48/5.69 U19_aag(x1, x2, x3, x4) = U19_aag(x4) 18.48/5.69 18.48/5.69 U25_aag(x1, x2, x3, x4) = U25_aag(x4) 18.48/5.69 18.48/5.69 addY_in_aag(x1, x2, x3) = addY_in_aag(x3) 18.48/5.69 18.48/5.69 U20_aag(x1, x2) = U20_aag(x1, x2) 18.48/5.69 18.48/5.69 addY_out_aag(x1, x2, x3) = addY_out_aag(x1, x2) 18.48/5.69 18.48/5.69 U21_aag(x1, x2, x3) = U21_aag(x3) 18.48/5.69 18.48/5.69 U22_aag(x1, x2, x3, x4) = U22_aag(x4) 18.48/5.69 18.48/5.69 U26_aag(x1, x2, x3, x4) = U26_aag(x4) 18.48/5.69 18.48/5.69 SUCC_IN_AA(x1, x2) = SUCC_IN_AA 18.48/5.69 18.48/5.69 18.48/5.69 We have to consider all (P,R,Pi)-chains 18.48/5.69 ---------------------------------------- 18.48/5.69 18.48/5.69 (84) UsableRulesProof (EQUIVALENT) 18.48/5.69 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 18.48/5.69 ---------------------------------------- 18.48/5.69 18.48/5.69 (85) 18.48/5.69 Obligation: 18.48/5.69 Pi DP problem: 18.48/5.69 The TRS P consists of the following rules: 18.48/5.69 18.48/5.69 SUCC_IN_AA(one(X), zero(Z)) -> SUCC_IN_AA(X, Z) 18.48/5.69 18.48/5.69 R is empty. 18.48/5.69 The argument filtering Pi contains the following mapping: 18.48/5.69 zero(x1) = zero(x1) 18.48/5.69 18.48/5.69 one(x1) = one(x1) 18.48/5.69 18.48/5.69 SUCC_IN_AA(x1, x2) = SUCC_IN_AA 18.48/5.69 18.48/5.69 18.48/5.69 We have to consider all (P,R,Pi)-chains 18.48/5.69 ---------------------------------------- 18.48/5.69 18.48/5.69 (86) PiDPToQDPProof (SOUND) 18.48/5.69 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 18.48/5.69 ---------------------------------------- 18.48/5.69 18.48/5.69 (87) 18.48/5.69 Obligation: 18.48/5.69 Q DP problem: 18.48/5.69 The TRS P consists of the following rules: 18.48/5.69 18.48/5.69 SUCC_IN_AA -> SUCC_IN_AA 18.48/5.69 18.48/5.69 R is empty. 18.48/5.69 Q is empty. 18.48/5.69 We have to consider all (P,Q,R)-chains. 18.48/5.69 ---------------------------------------- 18.48/5.69 18.48/5.69 (88) 18.48/5.69 Obligation: 18.48/5.69 Pi DP problem: 18.48/5.69 The TRS P consists of the following rules: 18.48/5.69 18.48/5.69 ADDX_IN_AAA(X, Y, Z) -> ADDZ_IN_AAA(X, Y, Z) 18.48/5.69 ADDZ_IN_AAA(zero(X), zero(Y), zero(Z)) -> ADDZ_IN_AAA(X, Y, Z) 18.48/5.69 ADDZ_IN_AAA(zero(X), one(Y), one(Z)) -> ADDX_IN_AAA(X, Y, Z) 18.48/5.69 ADDZ_IN_AAA(one(X), zero(Y), one(Z)) -> ADDY_IN_AAA(X, Y, Z) 18.48/5.69 ADDY_IN_AAA(X, Y, Z) -> ADDZ_IN_AAA(X, Y, Z) 18.48/5.69 ADDZ_IN_AAA(one(X), one(Y), zero(Z)) -> ADDC_IN_AAA(X, Y, Z) 18.48/5.69 ADDC_IN_AAA(X, Y, Z) -> ADDC_IN_AAA^1(X, Y, Z) 18.48/5.69 ADDC_IN_AAA^1(zero(X), zero(Y), one(Z)) -> ADDZ_IN_AAA(X, Y, Z) 18.48/5.69 ADDC_IN_AAA^1(zero(X), one(Y), zero(Z)) -> ADDX_IN_AAA^1(X, Y, Z) 18.48/5.69 ADDX_IN_AAA^1(X, Y, Z) -> ADDC_IN_AAA^1(X, Y, Z) 18.48/5.69 ADDC_IN_AAA^1(one(X), zero(Y), zero(Z)) -> ADDY_IN_AAA^1(X, Y, Z) 18.48/5.69 ADDY_IN_AAA^1(X, Y, Z) -> ADDC_IN_AAA^1(X, Y, Z) 18.48/5.69 ADDC_IN_AAA^1(one(X), one(Y), one(Z)) -> ADDC_IN_AAA(X, Y, Z) 18.48/5.69 18.48/5.69 The TRS R consists of the following rules: 18.48/5.69 18.48/5.69 times_in_aag(one(b), X, X) -> times_out_aag(one(b), X, X) 18.48/5.69 times_in_aag(zero(R), S, zero(RS)) -> U35_aag(R, S, RS, times_in_aag(R, S, RS)) 18.48/5.69 times_in_aag(one(R), S, RSS) -> U36_aag(R, S, RSS, times_in_aaa(R, S, RS)) 18.48/5.69 times_in_aaa(one(b), X, X) -> times_out_aaa(one(b), X, X) 18.48/5.69 times_in_aaa(zero(R), S, zero(RS)) -> U35_aaa(R, S, RS, times_in_aaa(R, S, RS)) 18.48/5.69 times_in_aaa(one(R), S, RSS) -> U36_aaa(R, S, RSS, times_in_aaa(R, S, RS)) 18.48/5.69 U36_aaa(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aaa(R, S, RSS, add_in_aaa(S, zero(RS), RSS)) 18.48/5.69 add_in_aaa(b, b, b) -> add_out_aaa(b, b, b) 18.48/5.69 add_in_aaa(X, b, X) -> U1_aaa(X, binaryZ_in_a(X)) 18.48/5.69 binaryZ_in_a(zero(X)) -> U29_a(X, binaryZ_in_a(X)) 18.48/5.69 binaryZ_in_a(one(X)) -> U30_a(X, binary_in_a(X)) 18.48/5.69 binary_in_a(b) -> binary_out_a(b) 18.48/5.69 binary_in_a(zero(X)) -> U27_a(X, binaryZ_in_a(X)) 18.48/5.69 U27_a(X, binaryZ_out_a(X)) -> binary_out_a(zero(X)) 18.48/5.69 binary_in_a(one(X)) -> U28_a(X, binary_in_a(X)) 18.48/5.69 U28_a(X, binary_out_a(X)) -> binary_out_a(one(X)) 18.48/5.69 U30_a(X, binary_out_a(X)) -> binaryZ_out_a(one(X)) 18.48/5.69 U29_a(X, binaryZ_out_a(X)) -> binaryZ_out_a(zero(X)) 18.48/5.69 U1_aaa(X, binaryZ_out_a(X)) -> add_out_aaa(X, b, X) 18.48/5.69 add_in_aaa(b, Y, Y) -> U2_aaa(Y, binaryZ_in_a(Y)) 18.48/5.69 U2_aaa(Y, binaryZ_out_a(Y)) -> add_out_aaa(b, Y, Y) 18.48/5.69 add_in_aaa(X, Y, Z) -> U3_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.48/5.69 addz_in_aaa(zero(X), zero(Y), zero(Z)) -> U10_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.48/5.69 addz_in_aaa(zero(X), one(Y), one(Z)) -> U11_aaa(X, Y, Z, addx_in_aaa(X, Y, Z)) 18.48/5.69 addx_in_aaa(one(X), b, one(X)) -> U4_aaa(X, binary_in_a(X)) 18.48/5.69 U4_aaa(X, binary_out_a(X)) -> addx_out_aaa(one(X), b, one(X)) 18.48/5.69 addx_in_aaa(zero(X), b, zero(X)) -> U5_aaa(X, binaryZ_in_a(X)) 18.48/5.69 U5_aaa(X, binaryZ_out_a(X)) -> addx_out_aaa(zero(X), b, zero(X)) 18.48/5.69 addx_in_aaa(X, Y, Z) -> U6_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.48/5.69 addz_in_aaa(one(X), zero(Y), one(Z)) -> U12_aaa(X, Y, Z, addy_in_aaa(X, Y, Z)) 18.48/5.69 addy_in_aaa(b, one(Y), one(Y)) -> U7_aaa(Y, binary_in_a(Y)) 18.48/5.69 U7_aaa(Y, binary_out_a(Y)) -> addy_out_aaa(b, one(Y), one(Y)) 18.48/5.69 addy_in_aaa(b, zero(Y), zero(Y)) -> U8_aaa(Y, binaryZ_in_a(Y)) 18.48/5.69 U8_aaa(Y, binaryZ_out_a(Y)) -> addy_out_aaa(b, zero(Y), zero(Y)) 18.48/5.69 addy_in_aaa(X, Y, Z) -> U9_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.48/5.69 addz_in_aaa(one(X), one(Y), zero(Z)) -> U13_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.48/5.69 addc_in_aaa(b, b, one(b)) -> addc_out_aaa(b, b, one(b)) 18.48/5.69 addc_in_aaa(X, b, Z) -> U14_aaa(X, Z, succZ_in_aa(X, Z)) 18.48/5.69 succZ_in_aa(zero(X), one(X)) -> U33_aa(X, binaryZ_in_a(X)) 18.48/5.69 U33_aa(X, binaryZ_out_a(X)) -> succZ_out_aa(zero(X), one(X)) 18.48/5.69 succZ_in_aa(one(X), zero(Z)) -> U34_aa(X, Z, succ_in_aa(X, Z)) 18.48/5.69 succ_in_aa(b, one(b)) -> succ_out_aa(b, one(b)) 18.48/5.69 succ_in_aa(zero(X), one(X)) -> U31_aa(X, binaryZ_in_a(X)) 18.48/5.69 U31_aa(X, binaryZ_out_a(X)) -> succ_out_aa(zero(X), one(X)) 18.48/5.69 succ_in_aa(one(X), zero(Z)) -> U32_aa(X, Z, succ_in_aa(X, Z)) 18.48/5.69 U32_aa(X, Z, succ_out_aa(X, Z)) -> succ_out_aa(one(X), zero(Z)) 18.48/5.69 U34_aa(X, Z, succ_out_aa(X, Z)) -> succZ_out_aa(one(X), zero(Z)) 18.48/5.69 U14_aaa(X, Z, succZ_out_aa(X, Z)) -> addc_out_aaa(X, b, Z) 18.48/5.69 addc_in_aaa(b, Y, Z) -> U15_aaa(Y, Z, succZ_in_aa(Y, Z)) 18.48/5.69 U15_aaa(Y, Z, succZ_out_aa(Y, Z)) -> addc_out_aaa(b, Y, Z) 18.48/5.69 addc_in_aaa(X, Y, Z) -> U16_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.48/5.69 addC_in_aaa(zero(X), zero(Y), one(Z)) -> U23_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.48/5.69 U23_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), zero(Y), one(Z)) 18.48/5.69 addC_in_aaa(zero(X), one(Y), zero(Z)) -> U24_aaa(X, Y, Z, addX_in_aaa(X, Y, Z)) 18.48/5.69 addX_in_aaa(zero(X), b, one(X)) -> U17_aaa(X, binaryZ_in_a(X)) 18.48/5.69 U17_aaa(X, binaryZ_out_a(X)) -> addX_out_aaa(zero(X), b, one(X)) 18.48/5.69 addX_in_aaa(one(X), b, zero(Z)) -> U18_aaa(X, Z, succ_in_aa(X, Z)) 18.48/5.69 U18_aaa(X, Z, succ_out_aa(X, Z)) -> addX_out_aaa(one(X), b, zero(Z)) 18.48/5.69 addX_in_aaa(X, Y, Z) -> U19_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.48/5.69 addC_in_aaa(one(X), zero(Y), zero(Z)) -> U25_aaa(X, Y, Z, addY_in_aaa(X, Y, Z)) 18.48/5.69 addY_in_aaa(b, zero(Y), one(Y)) -> U20_aaa(Y, binaryZ_in_a(Y)) 18.48/5.69 U20_aaa(Y, binaryZ_out_a(Y)) -> addY_out_aaa(b, zero(Y), one(Y)) 18.48/5.69 addY_in_aaa(b, one(Y), zero(Z)) -> U21_aaa(Y, Z, succ_in_aa(Y, Z)) 18.48/5.69 U21_aaa(Y, Z, succ_out_aa(Y, Z)) -> addY_out_aaa(b, one(Y), zero(Z)) 18.48/5.69 addY_in_aaa(X, Y, Z) -> U22_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.48/5.69 addC_in_aaa(one(X), one(Y), one(Z)) -> U26_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.48/5.69 U26_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), one(Y), one(Z)) 18.48/5.69 U22_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addY_out_aaa(X, Y, Z) 18.48/5.69 U25_aaa(X, Y, Z, addY_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), zero(Y), zero(Z)) 18.48/5.69 U19_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addX_out_aaa(X, Y, Z) 18.48/5.69 U24_aaa(X, Y, Z, addX_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), one(Y), zero(Z)) 18.48/5.69 U16_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addc_out_aaa(X, Y, Z) 18.48/5.69 U13_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), one(Y), zero(Z)) 18.48/5.69 U9_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addy_out_aaa(X, Y, Z) 18.48/5.69 U12_aaa(X, Y, Z, addy_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), zero(Y), one(Z)) 18.48/5.69 U6_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addx_out_aaa(X, Y, Z) 18.48/5.69 U11_aaa(X, Y, Z, addx_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), one(Y), one(Z)) 18.48/5.69 U10_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), zero(Y), zero(Z)) 18.48/5.69 U3_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> add_out_aaa(X, Y, Z) 18.48/5.69 U37_aaa(R, S, RSS, add_out_aaa(S, zero(RS), RSS)) -> times_out_aaa(one(R), S, RSS) 18.48/5.69 U35_aaa(R, S, RS, times_out_aaa(R, S, RS)) -> times_out_aaa(zero(R), S, zero(RS)) 18.48/5.69 U36_aag(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aag(R, S, RSS, add_in_aag(S, zero(RS), RSS)) 18.48/5.69 add_in_aag(b, b, b) -> add_out_aag(b, b, b) 18.48/5.69 add_in_aag(X, b, X) -> U1_aag(X, binaryZ_in_g(X)) 18.48/5.69 binaryZ_in_g(zero(X)) -> U29_g(X, binaryZ_in_g(X)) 18.48/5.69 binaryZ_in_g(one(X)) -> U30_g(X, binary_in_g(X)) 18.48/5.69 binary_in_g(b) -> binary_out_g(b) 18.48/5.69 binary_in_g(zero(X)) -> U27_g(X, binaryZ_in_g(X)) 18.48/5.69 U27_g(X, binaryZ_out_g(X)) -> binary_out_g(zero(X)) 18.48/5.69 binary_in_g(one(X)) -> U28_g(X, binary_in_g(X)) 18.48/5.69 U28_g(X, binary_out_g(X)) -> binary_out_g(one(X)) 18.48/5.69 U30_g(X, binary_out_g(X)) -> binaryZ_out_g(one(X)) 18.48/5.69 U29_g(X, binaryZ_out_g(X)) -> binaryZ_out_g(zero(X)) 18.48/5.69 U1_aag(X, binaryZ_out_g(X)) -> add_out_aag(X, b, X) 18.48/5.69 add_in_aag(b, Y, Y) -> U2_aag(Y, binaryZ_in_g(Y)) 18.48/5.69 U2_aag(Y, binaryZ_out_g(Y)) -> add_out_aag(b, Y, Y) 18.48/5.69 add_in_aag(X, Y, Z) -> U3_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.48/5.69 addz_in_aag(zero(X), zero(Y), zero(Z)) -> U10_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.48/5.69 addz_in_aag(zero(X), one(Y), one(Z)) -> U11_aag(X, Y, Z, addx_in_aag(X, Y, Z)) 18.48/5.69 addx_in_aag(one(X), b, one(X)) -> U4_aag(X, binary_in_g(X)) 18.48/5.69 U4_aag(X, binary_out_g(X)) -> addx_out_aag(one(X), b, one(X)) 18.48/5.69 addx_in_aag(zero(X), b, zero(X)) -> U5_aag(X, binaryZ_in_g(X)) 18.48/5.69 U5_aag(X, binaryZ_out_g(X)) -> addx_out_aag(zero(X), b, zero(X)) 18.48/5.69 addx_in_aag(X, Y, Z) -> U6_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.48/5.69 addz_in_aag(one(X), zero(Y), one(Z)) -> U12_aag(X, Y, Z, addy_in_aag(X, Y, Z)) 18.48/5.69 addy_in_aag(b, one(Y), one(Y)) -> U7_aag(Y, binary_in_g(Y)) 18.48/5.69 U7_aag(Y, binary_out_g(Y)) -> addy_out_aag(b, one(Y), one(Y)) 18.48/5.69 addy_in_aag(b, zero(Y), zero(Y)) -> U8_aag(Y, binaryZ_in_g(Y)) 18.48/5.69 U8_aag(Y, binaryZ_out_g(Y)) -> addy_out_aag(b, zero(Y), zero(Y)) 18.48/5.69 addy_in_aag(X, Y, Z) -> U9_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.48/5.69 addz_in_aag(one(X), one(Y), zero(Z)) -> U13_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.48/5.69 addc_in_aag(b, b, one(b)) -> addc_out_aag(b, b, one(b)) 18.48/5.69 addc_in_aag(X, b, Z) -> U14_aag(X, Z, succZ_in_ag(X, Z)) 18.48/5.69 succZ_in_ag(zero(X), one(X)) -> U33_ag(X, binaryZ_in_g(X)) 18.48/5.69 U33_ag(X, binaryZ_out_g(X)) -> succZ_out_ag(zero(X), one(X)) 18.48/5.69 succZ_in_ag(one(X), zero(Z)) -> U34_ag(X, Z, succ_in_ag(X, Z)) 18.48/5.69 succ_in_ag(b, one(b)) -> succ_out_ag(b, one(b)) 18.48/5.69 succ_in_ag(zero(X), one(X)) -> U31_ag(X, binaryZ_in_g(X)) 18.48/5.69 U31_ag(X, binaryZ_out_g(X)) -> succ_out_ag(zero(X), one(X)) 18.48/5.69 succ_in_ag(one(X), zero(Z)) -> U32_ag(X, Z, succ_in_ag(X, Z)) 18.48/5.69 U32_ag(X, Z, succ_out_ag(X, Z)) -> succ_out_ag(one(X), zero(Z)) 18.48/5.69 U34_ag(X, Z, succ_out_ag(X, Z)) -> succZ_out_ag(one(X), zero(Z)) 18.48/5.69 U14_aag(X, Z, succZ_out_ag(X, Z)) -> addc_out_aag(X, b, Z) 18.48/5.69 addc_in_aag(b, Y, Z) -> U15_aag(Y, Z, succZ_in_ag(Y, Z)) 18.48/5.69 U15_aag(Y, Z, succZ_out_ag(Y, Z)) -> addc_out_aag(b, Y, Z) 18.48/5.69 addc_in_aag(X, Y, Z) -> U16_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.48/5.69 addC_in_aag(zero(X), zero(Y), one(Z)) -> U23_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.48/5.69 U23_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), zero(Y), one(Z)) 18.48/5.69 addC_in_aag(zero(X), one(Y), zero(Z)) -> U24_aag(X, Y, Z, addX_in_aag(X, Y, Z)) 18.48/5.69 addX_in_aag(zero(X), b, one(X)) -> U17_aag(X, binaryZ_in_g(X)) 18.48/5.69 U17_aag(X, binaryZ_out_g(X)) -> addX_out_aag(zero(X), b, one(X)) 18.48/5.69 addX_in_aag(one(X), b, zero(Z)) -> U18_aag(X, Z, succ_in_ag(X, Z)) 18.48/5.69 U18_aag(X, Z, succ_out_ag(X, Z)) -> addX_out_aag(one(X), b, zero(Z)) 18.48/5.69 addX_in_aag(X, Y, Z) -> U19_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.48/5.69 addC_in_aag(one(X), zero(Y), zero(Z)) -> U25_aag(X, Y, Z, addY_in_aag(X, Y, Z)) 18.48/5.69 addY_in_aag(b, zero(Y), one(Y)) -> U20_aag(Y, binaryZ_in_g(Y)) 18.48/5.69 U20_aag(Y, binaryZ_out_g(Y)) -> addY_out_aag(b, zero(Y), one(Y)) 18.48/5.69 addY_in_aag(b, one(Y), zero(Z)) -> U21_aag(Y, Z, succ_in_ag(Y, Z)) 18.48/5.69 U21_aag(Y, Z, succ_out_ag(Y, Z)) -> addY_out_aag(b, one(Y), zero(Z)) 18.48/5.69 addY_in_aag(X, Y, Z) -> U22_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.48/5.69 addC_in_aag(one(X), one(Y), one(Z)) -> U26_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.48/5.69 U26_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addC_out_aag(one(X), one(Y), one(Z)) 18.48/5.69 U22_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addY_out_aag(X, Y, Z) 18.48/5.69 U25_aag(X, Y, Z, addY_out_aag(X, Y, Z)) -> addC_out_aag(one(X), zero(Y), zero(Z)) 18.48/5.69 U19_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addX_out_aag(X, Y, Z) 18.48/5.69 U24_aag(X, Y, Z, addX_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), one(Y), zero(Z)) 18.48/5.69 U16_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addc_out_aag(X, Y, Z) 18.48/5.69 U13_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addz_out_aag(one(X), one(Y), zero(Z)) 18.48/5.69 U9_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addy_out_aag(X, Y, Z) 18.48/5.69 U12_aag(X, Y, Z, addy_out_aag(X, Y, Z)) -> addz_out_aag(one(X), zero(Y), one(Z)) 18.48/5.69 U6_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addx_out_aag(X, Y, Z) 18.48/5.69 U11_aag(X, Y, Z, addx_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), one(Y), one(Z)) 18.48/5.69 U10_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), zero(Y), zero(Z)) 18.48/5.69 U3_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> add_out_aag(X, Y, Z) 18.48/5.69 U37_aag(R, S, RSS, add_out_aag(S, zero(RS), RSS)) -> times_out_aag(one(R), S, RSS) 18.48/5.69 U35_aag(R, S, RS, times_out_aag(R, S, RS)) -> times_out_aag(zero(R), S, zero(RS)) 18.48/5.69 18.48/5.69 The argument filtering Pi contains the following mapping: 18.48/5.69 times_in_aag(x1, x2, x3) = times_in_aag(x3) 18.48/5.69 18.48/5.69 times_out_aag(x1, x2, x3) = times_out_aag(x1, x2) 18.48/5.69 18.48/5.69 zero(x1) = zero(x1) 18.48/5.69 18.48/5.69 U35_aag(x1, x2, x3, x4) = U35_aag(x4) 18.48/5.69 18.48/5.69 U36_aag(x1, x2, x3, x4) = U36_aag(x3, x4) 18.48/5.69 18.48/5.69 times_in_aaa(x1, x2, x3) = times_in_aaa 18.48/5.69 18.48/5.69 times_out_aaa(x1, x2, x3) = times_out_aaa(x1) 18.48/5.69 18.48/5.69 U35_aaa(x1, x2, x3, x4) = U35_aaa(x4) 18.48/5.69 18.48/5.69 U36_aaa(x1, x2, x3, x4) = U36_aaa(x4) 18.48/5.69 18.48/5.69 U37_aaa(x1, x2, x3, x4) = U37_aaa(x1, x4) 18.48/5.69 18.48/5.69 add_in_aaa(x1, x2, x3) = add_in_aaa 18.48/5.69 18.48/5.69 add_out_aaa(x1, x2, x3) = add_out_aaa(x1, x2, x3) 18.48/5.69 18.48/5.69 U1_aaa(x1, x2) = U1_aaa(x2) 18.48/5.69 18.48/5.69 binaryZ_in_a(x1) = binaryZ_in_a 18.48/5.69 18.48/5.69 U29_a(x1, x2) = U29_a(x2) 18.48/5.69 18.48/5.69 U30_a(x1, x2) = U30_a(x2) 18.48/5.69 18.48/5.69 binary_in_a(x1) = binary_in_a 18.48/5.69 18.48/5.69 binary_out_a(x1) = binary_out_a(x1) 18.48/5.69 18.48/5.69 U27_a(x1, x2) = U27_a(x2) 18.48/5.69 18.48/5.69 binaryZ_out_a(x1) = binaryZ_out_a(x1) 18.48/5.69 18.48/5.69 U28_a(x1, x2) = U28_a(x2) 18.48/5.69 18.48/5.69 U2_aaa(x1, x2) = U2_aaa(x2) 18.48/5.69 18.48/5.69 U3_aaa(x1, x2, x3, x4) = U3_aaa(x4) 18.48/5.69 18.48/5.69 addz_in_aaa(x1, x2, x3) = addz_in_aaa 18.48/5.69 18.48/5.69 U10_aaa(x1, x2, x3, x4) = U10_aaa(x4) 18.48/5.69 18.48/5.69 U11_aaa(x1, x2, x3, x4) = U11_aaa(x4) 18.48/5.69 18.48/5.69 addx_in_aaa(x1, x2, x3) = addx_in_aaa 18.48/5.69 18.48/5.69 U4_aaa(x1, x2) = U4_aaa(x2) 18.48/5.69 18.48/5.69 addx_out_aaa(x1, x2, x3) = addx_out_aaa(x1, x2, x3) 18.48/5.69 18.48/5.69 U5_aaa(x1, x2) = U5_aaa(x2) 18.48/5.69 18.48/5.69 U6_aaa(x1, x2, x3, x4) = U6_aaa(x4) 18.48/5.69 18.48/5.69 U12_aaa(x1, x2, x3, x4) = U12_aaa(x4) 18.48/5.69 18.48/5.69 addy_in_aaa(x1, x2, x3) = addy_in_aaa 18.48/5.69 18.48/5.69 U7_aaa(x1, x2) = U7_aaa(x2) 18.48/5.69 18.48/5.69 addy_out_aaa(x1, x2, x3) = addy_out_aaa(x1, x2, x3) 18.48/5.69 18.48/5.69 U8_aaa(x1, x2) = U8_aaa(x2) 18.48/5.69 18.48/5.69 U9_aaa(x1, x2, x3, x4) = U9_aaa(x4) 18.48/5.69 18.48/5.69 U13_aaa(x1, x2, x3, x4) = U13_aaa(x4) 18.48/5.69 18.48/5.69 addc_in_aaa(x1, x2, x3) = addc_in_aaa 18.48/5.69 18.48/5.69 addc_out_aaa(x1, x2, x3) = addc_out_aaa(x1, x2, x3) 18.48/5.69 18.48/5.69 U14_aaa(x1, x2, x3) = U14_aaa(x3) 18.48/5.69 18.48/5.69 succZ_in_aa(x1, x2) = succZ_in_aa 18.48/5.69 18.48/5.69 U33_aa(x1, x2) = U33_aa(x2) 18.48/5.69 18.48/5.69 succZ_out_aa(x1, x2) = succZ_out_aa(x1, x2) 18.48/5.69 18.48/5.69 U34_aa(x1, x2, x3) = U34_aa(x3) 18.48/5.69 18.48/5.69 succ_in_aa(x1, x2) = succ_in_aa 18.48/5.69 18.48/5.69 succ_out_aa(x1, x2) = succ_out_aa(x1, x2) 18.48/5.69 18.48/5.69 U31_aa(x1, x2) = U31_aa(x2) 18.48/5.69 18.48/5.69 U32_aa(x1, x2, x3) = U32_aa(x3) 18.48/5.69 18.48/5.69 U15_aaa(x1, x2, x3) = U15_aaa(x3) 18.48/5.69 18.48/5.69 U16_aaa(x1, x2, x3, x4) = U16_aaa(x4) 18.48/5.69 18.48/5.69 addC_in_aaa(x1, x2, x3) = addC_in_aaa 18.48/5.69 18.48/5.69 U23_aaa(x1, x2, x3, x4) = U23_aaa(x4) 18.48/5.69 18.48/5.69 addz_out_aaa(x1, x2, x3) = addz_out_aaa(x1, x2, x3) 18.48/5.69 18.48/5.69 addC_out_aaa(x1, x2, x3) = addC_out_aaa(x1, x2, x3) 18.48/5.69 18.48/5.69 U24_aaa(x1, x2, x3, x4) = U24_aaa(x4) 18.48/5.69 18.48/5.69 addX_in_aaa(x1, x2, x3) = addX_in_aaa 18.48/5.69 18.48/5.69 U17_aaa(x1, x2) = U17_aaa(x2) 18.48/5.69 18.48/5.69 addX_out_aaa(x1, x2, x3) = addX_out_aaa(x1, x2, x3) 18.48/5.69 18.48/5.69 U18_aaa(x1, x2, x3) = U18_aaa(x3) 18.48/5.69 18.48/5.69 U19_aaa(x1, x2, x3, x4) = U19_aaa(x4) 18.48/5.69 18.48/5.69 U25_aaa(x1, x2, x3, x4) = U25_aaa(x4) 18.48/5.69 18.48/5.69 addY_in_aaa(x1, x2, x3) = addY_in_aaa 18.48/5.69 18.48/5.69 U20_aaa(x1, x2) = U20_aaa(x2) 18.48/5.69 18.48/5.69 addY_out_aaa(x1, x2, x3) = addY_out_aaa(x1, x2, x3) 18.48/5.69 18.48/5.69 U21_aaa(x1, x2, x3) = U21_aaa(x3) 18.48/5.69 18.48/5.69 U22_aaa(x1, x2, x3, x4) = U22_aaa(x4) 18.48/5.69 18.48/5.69 U26_aaa(x1, x2, x3, x4) = U26_aaa(x4) 18.48/5.69 18.48/5.69 U37_aag(x1, x2, x3, x4) = U37_aag(x1, x4) 18.48/5.69 18.48/5.69 add_in_aag(x1, x2, x3) = add_in_aag(x3) 18.48/5.69 18.48/5.69 b = b 18.48/5.69 18.48/5.69 add_out_aag(x1, x2, x3) = add_out_aag(x1, x2) 18.48/5.69 18.48/5.69 U1_aag(x1, x2) = U1_aag(x1, x2) 18.48/5.69 18.48/5.69 binaryZ_in_g(x1) = binaryZ_in_g(x1) 18.48/5.69 18.48/5.69 U29_g(x1, x2) = U29_g(x2) 18.48/5.69 18.48/5.69 one(x1) = one(x1) 18.48/5.69 18.48/5.69 U30_g(x1, x2) = U30_g(x2) 18.48/5.69 18.48/5.69 binary_in_g(x1) = binary_in_g(x1) 18.48/5.69 18.48/5.69 binary_out_g(x1) = binary_out_g 18.48/5.69 18.48/5.69 U27_g(x1, x2) = U27_g(x2) 18.48/5.69 18.48/5.69 binaryZ_out_g(x1) = binaryZ_out_g 18.48/5.69 18.48/5.69 U28_g(x1, x2) = U28_g(x2) 18.48/5.69 18.48/5.69 U2_aag(x1, x2) = U2_aag(x1, x2) 18.48/5.69 18.48/5.69 U3_aag(x1, x2, x3, x4) = U3_aag(x4) 18.48/5.69 18.48/5.69 addz_in_aag(x1, x2, x3) = addz_in_aag(x3) 18.48/5.69 18.48/5.69 U10_aag(x1, x2, x3, x4) = U10_aag(x4) 18.48/5.69 18.48/5.69 U11_aag(x1, x2, x3, x4) = U11_aag(x4) 18.48/5.69 18.48/5.69 addx_in_aag(x1, x2, x3) = addx_in_aag(x3) 18.48/5.69 18.48/5.69 U4_aag(x1, x2) = U4_aag(x1, x2) 18.48/5.69 18.48/5.69 addx_out_aag(x1, x2, x3) = addx_out_aag(x1, x2) 18.48/5.69 18.48/5.69 U5_aag(x1, x2) = U5_aag(x1, x2) 18.48/5.69 18.48/5.69 U6_aag(x1, x2, x3, x4) = U6_aag(x4) 18.48/5.69 18.48/5.69 U12_aag(x1, x2, x3, x4) = U12_aag(x4) 18.48/5.69 18.48/5.69 addy_in_aag(x1, x2, x3) = addy_in_aag(x3) 18.48/5.69 18.48/5.69 U7_aag(x1, x2) = U7_aag(x1, x2) 18.48/5.69 18.48/5.69 addy_out_aag(x1, x2, x3) = addy_out_aag(x1, x2) 18.48/5.69 18.48/5.69 U8_aag(x1, x2) = U8_aag(x1, x2) 18.48/5.69 18.48/5.69 U9_aag(x1, x2, x3, x4) = U9_aag(x4) 18.48/5.69 18.48/5.69 U13_aag(x1, x2, x3, x4) = U13_aag(x4) 18.48/5.69 18.48/5.69 addc_in_aag(x1, x2, x3) = addc_in_aag(x3) 18.48/5.69 18.48/5.69 addc_out_aag(x1, x2, x3) = addc_out_aag(x1, x2) 18.48/5.69 18.48/5.69 U14_aag(x1, x2, x3) = U14_aag(x3) 18.48/5.69 18.48/5.69 succZ_in_ag(x1, x2) = succZ_in_ag(x2) 18.48/5.69 18.48/5.69 U33_ag(x1, x2) = U33_ag(x1, x2) 18.48/5.69 18.48/5.69 succZ_out_ag(x1, x2) = succZ_out_ag(x1) 18.48/5.69 18.48/5.69 U34_ag(x1, x2, x3) = U34_ag(x3) 18.48/5.69 18.48/5.69 succ_in_ag(x1, x2) = succ_in_ag(x2) 18.48/5.69 18.48/5.69 succ_out_ag(x1, x2) = succ_out_ag(x1) 18.48/5.69 18.48/5.69 U31_ag(x1, x2) = U31_ag(x1, x2) 18.48/5.69 18.48/5.69 U32_ag(x1, x2, x3) = U32_ag(x3) 18.48/5.69 18.48/5.69 U15_aag(x1, x2, x3) = U15_aag(x3) 18.48/5.69 18.48/5.69 U16_aag(x1, x2, x3, x4) = U16_aag(x4) 18.48/5.69 18.48/5.69 addC_in_aag(x1, x2, x3) = addC_in_aag(x3) 18.48/5.69 18.48/5.69 U23_aag(x1, x2, x3, x4) = U23_aag(x4) 18.48/5.69 18.48/5.69 addz_out_aag(x1, x2, x3) = addz_out_aag(x1, x2) 18.48/5.69 18.48/5.69 addC_out_aag(x1, x2, x3) = addC_out_aag(x1, x2) 18.48/5.69 18.48/5.69 U24_aag(x1, x2, x3, x4) = U24_aag(x4) 18.48/5.69 18.48/5.69 addX_in_aag(x1, x2, x3) = addX_in_aag(x3) 18.48/5.69 18.48/5.69 U17_aag(x1, x2) = U17_aag(x1, x2) 18.48/5.69 18.48/5.69 addX_out_aag(x1, x2, x3) = addX_out_aag(x1, x2) 18.48/5.69 18.48/5.69 U18_aag(x1, x2, x3) = U18_aag(x3) 18.48/5.69 18.48/5.69 U19_aag(x1, x2, x3, x4) = U19_aag(x4) 18.48/5.69 18.48/5.69 U25_aag(x1, x2, x3, x4) = U25_aag(x4) 18.48/5.69 18.48/5.69 addY_in_aag(x1, x2, x3) = addY_in_aag(x3) 18.48/5.69 18.48/5.69 U20_aag(x1, x2) = U20_aag(x1, x2) 18.48/5.69 18.48/5.69 addY_out_aag(x1, x2, x3) = addY_out_aag(x1, x2) 18.48/5.69 18.48/5.69 U21_aag(x1, x2, x3) = U21_aag(x3) 18.48/5.69 18.48/5.69 U22_aag(x1, x2, x3, x4) = U22_aag(x4) 18.48/5.69 18.48/5.69 U26_aag(x1, x2, x3, x4) = U26_aag(x4) 18.48/5.69 18.48/5.69 ADDZ_IN_AAA(x1, x2, x3) = ADDZ_IN_AAA 18.48/5.69 18.48/5.69 ADDX_IN_AAA(x1, x2, x3) = ADDX_IN_AAA 18.48/5.69 18.48/5.69 ADDY_IN_AAA(x1, x2, x3) = ADDY_IN_AAA 18.48/5.69 18.48/5.69 ADDC_IN_AAA(x1, x2, x3) = ADDC_IN_AAA 18.48/5.69 18.48/5.69 ADDC_IN_AAA^1(x1, x2, x3) = ADDC_IN_AAA^1 18.48/5.69 18.48/5.69 ADDX_IN_AAA^1(x1, x2, x3) = ADDX_IN_AAA^1 18.48/5.69 18.48/5.69 ADDY_IN_AAA^1(x1, x2, x3) = ADDY_IN_AAA^1 18.48/5.69 18.48/5.69 18.48/5.69 We have to consider all (P,R,Pi)-chains 18.48/5.69 ---------------------------------------- 18.48/5.69 18.48/5.69 (89) UsableRulesProof (EQUIVALENT) 18.48/5.69 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 18.48/5.69 ---------------------------------------- 18.48/5.69 18.48/5.69 (90) 18.48/5.69 Obligation: 18.48/5.69 Pi DP problem: 18.48/5.69 The TRS P consists of the following rules: 18.48/5.69 18.48/5.69 ADDX_IN_AAA(X, Y, Z) -> ADDZ_IN_AAA(X, Y, Z) 18.48/5.69 ADDZ_IN_AAA(zero(X), zero(Y), zero(Z)) -> ADDZ_IN_AAA(X, Y, Z) 18.48/5.69 ADDZ_IN_AAA(zero(X), one(Y), one(Z)) -> ADDX_IN_AAA(X, Y, Z) 18.48/5.69 ADDZ_IN_AAA(one(X), zero(Y), one(Z)) -> ADDY_IN_AAA(X, Y, Z) 18.48/5.69 ADDY_IN_AAA(X, Y, Z) -> ADDZ_IN_AAA(X, Y, Z) 18.48/5.69 ADDZ_IN_AAA(one(X), one(Y), zero(Z)) -> ADDC_IN_AAA(X, Y, Z) 18.48/5.69 ADDC_IN_AAA(X, Y, Z) -> ADDC_IN_AAA^1(X, Y, Z) 18.48/5.69 ADDC_IN_AAA^1(zero(X), zero(Y), one(Z)) -> ADDZ_IN_AAA(X, Y, Z) 18.48/5.69 ADDC_IN_AAA^1(zero(X), one(Y), zero(Z)) -> ADDX_IN_AAA^1(X, Y, Z) 18.48/5.69 ADDX_IN_AAA^1(X, Y, Z) -> ADDC_IN_AAA^1(X, Y, Z) 18.48/5.69 ADDC_IN_AAA^1(one(X), zero(Y), zero(Z)) -> ADDY_IN_AAA^1(X, Y, Z) 18.48/5.69 ADDY_IN_AAA^1(X, Y, Z) -> ADDC_IN_AAA^1(X, Y, Z) 18.48/5.69 ADDC_IN_AAA^1(one(X), one(Y), one(Z)) -> ADDC_IN_AAA(X, Y, Z) 18.48/5.69 18.48/5.69 R is empty. 18.48/5.69 The argument filtering Pi contains the following mapping: 18.48/5.69 zero(x1) = zero(x1) 18.48/5.69 18.48/5.69 one(x1) = one(x1) 18.48/5.69 18.48/5.69 ADDZ_IN_AAA(x1, x2, x3) = ADDZ_IN_AAA 18.48/5.69 18.48/5.69 ADDX_IN_AAA(x1, x2, x3) = ADDX_IN_AAA 18.48/5.69 18.48/5.69 ADDY_IN_AAA(x1, x2, x3) = ADDY_IN_AAA 18.48/5.69 18.48/5.69 ADDC_IN_AAA(x1, x2, x3) = ADDC_IN_AAA 18.48/5.69 18.48/5.69 ADDC_IN_AAA^1(x1, x2, x3) = ADDC_IN_AAA^1 18.48/5.69 18.48/5.69 ADDX_IN_AAA^1(x1, x2, x3) = ADDX_IN_AAA^1 18.48/5.69 18.48/5.69 ADDY_IN_AAA^1(x1, x2, x3) = ADDY_IN_AAA^1 18.48/5.69 18.48/5.69 18.48/5.69 We have to consider all (P,R,Pi)-chains 18.48/5.69 ---------------------------------------- 18.48/5.69 18.48/5.69 (91) 18.48/5.69 Obligation: 18.48/5.69 Pi DP problem: 18.48/5.69 The TRS P consists of the following rules: 18.48/5.69 18.48/5.69 TIMES_IN_AAA(one(R), S, RSS) -> TIMES_IN_AAA(R, S, RS) 18.48/5.69 TIMES_IN_AAA(zero(R), S, zero(RS)) -> TIMES_IN_AAA(R, S, RS) 18.48/5.69 18.48/5.69 The TRS R consists of the following rules: 18.48/5.69 18.48/5.69 times_in_aag(one(b), X, X) -> times_out_aag(one(b), X, X) 18.48/5.69 times_in_aag(zero(R), S, zero(RS)) -> U35_aag(R, S, RS, times_in_aag(R, S, RS)) 18.48/5.69 times_in_aag(one(R), S, RSS) -> U36_aag(R, S, RSS, times_in_aaa(R, S, RS)) 18.48/5.69 times_in_aaa(one(b), X, X) -> times_out_aaa(one(b), X, X) 18.48/5.69 times_in_aaa(zero(R), S, zero(RS)) -> U35_aaa(R, S, RS, times_in_aaa(R, S, RS)) 18.48/5.69 times_in_aaa(one(R), S, RSS) -> U36_aaa(R, S, RSS, times_in_aaa(R, S, RS)) 18.48/5.69 U36_aaa(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aaa(R, S, RSS, add_in_aaa(S, zero(RS), RSS)) 18.48/5.69 add_in_aaa(b, b, b) -> add_out_aaa(b, b, b) 18.48/5.69 add_in_aaa(X, b, X) -> U1_aaa(X, binaryZ_in_a(X)) 18.48/5.69 binaryZ_in_a(zero(X)) -> U29_a(X, binaryZ_in_a(X)) 18.48/5.69 binaryZ_in_a(one(X)) -> U30_a(X, binary_in_a(X)) 18.48/5.69 binary_in_a(b) -> binary_out_a(b) 18.48/5.69 binary_in_a(zero(X)) -> U27_a(X, binaryZ_in_a(X)) 18.48/5.69 U27_a(X, binaryZ_out_a(X)) -> binary_out_a(zero(X)) 18.48/5.69 binary_in_a(one(X)) -> U28_a(X, binary_in_a(X)) 18.48/5.69 U28_a(X, binary_out_a(X)) -> binary_out_a(one(X)) 18.48/5.69 U30_a(X, binary_out_a(X)) -> binaryZ_out_a(one(X)) 18.48/5.69 U29_a(X, binaryZ_out_a(X)) -> binaryZ_out_a(zero(X)) 18.48/5.69 U1_aaa(X, binaryZ_out_a(X)) -> add_out_aaa(X, b, X) 18.48/5.69 add_in_aaa(b, Y, Y) -> U2_aaa(Y, binaryZ_in_a(Y)) 18.48/5.69 U2_aaa(Y, binaryZ_out_a(Y)) -> add_out_aaa(b, Y, Y) 18.48/5.69 add_in_aaa(X, Y, Z) -> U3_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.48/5.69 addz_in_aaa(zero(X), zero(Y), zero(Z)) -> U10_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.48/5.69 addz_in_aaa(zero(X), one(Y), one(Z)) -> U11_aaa(X, Y, Z, addx_in_aaa(X, Y, Z)) 18.48/5.69 addx_in_aaa(one(X), b, one(X)) -> U4_aaa(X, binary_in_a(X)) 18.48/5.69 U4_aaa(X, binary_out_a(X)) -> addx_out_aaa(one(X), b, one(X)) 18.48/5.69 addx_in_aaa(zero(X), b, zero(X)) -> U5_aaa(X, binaryZ_in_a(X)) 18.48/5.69 U5_aaa(X, binaryZ_out_a(X)) -> addx_out_aaa(zero(X), b, zero(X)) 18.48/5.69 addx_in_aaa(X, Y, Z) -> U6_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.48/5.69 addz_in_aaa(one(X), zero(Y), one(Z)) -> U12_aaa(X, Y, Z, addy_in_aaa(X, Y, Z)) 18.48/5.69 addy_in_aaa(b, one(Y), one(Y)) -> U7_aaa(Y, binary_in_a(Y)) 18.48/5.69 U7_aaa(Y, binary_out_a(Y)) -> addy_out_aaa(b, one(Y), one(Y)) 18.48/5.69 addy_in_aaa(b, zero(Y), zero(Y)) -> U8_aaa(Y, binaryZ_in_a(Y)) 18.48/5.69 U8_aaa(Y, binaryZ_out_a(Y)) -> addy_out_aaa(b, zero(Y), zero(Y)) 18.48/5.69 addy_in_aaa(X, Y, Z) -> U9_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.48/5.69 addz_in_aaa(one(X), one(Y), zero(Z)) -> U13_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.48/5.69 addc_in_aaa(b, b, one(b)) -> addc_out_aaa(b, b, one(b)) 18.48/5.69 addc_in_aaa(X, b, Z) -> U14_aaa(X, Z, succZ_in_aa(X, Z)) 18.48/5.69 succZ_in_aa(zero(X), one(X)) -> U33_aa(X, binaryZ_in_a(X)) 18.48/5.69 U33_aa(X, binaryZ_out_a(X)) -> succZ_out_aa(zero(X), one(X)) 18.48/5.69 succZ_in_aa(one(X), zero(Z)) -> U34_aa(X, Z, succ_in_aa(X, Z)) 18.48/5.69 succ_in_aa(b, one(b)) -> succ_out_aa(b, one(b)) 18.48/5.69 succ_in_aa(zero(X), one(X)) -> U31_aa(X, binaryZ_in_a(X)) 18.48/5.69 U31_aa(X, binaryZ_out_a(X)) -> succ_out_aa(zero(X), one(X)) 18.48/5.69 succ_in_aa(one(X), zero(Z)) -> U32_aa(X, Z, succ_in_aa(X, Z)) 18.48/5.69 U32_aa(X, Z, succ_out_aa(X, Z)) -> succ_out_aa(one(X), zero(Z)) 18.48/5.69 U34_aa(X, Z, succ_out_aa(X, Z)) -> succZ_out_aa(one(X), zero(Z)) 18.48/5.69 U14_aaa(X, Z, succZ_out_aa(X, Z)) -> addc_out_aaa(X, b, Z) 18.48/5.69 addc_in_aaa(b, Y, Z) -> U15_aaa(Y, Z, succZ_in_aa(Y, Z)) 18.48/5.69 U15_aaa(Y, Z, succZ_out_aa(Y, Z)) -> addc_out_aaa(b, Y, Z) 18.48/5.69 addc_in_aaa(X, Y, Z) -> U16_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.48/5.69 addC_in_aaa(zero(X), zero(Y), one(Z)) -> U23_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.48/5.69 U23_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), zero(Y), one(Z)) 18.48/5.69 addC_in_aaa(zero(X), one(Y), zero(Z)) -> U24_aaa(X, Y, Z, addX_in_aaa(X, Y, Z)) 18.48/5.69 addX_in_aaa(zero(X), b, one(X)) -> U17_aaa(X, binaryZ_in_a(X)) 18.48/5.69 U17_aaa(X, binaryZ_out_a(X)) -> addX_out_aaa(zero(X), b, one(X)) 18.48/5.69 addX_in_aaa(one(X), b, zero(Z)) -> U18_aaa(X, Z, succ_in_aa(X, Z)) 18.48/5.69 U18_aaa(X, Z, succ_out_aa(X, Z)) -> addX_out_aaa(one(X), b, zero(Z)) 18.48/5.69 addX_in_aaa(X, Y, Z) -> U19_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.48/5.69 addC_in_aaa(one(X), zero(Y), zero(Z)) -> U25_aaa(X, Y, Z, addY_in_aaa(X, Y, Z)) 18.48/5.69 addY_in_aaa(b, zero(Y), one(Y)) -> U20_aaa(Y, binaryZ_in_a(Y)) 18.48/5.69 U20_aaa(Y, binaryZ_out_a(Y)) -> addY_out_aaa(b, zero(Y), one(Y)) 18.48/5.69 addY_in_aaa(b, one(Y), zero(Z)) -> U21_aaa(Y, Z, succ_in_aa(Y, Z)) 18.48/5.69 U21_aaa(Y, Z, succ_out_aa(Y, Z)) -> addY_out_aaa(b, one(Y), zero(Z)) 18.48/5.69 addY_in_aaa(X, Y, Z) -> U22_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.48/5.69 addC_in_aaa(one(X), one(Y), one(Z)) -> U26_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.48/5.69 U26_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), one(Y), one(Z)) 18.48/5.69 U22_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addY_out_aaa(X, Y, Z) 18.48/5.69 U25_aaa(X, Y, Z, addY_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), zero(Y), zero(Z)) 18.48/5.69 U19_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addX_out_aaa(X, Y, Z) 18.48/5.69 U24_aaa(X, Y, Z, addX_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), one(Y), zero(Z)) 18.48/5.69 U16_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addc_out_aaa(X, Y, Z) 18.48/5.69 U13_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), one(Y), zero(Z)) 18.48/5.69 U9_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addy_out_aaa(X, Y, Z) 18.48/5.69 U12_aaa(X, Y, Z, addy_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), zero(Y), one(Z)) 18.48/5.69 U6_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addx_out_aaa(X, Y, Z) 18.48/5.69 U11_aaa(X, Y, Z, addx_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), one(Y), one(Z)) 18.48/5.69 U10_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), zero(Y), zero(Z)) 18.48/5.69 U3_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> add_out_aaa(X, Y, Z) 18.48/5.69 U37_aaa(R, S, RSS, add_out_aaa(S, zero(RS), RSS)) -> times_out_aaa(one(R), S, RSS) 18.48/5.69 U35_aaa(R, S, RS, times_out_aaa(R, S, RS)) -> times_out_aaa(zero(R), S, zero(RS)) 18.48/5.69 U36_aag(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aag(R, S, RSS, add_in_aag(S, zero(RS), RSS)) 18.48/5.69 add_in_aag(b, b, b) -> add_out_aag(b, b, b) 18.48/5.69 add_in_aag(X, b, X) -> U1_aag(X, binaryZ_in_g(X)) 18.48/5.69 binaryZ_in_g(zero(X)) -> U29_g(X, binaryZ_in_g(X)) 18.48/5.69 binaryZ_in_g(one(X)) -> U30_g(X, binary_in_g(X)) 18.48/5.69 binary_in_g(b) -> binary_out_g(b) 18.48/5.69 binary_in_g(zero(X)) -> U27_g(X, binaryZ_in_g(X)) 18.48/5.69 U27_g(X, binaryZ_out_g(X)) -> binary_out_g(zero(X)) 18.48/5.69 binary_in_g(one(X)) -> U28_g(X, binary_in_g(X)) 18.48/5.69 U28_g(X, binary_out_g(X)) -> binary_out_g(one(X)) 18.48/5.69 U30_g(X, binary_out_g(X)) -> binaryZ_out_g(one(X)) 18.48/5.69 U29_g(X, binaryZ_out_g(X)) -> binaryZ_out_g(zero(X)) 18.48/5.69 U1_aag(X, binaryZ_out_g(X)) -> add_out_aag(X, b, X) 18.48/5.69 add_in_aag(b, Y, Y) -> U2_aag(Y, binaryZ_in_g(Y)) 18.48/5.69 U2_aag(Y, binaryZ_out_g(Y)) -> add_out_aag(b, Y, Y) 18.48/5.69 add_in_aag(X, Y, Z) -> U3_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.48/5.69 addz_in_aag(zero(X), zero(Y), zero(Z)) -> U10_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.48/5.69 addz_in_aag(zero(X), one(Y), one(Z)) -> U11_aag(X, Y, Z, addx_in_aag(X, Y, Z)) 18.48/5.69 addx_in_aag(one(X), b, one(X)) -> U4_aag(X, binary_in_g(X)) 18.48/5.69 U4_aag(X, binary_out_g(X)) -> addx_out_aag(one(X), b, one(X)) 18.48/5.69 addx_in_aag(zero(X), b, zero(X)) -> U5_aag(X, binaryZ_in_g(X)) 18.48/5.69 U5_aag(X, binaryZ_out_g(X)) -> addx_out_aag(zero(X), b, zero(X)) 18.48/5.69 addx_in_aag(X, Y, Z) -> U6_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.48/5.69 addz_in_aag(one(X), zero(Y), one(Z)) -> U12_aag(X, Y, Z, addy_in_aag(X, Y, Z)) 18.48/5.69 addy_in_aag(b, one(Y), one(Y)) -> U7_aag(Y, binary_in_g(Y)) 18.48/5.69 U7_aag(Y, binary_out_g(Y)) -> addy_out_aag(b, one(Y), one(Y)) 18.48/5.69 addy_in_aag(b, zero(Y), zero(Y)) -> U8_aag(Y, binaryZ_in_g(Y)) 18.48/5.69 U8_aag(Y, binaryZ_out_g(Y)) -> addy_out_aag(b, zero(Y), zero(Y)) 18.48/5.69 addy_in_aag(X, Y, Z) -> U9_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.48/5.69 addz_in_aag(one(X), one(Y), zero(Z)) -> U13_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.48/5.69 addc_in_aag(b, b, one(b)) -> addc_out_aag(b, b, one(b)) 18.48/5.69 addc_in_aag(X, b, Z) -> U14_aag(X, Z, succZ_in_ag(X, Z)) 18.48/5.69 succZ_in_ag(zero(X), one(X)) -> U33_ag(X, binaryZ_in_g(X)) 18.48/5.69 U33_ag(X, binaryZ_out_g(X)) -> succZ_out_ag(zero(X), one(X)) 18.48/5.69 succZ_in_ag(one(X), zero(Z)) -> U34_ag(X, Z, succ_in_ag(X, Z)) 18.48/5.69 succ_in_ag(b, one(b)) -> succ_out_ag(b, one(b)) 18.48/5.69 succ_in_ag(zero(X), one(X)) -> U31_ag(X, binaryZ_in_g(X)) 18.48/5.69 U31_ag(X, binaryZ_out_g(X)) -> succ_out_ag(zero(X), one(X)) 18.48/5.69 succ_in_ag(one(X), zero(Z)) -> U32_ag(X, Z, succ_in_ag(X, Z)) 18.48/5.69 U32_ag(X, Z, succ_out_ag(X, Z)) -> succ_out_ag(one(X), zero(Z)) 18.48/5.69 U34_ag(X, Z, succ_out_ag(X, Z)) -> succZ_out_ag(one(X), zero(Z)) 18.48/5.69 U14_aag(X, Z, succZ_out_ag(X, Z)) -> addc_out_aag(X, b, Z) 18.48/5.69 addc_in_aag(b, Y, Z) -> U15_aag(Y, Z, succZ_in_ag(Y, Z)) 18.48/5.69 U15_aag(Y, Z, succZ_out_ag(Y, Z)) -> addc_out_aag(b, Y, Z) 18.48/5.69 addc_in_aag(X, Y, Z) -> U16_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.48/5.69 addC_in_aag(zero(X), zero(Y), one(Z)) -> U23_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.48/5.69 U23_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), zero(Y), one(Z)) 18.48/5.69 addC_in_aag(zero(X), one(Y), zero(Z)) -> U24_aag(X, Y, Z, addX_in_aag(X, Y, Z)) 18.48/5.69 addX_in_aag(zero(X), b, one(X)) -> U17_aag(X, binaryZ_in_g(X)) 18.48/5.69 U17_aag(X, binaryZ_out_g(X)) -> addX_out_aag(zero(X), b, one(X)) 18.48/5.69 addX_in_aag(one(X), b, zero(Z)) -> U18_aag(X, Z, succ_in_ag(X, Z)) 18.48/5.69 U18_aag(X, Z, succ_out_ag(X, Z)) -> addX_out_aag(one(X), b, zero(Z)) 18.48/5.69 addX_in_aag(X, Y, Z) -> U19_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.48/5.69 addC_in_aag(one(X), zero(Y), zero(Z)) -> U25_aag(X, Y, Z, addY_in_aag(X, Y, Z)) 18.48/5.69 addY_in_aag(b, zero(Y), one(Y)) -> U20_aag(Y, binaryZ_in_g(Y)) 18.48/5.69 U20_aag(Y, binaryZ_out_g(Y)) -> addY_out_aag(b, zero(Y), one(Y)) 18.48/5.69 addY_in_aag(b, one(Y), zero(Z)) -> U21_aag(Y, Z, succ_in_ag(Y, Z)) 18.48/5.69 U21_aag(Y, Z, succ_out_ag(Y, Z)) -> addY_out_aag(b, one(Y), zero(Z)) 18.48/5.69 addY_in_aag(X, Y, Z) -> U22_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.48/5.69 addC_in_aag(one(X), one(Y), one(Z)) -> U26_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.48/5.69 U26_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addC_out_aag(one(X), one(Y), one(Z)) 18.48/5.69 U22_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addY_out_aag(X, Y, Z) 18.48/5.69 U25_aag(X, Y, Z, addY_out_aag(X, Y, Z)) -> addC_out_aag(one(X), zero(Y), zero(Z)) 18.48/5.69 U19_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addX_out_aag(X, Y, Z) 18.48/5.69 U24_aag(X, Y, Z, addX_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), one(Y), zero(Z)) 18.48/5.69 U16_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addc_out_aag(X, Y, Z) 18.48/5.69 U13_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addz_out_aag(one(X), one(Y), zero(Z)) 18.48/5.69 U9_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addy_out_aag(X, Y, Z) 18.48/5.69 U12_aag(X, Y, Z, addy_out_aag(X, Y, Z)) -> addz_out_aag(one(X), zero(Y), one(Z)) 18.48/5.69 U6_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addx_out_aag(X, Y, Z) 18.48/5.69 U11_aag(X, Y, Z, addx_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), one(Y), one(Z)) 18.48/5.69 U10_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), zero(Y), zero(Z)) 18.48/5.69 U3_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> add_out_aag(X, Y, Z) 18.48/5.69 U37_aag(R, S, RSS, add_out_aag(S, zero(RS), RSS)) -> times_out_aag(one(R), S, RSS) 18.48/5.69 U35_aag(R, S, RS, times_out_aag(R, S, RS)) -> times_out_aag(zero(R), S, zero(RS)) 18.48/5.69 18.48/5.69 The argument filtering Pi contains the following mapping: 18.48/5.69 times_in_aag(x1, x2, x3) = times_in_aag(x3) 18.48/5.69 18.48/5.69 times_out_aag(x1, x2, x3) = times_out_aag(x1, x2) 18.48/5.69 18.48/5.69 zero(x1) = zero(x1) 18.48/5.69 18.48/5.69 U35_aag(x1, x2, x3, x4) = U35_aag(x4) 18.48/5.69 18.48/5.69 U36_aag(x1, x2, x3, x4) = U36_aag(x3, x4) 18.48/5.69 18.48/5.69 times_in_aaa(x1, x2, x3) = times_in_aaa 18.48/5.69 18.48/5.69 times_out_aaa(x1, x2, x3) = times_out_aaa(x1) 18.48/5.69 18.48/5.69 U35_aaa(x1, x2, x3, x4) = U35_aaa(x4) 18.48/5.69 18.48/5.69 U36_aaa(x1, x2, x3, x4) = U36_aaa(x4) 18.48/5.69 18.48/5.69 U37_aaa(x1, x2, x3, x4) = U37_aaa(x1, x4) 18.48/5.69 18.48/5.69 add_in_aaa(x1, x2, x3) = add_in_aaa 18.48/5.69 18.48/5.69 add_out_aaa(x1, x2, x3) = add_out_aaa(x1, x2, x3) 18.48/5.69 18.48/5.69 U1_aaa(x1, x2) = U1_aaa(x2) 18.48/5.69 18.48/5.69 binaryZ_in_a(x1) = binaryZ_in_a 18.48/5.69 18.48/5.69 U29_a(x1, x2) = U29_a(x2) 18.48/5.69 18.48/5.69 U30_a(x1, x2) = U30_a(x2) 18.48/5.69 18.48/5.69 binary_in_a(x1) = binary_in_a 18.48/5.69 18.48/5.69 binary_out_a(x1) = binary_out_a(x1) 18.48/5.69 18.48/5.69 U27_a(x1, x2) = U27_a(x2) 18.48/5.69 18.48/5.69 binaryZ_out_a(x1) = binaryZ_out_a(x1) 18.48/5.69 18.48/5.69 U28_a(x1, x2) = U28_a(x2) 18.48/5.69 18.48/5.69 U2_aaa(x1, x2) = U2_aaa(x2) 18.48/5.69 18.48/5.69 U3_aaa(x1, x2, x3, x4) = U3_aaa(x4) 18.48/5.69 18.48/5.69 addz_in_aaa(x1, x2, x3) = addz_in_aaa 18.48/5.69 18.48/5.69 U10_aaa(x1, x2, x3, x4) = U10_aaa(x4) 18.48/5.69 18.48/5.69 U11_aaa(x1, x2, x3, x4) = U11_aaa(x4) 18.48/5.69 18.48/5.69 addx_in_aaa(x1, x2, x3) = addx_in_aaa 18.48/5.69 18.48/5.69 U4_aaa(x1, x2) = U4_aaa(x2) 18.48/5.69 18.48/5.69 addx_out_aaa(x1, x2, x3) = addx_out_aaa(x1, x2, x3) 18.48/5.69 18.48/5.69 U5_aaa(x1, x2) = U5_aaa(x2) 18.48/5.69 18.48/5.69 U6_aaa(x1, x2, x3, x4) = U6_aaa(x4) 18.48/5.69 18.48/5.69 U12_aaa(x1, x2, x3, x4) = U12_aaa(x4) 18.48/5.69 18.48/5.69 addy_in_aaa(x1, x2, x3) = addy_in_aaa 18.48/5.69 18.48/5.69 U7_aaa(x1, x2) = U7_aaa(x2) 18.48/5.69 18.48/5.69 addy_out_aaa(x1, x2, x3) = addy_out_aaa(x1, x2, x3) 18.48/5.69 18.48/5.69 U8_aaa(x1, x2) = U8_aaa(x2) 18.48/5.69 18.48/5.69 U9_aaa(x1, x2, x3, x4) = U9_aaa(x4) 18.48/5.69 18.48/5.69 U13_aaa(x1, x2, x3, x4) = U13_aaa(x4) 18.48/5.69 18.48/5.69 addc_in_aaa(x1, x2, x3) = addc_in_aaa 18.48/5.69 18.48/5.69 addc_out_aaa(x1, x2, x3) = addc_out_aaa(x1, x2, x3) 18.48/5.69 18.48/5.69 U14_aaa(x1, x2, x3) = U14_aaa(x3) 18.48/5.69 18.48/5.69 succZ_in_aa(x1, x2) = succZ_in_aa 18.48/5.69 18.48/5.69 U33_aa(x1, x2) = U33_aa(x2) 18.48/5.69 18.48/5.69 succZ_out_aa(x1, x2) = succZ_out_aa(x1, x2) 18.48/5.69 18.48/5.69 U34_aa(x1, x2, x3) = U34_aa(x3) 18.48/5.69 18.48/5.69 succ_in_aa(x1, x2) = succ_in_aa 18.48/5.69 18.48/5.69 succ_out_aa(x1, x2) = succ_out_aa(x1, x2) 18.48/5.69 18.48/5.69 U31_aa(x1, x2) = U31_aa(x2) 18.48/5.69 18.48/5.69 U32_aa(x1, x2, x3) = U32_aa(x3) 18.48/5.69 18.48/5.69 U15_aaa(x1, x2, x3) = U15_aaa(x3) 18.48/5.69 18.48/5.69 U16_aaa(x1, x2, x3, x4) = U16_aaa(x4) 18.48/5.69 18.48/5.69 addC_in_aaa(x1, x2, x3) = addC_in_aaa 18.48/5.69 18.48/5.69 U23_aaa(x1, x2, x3, x4) = U23_aaa(x4) 18.48/5.69 18.48/5.69 addz_out_aaa(x1, x2, x3) = addz_out_aaa(x1, x2, x3) 18.48/5.69 18.48/5.69 addC_out_aaa(x1, x2, x3) = addC_out_aaa(x1, x2, x3) 18.48/5.69 18.48/5.69 U24_aaa(x1, x2, x3, x4) = U24_aaa(x4) 18.48/5.69 18.48/5.69 addX_in_aaa(x1, x2, x3) = addX_in_aaa 18.48/5.69 18.48/5.69 U17_aaa(x1, x2) = U17_aaa(x2) 18.48/5.69 18.48/5.69 addX_out_aaa(x1, x2, x3) = addX_out_aaa(x1, x2, x3) 18.48/5.69 18.48/5.69 U18_aaa(x1, x2, x3) = U18_aaa(x3) 18.48/5.69 18.48/5.69 U19_aaa(x1, x2, x3, x4) = U19_aaa(x4) 18.48/5.69 18.48/5.69 U25_aaa(x1, x2, x3, x4) = U25_aaa(x4) 18.48/5.69 18.48/5.69 addY_in_aaa(x1, x2, x3) = addY_in_aaa 18.48/5.69 18.48/5.69 U20_aaa(x1, x2) = U20_aaa(x2) 18.48/5.69 18.48/5.69 addY_out_aaa(x1, x2, x3) = addY_out_aaa(x1, x2, x3) 18.48/5.69 18.48/5.69 U21_aaa(x1, x2, x3) = U21_aaa(x3) 18.48/5.69 18.48/5.69 U22_aaa(x1, x2, x3, x4) = U22_aaa(x4) 18.48/5.69 18.48/5.69 U26_aaa(x1, x2, x3, x4) = U26_aaa(x4) 18.48/5.69 18.48/5.69 U37_aag(x1, x2, x3, x4) = U37_aag(x1, x4) 18.48/5.69 18.48/5.69 add_in_aag(x1, x2, x3) = add_in_aag(x3) 18.48/5.69 18.48/5.69 b = b 18.48/5.69 18.48/5.69 add_out_aag(x1, x2, x3) = add_out_aag(x1, x2) 18.48/5.69 18.48/5.69 U1_aag(x1, x2) = U1_aag(x1, x2) 18.48/5.69 18.48/5.69 binaryZ_in_g(x1) = binaryZ_in_g(x1) 18.48/5.69 18.48/5.69 U29_g(x1, x2) = U29_g(x2) 18.48/5.69 18.48/5.69 one(x1) = one(x1) 18.48/5.69 18.48/5.69 U30_g(x1, x2) = U30_g(x2) 18.48/5.69 18.48/5.69 binary_in_g(x1) = binary_in_g(x1) 18.48/5.69 18.48/5.69 binary_out_g(x1) = binary_out_g 18.48/5.69 18.48/5.69 U27_g(x1, x2) = U27_g(x2) 18.48/5.69 18.48/5.69 binaryZ_out_g(x1) = binaryZ_out_g 18.48/5.69 18.48/5.69 U28_g(x1, x2) = U28_g(x2) 18.48/5.69 18.48/5.69 U2_aag(x1, x2) = U2_aag(x1, x2) 18.48/5.69 18.48/5.69 U3_aag(x1, x2, x3, x4) = U3_aag(x4) 18.48/5.69 18.48/5.69 addz_in_aag(x1, x2, x3) = addz_in_aag(x3) 18.48/5.69 18.48/5.69 U10_aag(x1, x2, x3, x4) = U10_aag(x4) 18.48/5.69 18.48/5.69 U11_aag(x1, x2, x3, x4) = U11_aag(x4) 18.48/5.69 18.48/5.69 addx_in_aag(x1, x2, x3) = addx_in_aag(x3) 18.48/5.69 18.48/5.69 U4_aag(x1, x2) = U4_aag(x1, x2) 18.48/5.69 18.48/5.69 addx_out_aag(x1, x2, x3) = addx_out_aag(x1, x2) 18.48/5.69 18.48/5.69 U5_aag(x1, x2) = U5_aag(x1, x2) 18.48/5.69 18.48/5.69 U6_aag(x1, x2, x3, x4) = U6_aag(x4) 18.48/5.69 18.48/5.69 U12_aag(x1, x2, x3, x4) = U12_aag(x4) 18.48/5.69 18.48/5.69 addy_in_aag(x1, x2, x3) = addy_in_aag(x3) 18.48/5.69 18.48/5.69 U7_aag(x1, x2) = U7_aag(x1, x2) 18.48/5.69 18.48/5.69 addy_out_aag(x1, x2, x3) = addy_out_aag(x1, x2) 18.48/5.69 18.48/5.69 U8_aag(x1, x2) = U8_aag(x1, x2) 18.48/5.69 18.48/5.69 U9_aag(x1, x2, x3, x4) = U9_aag(x4) 18.48/5.69 18.48/5.69 U13_aag(x1, x2, x3, x4) = U13_aag(x4) 18.48/5.69 18.48/5.69 addc_in_aag(x1, x2, x3) = addc_in_aag(x3) 18.48/5.69 18.48/5.69 addc_out_aag(x1, x2, x3) = addc_out_aag(x1, x2) 18.48/5.69 18.48/5.69 U14_aag(x1, x2, x3) = U14_aag(x3) 18.48/5.69 18.48/5.69 succZ_in_ag(x1, x2) = succZ_in_ag(x2) 18.48/5.69 18.48/5.69 U33_ag(x1, x2) = U33_ag(x1, x2) 18.48/5.69 18.48/5.69 succZ_out_ag(x1, x2) = succZ_out_ag(x1) 18.48/5.69 18.48/5.69 U34_ag(x1, x2, x3) = U34_ag(x3) 18.48/5.69 18.48/5.69 succ_in_ag(x1, x2) = succ_in_ag(x2) 18.48/5.69 18.48/5.69 succ_out_ag(x1, x2) = succ_out_ag(x1) 18.48/5.69 18.48/5.69 U31_ag(x1, x2) = U31_ag(x1, x2) 18.48/5.69 18.48/5.69 U32_ag(x1, x2, x3) = U32_ag(x3) 18.48/5.69 18.48/5.69 U15_aag(x1, x2, x3) = U15_aag(x3) 18.48/5.69 18.48/5.69 U16_aag(x1, x2, x3, x4) = U16_aag(x4) 18.48/5.69 18.48/5.69 addC_in_aag(x1, x2, x3) = addC_in_aag(x3) 18.48/5.69 18.48/5.69 U23_aag(x1, x2, x3, x4) = U23_aag(x4) 18.48/5.69 18.48/5.69 addz_out_aag(x1, x2, x3) = addz_out_aag(x1, x2) 18.48/5.69 18.48/5.69 addC_out_aag(x1, x2, x3) = addC_out_aag(x1, x2) 18.48/5.69 18.48/5.69 U24_aag(x1, x2, x3, x4) = U24_aag(x4) 18.48/5.69 18.48/5.69 addX_in_aag(x1, x2, x3) = addX_in_aag(x3) 18.48/5.69 18.48/5.69 U17_aag(x1, x2) = U17_aag(x1, x2) 18.48/5.69 18.48/5.69 addX_out_aag(x1, x2, x3) = addX_out_aag(x1, x2) 18.48/5.69 18.48/5.69 U18_aag(x1, x2, x3) = U18_aag(x3) 18.48/5.69 18.48/5.69 U19_aag(x1, x2, x3, x4) = U19_aag(x4) 18.48/5.69 18.48/5.69 U25_aag(x1, x2, x3, x4) = U25_aag(x4) 18.48/5.69 18.48/5.69 addY_in_aag(x1, x2, x3) = addY_in_aag(x3) 18.48/5.69 18.48/5.69 U20_aag(x1, x2) = U20_aag(x1, x2) 18.48/5.69 18.48/5.69 addY_out_aag(x1, x2, x3) = addY_out_aag(x1, x2) 18.48/5.69 18.48/5.69 U21_aag(x1, x2, x3) = U21_aag(x3) 18.48/5.69 18.48/5.69 U22_aag(x1, x2, x3, x4) = U22_aag(x4) 18.48/5.69 18.48/5.69 U26_aag(x1, x2, x3, x4) = U26_aag(x4) 18.48/5.69 18.48/5.69 TIMES_IN_AAA(x1, x2, x3) = TIMES_IN_AAA 18.48/5.69 18.48/5.69 18.48/5.69 We have to consider all (P,R,Pi)-chains 18.48/5.69 ---------------------------------------- 18.48/5.69 18.48/5.69 (92) UsableRulesProof (EQUIVALENT) 18.48/5.69 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 18.48/5.69 ---------------------------------------- 18.48/5.69 18.48/5.69 (93) 18.48/5.69 Obligation: 18.48/5.69 Pi DP problem: 18.48/5.69 The TRS P consists of the following rules: 18.48/5.69 18.48/5.69 TIMES_IN_AAA(one(R), S, RSS) -> TIMES_IN_AAA(R, S, RS) 18.48/5.69 TIMES_IN_AAA(zero(R), S, zero(RS)) -> TIMES_IN_AAA(R, S, RS) 18.48/5.69 18.48/5.69 R is empty. 18.48/5.69 The argument filtering Pi contains the following mapping: 18.48/5.69 zero(x1) = zero(x1) 18.48/5.69 18.48/5.69 one(x1) = one(x1) 18.48/5.69 18.48/5.69 TIMES_IN_AAA(x1, x2, x3) = TIMES_IN_AAA 18.48/5.69 18.48/5.69 18.48/5.69 We have to consider all (P,R,Pi)-chains 18.48/5.69 ---------------------------------------- 18.48/5.69 18.48/5.69 (94) 18.48/5.69 Obligation: 18.48/5.69 Pi DP problem: 18.48/5.69 The TRS P consists of the following rules: 18.48/5.69 18.48/5.69 TIMES_IN_AAG(zero(R), S, zero(RS)) -> TIMES_IN_AAG(R, S, RS) 18.48/5.69 18.48/5.69 The TRS R consists of the following rules: 18.48/5.69 18.48/5.69 times_in_aag(one(b), X, X) -> times_out_aag(one(b), X, X) 18.48/5.69 times_in_aag(zero(R), S, zero(RS)) -> U35_aag(R, S, RS, times_in_aag(R, S, RS)) 18.48/5.69 times_in_aag(one(R), S, RSS) -> U36_aag(R, S, RSS, times_in_aaa(R, S, RS)) 18.48/5.69 times_in_aaa(one(b), X, X) -> times_out_aaa(one(b), X, X) 18.48/5.69 times_in_aaa(zero(R), S, zero(RS)) -> U35_aaa(R, S, RS, times_in_aaa(R, S, RS)) 18.48/5.69 times_in_aaa(one(R), S, RSS) -> U36_aaa(R, S, RSS, times_in_aaa(R, S, RS)) 18.48/5.69 U36_aaa(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aaa(R, S, RSS, add_in_aaa(S, zero(RS), RSS)) 18.48/5.69 add_in_aaa(b, b, b) -> add_out_aaa(b, b, b) 18.48/5.69 add_in_aaa(X, b, X) -> U1_aaa(X, binaryZ_in_a(X)) 18.48/5.69 binaryZ_in_a(zero(X)) -> U29_a(X, binaryZ_in_a(X)) 18.48/5.69 binaryZ_in_a(one(X)) -> U30_a(X, binary_in_a(X)) 18.48/5.69 binary_in_a(b) -> binary_out_a(b) 18.48/5.69 binary_in_a(zero(X)) -> U27_a(X, binaryZ_in_a(X)) 18.48/5.69 U27_a(X, binaryZ_out_a(X)) -> binary_out_a(zero(X)) 18.48/5.69 binary_in_a(one(X)) -> U28_a(X, binary_in_a(X)) 18.48/5.69 U28_a(X, binary_out_a(X)) -> binary_out_a(one(X)) 18.48/5.69 U30_a(X, binary_out_a(X)) -> binaryZ_out_a(one(X)) 18.48/5.69 U29_a(X, binaryZ_out_a(X)) -> binaryZ_out_a(zero(X)) 18.48/5.69 U1_aaa(X, binaryZ_out_a(X)) -> add_out_aaa(X, b, X) 18.48/5.69 add_in_aaa(b, Y, Y) -> U2_aaa(Y, binaryZ_in_a(Y)) 18.48/5.69 U2_aaa(Y, binaryZ_out_a(Y)) -> add_out_aaa(b, Y, Y) 18.48/5.69 add_in_aaa(X, Y, Z) -> U3_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.48/5.69 addz_in_aaa(zero(X), zero(Y), zero(Z)) -> U10_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.48/5.69 addz_in_aaa(zero(X), one(Y), one(Z)) -> U11_aaa(X, Y, Z, addx_in_aaa(X, Y, Z)) 18.48/5.69 addx_in_aaa(one(X), b, one(X)) -> U4_aaa(X, binary_in_a(X)) 18.48/5.69 U4_aaa(X, binary_out_a(X)) -> addx_out_aaa(one(X), b, one(X)) 18.48/5.69 addx_in_aaa(zero(X), b, zero(X)) -> U5_aaa(X, binaryZ_in_a(X)) 18.48/5.69 U5_aaa(X, binaryZ_out_a(X)) -> addx_out_aaa(zero(X), b, zero(X)) 18.48/5.69 addx_in_aaa(X, Y, Z) -> U6_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.48/5.69 addz_in_aaa(one(X), zero(Y), one(Z)) -> U12_aaa(X, Y, Z, addy_in_aaa(X, Y, Z)) 18.48/5.69 addy_in_aaa(b, one(Y), one(Y)) -> U7_aaa(Y, binary_in_a(Y)) 18.48/5.69 U7_aaa(Y, binary_out_a(Y)) -> addy_out_aaa(b, one(Y), one(Y)) 18.48/5.69 addy_in_aaa(b, zero(Y), zero(Y)) -> U8_aaa(Y, binaryZ_in_a(Y)) 18.48/5.69 U8_aaa(Y, binaryZ_out_a(Y)) -> addy_out_aaa(b, zero(Y), zero(Y)) 18.48/5.69 addy_in_aaa(X, Y, Z) -> U9_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.48/5.69 addz_in_aaa(one(X), one(Y), zero(Z)) -> U13_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.48/5.69 addc_in_aaa(b, b, one(b)) -> addc_out_aaa(b, b, one(b)) 18.48/5.69 addc_in_aaa(X, b, Z) -> U14_aaa(X, Z, succZ_in_aa(X, Z)) 18.48/5.69 succZ_in_aa(zero(X), one(X)) -> U33_aa(X, binaryZ_in_a(X)) 18.48/5.69 U33_aa(X, binaryZ_out_a(X)) -> succZ_out_aa(zero(X), one(X)) 18.48/5.69 succZ_in_aa(one(X), zero(Z)) -> U34_aa(X, Z, succ_in_aa(X, Z)) 18.48/5.69 succ_in_aa(b, one(b)) -> succ_out_aa(b, one(b)) 18.48/5.69 succ_in_aa(zero(X), one(X)) -> U31_aa(X, binaryZ_in_a(X)) 18.72/5.74 U31_aa(X, binaryZ_out_a(X)) -> succ_out_aa(zero(X), one(X)) 18.72/5.74 succ_in_aa(one(X), zero(Z)) -> U32_aa(X, Z, succ_in_aa(X, Z)) 18.72/5.74 U32_aa(X, Z, succ_out_aa(X, Z)) -> succ_out_aa(one(X), zero(Z)) 18.72/5.74 U34_aa(X, Z, succ_out_aa(X, Z)) -> succZ_out_aa(one(X), zero(Z)) 18.72/5.74 U14_aaa(X, Z, succZ_out_aa(X, Z)) -> addc_out_aaa(X, b, Z) 18.72/5.74 addc_in_aaa(b, Y, Z) -> U15_aaa(Y, Z, succZ_in_aa(Y, Z)) 18.72/5.74 U15_aaa(Y, Z, succZ_out_aa(Y, Z)) -> addc_out_aaa(b, Y, Z) 18.72/5.74 addc_in_aaa(X, Y, Z) -> U16_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.72/5.74 addC_in_aaa(zero(X), zero(Y), one(Z)) -> U23_aaa(X, Y, Z, addz_in_aaa(X, Y, Z)) 18.72/5.74 U23_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), zero(Y), one(Z)) 18.72/5.74 addC_in_aaa(zero(X), one(Y), zero(Z)) -> U24_aaa(X, Y, Z, addX_in_aaa(X, Y, Z)) 18.72/5.74 addX_in_aaa(zero(X), b, one(X)) -> U17_aaa(X, binaryZ_in_a(X)) 18.72/5.74 U17_aaa(X, binaryZ_out_a(X)) -> addX_out_aaa(zero(X), b, one(X)) 18.72/5.74 addX_in_aaa(one(X), b, zero(Z)) -> U18_aaa(X, Z, succ_in_aa(X, Z)) 18.72/5.74 U18_aaa(X, Z, succ_out_aa(X, Z)) -> addX_out_aaa(one(X), b, zero(Z)) 18.72/5.74 addX_in_aaa(X, Y, Z) -> U19_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.72/5.74 addC_in_aaa(one(X), zero(Y), zero(Z)) -> U25_aaa(X, Y, Z, addY_in_aaa(X, Y, Z)) 18.72/5.74 addY_in_aaa(b, zero(Y), one(Y)) -> U20_aaa(Y, binaryZ_in_a(Y)) 18.72/5.74 U20_aaa(Y, binaryZ_out_a(Y)) -> addY_out_aaa(b, zero(Y), one(Y)) 18.72/5.74 addY_in_aaa(b, one(Y), zero(Z)) -> U21_aaa(Y, Z, succ_in_aa(Y, Z)) 18.72/5.74 U21_aaa(Y, Z, succ_out_aa(Y, Z)) -> addY_out_aaa(b, one(Y), zero(Z)) 18.72/5.74 addY_in_aaa(X, Y, Z) -> U22_aaa(X, Y, Z, addC_in_aaa(X, Y, Z)) 18.72/5.74 addC_in_aaa(one(X), one(Y), one(Z)) -> U26_aaa(X, Y, Z, addc_in_aaa(X, Y, Z)) 18.72/5.74 U26_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), one(Y), one(Z)) 18.72/5.74 U22_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addY_out_aaa(X, Y, Z) 18.72/5.74 U25_aaa(X, Y, Z, addY_out_aaa(X, Y, Z)) -> addC_out_aaa(one(X), zero(Y), zero(Z)) 18.72/5.74 U19_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addX_out_aaa(X, Y, Z) 18.72/5.74 U24_aaa(X, Y, Z, addX_out_aaa(X, Y, Z)) -> addC_out_aaa(zero(X), one(Y), zero(Z)) 18.72/5.74 U16_aaa(X, Y, Z, addC_out_aaa(X, Y, Z)) -> addc_out_aaa(X, Y, Z) 18.72/5.74 U13_aaa(X, Y, Z, addc_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), one(Y), zero(Z)) 18.72/5.74 U9_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addy_out_aaa(X, Y, Z) 18.72/5.74 U12_aaa(X, Y, Z, addy_out_aaa(X, Y, Z)) -> addz_out_aaa(one(X), zero(Y), one(Z)) 18.72/5.74 U6_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addx_out_aaa(X, Y, Z) 18.72/5.74 U11_aaa(X, Y, Z, addx_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), one(Y), one(Z)) 18.72/5.74 U10_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> addz_out_aaa(zero(X), zero(Y), zero(Z)) 18.72/5.74 U3_aaa(X, Y, Z, addz_out_aaa(X, Y, Z)) -> add_out_aaa(X, Y, Z) 18.72/5.74 U37_aaa(R, S, RSS, add_out_aaa(S, zero(RS), RSS)) -> times_out_aaa(one(R), S, RSS) 18.72/5.74 U35_aaa(R, S, RS, times_out_aaa(R, S, RS)) -> times_out_aaa(zero(R), S, zero(RS)) 18.72/5.74 U36_aag(R, S, RSS, times_out_aaa(R, S, RS)) -> U37_aag(R, S, RSS, add_in_aag(S, zero(RS), RSS)) 18.72/5.74 add_in_aag(b, b, b) -> add_out_aag(b, b, b) 18.72/5.74 add_in_aag(X, b, X) -> U1_aag(X, binaryZ_in_g(X)) 18.72/5.74 binaryZ_in_g(zero(X)) -> U29_g(X, binaryZ_in_g(X)) 18.72/5.74 binaryZ_in_g(one(X)) -> U30_g(X, binary_in_g(X)) 18.72/5.74 binary_in_g(b) -> binary_out_g(b) 18.72/5.74 binary_in_g(zero(X)) -> U27_g(X, binaryZ_in_g(X)) 18.72/5.74 U27_g(X, binaryZ_out_g(X)) -> binary_out_g(zero(X)) 18.72/5.74 binary_in_g(one(X)) -> U28_g(X, binary_in_g(X)) 18.72/5.74 U28_g(X, binary_out_g(X)) -> binary_out_g(one(X)) 18.72/5.74 U30_g(X, binary_out_g(X)) -> binaryZ_out_g(one(X)) 18.72/5.74 U29_g(X, binaryZ_out_g(X)) -> binaryZ_out_g(zero(X)) 18.72/5.74 U1_aag(X, binaryZ_out_g(X)) -> add_out_aag(X, b, X) 18.72/5.74 add_in_aag(b, Y, Y) -> U2_aag(Y, binaryZ_in_g(Y)) 18.72/5.74 U2_aag(Y, binaryZ_out_g(Y)) -> add_out_aag(b, Y, Y) 18.72/5.74 add_in_aag(X, Y, Z) -> U3_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.72/5.74 addz_in_aag(zero(X), zero(Y), zero(Z)) -> U10_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.72/5.74 addz_in_aag(zero(X), one(Y), one(Z)) -> U11_aag(X, Y, Z, addx_in_aag(X, Y, Z)) 18.72/5.74 addx_in_aag(one(X), b, one(X)) -> U4_aag(X, binary_in_g(X)) 18.72/5.74 U4_aag(X, binary_out_g(X)) -> addx_out_aag(one(X), b, one(X)) 18.72/5.74 addx_in_aag(zero(X), b, zero(X)) -> U5_aag(X, binaryZ_in_g(X)) 18.72/5.74 U5_aag(X, binaryZ_out_g(X)) -> addx_out_aag(zero(X), b, zero(X)) 18.72/5.74 addx_in_aag(X, Y, Z) -> U6_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.72/5.74 addz_in_aag(one(X), zero(Y), one(Z)) -> U12_aag(X, Y, Z, addy_in_aag(X, Y, Z)) 18.72/5.74 addy_in_aag(b, one(Y), one(Y)) -> U7_aag(Y, binary_in_g(Y)) 18.72/5.74 U7_aag(Y, binary_out_g(Y)) -> addy_out_aag(b, one(Y), one(Y)) 18.72/5.74 addy_in_aag(b, zero(Y), zero(Y)) -> U8_aag(Y, binaryZ_in_g(Y)) 18.72/5.74 U8_aag(Y, binaryZ_out_g(Y)) -> addy_out_aag(b, zero(Y), zero(Y)) 18.72/5.74 addy_in_aag(X, Y, Z) -> U9_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.72/5.74 addz_in_aag(one(X), one(Y), zero(Z)) -> U13_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.72/5.74 addc_in_aag(b, b, one(b)) -> addc_out_aag(b, b, one(b)) 18.72/5.74 addc_in_aag(X, b, Z) -> U14_aag(X, Z, succZ_in_ag(X, Z)) 18.72/5.74 succZ_in_ag(zero(X), one(X)) -> U33_ag(X, binaryZ_in_g(X)) 18.72/5.74 U33_ag(X, binaryZ_out_g(X)) -> succZ_out_ag(zero(X), one(X)) 18.72/5.74 succZ_in_ag(one(X), zero(Z)) -> U34_ag(X, Z, succ_in_ag(X, Z)) 18.72/5.74 succ_in_ag(b, one(b)) -> succ_out_ag(b, one(b)) 18.72/5.74 succ_in_ag(zero(X), one(X)) -> U31_ag(X, binaryZ_in_g(X)) 18.72/5.74 U31_ag(X, binaryZ_out_g(X)) -> succ_out_ag(zero(X), one(X)) 18.72/5.74 succ_in_ag(one(X), zero(Z)) -> U32_ag(X, Z, succ_in_ag(X, Z)) 18.72/5.74 U32_ag(X, Z, succ_out_ag(X, Z)) -> succ_out_ag(one(X), zero(Z)) 18.72/5.74 U34_ag(X, Z, succ_out_ag(X, Z)) -> succZ_out_ag(one(X), zero(Z)) 18.72/5.74 U14_aag(X, Z, succZ_out_ag(X, Z)) -> addc_out_aag(X, b, Z) 18.72/5.74 addc_in_aag(b, Y, Z) -> U15_aag(Y, Z, succZ_in_ag(Y, Z)) 18.72/5.74 U15_aag(Y, Z, succZ_out_ag(Y, Z)) -> addc_out_aag(b, Y, Z) 18.72/5.74 addc_in_aag(X, Y, Z) -> U16_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.72/5.74 addC_in_aag(zero(X), zero(Y), one(Z)) -> U23_aag(X, Y, Z, addz_in_aag(X, Y, Z)) 18.72/5.74 U23_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), zero(Y), one(Z)) 18.72/5.74 addC_in_aag(zero(X), one(Y), zero(Z)) -> U24_aag(X, Y, Z, addX_in_aag(X, Y, Z)) 18.72/5.74 addX_in_aag(zero(X), b, one(X)) -> U17_aag(X, binaryZ_in_g(X)) 18.72/5.74 U17_aag(X, binaryZ_out_g(X)) -> addX_out_aag(zero(X), b, one(X)) 18.72/5.74 addX_in_aag(one(X), b, zero(Z)) -> U18_aag(X, Z, succ_in_ag(X, Z)) 18.72/5.74 U18_aag(X, Z, succ_out_ag(X, Z)) -> addX_out_aag(one(X), b, zero(Z)) 18.72/5.74 addX_in_aag(X, Y, Z) -> U19_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.72/5.74 addC_in_aag(one(X), zero(Y), zero(Z)) -> U25_aag(X, Y, Z, addY_in_aag(X, Y, Z)) 18.72/5.74 addY_in_aag(b, zero(Y), one(Y)) -> U20_aag(Y, binaryZ_in_g(Y)) 18.72/5.74 U20_aag(Y, binaryZ_out_g(Y)) -> addY_out_aag(b, zero(Y), one(Y)) 18.72/5.74 addY_in_aag(b, one(Y), zero(Z)) -> U21_aag(Y, Z, succ_in_ag(Y, Z)) 18.72/5.74 U21_aag(Y, Z, succ_out_ag(Y, Z)) -> addY_out_aag(b, one(Y), zero(Z)) 18.72/5.74 addY_in_aag(X, Y, Z) -> U22_aag(X, Y, Z, addC_in_aag(X, Y, Z)) 18.72/5.74 addC_in_aag(one(X), one(Y), one(Z)) -> U26_aag(X, Y, Z, addc_in_aag(X, Y, Z)) 18.72/5.74 U26_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addC_out_aag(one(X), one(Y), one(Z)) 18.72/5.74 U22_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addY_out_aag(X, Y, Z) 18.72/5.74 U25_aag(X, Y, Z, addY_out_aag(X, Y, Z)) -> addC_out_aag(one(X), zero(Y), zero(Z)) 18.72/5.74 U19_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addX_out_aag(X, Y, Z) 18.72/5.74 U24_aag(X, Y, Z, addX_out_aag(X, Y, Z)) -> addC_out_aag(zero(X), one(Y), zero(Z)) 18.72/5.74 U16_aag(X, Y, Z, addC_out_aag(X, Y, Z)) -> addc_out_aag(X, Y, Z) 18.72/5.74 U13_aag(X, Y, Z, addc_out_aag(X, Y, Z)) -> addz_out_aag(one(X), one(Y), zero(Z)) 18.72/5.74 U9_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addy_out_aag(X, Y, Z) 18.72/5.74 U12_aag(X, Y, Z, addy_out_aag(X, Y, Z)) -> addz_out_aag(one(X), zero(Y), one(Z)) 18.72/5.74 U6_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addx_out_aag(X, Y, Z) 18.72/5.74 U11_aag(X, Y, Z, addx_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), one(Y), one(Z)) 18.72/5.74 U10_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> addz_out_aag(zero(X), zero(Y), zero(Z)) 18.72/5.74 U3_aag(X, Y, Z, addz_out_aag(X, Y, Z)) -> add_out_aag(X, Y, Z) 18.72/5.74 U37_aag(R, S, RSS, add_out_aag(S, zero(RS), RSS)) -> times_out_aag(one(R), S, RSS) 18.72/5.74 U35_aag(R, S, RS, times_out_aag(R, S, RS)) -> times_out_aag(zero(R), S, zero(RS)) 18.72/5.74 18.72/5.74 The argument filtering Pi contains the following mapping: 18.72/5.74 times_in_aag(x1, x2, x3) = times_in_aag(x3) 18.72/5.74 18.72/5.74 times_out_aag(x1, x2, x3) = times_out_aag(x1, x2) 18.72/5.74 18.72/5.74 zero(x1) = zero(x1) 18.72/5.74 18.72/5.74 U35_aag(x1, x2, x3, x4) = U35_aag(x4) 18.72/5.74 18.72/5.74 U36_aag(x1, x2, x3, x4) = U36_aag(x3, x4) 18.72/5.74 18.72/5.74 times_in_aaa(x1, x2, x3) = times_in_aaa 18.72/5.74 18.72/5.74 times_out_aaa(x1, x2, x3) = times_out_aaa(x1) 18.72/5.74 18.72/5.74 U35_aaa(x1, x2, x3, x4) = U35_aaa(x4) 18.72/5.74 18.72/5.74 U36_aaa(x1, x2, x3, x4) = U36_aaa(x4) 18.72/5.74 18.72/5.74 U37_aaa(x1, x2, x3, x4) = U37_aaa(x1, x4) 18.72/5.74 18.72/5.74 add_in_aaa(x1, x2, x3) = add_in_aaa 18.72/5.74 18.72/5.74 add_out_aaa(x1, x2, x3) = add_out_aaa(x1, x2, x3) 18.72/5.74 18.72/5.74 U1_aaa(x1, x2) = U1_aaa(x2) 18.72/5.74 18.72/5.74 binaryZ_in_a(x1) = binaryZ_in_a 18.72/5.74 18.72/5.74 U29_a(x1, x2) = U29_a(x2) 18.72/5.74 18.72/5.74 U30_a(x1, x2) = U30_a(x2) 18.72/5.74 18.72/5.74 binary_in_a(x1) = binary_in_a 18.72/5.74 18.72/5.74 binary_out_a(x1) = binary_out_a(x1) 18.72/5.74 18.72/5.74 U27_a(x1, x2) = U27_a(x2) 18.72/5.74 18.72/5.74 binaryZ_out_a(x1) = binaryZ_out_a(x1) 18.72/5.74 18.72/5.74 U28_a(x1, x2) = U28_a(x2) 18.72/5.74 18.72/5.74 U2_aaa(x1, x2) = U2_aaa(x2) 18.72/5.74 18.72/5.74 U3_aaa(x1, x2, x3, x4) = U3_aaa(x4) 18.72/5.74 18.72/5.74 addz_in_aaa(x1, x2, x3) = addz_in_aaa 18.72/5.74 18.72/5.74 U10_aaa(x1, x2, x3, x4) = U10_aaa(x4) 18.72/5.74 18.72/5.74 U11_aaa(x1, x2, x3, x4) = U11_aaa(x4) 18.72/5.74 18.72/5.74 addx_in_aaa(x1, x2, x3) = addx_in_aaa 18.72/5.74 18.72/5.74 U4_aaa(x1, x2) = U4_aaa(x2) 18.72/5.74 18.72/5.74 addx_out_aaa(x1, x2, x3) = addx_out_aaa(x1, x2, x3) 18.72/5.74 18.72/5.74 U5_aaa(x1, x2) = U5_aaa(x2) 18.72/5.74 18.72/5.74 U6_aaa(x1, x2, x3, x4) = U6_aaa(x4) 18.72/5.74 18.72/5.74 U12_aaa(x1, x2, x3, x4) = U12_aaa(x4) 18.72/5.74 18.72/5.74 addy_in_aaa(x1, x2, x3) = addy_in_aaa 18.72/5.74 18.72/5.74 U7_aaa(x1, x2) = U7_aaa(x2) 18.72/5.74 18.72/5.74 addy_out_aaa(x1, x2, x3) = addy_out_aaa(x1, x2, x3) 18.72/5.74 18.72/5.74 U8_aaa(x1, x2) = U8_aaa(x2) 18.72/5.74 18.72/5.74 U9_aaa(x1, x2, x3, x4) = U9_aaa(x4) 18.72/5.74 18.72/5.74 U13_aaa(x1, x2, x3, x4) = U13_aaa(x4) 18.72/5.74 18.72/5.74 addc_in_aaa(x1, x2, x3) = addc_in_aaa 18.72/5.74 18.72/5.74 addc_out_aaa(x1, x2, x3) = addc_out_aaa(x1, x2, x3) 18.72/5.74 18.72/5.74 U14_aaa(x1, x2, x3) = U14_aaa(x3) 18.72/5.74 18.72/5.74 succZ_in_aa(x1, x2) = succZ_in_aa 18.72/5.74 18.72/5.74 U33_aa(x1, x2) = U33_aa(x2) 18.72/5.74 18.72/5.74 succZ_out_aa(x1, x2) = succZ_out_aa(x1, x2) 18.72/5.74 18.72/5.74 U34_aa(x1, x2, x3) = U34_aa(x3) 18.72/5.74 18.72/5.74 succ_in_aa(x1, x2) = succ_in_aa 18.72/5.74 18.72/5.74 succ_out_aa(x1, x2) = succ_out_aa(x1, x2) 18.72/5.74 18.72/5.74 U31_aa(x1, x2) = U31_aa(x2) 18.72/5.74 18.72/5.74 U32_aa(x1, x2, x3) = U32_aa(x3) 18.72/5.74 18.72/5.74 U15_aaa(x1, x2, x3) = U15_aaa(x3) 18.72/5.74 18.72/5.74 U16_aaa(x1, x2, x3, x4) = U16_aaa(x4) 18.72/5.74 18.72/5.74 addC_in_aaa(x1, x2, x3) = addC_in_aaa 18.72/5.74 18.72/5.74 U23_aaa(x1, x2, x3, x4) = U23_aaa(x4) 18.72/5.74 18.72/5.74 addz_out_aaa(x1, x2, x3) = addz_out_aaa(x1, x2, x3) 18.72/5.74 18.72/5.74 addC_out_aaa(x1, x2, x3) = addC_out_aaa(x1, x2, x3) 18.72/5.74 18.72/5.74 U24_aaa(x1, x2, x3, x4) = U24_aaa(x4) 18.72/5.74 18.72/5.74 addX_in_aaa(x1, x2, x3) = addX_in_aaa 18.72/5.74 18.72/5.74 U17_aaa(x1, x2) = U17_aaa(x2) 18.72/5.74 18.72/5.74 addX_out_aaa(x1, x2, x3) = addX_out_aaa(x1, x2, x3) 18.72/5.74 18.72/5.74 U18_aaa(x1, x2, x3) = U18_aaa(x3) 18.72/5.74 18.72/5.74 U19_aaa(x1, x2, x3, x4) = U19_aaa(x4) 18.72/5.74 18.72/5.74 U25_aaa(x1, x2, x3, x4) = U25_aaa(x4) 18.72/5.74 18.72/5.74 addY_in_aaa(x1, x2, x3) = addY_in_aaa 18.72/5.74 18.72/5.74 U20_aaa(x1, x2) = U20_aaa(x2) 18.72/5.74 18.72/5.74 addY_out_aaa(x1, x2, x3) = addY_out_aaa(x1, x2, x3) 18.72/5.74 18.72/5.74 U21_aaa(x1, x2, x3) = U21_aaa(x3) 18.72/5.74 18.72/5.74 U22_aaa(x1, x2, x3, x4) = U22_aaa(x4) 18.72/5.74 18.72/5.74 U26_aaa(x1, x2, x3, x4) = U26_aaa(x4) 18.72/5.74 18.72/5.74 U37_aag(x1, x2, x3, x4) = U37_aag(x1, x4) 18.72/5.74 18.72/5.74 add_in_aag(x1, x2, x3) = add_in_aag(x3) 18.72/5.74 18.72/5.74 b = b 18.72/5.74 18.72/5.74 add_out_aag(x1, x2, x3) = add_out_aag(x1, x2) 18.72/5.74 18.72/5.74 U1_aag(x1, x2) = U1_aag(x1, x2) 18.72/5.74 18.72/5.74 binaryZ_in_g(x1) = binaryZ_in_g(x1) 18.72/5.74 18.72/5.74 U29_g(x1, x2) = U29_g(x2) 18.72/5.74 18.72/5.74 one(x1) = one(x1) 18.72/5.74 18.72/5.74 U30_g(x1, x2) = U30_g(x2) 18.72/5.74 18.72/5.74 binary_in_g(x1) = binary_in_g(x1) 18.72/5.74 18.72/5.74 binary_out_g(x1) = binary_out_g 18.72/5.74 18.72/5.74 U27_g(x1, x2) = U27_g(x2) 18.72/5.74 18.72/5.74 binaryZ_out_g(x1) = binaryZ_out_g 18.72/5.74 18.72/5.74 U28_g(x1, x2) = U28_g(x2) 18.72/5.74 18.72/5.74 U2_aag(x1, x2) = U2_aag(x1, x2) 18.72/5.74 18.72/5.74 U3_aag(x1, x2, x3, x4) = U3_aag(x4) 18.72/5.74 18.72/5.74 addz_in_aag(x1, x2, x3) = addz_in_aag(x3) 18.72/5.74 18.72/5.74 U10_aag(x1, x2, x3, x4) = U10_aag(x4) 18.72/5.74 18.72/5.74 U11_aag(x1, x2, x3, x4) = U11_aag(x4) 18.72/5.74 18.72/5.74 addx_in_aag(x1, x2, x3) = addx_in_aag(x3) 18.72/5.74 18.72/5.74 U4_aag(x1, x2) = U4_aag(x1, x2) 18.72/5.74 18.72/5.74 addx_out_aag(x1, x2, x3) = addx_out_aag(x1, x2) 18.72/5.74 18.72/5.74 U5_aag(x1, x2) = U5_aag(x1, x2) 18.72/5.74 18.72/5.74 U6_aag(x1, x2, x3, x4) = U6_aag(x4) 18.72/5.74 18.72/5.74 U12_aag(x1, x2, x3, x4) = U12_aag(x4) 18.72/5.74 18.72/5.74 addy_in_aag(x1, x2, x3) = addy_in_aag(x3) 18.72/5.74 18.72/5.74 U7_aag(x1, x2) = U7_aag(x1, x2) 18.72/5.74 18.72/5.74 addy_out_aag(x1, x2, x3) = addy_out_aag(x1, x2) 18.72/5.74 18.72/5.74 U8_aag(x1, x2) = U8_aag(x1, x2) 18.72/5.74 18.72/5.74 U9_aag(x1, x2, x3, x4) = U9_aag(x4) 18.72/5.74 18.72/5.74 U13_aag(x1, x2, x3, x4) = U13_aag(x4) 18.72/5.74 18.72/5.74 addc_in_aag(x1, x2, x3) = addc_in_aag(x3) 18.72/5.74 18.72/5.74 addc_out_aag(x1, x2, x3) = addc_out_aag(x1, x2) 18.72/5.74 18.72/5.74 U14_aag(x1, x2, x3) = U14_aag(x3) 18.72/5.74 18.72/5.74 succZ_in_ag(x1, x2) = succZ_in_ag(x2) 18.72/5.74 18.72/5.74 U33_ag(x1, x2) = U33_ag(x1, x2) 18.72/5.74 18.72/5.74 succZ_out_ag(x1, x2) = succZ_out_ag(x1) 18.72/5.74 18.72/5.74 U34_ag(x1, x2, x3) = U34_ag(x3) 18.72/5.74 18.72/5.74 succ_in_ag(x1, x2) = succ_in_ag(x2) 18.72/5.74 18.72/5.74 succ_out_ag(x1, x2) = succ_out_ag(x1) 18.72/5.74 18.72/5.74 U31_ag(x1, x2) = U31_ag(x1, x2) 18.72/5.74 18.72/5.74 U32_ag(x1, x2, x3) = U32_ag(x3) 18.72/5.74 18.72/5.74 U15_aag(x1, x2, x3) = U15_aag(x3) 18.72/5.74 18.72/5.74 U16_aag(x1, x2, x3, x4) = U16_aag(x4) 18.72/5.74 18.72/5.74 addC_in_aag(x1, x2, x3) = addC_in_aag(x3) 18.72/5.74 18.72/5.74 U23_aag(x1, x2, x3, x4) = U23_aag(x4) 18.72/5.74 18.72/5.74 addz_out_aag(x1, x2, x3) = addz_out_aag(x1, x2) 18.72/5.74 18.72/5.74 addC_out_aag(x1, x2, x3) = addC_out_aag(x1, x2) 18.72/5.74 18.72/5.74 U24_aag(x1, x2, x3, x4) = U24_aag(x4) 18.72/5.74 18.72/5.74 addX_in_aag(x1, x2, x3) = addX_in_aag(x3) 18.72/5.74 18.72/5.74 U17_aag(x1, x2) = U17_aag(x1, x2) 18.72/5.74 18.72/5.74 addX_out_aag(x1, x2, x3) = addX_out_aag(x1, x2) 18.72/5.74 18.72/5.74 U18_aag(x1, x2, x3) = U18_aag(x3) 18.72/5.74 18.72/5.74 U19_aag(x1, x2, x3, x4) = U19_aag(x4) 18.72/5.74 18.72/5.74 U25_aag(x1, x2, x3, x4) = U25_aag(x4) 18.72/5.74 18.72/5.74 addY_in_aag(x1, x2, x3) = addY_in_aag(x3) 18.72/5.74 18.72/5.74 U20_aag(x1, x2) = U20_aag(x1, x2) 18.72/5.74 18.72/5.74 addY_out_aag(x1, x2, x3) = addY_out_aag(x1, x2) 18.72/5.74 18.72/5.74 U21_aag(x1, x2, x3) = U21_aag(x3) 18.72/5.74 18.72/5.74 U22_aag(x1, x2, x3, x4) = U22_aag(x4) 18.72/5.74 18.72/5.74 U26_aag(x1, x2, x3, x4) = U26_aag(x4) 18.72/5.74 18.72/5.74 TIMES_IN_AAG(x1, x2, x3) = TIMES_IN_AAG(x3) 18.72/5.74 18.72/5.74 18.72/5.74 We have to consider all (P,R,Pi)-chains 18.72/5.74 ---------------------------------------- 18.72/5.74 18.72/5.74 (95) UsableRulesProof (EQUIVALENT) 18.72/5.74 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 18.72/5.74 ---------------------------------------- 18.72/5.74 18.72/5.74 (96) 18.72/5.74 Obligation: 18.72/5.74 Pi DP problem: 18.72/5.74 The TRS P consists of the following rules: 18.72/5.74 18.72/5.74 TIMES_IN_AAG(zero(R), S, zero(RS)) -> TIMES_IN_AAG(R, S, RS) 18.72/5.74 18.72/5.74 R is empty. 18.72/5.74 The argument filtering Pi contains the following mapping: 18.72/5.74 zero(x1) = zero(x1) 18.72/5.74 18.72/5.74 TIMES_IN_AAG(x1, x2, x3) = TIMES_IN_AAG(x3) 18.72/5.74 18.72/5.74 18.72/5.74 We have to consider all (P,R,Pi)-chains 18.72/5.74 ---------------------------------------- 18.72/5.74 18.72/5.74 (97) PrologToTRSTransformerProof (SOUND) 18.72/5.74 Transformed Prolog program to TRS. 18.72/5.74 18.72/5.74 { 18.72/5.74 "root": 3, 18.72/5.74 "program": { 18.72/5.74 "directives": [], 18.72/5.74 "clauses": [ 18.72/5.74 [ 18.72/5.74 "(add (b) (b) (b))", 18.72/5.74 null 18.72/5.74 ], 18.72/5.74 [ 18.72/5.74 "(add X (b) X)", 18.72/5.74 "(binaryZ X)" 18.72/5.74 ], 18.72/5.74 [ 18.72/5.74 "(add (b) Y Y)", 18.72/5.74 "(binaryZ Y)" 18.72/5.74 ], 18.72/5.74 [ 18.72/5.74 "(add X Y Z)", 18.72/5.74 "(addz X Y Z)" 18.72/5.74 ], 18.72/5.74 [ 18.72/5.74 "(addx (one X) (b) (one X))", 18.72/5.74 "(binary X)" 18.72/5.74 ], 18.72/5.74 [ 18.72/5.74 "(addx (zero X) (b) (zero X))", 18.72/5.74 "(binaryZ X)" 18.72/5.74 ], 18.72/5.74 [ 18.72/5.74 "(addx X Y Z)", 18.72/5.74 "(addz X Y Z)" 18.72/5.74 ], 18.72/5.74 [ 18.72/5.74 "(addy (b) (one Y) (one Y))", 18.72/5.74 "(binary Y)" 18.72/5.74 ], 18.72/5.74 [ 18.72/5.74 "(addy (b) (zero Y) (zero Y))", 18.72/5.74 "(binaryZ Y)" 18.72/5.74 ], 18.72/5.74 [ 18.72/5.74 "(addy X Y Z)", 18.72/5.74 "(addz X Y Z)" 18.72/5.74 ], 18.72/5.74 [ 18.72/5.74 "(addz (zero X) (zero Y) (zero Z))", 18.72/5.74 "(addz X Y Z)" 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"relations": [] 18.82/5.77 }, 18.82/5.77 "ground": ["T644"], 18.82/5.77 "free": [], 18.82/5.77 "exprvars": [] 18.82/5.77 } 18.82/5.77 }, 18.82/5.77 "2402": { 18.82/5.77 "goal": [{ 18.82/5.77 "clause": 35, 18.82/5.77 "scope": 27, 18.82/5.77 "term": "(succ T639 T638)" 18.82/5.77 }], 18.82/5.77 "kb": { 18.82/5.77 "nonunifying": [], 18.82/5.77 "intvars": {}, 18.82/5.77 "arithmetic": { 18.82/5.77 "type": "PlainIntegerRelationState", 18.82/5.77 "relations": [] 18.82/5.77 }, 18.82/5.77 "ground": ["T638"], 18.82/5.77 "free": [], 18.82/5.77 "exprvars": [] 18.82/5.77 } 18.82/5.77 }, 18.82/5.77 "2401": { 18.82/5.77 "goal": [{ 18.82/5.77 "clause": 34, 18.82/5.77 "scope": 27, 18.82/5.77 "term": "(succ T639 T638)" 18.82/5.77 }], 18.82/5.77 "kb": { 18.82/5.77 "nonunifying": [], 18.82/5.77 "intvars": {}, 18.82/5.77 "arithmetic": { 18.82/5.77 "type": "PlainIntegerRelationState", 18.82/5.77 "relations": [] 18.82/5.77 }, 18.82/5.77 "ground": ["T638"], 18.82/5.77 "free": [], 18.82/5.77 "exprvars": [] 18.82/5.77 } 18.82/5.77 }, 18.82/5.77 "2400": { 18.82/5.77 "goal": [], 18.82/5.77 "kb": { 18.82/5.77 "nonunifying": [], 18.82/5.77 "intvars": {}, 18.82/5.77 "arithmetic": { 18.82/5.77 "type": "PlainIntegerRelationState", 18.82/5.77 "relations": [] 18.82/5.77 }, 18.82/5.77 "ground": [], 18.82/5.77 "free": [], 18.82/5.77 "exprvars": [] 18.82/5.77 } 18.82/5.77 }, 18.82/5.77 "1552": { 18.82/5.77 "goal": [{ 18.82/5.77 "clause": 13, 18.82/5.77 "scope": 8, 18.82/5.77 "term": "(addz T143 T144 X156)" 18.82/5.77 }], 18.82/5.77 "kb": { 18.82/5.77 "nonunifying": [], 18.82/5.77 "intvars": {}, 18.82/5.77 "arithmetic": { 18.82/5.77 "type": "PlainIntegerRelationState", 18.82/5.77 "relations": [] 18.82/5.77 }, 18.82/5.77 "ground": [], 18.82/5.77 "free": ["X156"], 18.82/5.77 "exprvars": [] 18.82/5.77 } 18.82/5.77 }, 18.82/5.77 "1551": { 18.82/5.77 "goal": [{ 18.82/5.77 "clause": 12, 18.82/5.77 "scope": 8, 18.82/5.77 "term": "(addz T143 T144 X156)" 18.82/5.77 }], 18.82/5.77 "kb": { 18.82/5.77 "nonunifying": [], 18.82/5.77 "intvars": {}, 18.82/5.77 "arithmetic": { 18.82/5.77 "type": "PlainIntegerRelationState", 18.82/5.77 "relations": [] 18.82/5.77 }, 18.82/5.77 "ground": [], 18.82/5.77 "free": ["X156"], 18.82/5.77 "exprvars": [] 18.82/5.77 } 18.82/5.77 }, 18.82/5.77 "2407": { 18.82/5.77 "goal": [], 18.82/5.77 "kb": { 18.82/5.77 "nonunifying": [], 18.82/5.77 "intvars": {}, 18.82/5.77 "arithmetic": { 18.82/5.77 "type": "PlainIntegerRelationState", 18.82/5.77 "relations": [] 18.82/5.77 }, 18.82/5.77 "ground": [], 18.82/5.77 "free": [], 18.82/5.77 "exprvars": [] 18.82/5.77 } 18.82/5.77 }, 18.82/5.77 "2406": { 18.82/5.77 "goal": [{ 18.82/5.77 "clause": -1, 18.82/5.77 "scope": -1, 18.82/5.77 "term": "(succ T652 T651)" 18.82/5.77 }], 18.82/5.77 "kb": { 18.82/5.77 "nonunifying": [], 18.82/5.77 "intvars": {}, 18.82/5.77 "arithmetic": { 18.82/5.77 "type": "PlainIntegerRelationState", 18.82/5.77 "relations": [] 18.82/5.77 }, 18.82/5.77 "ground": ["T651"], 18.82/5.77 "free": [], 18.82/5.77 "exprvars": [] 18.82/5.77 } 18.82/5.77 }, 18.82/5.77 "2540": { 18.82/5.77 "goal": [{ 18.82/5.77 "clause": -1, 18.82/5.77 "scope": -1, 18.82/5.77 "term": "(addy T839 T840 T838)" 18.82/5.77 }], 18.82/5.77 "kb": { 18.82/5.77 "nonunifying": [], 18.82/5.77 "intvars": {}, 18.82/5.77 "arithmetic": { 18.82/5.77 "type": "PlainIntegerRelationState", 18.82/5.77 "relations": [] 18.82/5.77 }, 18.82/5.77 "ground": ["T838"], 18.82/5.77 "free": [], 18.82/5.77 "exprvars": [] 18.82/5.77 } 18.82/5.77 }, 18.82/5.77 "1691": { 18.82/5.77 "goal": [], 18.82/5.77 "kb": { 18.82/5.77 "nonunifying": [], 18.82/5.77 "intvars": {}, 18.82/5.77 "arithmetic": { 18.82/5.77 "type": "PlainIntegerRelationState", 18.82/5.77 "relations": [] 18.82/5.77 }, 18.82/5.77 "ground": [], 18.82/5.77 "free": [], 18.82/5.77 "exprvars": [] 18.82/5.77 } 18.82/5.77 }, 18.82/5.77 "1690": { 18.82/5.77 "goal": [{ 18.82/5.77 "clause": -1, 18.82/5.77 "scope": -1, 18.82/5.77 "term": "(binaryZ T261)" 18.82/5.77 }], 18.82/5.77 "kb": { 18.82/5.77 "nonunifying": [], 18.82/5.77 "intvars": {}, 18.82/5.77 "arithmetic": { 18.82/5.77 "type": "PlainIntegerRelationState", 18.82/5.77 "relations": [] 18.82/5.77 }, 18.82/5.77 "ground": [], 18.82/5.77 "free": [], 18.82/5.77 "exprvars": [] 18.82/5.77 } 18.82/5.77 }, 18.82/5.77 "104": { 18.82/5.77 "goal": [{ 18.82/5.77 "clause": -1, 18.82/5.77 "scope": -1, 18.82/5.77 "term": "(times T37 T38 X33)" 18.82/5.77 }], 18.82/5.77 "kb": { 18.82/5.77 "nonunifying": [], 18.82/5.77 "intvars": {}, 18.82/5.77 "arithmetic": { 18.82/5.77 "type": "PlainIntegerRelationState", 18.82/5.77 "relations": [] 18.82/5.77 }, 18.82/5.77 "ground": [], 18.82/5.77 "free": ["X33"], 18.82/5.77 "exprvars": [] 18.82/5.77 } 18.82/5.77 }, 18.82/5.77 "1201": { 18.82/5.77 "goal": [], 18.82/5.77 "kb": { 18.82/5.77 "nonunifying": [], 18.82/5.77 "intvars": {}, 18.82/5.77 "arithmetic": { 18.82/5.77 "type": "PlainIntegerRelationState", 18.82/5.77 "relations": [] 18.82/5.77 }, 18.82/5.77 "ground": [], 18.82/5.77 "free": [], 18.82/5.77 "exprvars": [] 18.82/5.77 } 18.82/5.77 }, 18.82/5.77 "2411": { 18.82/5.77 "goal": [{ 18.82/5.77 "clause": 17, 18.82/5.77 "scope": 25, 18.82/5.77 "term": "(addc T613 T614 T612)" 18.82/5.77 }], 18.82/5.77 "kb": { 18.82/5.77 "nonunifying": [], 18.82/5.77 "intvars": {}, 18.82/5.77 "arithmetic": { 18.82/5.77 "type": "PlainIntegerRelationState", 18.82/5.77 "relations": [] 18.82/5.77 }, 18.82/5.77 "ground": ["T612"], 18.82/5.77 "free": [], 18.82/5.77 "exprvars": [] 18.82/5.77 } 18.82/5.77 }, 18.82/5.77 "2410": { 18.82/5.77 "goal": [{ 18.82/5.77 "clause": 16, 18.82/5.77 "scope": 25, 18.82/5.77 "term": "(addc T613 T614 T612)" 18.82/5.77 }], 18.82/5.77 "kb": { 18.82/5.77 "nonunifying": [], 18.82/5.77 "intvars": {}, 18.82/5.77 "arithmetic": { 18.82/5.77 "type": "PlainIntegerRelationState", 18.82/5.77 "relations": [] 18.82/5.77 }, 18.82/5.77 "ground": ["T612"], 18.82/5.77 "free": [], 18.82/5.77 "exprvars": [] 18.82/5.77 } 18.82/5.77 }, 18.82/5.77 "900": { 18.82/5.77 "goal": [ 18.82/5.77 { 18.82/5.77 "clause": 1, 18.82/5.77 "scope": 3, 18.82/5.77 "term": "(add T75 (zero T74) X78)" 18.82/5.77 }, 18.82/5.77 { 18.82/5.77 "clause": 2, 18.82/5.77 "scope": 3, 18.82/5.77 "term": "(add T75 (zero T74) X78)" 18.82/5.77 }, 18.82/5.77 { 18.82/5.77 "clause": 3, 18.82/5.77 "scope": 3, 18.82/5.77 "term": "(add T75 (zero T74) X78)" 18.82/5.77 } 18.82/5.77 ], 18.82/5.77 "kb": { 18.82/5.77 "nonunifying": [], 18.82/5.77 "intvars": {}, 18.82/5.77 "arithmetic": { 18.82/5.77 "type": "PlainIntegerRelationState", 18.82/5.77 "relations": [] 18.82/5.77 }, 18.82/5.77 "ground": [], 18.82/5.77 "free": ["X78"], 18.82/5.77 "exprvars": [] 18.82/5.77 } 18.82/5.77 }, 18.82/5.77 "109": { 18.82/5.77 "goal": [{ 18.82/5.77 "clause": -1, 18.82/5.77 "scope": -1, 18.82/5.77 "term": "(add T42 (zero T41) T36)" 18.82/5.77 }], 18.82/5.77 "kb": { 18.82/5.77 "nonunifying": [], 18.82/5.77 "intvars": {}, 18.82/5.77 "arithmetic": { 18.82/5.77 "type": "PlainIntegerRelationState", 18.82/5.77 "relations": [] 18.82/5.77 }, 18.82/5.77 "ground": ["T36"], 18.82/5.77 "free": [], 18.82/5.77 "exprvars": [] 18.82/5.77 } 18.82/5.77 }, 18.82/5.77 "901": { 18.82/5.77 "goal": [ 18.82/5.77 { 18.82/5.77 "clause": 2, 18.82/5.77 "scope": 3, 18.82/5.77 "term": "(add T75 (zero T74) X78)" 18.82/5.77 }, 18.82/5.77 { 18.82/5.77 "clause": 3, 18.82/5.77 "scope": 3, 18.82/5.77 "term": "(add T75 (zero T74) X78)" 18.82/5.77 } 18.82/5.77 ], 18.82/5.77 "kb": { 18.82/5.77 "nonunifying": [], 18.82/5.77 "intvars": {}, 18.82/5.77 "arithmetic": { 18.82/5.77 "type": "PlainIntegerRelationState", 18.82/5.77 "relations": [] 18.82/5.77 }, 18.82/5.77 "ground": [], 18.82/5.77 "free": ["X78"], 18.82/5.77 "exprvars": [] 18.82/5.77 } 18.82/5.77 }, 18.82/5.77 "902": { 18.82/5.77 "goal": [{ 18.82/5.77 "clause": 2, 18.82/5.77 "scope": 3, 18.82/5.77 "term": "(add T75 (zero T74) X78)" 18.82/5.77 }], 18.82/5.77 "kb": { 18.82/5.77 "nonunifying": [], 18.82/5.77 "intvars": {}, 18.82/5.77 "arithmetic": { 18.82/5.77 "type": "PlainIntegerRelationState", 18.82/5.77 "relations": [] 18.82/5.77 }, 18.82/5.77 "ground": [], 18.82/5.77 "free": ["X78"], 18.82/5.77 "exprvars": [] 18.82/5.77 } 18.82/5.77 }, 18.82/5.77 "903": { 18.82/5.77 "goal": [{ 18.82/5.77 "clause": 3, 18.82/5.77 "scope": 3, 18.82/5.77 "term": "(add T75 (zero T74) X78)" 18.82/5.77 }], 18.82/5.77 "kb": { 18.82/5.77 "nonunifying": [], 18.82/5.77 "intvars": {}, 18.82/5.77 "arithmetic": { 18.82/5.77 "type": "PlainIntegerRelationState", 18.82/5.77 "relations": [] 18.82/5.77 }, 18.82/5.77 "ground": [], 18.82/5.77 "free": ["X78"], 18.82/5.77 "exprvars": [] 18.82/5.77 } 18.82/5.77 }, 18.82/5.77 "2419": { 18.82/5.77 "goal": [], 18.82/5.77 "kb": { 18.82/5.77 "nonunifying": [], 18.82/5.77 "intvars": {}, 18.82/5.77 "arithmetic": { 18.82/5.77 "type": "PlainIntegerRelationState", 18.82/5.77 "relations": [] 18.82/5.77 }, 18.82/5.77 "ground": [], 18.82/5.77 "free": [], 18.82/5.77 "exprvars": [] 18.82/5.77 } 18.82/5.77 }, 18.82/5.77 "2418": { 18.82/5.77 "goal": [{ 18.82/5.77 "clause": -1, 18.82/5.77 "scope": -1, 18.82/5.77 "term": "(succZ T663 T662)" 18.82/5.77 }], 18.82/5.77 "kb": { 18.82/5.77 "nonunifying": [], 18.82/5.77 "intvars": {}, 18.82/5.77 "arithmetic": { 18.82/5.77 "type": "PlainIntegerRelationState", 18.82/5.77 "relations": [] 18.82/5.77 }, 18.82/5.77 "ground": ["T662"], 18.82/5.77 "free": [], 18.82/5.77 "exprvars": [] 18.82/5.77 } 18.82/5.77 } 18.82/5.77 }, 18.82/5.77 "edges": [ 18.82/5.77 { 18.82/5.77 "from": 3, 18.82/5.77 "to": 5, 18.82/5.77 "label": "CASE" 18.82/5.77 }, 18.82/5.77 { 18.82/5.77 "from": 5, 18.82/5.77 "to": 6, 18.82/5.77 "label": "PARALLEL" 18.82/5.77 }, 18.82/5.77 { 18.82/5.77 "from": 5, 18.82/5.77 "to": 7, 18.82/5.77 "label": "PARALLEL" 18.82/5.77 }, 18.82/5.77 { 18.82/5.77 "from": 6, 18.82/5.77 "to": 8, 18.82/5.77 "label": "EVAL with clause\ntimes(one(b), X5, X5).\nand substitutionT1 -> one(b),\nT2 -> T8,\nX5 -> T8,\nT3 -> T8" 18.82/5.77 }, 18.82/5.77 { 18.82/5.77 "from": 6, 18.82/5.77 "to": 9, 18.82/5.77 "label": "EVAL-BACKTRACK" 18.82/5.77 }, 18.82/5.77 { 18.82/5.77 "from": 7, 18.82/5.77 "to": 11, 18.82/5.77 "label": "PARALLEL" 18.82/5.77 }, 18.82/5.77 { 18.82/5.77 "from": 7, 18.82/5.77 "to": 12, 18.82/5.77 "label": "PARALLEL" 18.82/5.77 }, 18.82/5.77 { 18.82/5.77 "from": 8, 18.82/5.77 "to": 10, 18.82/5.77 "label": "SUCCESS" 18.82/5.77 }, 18.82/5.77 { 18.82/5.77 "from": 11, 18.82/5.77 "to": 13, 18.82/5.77 "label": "EVAL with clause\ntimes(zero(X18), X19, zero(X20)) :- times(X18, X19, X20).\nand substitutionX18 -> T24,\nT1 -> zero(T24),\nT2 -> T25,\nX19 -> T25,\nX20 -> T23,\nT3 -> zero(T23),\nT21 -> T24,\nT22 -> T25" 18.82/5.77 }, 18.82/5.77 { 18.82/5.77 "from": 11, 18.82/5.77 "to": 14, 18.82/5.77 "label": "EVAL-BACKTRACK" 18.82/5.77 }, 18.82/5.77 { 18.82/5.77 "from": 12, 18.82/5.77 "to": 42, 18.82/5.77 "label": "EVAL with clause\ntimes(one(X30), X31, X32) :- ','(times(X30, X31, X33), add(X31, zero(X33), X32)).\nand substitutionX30 -> T37,\nT1 -> one(T37),\nT2 -> T38,\nX31 -> T38,\nT3 -> T36,\nX32 -> T36,\nT34 -> T37,\nT35 -> T38" 18.82/5.77 }, 18.82/5.77 { 18.82/5.77 "from": 12, 18.82/5.77 "to": 43, 18.82/5.77 "label": "EVAL-BACKTRACK" 18.82/5.77 }, 18.82/5.77 { 18.82/5.77 "from": 13, 18.82/5.77 "to": 3, 18.82/5.77 "label": "INSTANCE with matching:\nT1 -> T24\nT2 -> T25\nT3 -> T23" 18.82/5.77 }, 18.82/5.77 { 18.82/5.77 "from": 42, 18.82/5.77 "to": 104, 18.82/5.77 "label": "SPLIT 1" 18.82/5.77 }, 18.82/5.77 { 18.82/5.77 "from": 42, 18.82/5.77 "to": 109, 18.82/5.77 "label": "SPLIT 2\nnew knowledge:\nT37 is ground\nreplacements:X33 -> T41,\nT38 -> T42" 18.82/5.77 }, 18.82/5.77 { 18.82/5.77 "from": 104, 18.82/5.77 "to": 127, 18.82/5.77 "label": "CASE" 18.82/5.77 }, 18.82/5.77 { 18.82/5.77 "from": 109, 18.82/5.77 "to": 2152, 18.82/5.77 "label": "CASE" 18.82/5.77 }, 18.82/5.77 { 18.82/5.77 "from": 127, 18.82/5.77 "to": 128, 18.82/5.77 "label": "PARALLEL" 18.82/5.77 }, 18.82/5.77 { 18.82/5.77 "from": 127, 18.82/5.77 "to": 129, 18.82/5.77 "label": "PARALLEL" 18.82/5.77 }, 18.82/5.77 { 18.82/5.78 "from": 128, 18.82/5.78 "to": 748, 18.82/5.78 "label": "EVAL with clause\ntimes(one(b), X42, X42).\nand substitutionT37 -> one(b),\nT38 -> T49,\nX42 -> T49,\nX33 -> T49" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 128, 18.82/5.78 "to": 758, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 129, 18.82/5.78 "to": 836, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 129, 18.82/5.78 "to": 837, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 748, 18.82/5.78 "to": 763, 18.82/5.78 "label": "SUCCESS" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 836, 18.82/5.78 "to": 886, 18.82/5.78 "label": "EVAL with clause\ntimes(zero(X59), X60, zero(X61)) :- times(X59, X60, X61).\nand substitutionX59 -> T60,\nT37 -> zero(T60),\nT38 -> T61,\nX60 -> T61,\nX61 -> X62,\nX33 -> zero(X62),\nT58 -> T60,\nT59 -> T61" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 836, 18.82/5.78 "to": 887, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 837, 18.82/5.78 "to": 888, 18.82/5.78 "label": "EVAL with clause\ntimes(one(X74), X75, X76) :- ','(times(X74, X75, X77), add(X75, zero(X77), X76)).\nand substitutionX74 -> T70,\nT37 -> one(T70),\nT38 -> T71,\nX75 -> T71,\nX33 -> X78,\nX76 -> X78,\nT68 -> T70,\nT69 -> T71" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 837, 18.82/5.78 "to": 889, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 886, 18.82/5.78 "to": 104, 18.82/5.78 "label": "INSTANCE with matching:\nT37 -> T60\nT38 -> T61\nX33 -> X62" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 888, 18.82/5.78 "to": 897, 18.82/5.78 "label": "SPLIT 1" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 888, 18.82/5.78 "to": 898, 18.82/5.78 "label": "SPLIT 2\nnew knowledge:\nT70 is ground\nreplacements:X77 -> T74,\nT71 -> T75" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 897, 18.82/5.78 "to": 104, 18.82/5.78 "label": "INSTANCE with matching:\nT37 -> T70\nT38 -> T71\nX33 -> X77" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 898, 18.82/5.78 "to": 899, 18.82/5.78 "label": "CASE" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 899, 18.82/5.78 "to": 900, 18.82/5.78 "label": "BACKTRACK\nfor clause: add(b, b, b)because of non-unification" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 900, 18.82/5.78 "to": 901, 18.82/5.78 "label": "BACKTRACK\nfor clause: add(X, b, X) :- binaryZ(X)because of non-unification" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 901, 18.82/5.78 "to": 902, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 901, 18.82/5.78 "to": 903, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 902, 18.82/5.78 "to": 917, 18.82/5.78 "label": "EVAL with clause\nadd(b, X88, X88) :- binaryZ(X88).\nand substitutionT75 -> b,\nT74 -> T84,\nX88 -> zero(T84),\nX78 -> zero(T84),\nT83 -> T84" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 902, 18.82/5.78 "to": 927, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 903, 18.82/5.78 "to": 1229, 18.82/5.78 "label": "ONLY EVAL with clause\nadd(X129, X130, X131) :- addz(X129, X130, X131).\nand substitutionT75 -> T129,\nX129 -> T129,\nT74 -> T130,\nX130 -> zero(T130),\nX78 -> X132,\nX131 -> X132,\nT127 -> T129,\nT128 -> T130" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 917, 18.82/5.78 "to": 983, 18.82/5.78 "label": "CASE" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 983, 18.82/5.78 "to": 985, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 983, 18.82/5.78 "to": 986, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 985, 18.82/5.78 "to": 1142, 18.82/5.78 "label": "ONLY EVAL with clause\nbinaryZ(zero(X96)) :- binaryZ(X96).\nand substitutionT84 -> T95,\nX96 -> T95,\nT94 -> T95" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 986, 18.82/5.78 "to": 1201, 18.82/5.78 "label": "BACKTRACK\nfor clause: binaryZ(one(X)) :- binary(X)because of non-unification" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1142, 18.82/5.78 "to": 1144, 18.82/5.78 "label": "CASE" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1144, 18.82/5.78 "to": 1145, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1144, 18.82/5.78 "to": 1146, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1145, 18.82/5.78 "to": 1147, 18.82/5.78 "label": "EVAL with clause\nbinaryZ(zero(X102)) :- binaryZ(X102).\nand substitutionX102 -> T102,\nT95 -> zero(T102),\nT101 -> T102" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1145, 18.82/5.78 "to": 1148, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1146, 18.82/5.78 "to": 1151, 18.82/5.78 "label": "EVAL with clause\nbinaryZ(one(X106)) :- binary(X106).\nand substitutionX106 -> T107,\nT95 -> one(T107),\nT106 -> T107" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1146, 18.82/5.78 "to": 1152, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1147, 18.82/5.78 "to": 1142, 18.82/5.78 "label": "INSTANCE with matching:\nT95 -> T102" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1151, 18.82/5.78 "to": 1153, 18.82/5.78 "label": "CASE" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1153, 18.82/5.78 "to": 1154, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1153, 18.82/5.78 "to": 1155, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1154, 18.82/5.78 "to": 1156, 18.82/5.78 "label": "EVAL with clause\nbinary(b).\nand substitutionT107 -> b" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1154, 18.82/5.78 "to": 1158, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1155, 18.82/5.78 "to": 1161, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1155, 18.82/5.78 "to": 1162, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1156, 18.82/5.78 "to": 1159, 18.82/5.78 "label": "SUCCESS" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1161, 18.82/5.78 "to": 1175, 18.82/5.78 "label": "EVAL with clause\nbinary(zero(X111)) :- binaryZ(X111).\nand substitutionX111 -> T113,\nT107 -> zero(T113),\nT112 -> T113" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1161, 18.82/5.78 "to": 1177, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1162, 18.82/5.78 "to": 1193, 18.82/5.78 "label": "EVAL with clause\nbinary(one(X115)) :- binary(X115).\nand substitutionX115 -> T118,\nT107 -> one(T118),\nT117 -> T118" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1162, 18.82/5.78 "to": 1194, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1175, 18.82/5.78 "to": 1142, 18.82/5.78 "label": "INSTANCE with matching:\nT95 -> T113" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1193, 18.82/5.78 "to": 1151, 18.82/5.78 "label": "INSTANCE with matching:\nT107 -> T118" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1229, 18.82/5.78 "to": 1242, 18.82/5.78 "label": "CASE" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1242, 18.82/5.78 "to": 1250, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1242, 18.82/5.78 "to": 1251, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1250, 18.82/5.78 "to": 1256, 18.82/5.78 "label": "EVAL with clause\naddz(zero(X153), zero(X154), zero(X155)) :- addz(X153, X154, X155).\nand substitutionX153 -> T143,\nT129 -> zero(T143),\nT130 -> T144,\nX154 -> T144,\nX155 -> X156,\nX132 -> zero(X156),\nT141 -> T143,\nT142 -> T144" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1250, 18.82/5.78 "to": 1257, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1251, 18.82/5.78 "to": 2121, 18.82/5.78 "label": "BACKTRACK\nfor clause: addz(zero(X), one(Y), one(Z)) :- addx(X, Y, Z)because of non-unification" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1256, 18.82/5.78 "to": 1260, 18.82/5.78 "label": "CASE" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1260, 18.82/5.78 "to": 1487, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1260, 18.82/5.78 "to": 1488, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1487, 18.82/5.78 "to": 1499, 18.82/5.78 "label": "EVAL with clause\naddz(zero(X177), zero(X178), zero(X179)) :- addz(X177, X178, X179).\nand substitutionX177 -> T157,\nT143 -> zero(T157),\nX178 -> T158,\nT144 -> zero(T158),\nX179 -> X180,\nX156 -> zero(X180),\nT155 -> T157,\nT156 -> T158" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1487, 18.82/5.78 "to": 1501, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1488, 18.82/5.78 "to": 1507, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1488, 18.82/5.78 "to": 1508, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1499, 18.82/5.78 "to": 1256, 18.82/5.78 "label": "INSTANCE with matching:\nT143 -> T157\nT144 -> T158\nX156 -> X180" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1507, 18.82/5.78 "to": 1512, 18.82/5.78 "label": "EVAL with clause\naddz(zero(X201), one(X202), one(X203)) :- addx(X201, X202, X203).\nand substitutionX201 -> T171,\nT143 -> zero(T171),\nX202 -> T172,\nT144 -> one(T172),\nX203 -> X204,\nX156 -> one(X204),\nT169 -> T171,\nT170 -> T172" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1507, 18.82/5.78 "to": 1513, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1508, 18.82/5.78 "to": 1551, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1508, 18.82/5.78 "to": 1552, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1512, 18.82/5.78 "to": 1514, 18.82/5.78 "label": "CASE" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1514, 18.82/5.78 "to": 1515, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1514, 18.82/5.78 "to": 1516, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1515, 18.82/5.78 "to": 1518, 18.82/5.78 "label": "EVAL with clause\naddx(one(X210), b, one(X210)) :- binary(X210).\nand substitutionX210 -> T179,\nT171 -> one(T179),\nT172 -> b,\nX204 -> one(T179),\nT178 -> T179" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1515, 18.82/5.78 "to": 1519, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1516, 18.82/5.78 "to": 1521, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1516, 18.82/5.78 "to": 1522, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1518, 18.82/5.78 "to": 1151, 18.82/5.78 "label": "INSTANCE with matching:\nT107 -> T179" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1521, 18.82/5.78 "to": 1525, 18.82/5.78 "label": "EVAL with clause\naddx(zero(X215), b, zero(X215)) :- binaryZ(X215).\nand substitutionX215 -> T185,\nT171 -> zero(T185),\nT172 -> b,\nX204 -> zero(T185),\nT184 -> T185" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1521, 18.82/5.78 "to": 1526, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1522, 18.82/5.78 "to": 1530, 18.82/5.78 "label": "ONLY EVAL with clause\naddx(X229, X230, X231) :- addz(X229, X230, X231).\nand substitutionT171 -> T197,\nX229 -> T197,\nT172 -> T198,\nX230 -> T198,\nX204 -> X232,\nX231 -> X232,\nT195 -> T197,\nT196 -> T198" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1525, 18.82/5.78 "to": 1142, 18.82/5.78 "label": "INSTANCE with matching:\nT95 -> T185" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1530, 18.82/5.78 "to": 1256, 18.82/5.78 "label": "INSTANCE with matching:\nT143 -> T197\nT144 -> T198\nX156 -> X232" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1551, 18.82/5.78 "to": 1592, 18.82/5.78 "label": "EVAL with clause\naddz(one(X253), zero(X254), one(X255)) :- addy(X253, X254, X255).\nand substitutionX253 -> T211,\nT143 -> one(T211),\nX254 -> T212,\nT144 -> zero(T212),\nX255 -> X256,\nX156 -> one(X256),\nT209 -> T211,\nT210 -> T212" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1551, 18.82/5.78 "to": 1597, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1552, 18.82/5.78 "to": 1650, 18.82/5.78 "label": "EVAL with clause\naddz(one(X297), one(X298), zero(X299)) :- addc(X297, X298, X299).\nand substitutionX297 -> T247,\nT143 -> one(T247),\nX298 -> T248,\nT144 -> one(T248),\nX299 -> X300,\nX156 -> zero(X300),\nT245 -> T247,\nT246 -> T248" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1552, 18.82/5.78 "to": 1651, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1592, 18.82/5.78 "to": 1600, 18.82/5.78 "label": "CASE" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1600, 18.82/5.78 "to": 1601, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1600, 18.82/5.78 "to": 1602, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1601, 18.82/5.78 "to": 1605, 18.82/5.78 "label": "EVAL with clause\naddy(b, one(X262), one(X262)) :- binary(X262).\nand substitutionT211 -> b,\nX262 -> T219,\nT212 -> one(T219),\nX256 -> one(T219),\nT218 -> T219" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1601, 18.82/5.78 "to": 1606, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1602, 18.82/5.78 "to": 1609, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1602, 18.82/5.78 "to": 1610, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1605, 18.82/5.78 "to": 1151, 18.82/5.78 "label": "INSTANCE with matching:\nT107 -> T219" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1609, 18.82/5.78 "to": 1613, 18.82/5.78 "label": "EVAL with clause\naddy(b, zero(X267), zero(X267)) :- binaryZ(X267).\nand substitutionT211 -> b,\nX267 -> T225,\nT212 -> zero(T225),\nX256 -> zero(T225),\nT224 -> T225" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1609, 18.82/5.78 "to": 1614, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1610, 18.82/5.78 "to": 1644, 18.82/5.78 "label": "ONLY EVAL with clause\naddy(X281, X282, X283) :- addz(X281, X282, X283).\nand substitutionT211 -> T237,\nX281 -> T237,\nT212 -> T238,\nX282 -> T238,\nX256 -> X284,\nX283 -> X284,\nT235 -> T237,\nT236 -> T238" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1613, 18.82/5.78 "to": 1142, 18.82/5.78 "label": "INSTANCE with matching:\nT95 -> T225" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1644, 18.82/5.78 "to": 1256, 18.82/5.78 "label": "INSTANCE with matching:\nT143 -> T237\nT144 -> T238\nX156 -> X284" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1650, 18.82/5.78 "to": 1656, 18.82/5.78 "label": "CASE" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1656, 18.82/5.78 "to": 1658, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1656, 18.82/5.78 "to": 1659, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1658, 18.82/5.78 "to": 1660, 18.82/5.78 "label": "EVAL with clause\naddc(b, b, one(b)).\nand substitutionT247 -> b,\nT248 -> b,\nX300 -> one(b)" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1658, 18.82/5.78 "to": 1661, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1659, 18.82/5.78 "to": 1665, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1659, 18.82/5.78 "to": 1666, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1660, 18.82/5.78 "to": 1662, 18.82/5.78 "label": "SUCCESS" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1665, 18.82/5.78 "to": 1677, 18.82/5.78 "label": "EVAL with clause\naddc(X313, b, X314) :- succZ(X313, X314).\nand substitutionT247 -> T254,\nX313 -> T254,\nT248 -> b,\nX300 -> X315,\nX314 -> X315,\nT253 -> T254" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1665, 18.82/5.78 "to": 1678, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1666, 18.82/5.78 "to": 1720, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1666, 18.82/5.78 "to": 1721, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1677, 18.82/5.78 "to": 1679, 18.82/5.78 "label": "CASE" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1679, 18.82/5.78 "to": 1680, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1679, 18.82/5.78 "to": 1681, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1680, 18.82/5.78 "to": 1690, 18.82/5.78 "label": "EVAL with clause\nsuccZ(zero(X321), one(X321)) :- binaryZ(X321).\nand substitutionX321 -> T261,\nT254 -> zero(T261),\nX315 -> one(T261),\nT260 -> T261" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1680, 18.82/5.78 "to": 1691, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1681, 18.82/5.78 "to": 1696, 18.82/5.78 "label": "EVAL with clause\nsuccZ(one(X329), zero(X330)) :- succ(X329, X330).\nand substitutionX329 -> T266,\nT254 -> one(T266),\nX330 -> X331,\nX315 -> zero(X331),\nT265 -> T266" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1681, 18.82/5.78 "to": 1697, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1690, 18.82/5.78 "to": 1142, 18.82/5.78 "label": "INSTANCE with matching:\nT95 -> T261" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1696, 18.82/5.78 "to": 1698, 18.82/5.78 "label": "CASE" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1698, 18.82/5.78 "to": 1699, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1698, 18.82/5.78 "to": 1701, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1699, 18.82/5.78 "to": 1703, 18.82/5.78 "label": "EVAL with clause\nsucc(b, one(b)).\nand substitutionT266 -> b,\nX331 -> one(b)" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1699, 18.82/5.78 "to": 1704, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1701, 18.82/5.78 "to": 1706, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1701, 18.82/5.78 "to": 1707, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1703, 18.82/5.78 "to": 1705, 18.82/5.78 "label": "SUCCESS" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1706, 18.82/5.78 "to": 1710, 18.82/5.78 "label": "EVAL with clause\nsucc(zero(X336), one(X336)) :- binaryZ(X336).\nand substitutionX336 -> T272,\nT266 -> zero(T272),\nX331 -> one(T272),\nT271 -> T272" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1706, 18.82/5.78 "to": 1711, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1707, 18.82/5.78 "to": 1716, 18.82/5.78 "label": "EVAL with clause\nsucc(one(X344), zero(X345)) :- succ(X344, X345).\nand substitutionX344 -> T277,\nT266 -> one(T277),\nX345 -> X346,\nX331 -> zero(X346),\nT276 -> T277" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1707, 18.82/5.78 "to": 1717, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1710, 18.82/5.78 "to": 1142, 18.82/5.78 "label": "INSTANCE with matching:\nT95 -> T272" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1716, 18.82/5.78 "to": 1696, 18.82/5.78 "label": "INSTANCE with matching:\nT266 -> T277\nX331 -> X346" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1720, 18.82/5.78 "to": 1725, 18.82/5.78 "label": "EVAL with clause\naddc(b, X359, X360) :- succZ(X359, X360).\nand substitutionT247 -> b,\nT248 -> T283,\nX359 -> T283,\nX300 -> X361,\nX360 -> X361,\nT282 -> T283" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1720, 18.82/5.78 "to": 1726, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1721, 18.82/5.78 "to": 1733, 18.82/5.78 "label": "ONLY EVAL with clause\naddc(X375, X376, X377) :- addC(X375, X376, X377).\nand substitutionT247 -> T295,\nX375 -> T295,\nT248 -> T296,\nX376 -> T296,\nX300 -> X378,\nX377 -> X378,\nT293 -> T295,\nT294 -> T296" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1725, 18.82/5.78 "to": 1677, 18.82/5.78 "label": "INSTANCE with matching:\nT254 -> T283\nX315 -> X361" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1733, 18.82/5.78 "to": 1735, 18.82/5.78 "label": "CASE" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1735, 18.82/5.78 "to": 1736, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1735, 18.82/5.78 "to": 1737, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1736, 18.82/5.78 "to": 1738, 18.82/5.78 "label": "EVAL with clause\naddC(zero(X399), zero(X400), one(X401)) :- addz(X399, X400, X401).\nand substitutionX399 -> T309,\nT295 -> zero(T309),\nX400 -> T310,\nT296 -> zero(T310),\nX401 -> X402,\nX378 -> one(X402),\nT307 -> T309,\nT308 -> T310" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1736, 18.82/5.78 "to": 1739, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1737, 18.82/5.78 "to": 1740, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1737, 18.82/5.78 "to": 1741, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1738, 18.82/5.78 "to": 1256, 18.82/5.78 "label": "INSTANCE with matching:\nT143 -> T309\nT144 -> T310\nX156 -> X402" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1740, 18.82/5.78 "to": 1742, 18.82/5.78 "label": "EVAL with clause\naddC(zero(X423), one(X424), zero(X425)) :- addX(X423, X424, X425).\nand substitutionX423 -> T323,\nT295 -> zero(T323),\nX424 -> T324,\nT296 -> one(T324),\nX425 -> X426,\nX378 -> zero(X426),\nT321 -> T323,\nT322 -> T324" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1740, 18.82/5.78 "to": 1743, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1741, 18.82/5.78 "to": 2083, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1741, 18.82/5.78 "to": 2084, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1742, 18.82/5.78 "to": 1744, 18.82/5.78 "label": "CASE" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1744, 18.82/5.78 "to": 1745, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1744, 18.82/5.78 "to": 1746, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1745, 18.82/5.78 "to": 1747, 18.82/5.78 "label": "EVAL with clause\naddX(zero(X432), b, one(X432)) :- binaryZ(X432).\nand substitutionX432 -> T331,\nT323 -> zero(T331),\nT324 -> b,\nX426 -> one(T331),\nT330 -> T331" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1745, 18.82/5.78 "to": 1748, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1746, 18.82/5.78 "to": 1749, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1746, 18.82/5.78 "to": 1750, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1747, 18.82/5.78 "to": 1142, 18.82/5.78 "label": "INSTANCE with matching:\nT95 -> T331" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1749, 18.82/5.78 "to": 1751, 18.82/5.78 "label": "EVAL with clause\naddX(one(X446), b, zero(X447)) :- succ(X446, X447).\nand substitutionX446 -> T338,\nT323 -> one(T338),\nT324 -> b,\nX447 -> X448,\nX426 -> zero(X448),\nT337 -> T338" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1749, 18.82/5.78 "to": 1752, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1750, 18.82/5.78 "to": 1931, 18.82/5.78 "label": "ONLY EVAL with clause\naddX(X461, X462, X463) :- addC(X461, X462, X463).\nand substitutionT323 -> T349,\nX461 -> T349,\nT324 -> T350,\nX462 -> T350,\nX426 -> X464,\nX463 -> X464,\nT347 -> T349,\nT348 -> T350" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1751, 18.82/5.78 "to": 1696, 18.82/5.78 "label": "INSTANCE with matching:\nT266 -> T338\nX331 -> X448" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 1931, 18.82/5.78 "to": 1733, 18.82/5.78 "label": "INSTANCE with matching:\nT295 -> T349\nT296 -> T350\nX378 -> X464" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2083, 18.82/5.78 "to": 2089, 18.82/5.78 "label": "EVAL with clause\naddC(one(X485), zero(X486), zero(X487)) :- addY(X485, X486, X487).\nand substitutionX485 -> T363,\nT295 -> one(T363),\nX486 -> T364,\nT296 -> zero(T364),\nX487 -> X488,\nX378 -> zero(X488),\nT361 -> T363,\nT362 -> T364" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2083, 18.82/5.78 "to": 2090, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2084, 18.82/5.78 "to": 2119, 18.82/5.78 "label": "EVAL with clause\naddC(one(X539), one(X540), one(X541)) :- addc(X539, X540, X541).\nand substitutionX539 -> T399,\nT295 -> one(T399),\nX540 -> T400,\nT296 -> one(T400),\nX541 -> X542,\nX378 -> one(X542),\nT397 -> T399,\nT398 -> T400" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2084, 18.82/5.78 "to": 2120, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2089, 18.82/5.78 "to": 2091, 18.82/5.78 "label": "CASE" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2091, 18.82/5.78 "to": 2092, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2091, 18.82/5.78 "to": 2093, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2092, 18.82/5.78 "to": 2094, 18.82/5.78 "label": "EVAL with clause\naddY(b, zero(X494), one(X494)) :- binaryZ(X494).\nand substitutionT363 -> b,\nX494 -> T371,\nT364 -> zero(T371),\nX488 -> one(T371),\nT370 -> T371" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2092, 18.82/5.78 "to": 2095, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2093, 18.82/5.78 "to": 2096, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2093, 18.82/5.78 "to": 2097, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2094, 18.82/5.78 "to": 1142, 18.82/5.78 "label": "INSTANCE with matching:\nT95 -> T371" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2096, 18.82/5.78 "to": 2115, 18.82/5.78 "label": "EVAL with clause\naddY(b, one(X508), zero(X509)) :- succ(X508, X509).\nand substitutionT363 -> b,\nX508 -> T378,\nT364 -> one(T378),\nX509 -> X510,\nX488 -> zero(X510),\nT377 -> T378" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2096, 18.82/5.78 "to": 2116, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2097, 18.82/5.78 "to": 2118, 18.82/5.78 "label": "ONLY EVAL with clause\naddY(X523, X524, X525) :- addC(X523, X524, X525).\nand substitutionT363 -> T389,\nX523 -> T389,\nT364 -> T390,\nX524 -> T390,\nX488 -> X526,\nX525 -> X526,\nT387 -> T389,\nT388 -> T390" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2115, 18.82/5.78 "to": 1696, 18.82/5.78 "label": "INSTANCE with matching:\nT266 -> T378\nX331 -> X510" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2118, 18.82/5.78 "to": 1733, 18.82/5.78 "label": "INSTANCE with matching:\nT295 -> T389\nT296 -> T390\nX378 -> X526" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2119, 18.82/5.78 "to": 1650, 18.82/5.78 "label": "INSTANCE with matching:\nT247 -> T399\nT248 -> T400\nX300 -> X542" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2121, 18.82/5.78 "to": 2140, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2121, 18.82/5.78 "to": 2141, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2140, 18.82/5.78 "to": 2144, 18.82/5.78 "label": "EVAL with clause\naddz(one(X562), zero(X563), one(X564)) :- addy(X562, X563, X564).\nand substitutionX562 -> T412,\nT129 -> one(T412),\nT130 -> T413,\nX563 -> T413,\nX564 -> X565,\nX132 -> one(X565),\nT410 -> T412,\nT411 -> T413" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2140, 18.82/5.78 "to": 2145, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2141, 18.82/5.78 "to": 2149, 18.82/5.78 "label": "BACKTRACK\nfor clause: addz(one(X), one(Y), zero(Z)) :- addc(X, Y, Z)because of non-unification" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2144, 18.82/5.78 "to": 1592, 18.82/5.78 "label": "INSTANCE with matching:\nT211 -> T412\nT212 -> T413\nX256 -> X565" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2152, 18.82/5.78 "to": 2153, 18.82/5.78 "label": "BACKTRACK\nfor clause: add(b, b, b)because of non-unification" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2153, 18.82/5.78 "to": 2154, 18.82/5.78 "label": "BACKTRACK\nfor clause: add(X, b, X) :- binaryZ(X)because of non-unification" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2154, 18.82/5.78 "to": 2157, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2154, 18.82/5.78 "to": 2158, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2157, 18.82/5.78 "to": 2161, 18.82/5.78 "label": "EVAL with clause\nadd(b, X575, X575) :- binaryZ(X575).\nand substitutionT42 -> b,\nT41 -> T421,\nX575 -> zero(T421),\nT36 -> zero(T421)" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2157, 18.82/5.78 "to": 2162, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2158, 18.82/5.78 "to": 2225, 18.82/5.78 "label": "ONLY EVAL with clause\nadd(X613, X614, X615) :- addz(X613, X614, X615).\nand substitutionT42 -> T463,\nX613 -> T463,\nT41 -> T464,\nX614 -> zero(T464),\nT36 -> T462,\nX615 -> T462,\nT460 -> T463,\nT461 -> T464" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2161, 18.82/5.78 "to": 2163, 18.82/5.78 "label": "CASE" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2163, 18.82/5.78 "to": 2173, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2163, 18.82/5.78 "to": 2174, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2173, 18.82/5.78 "to": 2175, 18.82/5.78 "label": "ONLY EVAL with clause\nbinaryZ(zero(X583)) :- binaryZ(X583).\nand substitutionT421 -> T429,\nX583 -> T429" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2174, 18.82/5.78 "to": 2224, 18.82/5.78 "label": "BACKTRACK\nfor clause: binaryZ(one(X)) :- binary(X)because of non-unification" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2175, 18.82/5.78 "to": 2176, 18.82/5.78 "label": "CASE" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2176, 18.82/5.78 "to": 2177, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2176, 18.82/5.78 "to": 2178, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2177, 18.82/5.78 "to": 2180, 18.82/5.78 "label": "EVAL with clause\nbinaryZ(zero(X589)) :- binaryZ(X589).\nand substitutionX589 -> T435,\nT429 -> zero(T435)" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2177, 18.82/5.78 "to": 2181, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2178, 18.82/5.78 "to": 2182, 18.82/5.78 "label": "EVAL with clause\nbinaryZ(one(X593)) :- binary(X593).\nand substitutionX593 -> T439,\nT429 -> one(T439)" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2178, 18.82/5.78 "to": 2183, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2180, 18.82/5.78 "to": 2175, 18.82/5.78 "label": "INSTANCE with matching:\nT429 -> T435" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2182, 18.82/5.78 "to": 2184, 18.82/5.78 "label": "CASE" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2184, 18.82/5.78 "to": 2187, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2184, 18.82/5.78 "to": 2188, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2187, 18.82/5.78 "to": 2189, 18.82/5.78 "label": "EVAL with clause\nbinary(b).\nand substitutionT439 -> b" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2187, 18.82/5.78 "to": 2190, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2188, 18.82/5.78 "to": 2192, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2188, 18.82/5.78 "to": 2193, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2189, 18.82/5.78 "to": 2191, 18.82/5.78 "label": "SUCCESS" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2192, 18.82/5.78 "to": 2194, 18.82/5.78 "label": "EVAL with clause\nbinary(zero(X598)) :- binaryZ(X598).\nand substitutionX598 -> T444,\nT439 -> zero(T444)" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2192, 18.82/5.78 "to": 2195, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2193, 18.82/5.78 "to": 2222, 18.82/5.78 "label": "EVAL with clause\nbinary(one(X602)) :- binary(X602).\nand substitutionX602 -> T448,\nT439 -> one(T448)" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2193, 18.82/5.78 "to": 2223, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2194, 18.82/5.78 "to": 2175, 18.82/5.78 "label": "INSTANCE with matching:\nT429 -> T444" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2222, 18.82/5.78 "to": 2182, 18.82/5.78 "label": "INSTANCE with matching:\nT439 -> T448" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2225, 18.82/5.78 "to": 2226, 18.82/5.78 "label": "CASE" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2226, 18.82/5.78 "to": 2227, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2226, 18.82/5.78 "to": 2228, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2227, 18.82/5.78 "to": 2229, 18.82/5.78 "label": "EVAL with clause\naddz(zero(X631), zero(X632), zero(X633)) :- addz(X631, X632, X633).\nand substitutionX631 -> T483,\nT463 -> zero(T483),\nT464 -> T484,\nX632 -> T484,\nX633 -> T482,\nT462 -> zero(T482),\nT480 -> T483,\nT481 -> T484" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2227, 18.82/5.78 "to": 2230, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2228, 18.82/5.78 "to": 2511, 18.82/5.78 "label": "BACKTRACK\nfor clause: addz(zero(X), one(Y), one(Z)) :- addx(X, Y, Z)because of non-unification" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2229, 18.82/5.78 "to": 2251, 18.82/5.78 "label": "CASE" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2251, 18.82/5.78 "to": 2252, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2251, 18.82/5.78 "to": 2253, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2252, 18.82/5.78 "to": 2254, 18.82/5.78 "label": "EVAL with clause\naddz(zero(X649), zero(X650), zero(X651)) :- addz(X649, X650, X651).\nand substitutionX649 -> T503,\nT483 -> zero(T503),\nX650 -> T504,\nT484 -> zero(T504),\nX651 -> T502,\nT482 -> zero(T502),\nT500 -> T503,\nT501 -> T504" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2252, 18.82/5.78 "to": 2255, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2253, 18.82/5.78 "to": 2256, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2253, 18.82/5.78 "to": 2257, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2254, 18.82/5.78 "to": 2229, 18.82/5.78 "label": "INSTANCE with matching:\nT483 -> T503\nT484 -> T504\nT482 -> T502" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2256, 18.82/5.78 "to": 2271, 18.82/5.78 "label": "EVAL with clause\naddz(zero(X667), one(X668), one(X669)) :- addx(X667, X668, X669).\nand substitutionX667 -> T523,\nT483 -> zero(T523),\nX668 -> T524,\nT484 -> one(T524),\nX669 -> T522,\nT482 -> one(T522),\nT520 -> T523,\nT521 -> T524" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2256, 18.82/5.78 "to": 2272, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2257, 18.82/5.78 "to": 2298, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2257, 18.82/5.78 "to": 2299, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2271, 18.82/5.78 "to": 2276, 18.82/5.78 "label": "CASE" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2276, 18.82/5.78 "to": 2280, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2276, 18.82/5.78 "to": 2281, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2280, 18.82/5.78 "to": 2283, 18.82/5.78 "label": "EVAL with clause\naddx(one(X675), b, one(X675)) :- binary(X675).\nand substitutionX675 -> T530,\nT523 -> one(T530),\nT524 -> b,\nT522 -> one(T530)" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2280, 18.82/5.78 "to": 2284, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2281, 18.82/5.78 "to": 2286, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2281, 18.82/5.78 "to": 2287, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2283, 18.82/5.78 "to": 2182, 18.82/5.78 "label": "INSTANCE with matching:\nT439 -> T530" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2286, 18.82/5.78 "to": 2288, 18.82/5.78 "label": "EVAL with clause\naddx(zero(X680), b, zero(X680)) :- binaryZ(X680).\nand substitutionX680 -> T535,\nT523 -> zero(T535),\nT524 -> b,\nT522 -> zero(T535)" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2286, 18.82/5.78 "to": 2289, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2287, 18.82/5.78 "to": 2297, 18.82/5.78 "label": "ONLY EVAL with clause\naddx(X691, X692, X693) :- addz(X691, X692, X693).\nand substitutionT523 -> T551,\nX691 -> T551,\nT524 -> T552,\nX692 -> T552,\nT522 -> T550,\nX693 -> T550,\nT548 -> T551,\nT549 -> T552" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2288, 18.82/5.78 "to": 2175, 18.82/5.78 "label": "INSTANCE with matching:\nT429 -> T535" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2297, 18.82/5.78 "to": 2229, 18.82/5.78 "label": "INSTANCE with matching:\nT483 -> T551\nT484 -> T552\nT482 -> T550" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2298, 18.82/5.78 "to": 2300, 18.82/5.78 "label": "EVAL with clause\naddz(one(X709), zero(X710), one(X711)) :- addy(X709, X710, X711).\nand substitutionX709 -> T571,\nT483 -> one(T571),\nX710 -> T572,\nT484 -> zero(T572),\nX711 -> T570,\nT482 -> one(T570),\nT568 -> T571,\nT569 -> T572" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2298, 18.82/5.78 "to": 2301, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2299, 18.82/5.78 "to": 2342, 18.82/5.78 "label": "EVAL with clause\naddz(one(X745), one(X746), zero(X747)) :- addc(X745, X746, X747).\nand substitutionX745 -> T613,\nT483 -> one(T613),\nX746 -> T614,\nT484 -> one(T614),\nX747 -> T612,\nT482 -> zero(T612),\nT610 -> T613,\nT611 -> T614" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2299, 18.82/5.78 "to": 2343, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2300, 18.82/5.78 "to": 2302, 18.82/5.78 "label": "CASE" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2302, 18.82/5.78 "to": 2303, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2302, 18.82/5.78 "to": 2304, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2303, 18.82/5.78 "to": 2305, 18.82/5.78 "label": "EVAL with clause\naddy(b, one(X717), one(X717)) :- binary(X717).\nand substitutionT571 -> b,\nX717 -> T578,\nT572 -> one(T578),\nT570 -> one(T578)" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2303, 18.82/5.78 "to": 2306, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2304, 18.82/5.78 "to": 2324, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2304, 18.82/5.78 "to": 2325, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2305, 18.82/5.78 "to": 2182, 18.82/5.78 "label": "INSTANCE with matching:\nT439 -> T578" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2324, 18.82/5.78 "to": 2327, 18.82/5.78 "label": "EVAL with clause\naddy(b, zero(X722), zero(X722)) :- binaryZ(X722).\nand substitutionT571 -> b,\nX722 -> T583,\nT572 -> zero(T583),\nT570 -> zero(T583)" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2324, 18.82/5.78 "to": 2328, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2325, 18.82/5.78 "to": 2333, 18.82/5.78 "label": "ONLY EVAL with clause\naddy(X733, X734, X735) :- addz(X733, X734, X735).\nand substitutionT571 -> T599,\nX733 -> T599,\nT572 -> T600,\nX734 -> T600,\nT570 -> T598,\nX735 -> T598,\nT596 -> T599,\nT597 -> T600" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2327, 18.82/5.78 "to": 2175, 18.82/5.78 "label": "INSTANCE with matching:\nT429 -> T583" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2333, 18.82/5.78 "to": 2229, 18.82/5.78 "label": "INSTANCE with matching:\nT483 -> T599\nT484 -> T600\nT482 -> T598" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2342, 18.82/5.78 "to": 2344, 18.82/5.78 "label": "CASE" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2344, 18.82/5.78 "to": 2345, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2344, 18.82/5.78 "to": 2346, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2345, 18.82/5.78 "to": 2347, 18.82/5.78 "label": "EVAL with clause\naddc(b, b, one(b)).\nand substitutionT613 -> b,\nT614 -> b,\nT612 -> one(b)" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2345, 18.82/5.78 "to": 2348, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2346, 18.82/5.78 "to": 2350, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2346, 18.82/5.78 "to": 2351, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2347, 18.82/5.78 "to": 2349, 18.82/5.78 "label": "SUCCESS" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2350, 18.82/5.78 "to": 2352, 18.82/5.78 "label": "EVAL with clause\naddc(X756, b, X757) :- succZ(X756, X757).\nand substitutionT613 -> T625,\nX756 -> T625,\nT614 -> b,\nT612 -> T624,\nX757 -> T624,\nT623 -> T625" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2350, 18.82/5.78 "to": 2353, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2351, 18.82/5.78 "to": 2410, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2351, 18.82/5.78 "to": 2411, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2352, 18.82/5.78 "to": 2354, 18.82/5.78 "label": "CASE" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2354, 18.82/5.78 "to": 2355, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2354, 18.82/5.78 "to": 2356, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2355, 18.82/5.78 "to": 2359, 18.82/5.78 "label": "EVAL with clause\nsuccZ(zero(X763), one(X763)) :- binaryZ(X763).\nand substitutionX763 -> T631,\nT625 -> zero(T631),\nT624 -> one(T631)" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2355, 18.82/5.78 "to": 2378, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2356, 18.82/5.78 "to": 2393, 18.82/5.78 "label": "EVAL with clause\nsuccZ(one(X769), zero(X770)) :- succ(X769, X770).\nand substitutionX769 -> T639,\nT625 -> one(T639),\nX770 -> T638,\nT624 -> zero(T638),\nT637 -> T639" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2356, 18.82/5.78 "to": 2394, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2359, 18.82/5.78 "to": 2175, 18.82/5.78 "label": "INSTANCE with matching:\nT429 -> T631" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2393, 18.82/5.78 "to": 2395, 18.82/5.78 "label": "CASE" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2395, 18.82/5.78 "to": 2396, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2395, 18.82/5.78 "to": 2397, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2396, 18.82/5.78 "to": 2398, 18.82/5.78 "label": "EVAL with clause\nsucc(b, one(b)).\nand substitutionT639 -> b,\nT638 -> one(b)" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2396, 18.82/5.78 "to": 2399, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2397, 18.82/5.78 "to": 2401, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2397, 18.82/5.78 "to": 2402, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2398, 18.82/5.78 "to": 2400, 18.82/5.78 "label": "SUCCESS" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2401, 18.82/5.78 "to": 2403, 18.82/5.78 "label": "EVAL with clause\nsucc(zero(X775), one(X775)) :- binaryZ(X775).\nand substitutionX775 -> T644,\nT639 -> zero(T644),\nT638 -> one(T644)" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2401, 18.82/5.78 "to": 2404, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2402, 18.82/5.78 "to": 2406, 18.82/5.78 "label": "EVAL with clause\nsucc(one(X781), zero(X782)) :- succ(X781, X782).\nand substitutionX781 -> T652,\nT639 -> one(T652),\nX782 -> T651,\nT638 -> zero(T651),\nT650 -> T652" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2402, 18.82/5.78 "to": 2407, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2403, 18.82/5.78 "to": 2175, 18.82/5.78 "label": "INSTANCE with matching:\nT429 -> T644" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2406, 18.82/5.78 "to": 2393, 18.82/5.78 "label": "INSTANCE with matching:\nT639 -> T652\nT638 -> T651" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2410, 18.82/5.78 "to": 2418, 18.82/5.78 "label": "EVAL with clause\naddc(b, X791, X792) :- succZ(X791, X792).\nand substitutionT613 -> b,\nT614 -> T663,\nX791 -> T663,\nT612 -> T662,\nX792 -> T662,\nT661 -> T663" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2410, 18.82/5.78 "to": 2419, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2411, 18.82/5.78 "to": 2435, 18.82/5.78 "label": "ONLY EVAL with clause\naddc(X803, X804, X805) :- addC(X803, X804, X805).\nand substitutionT613 -> T679,\nX803 -> T679,\nT614 -> T680,\nX804 -> T680,\nT612 -> T678,\nX805 -> T678,\nT676 -> T679,\nT677 -> T680" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2418, 18.82/5.78 "to": 2352, 18.82/5.78 "label": "INSTANCE with matching:\nT625 -> T663\nT624 -> T662" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2435, 18.82/5.78 "to": 2442, 18.82/5.78 "label": "CASE" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2442, 18.82/5.78 "to": 2448, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2442, 18.82/5.78 "to": 2449, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2448, 18.82/5.78 "to": 2452, 18.82/5.78 "label": "EVAL with clause\naddC(zero(X821), zero(X822), one(X823)) :- addz(X821, X822, X823).\nand substitutionX821 -> T699,\nT679 -> zero(T699),\nX822 -> T700,\nT680 -> zero(T700),\nX823 -> T698,\nT678 -> one(T698),\nT696 -> T699,\nT697 -> T700" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2448, 18.82/5.78 "to": 2453, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2449, 18.82/5.78 "to": 2466, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2449, 18.82/5.78 "to": 2467, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2452, 18.82/5.78 "to": 2229, 18.82/5.78 "label": "INSTANCE with matching:\nT483 -> T699\nT484 -> T700\nT482 -> T698" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2466, 18.82/5.78 "to": 2472, 18.82/5.78 "label": "EVAL with clause\naddC(zero(X839), one(X840), zero(X841)) :- addX(X839, X840, X841).\nand substitutionX839 -> T719,\nT679 -> zero(T719),\nX840 -> T720,\nT680 -> one(T720),\nX841 -> T718,\nT678 -> zero(T718),\nT716 -> T719,\nT717 -> T720" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2466, 18.82/5.78 "to": 2473, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2467, 18.82/5.78 "to": 2484, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2467, 18.82/5.78 "to": 2485, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2472, 18.82/5.78 "to": 2474, 18.82/5.78 "label": "CASE" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2474, 18.82/5.78 "to": 2475, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2474, 18.82/5.78 "to": 2476, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2475, 18.82/5.78 "to": 2477, 18.82/5.78 "label": "EVAL with clause\naddX(zero(X847), b, one(X847)) :- binaryZ(X847).\nand substitutionX847 -> T726,\nT719 -> zero(T726),\nT720 -> b,\nT718 -> one(T726)" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2475, 18.82/5.78 "to": 2478, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2476, 18.82/5.78 "to": 2479, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2476, 18.82/5.78 "to": 2480, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2477, 18.82/5.78 "to": 2175, 18.82/5.78 "label": "INSTANCE with matching:\nT429 -> T726" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2479, 18.82/5.78 "to": 2481, 18.82/5.78 "label": "EVAL with clause\naddX(one(X857), b, zero(X858)) :- succ(X857, X858).\nand substitutionX857 -> T738,\nT719 -> one(T738),\nT720 -> b,\nX858 -> T737,\nT718 -> zero(T737),\nT736 -> T738" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2479, 18.82/5.78 "to": 2482, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2480, 18.82/5.78 "to": 2483, 18.82/5.78 "label": "ONLY EVAL with clause\naddX(X868, X869, X870) :- addC(X868, X869, X870).\nand substitutionT719 -> T753,\nX868 -> T753,\nT720 -> T754,\nX869 -> T754,\nT718 -> T752,\nX870 -> T752,\nT750 -> T753,\nT751 -> T754" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2481, 18.82/5.78 "to": 2393, 18.82/5.78 "label": "INSTANCE with matching:\nT639 -> T738\nT638 -> T737" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2483, 18.82/5.78 "to": 2435, 18.82/5.78 "label": "INSTANCE with matching:\nT679 -> T753\nT680 -> T754\nT678 -> T752" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2484, 18.82/5.78 "to": 2486, 18.82/5.78 "label": "EVAL with clause\naddC(one(X886), zero(X887), zero(X888)) :- addY(X886, X887, X888).\nand substitutionX886 -> T773,\nT679 -> one(T773),\nX887 -> T774,\nT680 -> zero(T774),\nX888 -> T772,\nT678 -> zero(T772),\nT770 -> T773,\nT771 -> T774" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2484, 18.82/5.78 "to": 2487, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2485, 18.82/5.78 "to": 2508, 18.82/5.78 "label": "EVAL with clause\naddC(one(X927), one(X928), one(X929)) :- addc(X927, X928, X929).\nand substitutionX927 -> T821,\nT679 -> one(T821),\nX928 -> T822,\nT680 -> one(T822),\nX929 -> T820,\nT678 -> one(T820),\nT818 -> T821,\nT819 -> T822" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2485, 18.82/5.78 "to": 2509, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2486, 18.82/5.78 "to": 2488, 18.82/5.78 "label": "CASE" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2488, 18.82/5.78 "to": 2489, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2488, 18.82/5.78 "to": 2490, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2489, 18.82/5.78 "to": 2491, 18.82/5.78 "label": "EVAL with clause\naddY(b, zero(X894), one(X894)) :- binaryZ(X894).\nand substitutionT773 -> b,\nX894 -> T780,\nT774 -> zero(T780),\nT772 -> one(T780)" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2489, 18.82/5.78 "to": 2492, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2490, 18.82/5.78 "to": 2494, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2490, 18.82/5.78 "to": 2495, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2491, 18.82/5.78 "to": 2175, 18.82/5.78 "label": "INSTANCE with matching:\nT429 -> T780" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2494, 18.82/5.78 "to": 2497, 18.82/5.78 "label": "EVAL with clause\naddY(b, one(X904), zero(X905)) :- succ(X904, X905).\nand substitutionT773 -> b,\nX904 -> T792,\nT774 -> one(T792),\nX905 -> T791,\nT772 -> zero(T791),\nT790 -> T792" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2494, 18.82/5.78 "to": 2498, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2495, 18.82/5.78 "to": 2503, 18.82/5.78 "label": "ONLY EVAL with clause\naddY(X915, X916, X917) :- addC(X915, X916, X917).\nand substitutionT773 -> T807,\nX915 -> T807,\nT774 -> T808,\nX916 -> T808,\nT772 -> T806,\nX917 -> T806,\nT804 -> T807,\nT805 -> T808" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2497, 18.82/5.78 "to": 2393, 18.82/5.78 "label": "INSTANCE with matching:\nT639 -> T792\nT638 -> T791" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2503, 18.82/5.78 "to": 2435, 18.82/5.78 "label": "INSTANCE with matching:\nT679 -> T807\nT680 -> T808\nT678 -> T806" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2508, 18.82/5.78 "to": 2342, 18.82/5.78 "label": "INSTANCE with matching:\nT613 -> T821\nT614 -> T822\nT612 -> T820" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2511, 18.82/5.78 "to": 2516, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2511, 18.82/5.78 "to": 2517, 18.82/5.78 "label": "PARALLEL" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2516, 18.82/5.78 "to": 2540, 18.82/5.78 "label": "EVAL with clause\naddz(one(X945), zero(X946), one(X947)) :- addy(X945, X946, X947).\nand substitutionX945 -> T839,\nT463 -> one(T839),\nT464 -> T840,\nX946 -> T840,\nX947 -> T838,\nT462 -> one(T838),\nT836 -> T839,\nT837 -> T840" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2516, 18.82/5.78 "to": 2541, 18.82/5.78 "label": "EVAL-BACKTRACK" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2517, 18.82/5.78 "to": 2565, 18.82/5.78 "label": "BACKTRACK\nfor clause: addz(one(X), one(Y), zero(Z)) :- addc(X, Y, Z)because of non-unification" 18.82/5.78 }, 18.82/5.78 { 18.82/5.78 "from": 2540, 18.82/5.78 "to": 2300, 18.82/5.78 "label": "INSTANCE with matching:\nT571 -> T839\nT572 -> T840\nT570 -> T838" 18.82/5.78 } 18.82/5.78 ], 18.82/5.78 "type": "Graph" 18.82/5.78 } 18.82/5.78 } 18.82/5.78 18.82/5.78 ---------------------------------------- 18.82/5.78 18.82/5.78 (98) 18.82/5.78 Obligation: 18.82/5.78 Q restricted rewrite system: 18.82/5.78 The TRS R consists of the following rules: 18.82/5.78 18.82/5.78 f3_in(T8) -> f3_out1(one(b), T8) 18.82/5.78 f3_in(zero(T23)) -> U1(f3_in(T23), zero(T23)) 18.82/5.78 U1(f3_out1(T24, T25), zero(T23)) -> f3_out1(zero(T24), T25) 18.82/5.78 f3_in(T36) -> U2(f42_in(T36), T36) 18.82/5.78 U2(f42_out1(T37, T38, X33), T36) -> f3_out1(one(T37), T38) 18.82/5.78 f104_in -> f104_out1(one(b)) 18.82/5.78 f104_in -> U3(f104_in) 18.82/5.78 U3(f104_out1(T60)) -> f104_out1(zero(T60)) 18.82/5.78 f104_in -> U4(f888_in) 18.82/5.78 U4(f888_out1(T70, T71, X77, X78)) -> f104_out1(one(T70)) 18.82/5.78 f1142_in -> U5(f1142_in) 18.82/5.78 U5(f1142_out1(T102)) -> f1142_out1(zero(T102)) 18.82/5.78 f1142_in -> U6(f1151_in) 18.82/5.78 U6(f1151_out1(T107)) -> f1142_out1(one(T107)) 18.82/5.78 f1151_in -> f1151_out1(b) 18.82/5.78 f1151_in -> U7(f1142_in) 18.82/5.78 U7(f1142_out1(T113)) -> f1151_out1(zero(T113)) 18.82/5.78 f1151_in -> U8(f1151_in) 18.82/5.78 U8(f1151_out1(T118)) -> f1151_out1(one(T118)) 18.82/5.78 f1256_in -> U9(f1256_in) 18.82/5.78 U9(f1256_out1(T157, T158, X180)) -> f1256_out1(zero(T157), zero(T158), zero(X180)) 18.82/5.78 f1256_in -> U10(f1151_in) 18.82/5.78 U10(f1151_out1(T179)) -> f1256_out1(zero(one(T179)), one(b), one(one(T179))) 18.82/5.78 f1256_in -> U11(f1142_in) 18.82/5.78 U11(f1142_out1(T185)) -> f1256_out1(zero(zero(T185)), one(b), one(zero(T185))) 18.82/5.78 f1256_in -> U12(f1256_in) 18.82/5.78 U12(f1256_out1(T197, T198, X232)) -> f1256_out1(zero(T197), one(T198), one(X232)) 18.82/5.78 f1256_in -> U13(f1592_in) 18.82/5.78 U13(f1592_out1(T211, T212, X256)) -> f1256_out1(one(T211), zero(T212), one(X256)) 18.82/5.78 f1256_in -> U14(f1650_in) 18.82/5.78 U14(f1650_out1(T247, T248, X300)) -> f1256_out1(one(T247), one(T248), zero(X300)) 18.82/5.78 f1696_in -> f1696_out1(b, one(b)) 18.82/5.78 f1696_in -> U15(f1142_in) 18.82/5.78 U15(f1142_out1(T272)) -> f1696_out1(zero(T272), one(T272)) 18.82/5.78 f1696_in -> U16(f1696_in) 18.82/5.78 U16(f1696_out1(T277, X346)) -> f1696_out1(one(T277), zero(X346)) 18.82/5.78 f1677_in -> U17(f1142_in) 18.82/5.78 U17(f1142_out1(T261)) -> f1677_out1(zero(T261), one(T261)) 18.82/5.78 f1677_in -> U18(f1696_in) 18.82/5.78 U18(f1696_out1(T266, X331)) -> f1677_out1(one(T266), zero(X331)) 18.82/5.78 f1733_in -> U19(f1256_in) 18.82/5.78 U19(f1256_out1(T309, T310, X402)) -> f1733_out1(zero(T309), zero(T310), one(X402)) 18.82/5.78 f1733_in -> U20(f1142_in) 18.82/5.78 U20(f1142_out1(T331)) -> f1733_out1(zero(zero(T331)), one(b), zero(one(T331))) 18.82/5.78 f1733_in -> U21(f1696_in) 18.82/5.78 U21(f1696_out1(T338, X448)) -> f1733_out1(zero(one(T338)), one(b), zero(zero(X448))) 18.82/5.78 f1733_in -> U22(f1733_in) 18.82/5.78 U22(f1733_out1(T349, T350, X464)) -> f1733_out1(zero(T349), one(T350), zero(X464)) 18.82/5.78 f1733_in -> U23(f1142_in) 18.82/5.78 U23(f1142_out1(T371)) -> f1733_out1(one(b), zero(zero(T371)), zero(one(T371))) 18.82/5.78 f1733_in -> U24(f1696_in) 18.82/5.78 U24(f1696_out1(T378, X510)) -> f1733_out1(one(b), zero(one(T378)), zero(zero(X510))) 18.82/5.78 f1733_in -> U25(f1733_in) 18.82/5.78 U25(f1733_out1(T389, T390, X526)) -> f1733_out1(one(T389), zero(T390), zero(X526)) 18.82/5.78 f1733_in -> U26(f1650_in) 18.82/5.78 U26(f1650_out1(T399, T400, X542)) -> f1733_out1(one(T399), one(T400), one(X542)) 18.82/5.78 f1650_in -> f1650_out1(b, b, one(b)) 18.82/5.78 f1650_in -> U27(f1677_in) 18.82/5.78 U27(f1677_out1(T254, X315)) -> f1650_out1(T254, b, X315) 18.82/5.78 f1650_in -> U28(f1677_in) 18.82/5.78 U28(f1677_out1(T283, X361)) -> f1650_out1(b, T283, X361) 18.82/5.78 f1650_in -> U29(f1733_in) 18.82/5.78 U29(f1733_out1(T295, T296, X378)) -> f1650_out1(T295, T296, X378) 18.82/5.78 f1592_in -> U30(f1151_in) 18.82/5.78 U30(f1151_out1(T219)) -> f1592_out1(b, one(T219), one(T219)) 18.82/5.78 f1592_in -> U31(f1142_in) 18.82/5.78 U31(f1142_out1(T225)) -> f1592_out1(b, zero(T225), zero(T225)) 18.82/5.78 f1592_in -> U32(f1256_in) 18.82/5.78 U32(f1256_out1(T237, T238, X284)) -> f1592_out1(T237, T238, X284) 18.82/5.78 f2175_in(zero(T435)) -> U33(f2175_in(T435), zero(T435)) 18.82/5.78 U33(f2175_out1, zero(T435)) -> f2175_out1 18.82/5.78 f2175_in(one(T439)) -> U34(f2182_in(T439), one(T439)) 18.82/5.78 U34(f2182_out1, one(T439)) -> f2175_out1 18.82/5.78 f2182_in(b) -> f2182_out1 18.82/5.78 f2182_in(zero(T444)) -> U35(f2175_in(T444), zero(T444)) 18.82/5.78 U35(f2175_out1, zero(T444)) -> f2182_out1 18.82/5.78 f2182_in(one(T448)) -> U36(f2182_in(T448), one(T448)) 18.82/5.78 U36(f2182_out1, one(T448)) -> f2182_out1 18.82/5.78 f2229_in(zero(T502)) -> U37(f2229_in(T502), zero(T502)) 18.82/5.78 U37(f2229_out1(T503, T504), zero(T502)) -> f2229_out1(zero(T503), zero(T504)) 18.82/5.78 f2229_in(one(one(T530))) -> U38(f2182_in(T530), one(one(T530))) 18.82/5.78 U38(f2182_out1, one(one(T530))) -> f2229_out1(zero(one(T530)), one(b)) 18.82/5.78 f2229_in(one(zero(T535))) -> U39(f2175_in(T535), one(zero(T535))) 18.82/5.78 U39(f2175_out1, one(zero(T535))) -> f2229_out1(zero(zero(T535)), one(b)) 18.82/5.78 f2229_in(one(T550)) -> U40(f2229_in(T550), one(T550)) 18.82/5.78 U40(f2229_out1(T551, T552), one(T550)) -> f2229_out1(zero(T551), one(T552)) 18.82/5.78 f2229_in(one(T570)) -> U41(f2300_in(T570), one(T570)) 18.82/5.78 U41(f2300_out1(T571, T572), one(T570)) -> f2229_out1(one(T571), zero(T572)) 18.82/5.78 f2229_in(zero(T612)) -> U42(f2342_in(T612), zero(T612)) 18.82/5.78 U42(f2342_out1(T613, T614), zero(T612)) -> f2229_out1(one(T613), one(T614)) 18.82/5.78 f2393_in(one(b)) -> f2393_out1(b) 18.82/5.78 f2393_in(one(T644)) -> U43(f2175_in(T644), one(T644)) 18.82/5.78 U43(f2175_out1, one(T644)) -> f2393_out1(zero(T644)) 18.82/5.78 f2393_in(zero(T651)) -> U44(f2393_in(T651), zero(T651)) 18.82/5.78 U44(f2393_out1(T652), zero(T651)) -> f2393_out1(one(T652)) 18.82/5.78 f2352_in(one(T631)) -> U45(f2175_in(T631), one(T631)) 18.82/5.78 U45(f2175_out1, one(T631)) -> f2352_out1(zero(T631)) 18.82/5.78 f2352_in(zero(T638)) -> U46(f2393_in(T638), zero(T638)) 18.82/5.78 U46(f2393_out1(T639), zero(T638)) -> f2352_out1(one(T639)) 18.82/5.78 f2435_in(one(T698)) -> U47(f2229_in(T698), one(T698)) 18.82/5.78 U47(f2229_out1(T699, T700), one(T698)) -> f2435_out1(zero(T699), zero(T700)) 18.82/5.78 f2435_in(zero(one(T726))) -> U48(f2175_in(T726), zero(one(T726))) 18.82/5.78 U48(f2175_out1, zero(one(T726))) -> f2435_out1(zero(zero(T726)), one(b)) 18.82/5.78 f2435_in(zero(zero(T737))) -> U49(f2393_in(T737), zero(zero(T737))) 18.82/5.78 U49(f2393_out1(T738), zero(zero(T737))) -> f2435_out1(zero(one(T738)), one(b)) 18.82/5.78 f2435_in(zero(T752)) -> U50(f2435_in(T752), zero(T752)) 18.82/5.78 U50(f2435_out1(T753, T754), zero(T752)) -> f2435_out1(zero(T753), one(T754)) 18.82/5.78 f2435_in(zero(one(T780))) -> U51(f2175_in(T780), zero(one(T780))) 18.82/5.78 U51(f2175_out1, zero(one(T780))) -> f2435_out1(one(b), zero(zero(T780))) 18.82/5.78 f2435_in(zero(zero(T791))) -> U52(f2393_in(T791), zero(zero(T791))) 18.82/5.78 U52(f2393_out1(T792), zero(zero(T791))) -> f2435_out1(one(b), zero(one(T792))) 18.82/5.78 f2435_in(zero(T806)) -> U53(f2435_in(T806), zero(T806)) 18.82/5.78 U53(f2435_out1(T807, T808), zero(T806)) -> f2435_out1(one(T807), zero(T808)) 18.82/5.78 f2435_in(one(T820)) -> U54(f2342_in(T820), one(T820)) 18.82/5.78 U54(f2342_out1(T821, T822), one(T820)) -> f2435_out1(one(T821), one(T822)) 18.82/5.78 f2342_in(one(b)) -> f2342_out1(b, b) 18.82/5.78 f2342_in(T624) -> U55(f2352_in(T624), T624) 18.82/5.78 U55(f2352_out1(T625), T624) -> f2342_out1(T625, b) 18.82/5.78 f2342_in(T662) -> U56(f2352_in(T662), T662) 18.82/5.78 U56(f2352_out1(T663), T662) -> f2342_out1(b, T663) 18.82/5.78 f2342_in(T678) -> U57(f2435_in(T678), T678) 18.82/5.78 U57(f2435_out1(T679, T680), T678) -> f2342_out1(T679, T680) 18.82/5.78 f2300_in(one(T578)) -> U58(f2182_in(T578), one(T578)) 18.82/5.78 U58(f2182_out1, one(T578)) -> f2300_out1(b, one(T578)) 18.82/5.78 f2300_in(zero(T583)) -> U59(f2175_in(T583), zero(T583)) 18.82/5.78 U59(f2175_out1, zero(T583)) -> f2300_out1(b, zero(T583)) 18.82/5.78 f2300_in(T598) -> U60(f2229_in(T598), T598) 18.82/5.78 U60(f2229_out1(T599, T600), T598) -> f2300_out1(T599, T600) 18.82/5.78 f109_in(zero(T429)) -> U61(f2175_in(T429), zero(T429)) 18.82/5.78 U61(f2175_out1, zero(T429)) -> f109_out1(b, T429) 18.82/5.78 f109_in(zero(T482)) -> U62(f2229_in(T482), zero(T482)) 18.82/5.78 U62(f2229_out1(T483, T484), zero(T482)) -> f109_out1(zero(T483), T484) 18.82/5.78 f109_in(one(T838)) -> U63(f2300_in(T838), one(T838)) 18.82/5.78 U63(f2300_out1(T839, T840), one(T838)) -> f109_out1(one(T839), T840) 18.82/5.78 f898_in -> U64(f1142_in) 18.82/5.78 U64(f1142_out1(T95)) -> f898_out1(b, T95, zero(T95)) 18.82/5.78 f898_in -> U65(f1256_in) 18.82/5.78 U65(f1256_out1(T143, T144, X156)) -> f898_out1(zero(T143), T144, zero(X156)) 18.82/5.78 f898_in -> U66(f1592_in) 18.82/5.78 U66(f1592_out1(T412, T413, X565)) -> f898_out1(one(T412), T413, one(X565)) 18.82/5.78 f42_in(T36) -> U67(f104_in, T36) 18.82/5.78 U67(f104_out1(T37), T36) -> U68(f109_in(T36), T36, T37) 18.82/5.78 U68(f109_out1(T42, T41), T36, T37) -> f42_out1(T37, T42, T41) 18.82/5.78 f888_in -> U69(f104_in) 18.82/5.78 U69(f104_out1(T70)) -> U70(f898_in, T70) 18.82/5.78 U70(f898_out1(T75, T74, X78), T70) -> f888_out1(T70, T75, T74, X78) 18.82/5.78 18.82/5.78 Q is empty. 18.82/5.78 18.82/5.78 ---------------------------------------- 18.82/5.78 18.82/5.78 (99) DependencyPairsProof (EQUIVALENT) 18.82/5.78 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 18.82/5.78 ---------------------------------------- 18.82/5.78 18.82/5.78 (100) 18.82/5.78 Obligation: 18.82/5.78 Q DP problem: 18.82/5.78 The TRS P consists of the following rules: 18.82/5.78 18.82/5.78 F3_IN(zero(T23)) -> U1^1(f3_in(T23), zero(T23)) 18.82/5.78 F3_IN(zero(T23)) -> F3_IN(T23) 18.82/5.78 F3_IN(T36) -> U2^1(f42_in(T36), T36) 18.82/5.78 F3_IN(T36) -> F42_IN(T36) 18.82/5.78 F104_IN -> U3^1(f104_in) 18.82/5.78 F104_IN -> F104_IN 18.82/5.78 F104_IN -> U4^1(f888_in) 18.82/5.78 F104_IN -> F888_IN 18.82/5.78 F1142_IN -> U5^1(f1142_in) 18.82/5.78 F1142_IN -> F1142_IN 18.82/5.78 F1142_IN -> U6^1(f1151_in) 18.82/5.78 F1142_IN -> F1151_IN 18.82/5.78 F1151_IN -> U7^1(f1142_in) 18.82/5.78 F1151_IN -> F1142_IN 18.82/5.78 F1151_IN -> U8^1(f1151_in) 18.82/5.78 F1151_IN -> F1151_IN 18.82/5.78 F1256_IN -> U9^1(f1256_in) 18.82/5.78 F1256_IN -> F1256_IN 18.82/5.78 F1256_IN -> U10^1(f1151_in) 18.82/5.78 F1256_IN -> F1151_IN 18.82/5.78 F1256_IN -> U11^1(f1142_in) 18.82/5.78 F1256_IN -> F1142_IN 18.82/5.78 F1256_IN -> U12^1(f1256_in) 18.82/5.78 F1256_IN -> U13^1(f1592_in) 18.82/5.78 F1256_IN -> F1592_IN 18.82/5.78 F1256_IN -> U14^1(f1650_in) 18.82/5.78 F1256_IN -> F1650_IN 18.82/5.78 F1696_IN -> U15^1(f1142_in) 18.82/5.78 F1696_IN -> F1142_IN 18.82/5.78 F1696_IN -> U16^1(f1696_in) 18.82/5.78 F1696_IN -> F1696_IN 18.82/5.78 F1677_IN -> U17^1(f1142_in) 18.82/5.78 F1677_IN -> F1142_IN 18.82/5.78 F1677_IN -> U18^1(f1696_in) 18.82/5.78 F1677_IN -> F1696_IN 18.82/5.78 F1733_IN -> U19^1(f1256_in) 18.82/5.78 F1733_IN -> F1256_IN 18.82/5.78 F1733_IN -> U20^1(f1142_in) 18.82/5.78 F1733_IN -> F1142_IN 18.82/5.78 F1733_IN -> U21^1(f1696_in) 18.82/5.78 F1733_IN -> F1696_IN 18.82/5.78 F1733_IN -> U22^1(f1733_in) 18.82/5.78 F1733_IN -> F1733_IN 18.82/5.78 F1733_IN -> U23^1(f1142_in) 18.82/5.78 F1733_IN -> U24^1(f1696_in) 18.82/5.78 F1733_IN -> U25^1(f1733_in) 18.82/5.78 F1733_IN -> U26^1(f1650_in) 18.82/5.78 F1733_IN -> F1650_IN 18.82/5.78 F1650_IN -> U27^1(f1677_in) 18.82/5.78 F1650_IN -> F1677_IN 18.82/5.78 F1650_IN -> U28^1(f1677_in) 18.82/5.78 F1650_IN -> U29^1(f1733_in) 18.82/5.78 F1650_IN -> F1733_IN 18.82/5.78 F1592_IN -> U30^1(f1151_in) 18.82/5.78 F1592_IN -> F1151_IN 18.82/5.78 F1592_IN -> U31^1(f1142_in) 18.82/5.78 F1592_IN -> F1142_IN 18.82/5.78 F1592_IN -> U32^1(f1256_in) 18.82/5.78 F1592_IN -> F1256_IN 18.82/5.78 F2175_IN(zero(T435)) -> U33^1(f2175_in(T435), zero(T435)) 18.82/5.78 F2175_IN(zero(T435)) -> F2175_IN(T435) 18.82/5.78 F2175_IN(one(T439)) -> U34^1(f2182_in(T439), one(T439)) 18.82/5.78 F2175_IN(one(T439)) -> F2182_IN(T439) 18.82/5.78 F2182_IN(zero(T444)) -> U35^1(f2175_in(T444), zero(T444)) 18.82/5.78 F2182_IN(zero(T444)) -> F2175_IN(T444) 18.82/5.78 F2182_IN(one(T448)) -> U36^1(f2182_in(T448), one(T448)) 18.82/5.78 F2182_IN(one(T448)) -> F2182_IN(T448) 18.82/5.78 F2229_IN(zero(T502)) -> U37^1(f2229_in(T502), zero(T502)) 18.82/5.78 F2229_IN(zero(T502)) -> F2229_IN(T502) 18.82/5.78 F2229_IN(one(one(T530))) -> U38^1(f2182_in(T530), one(one(T530))) 18.82/5.78 F2229_IN(one(one(T530))) -> F2182_IN(T530) 18.82/5.78 F2229_IN(one(zero(T535))) -> U39^1(f2175_in(T535), one(zero(T535))) 18.82/5.78 F2229_IN(one(zero(T535))) -> F2175_IN(T535) 18.82/5.78 F2229_IN(one(T550)) -> U40^1(f2229_in(T550), one(T550)) 18.82/5.78 F2229_IN(one(T550)) -> F2229_IN(T550) 18.82/5.78 F2229_IN(one(T570)) -> U41^1(f2300_in(T570), one(T570)) 18.82/5.78 F2229_IN(one(T570)) -> F2300_IN(T570) 18.82/5.78 F2229_IN(zero(T612)) -> U42^1(f2342_in(T612), zero(T612)) 18.82/5.78 F2229_IN(zero(T612)) -> F2342_IN(T612) 18.82/5.78 F2393_IN(one(T644)) -> U43^1(f2175_in(T644), one(T644)) 18.82/5.78 F2393_IN(one(T644)) -> F2175_IN(T644) 18.82/5.78 F2393_IN(zero(T651)) -> U44^1(f2393_in(T651), zero(T651)) 18.82/5.78 F2393_IN(zero(T651)) -> F2393_IN(T651) 18.82/5.78 F2352_IN(one(T631)) -> U45^1(f2175_in(T631), one(T631)) 18.82/5.78 F2352_IN(one(T631)) -> F2175_IN(T631) 18.82/5.78 F2352_IN(zero(T638)) -> U46^1(f2393_in(T638), zero(T638)) 18.82/5.78 F2352_IN(zero(T638)) -> F2393_IN(T638) 18.82/5.78 F2435_IN(one(T698)) -> U47^1(f2229_in(T698), one(T698)) 18.82/5.78 F2435_IN(one(T698)) -> F2229_IN(T698) 18.82/5.78 F2435_IN(zero(one(T726))) -> U48^1(f2175_in(T726), zero(one(T726))) 18.82/5.78 F2435_IN(zero(one(T726))) -> F2175_IN(T726) 18.82/5.78 F2435_IN(zero(zero(T737))) -> U49^1(f2393_in(T737), zero(zero(T737))) 18.82/5.78 F2435_IN(zero(zero(T737))) -> F2393_IN(T737) 18.82/5.78 F2435_IN(zero(T752)) -> U50^1(f2435_in(T752), zero(T752)) 18.82/5.78 F2435_IN(zero(T752)) -> F2435_IN(T752) 18.82/5.78 F2435_IN(zero(one(T780))) -> U51^1(f2175_in(T780), zero(one(T780))) 18.82/5.78 F2435_IN(zero(zero(T791))) -> U52^1(f2393_in(T791), zero(zero(T791))) 18.82/5.78 F2435_IN(zero(T806)) -> U53^1(f2435_in(T806), zero(T806)) 18.82/5.78 F2435_IN(one(T820)) -> U54^1(f2342_in(T820), one(T820)) 18.82/5.78 F2435_IN(one(T820)) -> F2342_IN(T820) 18.82/5.78 F2342_IN(T624) -> U55^1(f2352_in(T624), T624) 18.82/5.78 F2342_IN(T624) -> F2352_IN(T624) 18.82/5.78 F2342_IN(T662) -> U56^1(f2352_in(T662), T662) 18.82/5.78 F2342_IN(T678) -> U57^1(f2435_in(T678), T678) 18.82/5.78 F2342_IN(T678) -> F2435_IN(T678) 18.82/5.78 F2300_IN(one(T578)) -> U58^1(f2182_in(T578), one(T578)) 18.82/5.78 F2300_IN(one(T578)) -> F2182_IN(T578) 18.82/5.78 F2300_IN(zero(T583)) -> U59^1(f2175_in(T583), zero(T583)) 18.82/5.78 F2300_IN(zero(T583)) -> F2175_IN(T583) 18.82/5.78 F2300_IN(T598) -> U60^1(f2229_in(T598), T598) 18.82/5.78 F2300_IN(T598) -> F2229_IN(T598) 18.82/5.78 F109_IN(zero(T429)) -> U61^1(f2175_in(T429), zero(T429)) 18.82/5.78 F109_IN(zero(T429)) -> F2175_IN(T429) 18.82/5.78 F109_IN(zero(T482)) -> U62^1(f2229_in(T482), zero(T482)) 18.82/5.78 F109_IN(zero(T482)) -> F2229_IN(T482) 18.82/5.79 F109_IN(one(T838)) -> U63^1(f2300_in(T838), one(T838)) 18.82/5.79 F109_IN(one(T838)) -> F2300_IN(T838) 18.82/5.79 F898_IN -> U64^1(f1142_in) 18.82/5.79 F898_IN -> F1142_IN 18.82/5.79 F898_IN -> U65^1(f1256_in) 18.82/5.79 F898_IN -> F1256_IN 18.82/5.79 F898_IN -> U66^1(f1592_in) 18.82/5.79 F898_IN -> F1592_IN 18.82/5.79 F42_IN(T36) -> U67^1(f104_in, T36) 18.82/5.79 F42_IN(T36) -> F104_IN 18.82/5.79 U67^1(f104_out1(T37), T36) -> U68^1(f109_in(T36), T36, T37) 18.82/5.79 U67^1(f104_out1(T37), T36) -> F109_IN(T36) 18.82/5.79 F888_IN -> U69^1(f104_in) 18.82/5.79 F888_IN -> F104_IN 18.82/5.79 U69^1(f104_out1(T70)) -> U70^1(f898_in, T70) 18.82/5.79 U69^1(f104_out1(T70)) -> F898_IN 18.82/5.79 18.82/5.79 The TRS R consists of the following rules: 18.82/5.79 18.82/5.79 f3_in(T8) -> f3_out1(one(b), T8) 18.82/5.79 f3_in(zero(T23)) -> U1(f3_in(T23), zero(T23)) 18.82/5.79 U1(f3_out1(T24, T25), zero(T23)) -> f3_out1(zero(T24), T25) 18.82/5.79 f3_in(T36) -> U2(f42_in(T36), T36) 18.82/5.79 U2(f42_out1(T37, T38, X33), T36) -> f3_out1(one(T37), T38) 18.82/5.79 f104_in -> f104_out1(one(b)) 18.82/5.79 f104_in -> U3(f104_in) 18.82/5.79 U3(f104_out1(T60)) -> f104_out1(zero(T60)) 18.82/5.79 f104_in -> U4(f888_in) 18.82/5.79 U4(f888_out1(T70, T71, X77, X78)) -> f104_out1(one(T70)) 18.82/5.79 f1142_in -> U5(f1142_in) 18.82/5.79 U5(f1142_out1(T102)) -> f1142_out1(zero(T102)) 18.82/5.79 f1142_in -> U6(f1151_in) 18.82/5.79 U6(f1151_out1(T107)) -> f1142_out1(one(T107)) 18.82/5.79 f1151_in -> f1151_out1(b) 18.82/5.79 f1151_in -> U7(f1142_in) 18.82/5.79 U7(f1142_out1(T113)) -> f1151_out1(zero(T113)) 18.82/5.79 f1151_in -> U8(f1151_in) 18.82/5.79 U8(f1151_out1(T118)) -> f1151_out1(one(T118)) 18.82/5.79 f1256_in -> U9(f1256_in) 18.82/5.79 U9(f1256_out1(T157, T158, X180)) -> f1256_out1(zero(T157), zero(T158), zero(X180)) 18.82/5.79 f1256_in -> U10(f1151_in) 18.82/5.79 U10(f1151_out1(T179)) -> f1256_out1(zero(one(T179)), one(b), one(one(T179))) 18.82/5.79 f1256_in -> U11(f1142_in) 18.82/5.79 U11(f1142_out1(T185)) -> f1256_out1(zero(zero(T185)), one(b), one(zero(T185))) 18.82/5.79 f1256_in -> U12(f1256_in) 18.82/5.79 U12(f1256_out1(T197, T198, X232)) -> f1256_out1(zero(T197), one(T198), one(X232)) 18.82/5.79 f1256_in -> U13(f1592_in) 18.82/5.79 U13(f1592_out1(T211, T212, X256)) -> f1256_out1(one(T211), zero(T212), one(X256)) 18.82/5.79 f1256_in -> U14(f1650_in) 18.82/5.79 U14(f1650_out1(T247, T248, X300)) -> f1256_out1(one(T247), one(T248), zero(X300)) 18.82/5.79 f1696_in -> f1696_out1(b, one(b)) 18.82/5.79 f1696_in -> U15(f1142_in) 18.82/5.79 U15(f1142_out1(T272)) -> f1696_out1(zero(T272), one(T272)) 18.82/5.79 f1696_in -> U16(f1696_in) 18.82/5.79 U16(f1696_out1(T277, X346)) -> f1696_out1(one(T277), zero(X346)) 18.82/5.79 f1677_in -> U17(f1142_in) 18.82/5.79 U17(f1142_out1(T261)) -> f1677_out1(zero(T261), one(T261)) 18.82/5.79 f1677_in -> U18(f1696_in) 18.82/5.79 U18(f1696_out1(T266, X331)) -> f1677_out1(one(T266), zero(X331)) 18.82/5.79 f1733_in -> U19(f1256_in) 18.82/5.79 U19(f1256_out1(T309, T310, X402)) -> f1733_out1(zero(T309), zero(T310), one(X402)) 18.82/5.79 f1733_in -> U20(f1142_in) 18.82/5.79 U20(f1142_out1(T331)) -> f1733_out1(zero(zero(T331)), one(b), zero(one(T331))) 18.82/5.79 f1733_in -> U21(f1696_in) 18.82/5.79 U21(f1696_out1(T338, X448)) -> f1733_out1(zero(one(T338)), one(b), zero(zero(X448))) 18.82/5.79 f1733_in -> U22(f1733_in) 18.82/5.79 U22(f1733_out1(T349, T350, X464)) -> f1733_out1(zero(T349), one(T350), zero(X464)) 18.82/5.79 f1733_in -> U23(f1142_in) 18.82/5.79 U23(f1142_out1(T371)) -> f1733_out1(one(b), zero(zero(T371)), zero(one(T371))) 18.82/5.79 f1733_in -> U24(f1696_in) 18.82/5.79 U24(f1696_out1(T378, X510)) -> f1733_out1(one(b), zero(one(T378)), zero(zero(X510))) 18.82/5.79 f1733_in -> U25(f1733_in) 18.82/5.79 U25(f1733_out1(T389, T390, X526)) -> f1733_out1(one(T389), zero(T390), zero(X526)) 18.82/5.79 f1733_in -> U26(f1650_in) 18.82/5.79 U26(f1650_out1(T399, T400, X542)) -> f1733_out1(one(T399), one(T400), one(X542)) 18.82/5.79 f1650_in -> f1650_out1(b, b, one(b)) 18.82/5.79 f1650_in -> U27(f1677_in) 18.82/5.79 U27(f1677_out1(T254, X315)) -> f1650_out1(T254, b, X315) 18.82/5.79 f1650_in -> U28(f1677_in) 18.82/5.79 U28(f1677_out1(T283, X361)) -> f1650_out1(b, T283, X361) 18.82/5.79 f1650_in -> U29(f1733_in) 18.82/5.79 U29(f1733_out1(T295, T296, X378)) -> f1650_out1(T295, T296, X378) 18.82/5.79 f1592_in -> U30(f1151_in) 18.82/5.79 U30(f1151_out1(T219)) -> f1592_out1(b, one(T219), one(T219)) 18.82/5.79 f1592_in -> U31(f1142_in) 18.82/5.79 U31(f1142_out1(T225)) -> f1592_out1(b, zero(T225), zero(T225)) 18.82/5.79 f1592_in -> U32(f1256_in) 18.82/5.79 U32(f1256_out1(T237, T238, X284)) -> f1592_out1(T237, T238, X284) 18.82/5.79 f2175_in(zero(T435)) -> U33(f2175_in(T435), zero(T435)) 18.82/5.79 U33(f2175_out1, zero(T435)) -> f2175_out1 18.82/5.79 f2175_in(one(T439)) -> U34(f2182_in(T439), one(T439)) 18.82/5.79 U34(f2182_out1, one(T439)) -> f2175_out1 18.82/5.79 f2182_in(b) -> f2182_out1 18.82/5.79 f2182_in(zero(T444)) -> U35(f2175_in(T444), zero(T444)) 18.82/5.79 U35(f2175_out1, zero(T444)) -> f2182_out1 18.82/5.79 f2182_in(one(T448)) -> U36(f2182_in(T448), one(T448)) 18.82/5.79 U36(f2182_out1, one(T448)) -> f2182_out1 18.82/5.79 f2229_in(zero(T502)) -> U37(f2229_in(T502), zero(T502)) 18.82/5.79 U37(f2229_out1(T503, T504), zero(T502)) -> f2229_out1(zero(T503), zero(T504)) 18.82/5.79 f2229_in(one(one(T530))) -> U38(f2182_in(T530), one(one(T530))) 18.82/5.79 U38(f2182_out1, one(one(T530))) -> f2229_out1(zero(one(T530)), one(b)) 18.82/5.79 f2229_in(one(zero(T535))) -> U39(f2175_in(T535), one(zero(T535))) 18.82/5.79 U39(f2175_out1, one(zero(T535))) -> f2229_out1(zero(zero(T535)), one(b)) 18.82/5.79 f2229_in(one(T550)) -> U40(f2229_in(T550), one(T550)) 18.82/5.79 U40(f2229_out1(T551, T552), one(T550)) -> f2229_out1(zero(T551), one(T552)) 18.82/5.79 f2229_in(one(T570)) -> U41(f2300_in(T570), one(T570)) 18.82/5.79 U41(f2300_out1(T571, T572), one(T570)) -> f2229_out1(one(T571), zero(T572)) 18.82/5.79 f2229_in(zero(T612)) -> U42(f2342_in(T612), zero(T612)) 18.82/5.79 U42(f2342_out1(T613, T614), zero(T612)) -> f2229_out1(one(T613), one(T614)) 18.82/5.79 f2393_in(one(b)) -> f2393_out1(b) 18.82/5.79 f2393_in(one(T644)) -> U43(f2175_in(T644), one(T644)) 18.82/5.79 U43(f2175_out1, one(T644)) -> f2393_out1(zero(T644)) 18.82/5.79 f2393_in(zero(T651)) -> U44(f2393_in(T651), zero(T651)) 18.82/5.79 U44(f2393_out1(T652), zero(T651)) -> f2393_out1(one(T652)) 18.82/5.79 f2352_in(one(T631)) -> U45(f2175_in(T631), one(T631)) 18.82/5.79 U45(f2175_out1, one(T631)) -> f2352_out1(zero(T631)) 18.82/5.79 f2352_in(zero(T638)) -> U46(f2393_in(T638), zero(T638)) 18.82/5.79 U46(f2393_out1(T639), zero(T638)) -> f2352_out1(one(T639)) 18.82/5.79 f2435_in(one(T698)) -> U47(f2229_in(T698), one(T698)) 18.82/5.79 U47(f2229_out1(T699, T700), one(T698)) -> f2435_out1(zero(T699), zero(T700)) 18.82/5.79 f2435_in(zero(one(T726))) -> U48(f2175_in(T726), zero(one(T726))) 18.82/5.79 U48(f2175_out1, zero(one(T726))) -> f2435_out1(zero(zero(T726)), one(b)) 18.82/5.79 f2435_in(zero(zero(T737))) -> U49(f2393_in(T737), zero(zero(T737))) 18.82/5.79 U49(f2393_out1(T738), zero(zero(T737))) -> f2435_out1(zero(one(T738)), one(b)) 18.82/5.79 f2435_in(zero(T752)) -> U50(f2435_in(T752), zero(T752)) 18.82/5.79 U50(f2435_out1(T753, T754), zero(T752)) -> f2435_out1(zero(T753), one(T754)) 18.82/5.79 f2435_in(zero(one(T780))) -> U51(f2175_in(T780), zero(one(T780))) 18.82/5.79 U51(f2175_out1, zero(one(T780))) -> f2435_out1(one(b), zero(zero(T780))) 18.82/5.79 f2435_in(zero(zero(T791))) -> U52(f2393_in(T791), zero(zero(T791))) 18.82/5.79 U52(f2393_out1(T792), zero(zero(T791))) -> f2435_out1(one(b), zero(one(T792))) 18.82/5.79 f2435_in(zero(T806)) -> U53(f2435_in(T806), zero(T806)) 18.82/5.79 U53(f2435_out1(T807, T808), zero(T806)) -> f2435_out1(one(T807), zero(T808)) 18.82/5.79 f2435_in(one(T820)) -> U54(f2342_in(T820), one(T820)) 18.82/5.79 U54(f2342_out1(T821, T822), one(T820)) -> f2435_out1(one(T821), one(T822)) 18.82/5.79 f2342_in(one(b)) -> f2342_out1(b, b) 18.82/5.79 f2342_in(T624) -> U55(f2352_in(T624), T624) 18.82/5.79 U55(f2352_out1(T625), T624) -> f2342_out1(T625, b) 18.82/5.79 f2342_in(T662) -> U56(f2352_in(T662), T662) 18.82/5.79 U56(f2352_out1(T663), T662) -> f2342_out1(b, T663) 18.82/5.79 f2342_in(T678) -> U57(f2435_in(T678), T678) 18.82/5.79 U57(f2435_out1(T679, T680), T678) -> f2342_out1(T679, T680) 18.82/5.79 f2300_in(one(T578)) -> U58(f2182_in(T578), one(T578)) 18.82/5.79 U58(f2182_out1, one(T578)) -> f2300_out1(b, one(T578)) 18.82/5.79 f2300_in(zero(T583)) -> U59(f2175_in(T583), zero(T583)) 18.82/5.79 U59(f2175_out1, zero(T583)) -> f2300_out1(b, zero(T583)) 18.82/5.79 f2300_in(T598) -> U60(f2229_in(T598), T598) 18.82/5.79 U60(f2229_out1(T599, T600), T598) -> f2300_out1(T599, T600) 18.82/5.79 f109_in(zero(T429)) -> U61(f2175_in(T429), zero(T429)) 18.82/5.79 U61(f2175_out1, zero(T429)) -> f109_out1(b, T429) 18.82/5.79 f109_in(zero(T482)) -> U62(f2229_in(T482), zero(T482)) 18.82/5.79 U62(f2229_out1(T483, T484), zero(T482)) -> f109_out1(zero(T483), T484) 18.82/5.79 f109_in(one(T838)) -> U63(f2300_in(T838), one(T838)) 18.82/5.79 U63(f2300_out1(T839, T840), one(T838)) -> f109_out1(one(T839), T840) 18.82/5.79 f898_in -> U64(f1142_in) 18.82/5.79 U64(f1142_out1(T95)) -> f898_out1(b, T95, zero(T95)) 18.82/5.79 f898_in -> U65(f1256_in) 18.82/5.79 U65(f1256_out1(T143, T144, X156)) -> f898_out1(zero(T143), T144, zero(X156)) 18.82/5.79 f898_in -> U66(f1592_in) 18.82/5.79 U66(f1592_out1(T412, T413, X565)) -> f898_out1(one(T412), T413, one(X565)) 18.82/5.79 f42_in(T36) -> U67(f104_in, T36) 18.82/5.79 U67(f104_out1(T37), T36) -> U68(f109_in(T36), T36, T37) 18.82/5.79 U68(f109_out1(T42, T41), T36, T37) -> f42_out1(T37, T42, T41) 18.82/5.79 f888_in -> U69(f104_in) 18.82/5.79 U69(f104_out1(T70)) -> U70(f898_in, T70) 18.82/5.79 U70(f898_out1(T75, T74, X78), T70) -> f888_out1(T70, T75, T74, X78) 18.82/5.79 18.82/5.79 Q is empty. 18.82/5.79 We have to consider all minimal (P,Q,R)-chains. 18.82/5.79 ---------------------------------------- 18.82/5.79 18.82/5.79 (101) DependencyGraphProof (EQUIVALENT) 18.82/5.79 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 8 SCCs with 100 less nodes. 18.82/5.79 ---------------------------------------- 18.82/5.79 18.82/5.79 (102) 18.82/5.79 Complex Obligation (AND) 18.82/5.79 18.82/5.79 ---------------------------------------- 18.82/5.79 18.82/5.79 (103) 18.82/5.79 Obligation: 18.82/5.79 Q DP problem: 18.82/5.79 The TRS P consists of the following rules: 18.82/5.79 18.82/5.79 F2175_IN(one(T439)) -> F2182_IN(T439) 18.82/5.79 F2182_IN(zero(T444)) -> F2175_IN(T444) 18.82/5.79 F2175_IN(zero(T435)) -> F2175_IN(T435) 18.82/5.79 F2182_IN(one(T448)) -> F2182_IN(T448) 18.82/5.79 18.82/5.79 The TRS R consists of the following rules: 18.82/5.79 18.82/5.79 f3_in(T8) -> f3_out1(one(b), T8) 18.82/5.79 f3_in(zero(T23)) -> U1(f3_in(T23), zero(T23)) 18.82/5.79 U1(f3_out1(T24, T25), zero(T23)) -> f3_out1(zero(T24), T25) 18.82/5.79 f3_in(T36) -> U2(f42_in(T36), T36) 18.82/5.79 U2(f42_out1(T37, T38, X33), T36) -> f3_out1(one(T37), T38) 18.82/5.79 f104_in -> f104_out1(one(b)) 18.82/5.79 f104_in -> U3(f104_in) 18.82/5.79 U3(f104_out1(T60)) -> f104_out1(zero(T60)) 18.82/5.79 f104_in -> U4(f888_in) 18.82/5.79 U4(f888_out1(T70, T71, X77, X78)) -> f104_out1(one(T70)) 18.82/5.79 f1142_in -> U5(f1142_in) 18.82/5.79 U5(f1142_out1(T102)) -> f1142_out1(zero(T102)) 18.82/5.79 f1142_in -> U6(f1151_in) 18.82/5.79 U6(f1151_out1(T107)) -> f1142_out1(one(T107)) 18.82/5.79 f1151_in -> f1151_out1(b) 18.82/5.79 f1151_in -> U7(f1142_in) 18.82/5.79 U7(f1142_out1(T113)) -> f1151_out1(zero(T113)) 18.82/5.79 f1151_in -> U8(f1151_in) 18.82/5.79 U8(f1151_out1(T118)) -> f1151_out1(one(T118)) 18.82/5.79 f1256_in -> U9(f1256_in) 18.82/5.79 U9(f1256_out1(T157, T158, X180)) -> f1256_out1(zero(T157), zero(T158), zero(X180)) 18.82/5.79 f1256_in -> U10(f1151_in) 18.82/5.79 U10(f1151_out1(T179)) -> f1256_out1(zero(one(T179)), one(b), one(one(T179))) 18.82/5.79 f1256_in -> U11(f1142_in) 18.82/5.79 U11(f1142_out1(T185)) -> f1256_out1(zero(zero(T185)), one(b), one(zero(T185))) 18.82/5.79 f1256_in -> U12(f1256_in) 18.82/5.79 U12(f1256_out1(T197, T198, X232)) -> f1256_out1(zero(T197), one(T198), one(X232)) 18.82/5.79 f1256_in -> U13(f1592_in) 18.82/5.79 U13(f1592_out1(T211, T212, X256)) -> f1256_out1(one(T211), zero(T212), one(X256)) 18.82/5.79 f1256_in -> U14(f1650_in) 18.82/5.79 U14(f1650_out1(T247, T248, X300)) -> f1256_out1(one(T247), one(T248), zero(X300)) 18.82/5.79 f1696_in -> f1696_out1(b, one(b)) 18.82/5.79 f1696_in -> U15(f1142_in) 18.82/5.79 U15(f1142_out1(T272)) -> f1696_out1(zero(T272), one(T272)) 18.82/5.79 f1696_in -> U16(f1696_in) 18.82/5.79 U16(f1696_out1(T277, X346)) -> f1696_out1(one(T277), zero(X346)) 18.82/5.79 f1677_in -> U17(f1142_in) 18.82/5.79 U17(f1142_out1(T261)) -> f1677_out1(zero(T261), one(T261)) 18.82/5.79 f1677_in -> U18(f1696_in) 18.82/5.79 U18(f1696_out1(T266, X331)) -> f1677_out1(one(T266), zero(X331)) 18.82/5.79 f1733_in -> U19(f1256_in) 18.82/5.79 U19(f1256_out1(T309, T310, X402)) -> f1733_out1(zero(T309), zero(T310), one(X402)) 18.82/5.79 f1733_in -> U20(f1142_in) 18.82/5.79 U20(f1142_out1(T331)) -> f1733_out1(zero(zero(T331)), one(b), zero(one(T331))) 18.82/5.79 f1733_in -> U21(f1696_in) 18.82/5.79 U21(f1696_out1(T338, X448)) -> f1733_out1(zero(one(T338)), one(b), zero(zero(X448))) 18.82/5.79 f1733_in -> U22(f1733_in) 18.82/5.79 U22(f1733_out1(T349, T350, X464)) -> f1733_out1(zero(T349), one(T350), zero(X464)) 18.82/5.79 f1733_in -> U23(f1142_in) 18.82/5.79 U23(f1142_out1(T371)) -> f1733_out1(one(b), zero(zero(T371)), zero(one(T371))) 18.82/5.79 f1733_in -> U24(f1696_in) 18.82/5.79 U24(f1696_out1(T378, X510)) -> f1733_out1(one(b), zero(one(T378)), zero(zero(X510))) 18.82/5.79 f1733_in -> U25(f1733_in) 18.82/5.79 U25(f1733_out1(T389, T390, X526)) -> f1733_out1(one(T389), zero(T390), zero(X526)) 18.82/5.79 f1733_in -> U26(f1650_in) 18.82/5.79 U26(f1650_out1(T399, T400, X542)) -> f1733_out1(one(T399), one(T400), one(X542)) 18.82/5.79 f1650_in -> f1650_out1(b, b, one(b)) 18.82/5.79 f1650_in -> U27(f1677_in) 18.82/5.79 U27(f1677_out1(T254, X315)) -> f1650_out1(T254, b, X315) 18.82/5.79 f1650_in -> U28(f1677_in) 18.82/5.79 U28(f1677_out1(T283, X361)) -> f1650_out1(b, T283, X361) 18.82/5.79 f1650_in -> U29(f1733_in) 18.82/5.79 U29(f1733_out1(T295, T296, X378)) -> f1650_out1(T295, T296, X378) 18.82/5.79 f1592_in -> U30(f1151_in) 18.82/5.79 U30(f1151_out1(T219)) -> f1592_out1(b, one(T219), one(T219)) 18.82/5.79 f1592_in -> U31(f1142_in) 18.82/5.79 U31(f1142_out1(T225)) -> f1592_out1(b, zero(T225), zero(T225)) 18.82/5.79 f1592_in -> U32(f1256_in) 18.82/5.79 U32(f1256_out1(T237, T238, X284)) -> f1592_out1(T237, T238, X284) 18.82/5.79 f2175_in(zero(T435)) -> U33(f2175_in(T435), zero(T435)) 18.82/5.79 U33(f2175_out1, zero(T435)) -> f2175_out1 18.82/5.79 f2175_in(one(T439)) -> U34(f2182_in(T439), one(T439)) 18.82/5.79 U34(f2182_out1, one(T439)) -> f2175_out1 18.82/5.79 f2182_in(b) -> f2182_out1 18.82/5.79 f2182_in(zero(T444)) -> U35(f2175_in(T444), zero(T444)) 18.82/5.79 U35(f2175_out1, zero(T444)) -> f2182_out1 18.82/5.79 f2182_in(one(T448)) -> U36(f2182_in(T448), one(T448)) 18.82/5.79 U36(f2182_out1, one(T448)) -> f2182_out1 18.82/5.79 f2229_in(zero(T502)) -> U37(f2229_in(T502), zero(T502)) 18.82/5.79 U37(f2229_out1(T503, T504), zero(T502)) -> f2229_out1(zero(T503), zero(T504)) 18.82/5.79 f2229_in(one(one(T530))) -> U38(f2182_in(T530), one(one(T530))) 18.82/5.79 U38(f2182_out1, one(one(T530))) -> f2229_out1(zero(one(T530)), one(b)) 18.82/5.79 f2229_in(one(zero(T535))) -> U39(f2175_in(T535), one(zero(T535))) 18.82/5.79 U39(f2175_out1, one(zero(T535))) -> f2229_out1(zero(zero(T535)), one(b)) 18.82/5.79 f2229_in(one(T550)) -> U40(f2229_in(T550), one(T550)) 18.82/5.79 U40(f2229_out1(T551, T552), one(T550)) -> f2229_out1(zero(T551), one(T552)) 18.82/5.79 f2229_in(one(T570)) -> U41(f2300_in(T570), one(T570)) 18.82/5.79 U41(f2300_out1(T571, T572), one(T570)) -> f2229_out1(one(T571), zero(T572)) 18.82/5.79 f2229_in(zero(T612)) -> U42(f2342_in(T612), zero(T612)) 18.82/5.79 U42(f2342_out1(T613, T614), zero(T612)) -> f2229_out1(one(T613), one(T614)) 18.82/5.79 f2393_in(one(b)) -> f2393_out1(b) 18.82/5.79 f2393_in(one(T644)) -> U43(f2175_in(T644), one(T644)) 18.82/5.79 U43(f2175_out1, one(T644)) -> f2393_out1(zero(T644)) 18.82/5.79 f2393_in(zero(T651)) -> U44(f2393_in(T651), zero(T651)) 18.82/5.79 U44(f2393_out1(T652), zero(T651)) -> f2393_out1(one(T652)) 18.82/5.79 f2352_in(one(T631)) -> U45(f2175_in(T631), one(T631)) 18.82/5.79 U45(f2175_out1, one(T631)) -> f2352_out1(zero(T631)) 18.82/5.79 f2352_in(zero(T638)) -> U46(f2393_in(T638), zero(T638)) 18.82/5.79 U46(f2393_out1(T639), zero(T638)) -> f2352_out1(one(T639)) 18.82/5.79 f2435_in(one(T698)) -> U47(f2229_in(T698), one(T698)) 18.82/5.79 U47(f2229_out1(T699, T700), one(T698)) -> f2435_out1(zero(T699), zero(T700)) 18.82/5.79 f2435_in(zero(one(T726))) -> U48(f2175_in(T726), zero(one(T726))) 18.82/5.79 U48(f2175_out1, zero(one(T726))) -> f2435_out1(zero(zero(T726)), one(b)) 18.82/5.79 f2435_in(zero(zero(T737))) -> U49(f2393_in(T737), zero(zero(T737))) 18.82/5.79 U49(f2393_out1(T738), zero(zero(T737))) -> f2435_out1(zero(one(T738)), one(b)) 18.82/5.79 f2435_in(zero(T752)) -> U50(f2435_in(T752), zero(T752)) 18.82/5.79 U50(f2435_out1(T753, T754), zero(T752)) -> f2435_out1(zero(T753), one(T754)) 18.82/5.79 f2435_in(zero(one(T780))) -> U51(f2175_in(T780), zero(one(T780))) 18.82/5.79 U51(f2175_out1, zero(one(T780))) -> f2435_out1(one(b), zero(zero(T780))) 18.82/5.79 f2435_in(zero(zero(T791))) -> U52(f2393_in(T791), zero(zero(T791))) 18.82/5.79 U52(f2393_out1(T792), zero(zero(T791))) -> f2435_out1(one(b), zero(one(T792))) 18.82/5.79 f2435_in(zero(T806)) -> U53(f2435_in(T806), zero(T806)) 18.82/5.79 U53(f2435_out1(T807, T808), zero(T806)) -> f2435_out1(one(T807), zero(T808)) 18.82/5.79 f2435_in(one(T820)) -> U54(f2342_in(T820), one(T820)) 18.82/5.79 U54(f2342_out1(T821, T822), one(T820)) -> f2435_out1(one(T821), one(T822)) 18.82/5.79 f2342_in(one(b)) -> f2342_out1(b, b) 18.82/5.79 f2342_in(T624) -> U55(f2352_in(T624), T624) 18.82/5.79 U55(f2352_out1(T625), T624) -> f2342_out1(T625, b) 18.82/5.79 f2342_in(T662) -> U56(f2352_in(T662), T662) 18.82/5.79 U56(f2352_out1(T663), T662) -> f2342_out1(b, T663) 18.82/5.79 f2342_in(T678) -> U57(f2435_in(T678), T678) 18.82/5.79 U57(f2435_out1(T679, T680), T678) -> f2342_out1(T679, T680) 18.82/5.79 f2300_in(one(T578)) -> U58(f2182_in(T578), one(T578)) 18.82/5.79 U58(f2182_out1, one(T578)) -> f2300_out1(b, one(T578)) 18.82/5.79 f2300_in(zero(T583)) -> U59(f2175_in(T583), zero(T583)) 18.82/5.79 U59(f2175_out1, zero(T583)) -> f2300_out1(b, zero(T583)) 18.82/5.79 f2300_in(T598) -> U60(f2229_in(T598), T598) 18.82/5.79 U60(f2229_out1(T599, T600), T598) -> f2300_out1(T599, T600) 18.82/5.79 f109_in(zero(T429)) -> U61(f2175_in(T429), zero(T429)) 18.82/5.79 U61(f2175_out1, zero(T429)) -> f109_out1(b, T429) 18.82/5.79 f109_in(zero(T482)) -> U62(f2229_in(T482), zero(T482)) 18.82/5.79 U62(f2229_out1(T483, T484), zero(T482)) -> f109_out1(zero(T483), T484) 18.82/5.79 f109_in(one(T838)) -> U63(f2300_in(T838), one(T838)) 18.82/5.79 U63(f2300_out1(T839, T840), one(T838)) -> f109_out1(one(T839), T840) 18.82/5.79 f898_in -> U64(f1142_in) 18.82/5.79 U64(f1142_out1(T95)) -> f898_out1(b, T95, zero(T95)) 18.82/5.79 f898_in -> U65(f1256_in) 18.82/5.79 U65(f1256_out1(T143, T144, X156)) -> f898_out1(zero(T143), T144, zero(X156)) 18.82/5.79 f898_in -> U66(f1592_in) 18.82/5.79 U66(f1592_out1(T412, T413, X565)) -> f898_out1(one(T412), T413, one(X565)) 18.82/5.79 f42_in(T36) -> U67(f104_in, T36) 18.82/5.79 U67(f104_out1(T37), T36) -> U68(f109_in(T36), T36, T37) 18.82/5.79 U68(f109_out1(T42, T41), T36, T37) -> f42_out1(T37, T42, T41) 18.82/5.79 f888_in -> U69(f104_in) 18.82/5.79 U69(f104_out1(T70)) -> U70(f898_in, T70) 18.82/5.79 U70(f898_out1(T75, T74, X78), T70) -> f888_out1(T70, T75, T74, X78) 18.82/5.79 18.82/5.79 Q is empty. 18.82/5.79 We have to consider all minimal (P,Q,R)-chains. 18.82/5.79 ---------------------------------------- 18.82/5.79 18.82/5.79 (104) UsableRulesProof (EQUIVALENT) 18.82/5.79 We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R. 18.82/5.79 ---------------------------------------- 18.82/5.79 18.82/5.79 (105) 18.82/5.79 Obligation: 18.82/5.79 Q DP problem: 18.82/5.79 The TRS P consists of the following rules: 18.82/5.79 18.82/5.79 F2175_IN(one(T439)) -> F2182_IN(T439) 18.82/5.79 F2182_IN(zero(T444)) -> F2175_IN(T444) 18.82/5.79 F2175_IN(zero(T435)) -> F2175_IN(T435) 18.82/5.79 F2182_IN(one(T448)) -> F2182_IN(T448) 18.82/5.79 18.82/5.79 R is empty. 18.82/5.79 Q is empty. 18.82/5.79 We have to consider all minimal (P,Q,R)-chains. 18.82/5.79 ---------------------------------------- 18.82/5.79 18.82/5.79 (106) QDPSizeChangeProof (EQUIVALENT) 18.82/5.79 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 18.82/5.79 18.82/5.79 From the DPs we obtained the following set of size-change graphs: 18.82/5.79 *F2182_IN(zero(T444)) -> F2175_IN(T444) 18.82/5.79 The graph contains the following edges 1 > 1 18.82/5.79 18.82/5.79 18.82/5.79 *F2182_IN(one(T448)) -> F2182_IN(T448) 18.82/5.79 The graph contains the following edges 1 > 1 18.82/5.79 18.82/5.79 18.82/5.79 *F2175_IN(zero(T435)) -> F2175_IN(T435) 18.82/5.79 The graph contains the following edges 1 > 1 18.82/5.79 18.82/5.79 18.82/5.79 *F2175_IN(one(T439)) -> F2182_IN(T439) 18.82/5.79 The graph contains the following edges 1 > 1 18.82/5.79 18.82/5.79 18.82/5.79 ---------------------------------------- 18.82/5.79 18.82/5.79 (107) 18.82/5.79 YES 18.82/5.79 18.82/5.79 ---------------------------------------- 18.82/5.79 18.82/5.79 (108) 18.82/5.79 Obligation: 18.82/5.79 Q DP problem: 18.82/5.79 The TRS P consists of the following rules: 18.82/5.79 18.82/5.79 F2393_IN(zero(T651)) -> F2393_IN(T651) 18.82/5.79 18.82/5.79 The TRS R consists of the following rules: 18.82/5.79 18.82/5.79 f3_in(T8) -> f3_out1(one(b), T8) 18.82/5.79 f3_in(zero(T23)) -> U1(f3_in(T23), zero(T23)) 18.82/5.79 U1(f3_out1(T24, T25), zero(T23)) -> f3_out1(zero(T24), T25) 18.82/5.79 f3_in(T36) -> U2(f42_in(T36), T36) 18.82/5.79 U2(f42_out1(T37, T38, X33), T36) -> f3_out1(one(T37), T38) 18.82/5.79 f104_in -> f104_out1(one(b)) 18.82/5.79 f104_in -> U3(f104_in) 18.82/5.79 U3(f104_out1(T60)) -> f104_out1(zero(T60)) 18.82/5.79 f104_in -> U4(f888_in) 18.82/5.79 U4(f888_out1(T70, T71, X77, X78)) -> f104_out1(one(T70)) 18.82/5.79 f1142_in -> U5(f1142_in) 18.82/5.79 U5(f1142_out1(T102)) -> f1142_out1(zero(T102)) 18.82/5.79 f1142_in -> U6(f1151_in) 18.82/5.79 U6(f1151_out1(T107)) -> f1142_out1(one(T107)) 18.82/5.79 f1151_in -> f1151_out1(b) 18.82/5.79 f1151_in -> U7(f1142_in) 18.82/5.79 U7(f1142_out1(T113)) -> f1151_out1(zero(T113)) 18.82/5.79 f1151_in -> U8(f1151_in) 18.82/5.79 U8(f1151_out1(T118)) -> f1151_out1(one(T118)) 18.82/5.79 f1256_in -> U9(f1256_in) 18.82/5.79 U9(f1256_out1(T157, T158, X180)) -> f1256_out1(zero(T157), zero(T158), zero(X180)) 18.82/5.79 f1256_in -> U10(f1151_in) 18.82/5.79 U10(f1151_out1(T179)) -> f1256_out1(zero(one(T179)), one(b), one(one(T179))) 18.82/5.79 f1256_in -> U11(f1142_in) 18.82/5.79 U11(f1142_out1(T185)) -> f1256_out1(zero(zero(T185)), one(b), one(zero(T185))) 18.82/5.79 f1256_in -> U12(f1256_in) 18.82/5.79 U12(f1256_out1(T197, T198, X232)) -> f1256_out1(zero(T197), one(T198), one(X232)) 18.82/5.79 f1256_in -> U13(f1592_in) 18.82/5.79 U13(f1592_out1(T211, T212, X256)) -> f1256_out1(one(T211), zero(T212), one(X256)) 18.82/5.79 f1256_in -> U14(f1650_in) 18.82/5.79 U14(f1650_out1(T247, T248, X300)) -> f1256_out1(one(T247), one(T248), zero(X300)) 18.82/5.79 f1696_in -> f1696_out1(b, one(b)) 18.82/5.79 f1696_in -> U15(f1142_in) 18.82/5.79 U15(f1142_out1(T272)) -> f1696_out1(zero(T272), one(T272)) 18.82/5.79 f1696_in -> U16(f1696_in) 18.82/5.79 U16(f1696_out1(T277, X346)) -> f1696_out1(one(T277), zero(X346)) 18.82/5.79 f1677_in -> U17(f1142_in) 18.82/5.79 U17(f1142_out1(T261)) -> f1677_out1(zero(T261), one(T261)) 18.82/5.79 f1677_in -> U18(f1696_in) 18.82/5.79 U18(f1696_out1(T266, X331)) -> f1677_out1(one(T266), zero(X331)) 18.82/5.79 f1733_in -> U19(f1256_in) 18.82/5.79 U19(f1256_out1(T309, T310, X402)) -> f1733_out1(zero(T309), zero(T310), one(X402)) 18.82/5.79 f1733_in -> U20(f1142_in) 18.82/5.79 U20(f1142_out1(T331)) -> f1733_out1(zero(zero(T331)), one(b), zero(one(T331))) 18.82/5.79 f1733_in -> U21(f1696_in) 18.82/5.79 U21(f1696_out1(T338, X448)) -> f1733_out1(zero(one(T338)), one(b), zero(zero(X448))) 18.82/5.79 f1733_in -> U22(f1733_in) 18.82/5.79 U22(f1733_out1(T349, T350, X464)) -> f1733_out1(zero(T349), one(T350), zero(X464)) 18.82/5.79 f1733_in -> U23(f1142_in) 18.82/5.79 U23(f1142_out1(T371)) -> f1733_out1(one(b), zero(zero(T371)), zero(one(T371))) 18.82/5.79 f1733_in -> U24(f1696_in) 18.82/5.79 U24(f1696_out1(T378, X510)) -> f1733_out1(one(b), zero(one(T378)), zero(zero(X510))) 18.82/5.79 f1733_in -> U25(f1733_in) 18.82/5.79 U25(f1733_out1(T389, T390, X526)) -> f1733_out1(one(T389), zero(T390), zero(X526)) 18.82/5.79 f1733_in -> U26(f1650_in) 18.82/5.79 U26(f1650_out1(T399, T400, X542)) -> f1733_out1(one(T399), one(T400), one(X542)) 18.82/5.79 f1650_in -> f1650_out1(b, b, one(b)) 18.82/5.79 f1650_in -> U27(f1677_in) 18.82/5.79 U27(f1677_out1(T254, X315)) -> f1650_out1(T254, b, X315) 18.82/5.79 f1650_in -> U28(f1677_in) 18.82/5.79 U28(f1677_out1(T283, X361)) -> f1650_out1(b, T283, X361) 18.82/5.79 f1650_in -> U29(f1733_in) 18.82/5.79 U29(f1733_out1(T295, T296, X378)) -> f1650_out1(T295, T296, X378) 18.82/5.79 f1592_in -> U30(f1151_in) 18.82/5.79 U30(f1151_out1(T219)) -> f1592_out1(b, one(T219), one(T219)) 18.82/5.79 f1592_in -> U31(f1142_in) 18.82/5.79 U31(f1142_out1(T225)) -> f1592_out1(b, zero(T225), zero(T225)) 18.82/5.79 f1592_in -> U32(f1256_in) 18.82/5.79 U32(f1256_out1(T237, T238, X284)) -> f1592_out1(T237, T238, X284) 18.82/5.79 f2175_in(zero(T435)) -> U33(f2175_in(T435), zero(T435)) 18.82/5.79 U33(f2175_out1, zero(T435)) -> f2175_out1 18.82/5.79 f2175_in(one(T439)) -> U34(f2182_in(T439), one(T439)) 18.82/5.79 U34(f2182_out1, one(T439)) -> f2175_out1 18.82/5.79 f2182_in(b) -> f2182_out1 18.82/5.79 f2182_in(zero(T444)) -> U35(f2175_in(T444), zero(T444)) 18.82/5.79 U35(f2175_out1, zero(T444)) -> f2182_out1 18.82/5.79 f2182_in(one(T448)) -> U36(f2182_in(T448), one(T448)) 18.82/5.79 U36(f2182_out1, one(T448)) -> f2182_out1 18.82/5.79 f2229_in(zero(T502)) -> U37(f2229_in(T502), zero(T502)) 18.82/5.79 U37(f2229_out1(T503, T504), zero(T502)) -> f2229_out1(zero(T503), zero(T504)) 18.82/5.79 f2229_in(one(one(T530))) -> U38(f2182_in(T530), one(one(T530))) 18.82/5.79 U38(f2182_out1, one(one(T530))) -> f2229_out1(zero(one(T530)), one(b)) 18.82/5.79 f2229_in(one(zero(T535))) -> U39(f2175_in(T535), one(zero(T535))) 18.82/5.79 U39(f2175_out1, one(zero(T535))) -> f2229_out1(zero(zero(T535)), one(b)) 18.82/5.79 f2229_in(one(T550)) -> U40(f2229_in(T550), one(T550)) 18.82/5.79 U40(f2229_out1(T551, T552), one(T550)) -> f2229_out1(zero(T551), one(T552)) 18.82/5.79 f2229_in(one(T570)) -> U41(f2300_in(T570), one(T570)) 18.82/5.79 U41(f2300_out1(T571, T572), one(T570)) -> f2229_out1(one(T571), zero(T572)) 18.82/5.79 f2229_in(zero(T612)) -> U42(f2342_in(T612), zero(T612)) 18.82/5.79 U42(f2342_out1(T613, T614), zero(T612)) -> f2229_out1(one(T613), one(T614)) 18.82/5.79 f2393_in(one(b)) -> f2393_out1(b) 18.82/5.79 f2393_in(one(T644)) -> U43(f2175_in(T644), one(T644)) 18.82/5.79 U43(f2175_out1, one(T644)) -> f2393_out1(zero(T644)) 18.82/5.79 f2393_in(zero(T651)) -> U44(f2393_in(T651), zero(T651)) 18.82/5.79 U44(f2393_out1(T652), zero(T651)) -> f2393_out1(one(T652)) 18.82/5.79 f2352_in(one(T631)) -> U45(f2175_in(T631), one(T631)) 18.82/5.79 U45(f2175_out1, one(T631)) -> f2352_out1(zero(T631)) 18.82/5.79 f2352_in(zero(T638)) -> U46(f2393_in(T638), zero(T638)) 18.82/5.79 U46(f2393_out1(T639), zero(T638)) -> f2352_out1(one(T639)) 18.82/5.79 f2435_in(one(T698)) -> U47(f2229_in(T698), one(T698)) 18.82/5.79 U47(f2229_out1(T699, T700), one(T698)) -> f2435_out1(zero(T699), zero(T700)) 18.82/5.79 f2435_in(zero(one(T726))) -> U48(f2175_in(T726), zero(one(T726))) 18.82/5.79 U48(f2175_out1, zero(one(T726))) -> f2435_out1(zero(zero(T726)), one(b)) 18.82/5.79 f2435_in(zero(zero(T737))) -> U49(f2393_in(T737), zero(zero(T737))) 18.82/5.79 U49(f2393_out1(T738), zero(zero(T737))) -> f2435_out1(zero(one(T738)), one(b)) 18.82/5.79 f2435_in(zero(T752)) -> U50(f2435_in(T752), zero(T752)) 18.82/5.79 U50(f2435_out1(T753, T754), zero(T752)) -> f2435_out1(zero(T753), one(T754)) 18.82/5.79 f2435_in(zero(one(T780))) -> U51(f2175_in(T780), zero(one(T780))) 18.82/5.79 U51(f2175_out1, zero(one(T780))) -> f2435_out1(one(b), zero(zero(T780))) 18.82/5.79 f2435_in(zero(zero(T791))) -> U52(f2393_in(T791), zero(zero(T791))) 18.82/5.79 U52(f2393_out1(T792), zero(zero(T791))) -> f2435_out1(one(b), zero(one(T792))) 18.82/5.79 f2435_in(zero(T806)) -> U53(f2435_in(T806), zero(T806)) 18.82/5.79 U53(f2435_out1(T807, T808), zero(T806)) -> f2435_out1(one(T807), zero(T808)) 18.82/5.79 f2435_in(one(T820)) -> U54(f2342_in(T820), one(T820)) 18.82/5.79 U54(f2342_out1(T821, T822), one(T820)) -> f2435_out1(one(T821), one(T822)) 18.82/5.79 f2342_in(one(b)) -> f2342_out1(b, b) 18.82/5.79 f2342_in(T624) -> U55(f2352_in(T624), T624) 18.82/5.79 U55(f2352_out1(T625), T624) -> f2342_out1(T625, b) 18.82/5.79 f2342_in(T662) -> U56(f2352_in(T662), T662) 18.82/5.79 U56(f2352_out1(T663), T662) -> f2342_out1(b, T663) 18.82/5.79 f2342_in(T678) -> U57(f2435_in(T678), T678) 18.82/5.79 U57(f2435_out1(T679, T680), T678) -> f2342_out1(T679, T680) 18.82/5.79 f2300_in(one(T578)) -> U58(f2182_in(T578), one(T578)) 18.82/5.79 U58(f2182_out1, one(T578)) -> f2300_out1(b, one(T578)) 18.82/5.79 f2300_in(zero(T583)) -> U59(f2175_in(T583), zero(T583)) 18.82/5.79 U59(f2175_out1, zero(T583)) -> f2300_out1(b, zero(T583)) 18.82/5.79 f2300_in(T598) -> U60(f2229_in(T598), T598) 18.82/5.79 U60(f2229_out1(T599, T600), T598) -> f2300_out1(T599, T600) 18.82/5.79 f109_in(zero(T429)) -> U61(f2175_in(T429), zero(T429)) 18.82/5.79 U61(f2175_out1, zero(T429)) -> f109_out1(b, T429) 18.82/5.79 f109_in(zero(T482)) -> U62(f2229_in(T482), zero(T482)) 18.82/5.79 U62(f2229_out1(T483, T484), zero(T482)) -> f109_out1(zero(T483), T484) 18.82/5.79 f109_in(one(T838)) -> U63(f2300_in(T838), one(T838)) 18.82/5.79 U63(f2300_out1(T839, T840), one(T838)) -> f109_out1(one(T839), T840) 18.82/5.79 f898_in -> U64(f1142_in) 18.82/5.79 U64(f1142_out1(T95)) -> f898_out1(b, T95, zero(T95)) 18.82/5.79 f898_in -> U65(f1256_in) 18.82/5.79 U65(f1256_out1(T143, T144, X156)) -> f898_out1(zero(T143), T144, zero(X156)) 18.82/5.79 f898_in -> U66(f1592_in) 18.82/5.79 U66(f1592_out1(T412, T413, X565)) -> f898_out1(one(T412), T413, one(X565)) 18.82/5.79 f42_in(T36) -> U67(f104_in, T36) 18.82/5.79 U67(f104_out1(T37), T36) -> U68(f109_in(T36), T36, T37) 18.82/5.79 U68(f109_out1(T42, T41), T36, T37) -> f42_out1(T37, T42, T41) 18.82/5.79 f888_in -> U69(f104_in) 18.82/5.79 U69(f104_out1(T70)) -> U70(f898_in, T70) 18.82/5.79 U70(f898_out1(T75, T74, X78), T70) -> f888_out1(T70, T75, T74, X78) 18.82/5.79 18.82/5.79 Q is empty. 18.82/5.79 We have to consider all minimal (P,Q,R)-chains. 18.82/5.79 ---------------------------------------- 18.82/5.79 18.82/5.79 (109) UsableRulesProof (EQUIVALENT) 18.82/5.79 We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R. 18.82/5.79 ---------------------------------------- 18.82/5.79 18.82/5.79 (110) 18.82/5.79 Obligation: 18.82/5.79 Q DP problem: 18.82/5.79 The TRS P consists of the following rules: 18.82/5.79 18.82/5.79 F2393_IN(zero(T651)) -> F2393_IN(T651) 18.82/5.79 18.82/5.79 R is empty. 18.82/5.79 Q is empty. 18.82/5.79 We have to consider all minimal (P,Q,R)-chains. 18.82/5.79 ---------------------------------------- 18.82/5.79 18.82/5.79 (111) QDPSizeChangeProof (EQUIVALENT) 18.82/5.79 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 18.82/5.79 18.82/5.79 From the DPs we obtained the following set of size-change graphs: 18.82/5.79 *F2393_IN(zero(T651)) -> F2393_IN(T651) 18.82/5.79 The graph contains the following edges 1 > 1 18.82/5.79 18.82/5.79 18.82/5.79 ---------------------------------------- 18.82/5.79 18.82/5.79 (112) 18.82/5.79 YES 18.82/5.79 18.82/5.79 ---------------------------------------- 18.82/5.79 18.82/5.79 (113) 18.82/5.79 Obligation: 18.82/5.79 Q DP problem: 18.82/5.79 The TRS P consists of the following rules: 18.82/5.79 18.82/5.79 F2229_IN(one(T550)) -> F2229_IN(T550) 18.82/5.79 F2229_IN(zero(T502)) -> F2229_IN(T502) 18.82/5.79 F2229_IN(one(T570)) -> F2300_IN(T570) 18.82/5.79 F2300_IN(T598) -> F2229_IN(T598) 18.82/5.79 F2229_IN(zero(T612)) -> F2342_IN(T612) 18.82/5.79 F2342_IN(T678) -> F2435_IN(T678) 18.82/5.79 F2435_IN(one(T698)) -> F2229_IN(T698) 18.82/5.79 F2435_IN(zero(T752)) -> F2435_IN(T752) 18.82/5.79 F2435_IN(one(T820)) -> F2342_IN(T820) 18.82/5.79 18.82/5.79 The TRS R consists of the following rules: 18.82/5.79 18.82/5.79 f3_in(T8) -> f3_out1(one(b), T8) 18.82/5.79 f3_in(zero(T23)) -> U1(f3_in(T23), zero(T23)) 18.82/5.79 U1(f3_out1(T24, T25), zero(T23)) -> f3_out1(zero(T24), T25) 18.82/5.79 f3_in(T36) -> U2(f42_in(T36), T36) 18.82/5.79 U2(f42_out1(T37, T38, X33), T36) -> f3_out1(one(T37), T38) 18.82/5.79 f104_in -> f104_out1(one(b)) 18.82/5.79 f104_in -> U3(f104_in) 18.82/5.79 U3(f104_out1(T60)) -> f104_out1(zero(T60)) 18.82/5.79 f104_in -> U4(f888_in) 18.82/5.79 U4(f888_out1(T70, T71, X77, X78)) -> f104_out1(one(T70)) 18.82/5.79 f1142_in -> U5(f1142_in) 18.82/5.79 U5(f1142_out1(T102)) -> f1142_out1(zero(T102)) 18.82/5.79 f1142_in -> U6(f1151_in) 18.82/5.79 U6(f1151_out1(T107)) -> f1142_out1(one(T107)) 18.82/5.79 f1151_in -> f1151_out1(b) 18.82/5.79 f1151_in -> U7(f1142_in) 18.82/5.79 U7(f1142_out1(T113)) -> f1151_out1(zero(T113)) 18.82/5.79 f1151_in -> U8(f1151_in) 18.82/5.79 U8(f1151_out1(T118)) -> f1151_out1(one(T118)) 18.82/5.79 f1256_in -> U9(f1256_in) 18.82/5.79 U9(f1256_out1(T157, T158, X180)) -> f1256_out1(zero(T157), zero(T158), zero(X180)) 18.82/5.79 f1256_in -> U10(f1151_in) 18.82/5.79 U10(f1151_out1(T179)) -> f1256_out1(zero(one(T179)), one(b), one(one(T179))) 18.82/5.79 f1256_in -> U11(f1142_in) 18.82/5.79 U11(f1142_out1(T185)) -> f1256_out1(zero(zero(T185)), one(b), one(zero(T185))) 18.82/5.79 f1256_in -> U12(f1256_in) 18.82/5.79 U12(f1256_out1(T197, T198, X232)) -> f1256_out1(zero(T197), one(T198), one(X232)) 18.82/5.79 f1256_in -> U13(f1592_in) 18.82/5.79 U13(f1592_out1(T211, T212, X256)) -> f1256_out1(one(T211), zero(T212), one(X256)) 18.82/5.79 f1256_in -> U14(f1650_in) 18.82/5.79 U14(f1650_out1(T247, T248, X300)) -> f1256_out1(one(T247), one(T248), zero(X300)) 18.82/5.79 f1696_in -> f1696_out1(b, one(b)) 18.82/5.79 f1696_in -> U15(f1142_in) 18.82/5.79 U15(f1142_out1(T272)) -> f1696_out1(zero(T272), one(T272)) 18.82/5.79 f1696_in -> U16(f1696_in) 18.82/5.79 U16(f1696_out1(T277, X346)) -> f1696_out1(one(T277), zero(X346)) 18.82/5.79 f1677_in -> U17(f1142_in) 18.82/5.79 U17(f1142_out1(T261)) -> f1677_out1(zero(T261), one(T261)) 18.82/5.79 f1677_in -> U18(f1696_in) 18.82/5.79 U18(f1696_out1(T266, X331)) -> f1677_out1(one(T266), zero(X331)) 18.82/5.79 f1733_in -> U19(f1256_in) 18.82/5.79 U19(f1256_out1(T309, T310, X402)) -> f1733_out1(zero(T309), zero(T310), one(X402)) 18.82/5.79 f1733_in -> U20(f1142_in) 18.82/5.79 U20(f1142_out1(T331)) -> f1733_out1(zero(zero(T331)), one(b), zero(one(T331))) 18.82/5.79 f1733_in -> U21(f1696_in) 18.82/5.79 U21(f1696_out1(T338, X448)) -> f1733_out1(zero(one(T338)), one(b), zero(zero(X448))) 18.82/5.79 f1733_in -> U22(f1733_in) 18.82/5.79 U22(f1733_out1(T349, T350, X464)) -> f1733_out1(zero(T349), one(T350), zero(X464)) 18.82/5.79 f1733_in -> U23(f1142_in) 18.82/5.79 U23(f1142_out1(T371)) -> f1733_out1(one(b), zero(zero(T371)), zero(one(T371))) 18.82/5.79 f1733_in -> U24(f1696_in) 18.82/5.79 U24(f1696_out1(T378, X510)) -> f1733_out1(one(b), zero(one(T378)), zero(zero(X510))) 18.82/5.79 f1733_in -> U25(f1733_in) 18.82/5.79 U25(f1733_out1(T389, T390, X526)) -> f1733_out1(one(T389), zero(T390), zero(X526)) 18.82/5.79 f1733_in -> U26(f1650_in) 18.82/5.79 U26(f1650_out1(T399, T400, X542)) -> f1733_out1(one(T399), one(T400), one(X542)) 18.82/5.79 f1650_in -> f1650_out1(b, b, one(b)) 18.82/5.79 f1650_in -> U27(f1677_in) 18.82/5.79 U27(f1677_out1(T254, X315)) -> f1650_out1(T254, b, X315) 18.82/5.79 f1650_in -> U28(f1677_in) 18.82/5.79 U28(f1677_out1(T283, X361)) -> f1650_out1(b, T283, X361) 18.82/5.79 f1650_in -> U29(f1733_in) 18.82/5.79 U29(f1733_out1(T295, T296, X378)) -> f1650_out1(T295, T296, X378) 18.82/5.79 f1592_in -> U30(f1151_in) 18.82/5.79 U30(f1151_out1(T219)) -> f1592_out1(b, one(T219), one(T219)) 18.82/5.79 f1592_in -> U31(f1142_in) 18.82/5.79 U31(f1142_out1(T225)) -> f1592_out1(b, zero(T225), zero(T225)) 18.82/5.79 f1592_in -> U32(f1256_in) 18.82/5.79 U32(f1256_out1(T237, T238, X284)) -> f1592_out1(T237, T238, X284) 18.82/5.79 f2175_in(zero(T435)) -> U33(f2175_in(T435), zero(T435)) 18.82/5.79 U33(f2175_out1, zero(T435)) -> f2175_out1 18.82/5.79 f2175_in(one(T439)) -> U34(f2182_in(T439), one(T439)) 18.82/5.79 U34(f2182_out1, one(T439)) -> f2175_out1 18.82/5.79 f2182_in(b) -> f2182_out1 18.82/5.79 f2182_in(zero(T444)) -> U35(f2175_in(T444), zero(T444)) 18.82/5.79 U35(f2175_out1, zero(T444)) -> f2182_out1 18.82/5.79 f2182_in(one(T448)) -> U36(f2182_in(T448), one(T448)) 18.82/5.79 U36(f2182_out1, one(T448)) -> f2182_out1 18.82/5.79 f2229_in(zero(T502)) -> U37(f2229_in(T502), zero(T502)) 18.82/5.79 U37(f2229_out1(T503, T504), zero(T502)) -> f2229_out1(zero(T503), zero(T504)) 18.82/5.79 f2229_in(one(one(T530))) -> U38(f2182_in(T530), one(one(T530))) 18.82/5.79 U38(f2182_out1, one(one(T530))) -> f2229_out1(zero(one(T530)), one(b)) 18.82/5.79 f2229_in(one(zero(T535))) -> U39(f2175_in(T535), one(zero(T535))) 18.82/5.79 U39(f2175_out1, one(zero(T535))) -> f2229_out1(zero(zero(T535)), one(b)) 18.82/5.79 f2229_in(one(T550)) -> U40(f2229_in(T550), one(T550)) 18.82/5.79 U40(f2229_out1(T551, T552), one(T550)) -> f2229_out1(zero(T551), one(T552)) 18.82/5.79 f2229_in(one(T570)) -> U41(f2300_in(T570), one(T570)) 18.82/5.79 U41(f2300_out1(T571, T572), one(T570)) -> f2229_out1(one(T571), zero(T572)) 18.82/5.79 f2229_in(zero(T612)) -> U42(f2342_in(T612), zero(T612)) 18.82/5.79 U42(f2342_out1(T613, T614), zero(T612)) -> f2229_out1(one(T613), one(T614)) 18.82/5.79 f2393_in(one(b)) -> f2393_out1(b) 18.82/5.79 f2393_in(one(T644)) -> U43(f2175_in(T644), one(T644)) 18.82/5.79 U43(f2175_out1, one(T644)) -> f2393_out1(zero(T644)) 18.82/5.79 f2393_in(zero(T651)) -> U44(f2393_in(T651), zero(T651)) 18.82/5.79 U44(f2393_out1(T652), zero(T651)) -> f2393_out1(one(T652)) 18.82/5.79 f2352_in(one(T631)) -> U45(f2175_in(T631), one(T631)) 18.82/5.79 U45(f2175_out1, one(T631)) -> f2352_out1(zero(T631)) 18.82/5.79 f2352_in(zero(T638)) -> U46(f2393_in(T638), zero(T638)) 18.82/5.79 U46(f2393_out1(T639), zero(T638)) -> f2352_out1(one(T639)) 18.82/5.79 f2435_in(one(T698)) -> U47(f2229_in(T698), one(T698)) 18.82/5.79 U47(f2229_out1(T699, T700), one(T698)) -> f2435_out1(zero(T699), zero(T700)) 18.82/5.79 f2435_in(zero(one(T726))) -> U48(f2175_in(T726), zero(one(T726))) 18.82/5.79 U48(f2175_out1, zero(one(T726))) -> f2435_out1(zero(zero(T726)), one(b)) 18.82/5.79 f2435_in(zero(zero(T737))) -> U49(f2393_in(T737), zero(zero(T737))) 18.82/5.79 U49(f2393_out1(T738), zero(zero(T737))) -> f2435_out1(zero(one(T738)), one(b)) 18.82/5.79 f2435_in(zero(T752)) -> U50(f2435_in(T752), zero(T752)) 18.82/5.79 U50(f2435_out1(T753, T754), zero(T752)) -> f2435_out1(zero(T753), one(T754)) 18.82/5.79 f2435_in(zero(one(T780))) -> U51(f2175_in(T780), zero(one(T780))) 18.82/5.79 U51(f2175_out1, zero(one(T780))) -> f2435_out1(one(b), zero(zero(T780))) 18.82/5.79 f2435_in(zero(zero(T791))) -> U52(f2393_in(T791), zero(zero(T791))) 18.82/5.79 U52(f2393_out1(T792), zero(zero(T791))) -> f2435_out1(one(b), zero(one(T792))) 18.82/5.79 f2435_in(zero(T806)) -> U53(f2435_in(T806), zero(T806)) 18.82/5.79 U53(f2435_out1(T807, T808), zero(T806)) -> f2435_out1(one(T807), zero(T808)) 18.82/5.79 f2435_in(one(T820)) -> U54(f2342_in(T820), one(T820)) 18.82/5.79 U54(f2342_out1(T821, T822), one(T820)) -> f2435_out1(one(T821), one(T822)) 18.82/5.79 f2342_in(one(b)) -> f2342_out1(b, b) 18.82/5.79 f2342_in(T624) -> U55(f2352_in(T624), T624) 18.82/5.79 U55(f2352_out1(T625), T624) -> f2342_out1(T625, b) 18.82/5.79 f2342_in(T662) -> U56(f2352_in(T662), T662) 18.82/5.79 U56(f2352_out1(T663), T662) -> f2342_out1(b, T663) 18.82/5.79 f2342_in(T678) -> U57(f2435_in(T678), T678) 18.82/5.79 U57(f2435_out1(T679, T680), T678) -> f2342_out1(T679, T680) 18.82/5.79 f2300_in(one(T578)) -> U58(f2182_in(T578), one(T578)) 18.82/5.79 U58(f2182_out1, one(T578)) -> f2300_out1(b, one(T578)) 18.82/5.79 f2300_in(zero(T583)) -> U59(f2175_in(T583), zero(T583)) 18.82/5.79 U59(f2175_out1, zero(T583)) -> f2300_out1(b, zero(T583)) 18.82/5.79 f2300_in(T598) -> U60(f2229_in(T598), T598) 18.82/5.79 U60(f2229_out1(T599, T600), T598) -> f2300_out1(T599, T600) 18.82/5.79 f109_in(zero(T429)) -> U61(f2175_in(T429), zero(T429)) 18.82/5.79 U61(f2175_out1, zero(T429)) -> f109_out1(b, T429) 18.82/5.79 f109_in(zero(T482)) -> U62(f2229_in(T482), zero(T482)) 18.82/5.79 U62(f2229_out1(T483, T484), zero(T482)) -> f109_out1(zero(T483), T484) 18.82/5.79 f109_in(one(T838)) -> U63(f2300_in(T838), one(T838)) 18.82/5.79 U63(f2300_out1(T839, T840), one(T838)) -> f109_out1(one(T839), T840) 18.82/5.79 f898_in -> U64(f1142_in) 18.82/5.79 U64(f1142_out1(T95)) -> f898_out1(b, T95, zero(T95)) 18.82/5.79 f898_in -> U65(f1256_in) 18.82/5.79 U65(f1256_out1(T143, T144, X156)) -> f898_out1(zero(T143), T144, zero(X156)) 18.82/5.79 f898_in -> U66(f1592_in) 18.82/5.79 U66(f1592_out1(T412, T413, X565)) -> f898_out1(one(T412), T413, one(X565)) 18.82/5.79 f42_in(T36) -> U67(f104_in, T36) 18.82/5.79 U67(f104_out1(T37), T36) -> U68(f109_in(T36), T36, T37) 18.82/5.79 U68(f109_out1(T42, T41), T36, T37) -> f42_out1(T37, T42, T41) 18.82/5.79 f888_in -> U69(f104_in) 18.82/5.79 U69(f104_out1(T70)) -> U70(f898_in, T70) 18.82/5.79 U70(f898_out1(T75, T74, X78), T70) -> f888_out1(T70, T75, T74, X78) 18.82/5.79 18.82/5.79 Q is empty. 18.82/5.79 We have to consider all minimal (P,Q,R)-chains. 18.82/5.79 ---------------------------------------- 18.82/5.79 18.82/5.79 (114) UsableRulesProof (EQUIVALENT) 18.82/5.79 We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R. 18.82/5.79 ---------------------------------------- 18.82/5.79 18.82/5.79 (115) 18.82/5.79 Obligation: 18.82/5.79 Q DP problem: 18.82/5.79 The TRS P consists of the following rules: 18.82/5.79 18.82/5.79 F2229_IN(one(T550)) -> F2229_IN(T550) 18.82/5.79 F2229_IN(zero(T502)) -> F2229_IN(T502) 18.82/5.79 F2229_IN(one(T570)) -> F2300_IN(T570) 18.82/5.79 F2300_IN(T598) -> F2229_IN(T598) 18.82/5.79 F2229_IN(zero(T612)) -> F2342_IN(T612) 18.82/5.79 F2342_IN(T678) -> F2435_IN(T678) 18.82/5.79 F2435_IN(one(T698)) -> F2229_IN(T698) 18.82/5.79 F2435_IN(zero(T752)) -> F2435_IN(T752) 18.82/5.79 F2435_IN(one(T820)) -> F2342_IN(T820) 18.82/5.79 18.82/5.79 R is empty. 18.82/5.79 Q is empty. 18.82/5.79 We have to consider all minimal (P,Q,R)-chains. 18.82/5.79 ---------------------------------------- 18.82/5.79 18.82/5.79 (116) QDPSizeChangeProof (EQUIVALENT) 18.82/5.79 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 18.82/5.79 18.82/5.79 From the DPs we obtained the following set of size-change graphs: 18.82/5.79 *F2300_IN(T598) -> F2229_IN(T598) 18.82/5.79 The graph contains the following edges 1 >= 1 18.82/5.79 18.82/5.79 18.82/5.79 *F2435_IN(one(T698)) -> F2229_IN(T698) 18.82/5.79 The graph contains the following edges 1 > 1 18.82/5.79 18.82/5.79 18.82/5.79 *F2229_IN(one(T570)) -> F2300_IN(T570) 18.82/5.79 The graph contains the following edges 1 > 1 18.82/5.79 18.82/5.79 18.82/5.79 *F2229_IN(zero(T612)) -> F2342_IN(T612) 18.82/5.79 The graph contains the following edges 1 > 1 18.82/5.79 18.82/5.79 18.82/5.79 *F2342_IN(T678) -> F2435_IN(T678) 18.82/5.79 The graph contains the following edges 1 >= 1 18.82/5.79 18.82/5.79 18.82/5.79 *F2435_IN(one(T820)) -> F2342_IN(T820) 18.82/5.79 The graph contains the following edges 1 > 1 18.82/5.79 18.82/5.79 18.82/5.79 *F2435_IN(zero(T752)) -> F2435_IN(T752) 18.82/5.79 The graph contains the following edges 1 > 1 18.82/5.79 18.82/5.79 18.82/5.79 *F2229_IN(one(T550)) -> F2229_IN(T550) 18.82/5.79 The graph contains the following edges 1 > 1 18.82/5.79 18.82/5.79 18.82/5.79 *F2229_IN(zero(T502)) -> F2229_IN(T502) 18.82/5.79 The graph contains the following edges 1 > 1 18.82/5.79 18.82/5.79 18.82/5.79 ---------------------------------------- 18.82/5.79 18.82/5.79 (117) 18.82/5.79 YES 18.82/5.79 18.82/5.79 ---------------------------------------- 18.82/5.79 18.82/5.79 (118) 18.82/5.79 Obligation: 18.82/5.79 Q DP problem: 18.82/5.79 The TRS P consists of the following rules: 18.82/5.79 18.82/5.79 F1142_IN -> F1151_IN 18.82/5.79 F1151_IN -> F1142_IN 18.82/5.79 F1142_IN -> F1142_IN 18.82/5.79 F1151_IN -> F1151_IN 18.82/5.79 18.82/5.79 The TRS R consists of the following rules: 18.82/5.79 18.82/5.79 f3_in(T8) -> f3_out1(one(b), T8) 18.82/5.79 f3_in(zero(T23)) -> U1(f3_in(T23), zero(T23)) 18.82/5.79 U1(f3_out1(T24, T25), zero(T23)) -> f3_out1(zero(T24), T25) 18.82/5.79 f3_in(T36) -> U2(f42_in(T36), T36) 18.82/5.79 U2(f42_out1(T37, T38, X33), T36) -> f3_out1(one(T37), T38) 18.82/5.79 f104_in -> f104_out1(one(b)) 18.82/5.79 f104_in -> U3(f104_in) 18.82/5.79 U3(f104_out1(T60)) -> f104_out1(zero(T60)) 18.82/5.79 f104_in -> U4(f888_in) 18.82/5.79 U4(f888_out1(T70, T71, X77, X78)) -> f104_out1(one(T70)) 18.82/5.79 f1142_in -> U5(f1142_in) 18.82/5.79 U5(f1142_out1(T102)) -> f1142_out1(zero(T102)) 18.82/5.79 f1142_in -> U6(f1151_in) 18.82/5.79 U6(f1151_out1(T107)) -> f1142_out1(one(T107)) 18.82/5.79 f1151_in -> f1151_out1(b) 18.82/5.79 f1151_in -> U7(f1142_in) 18.82/5.79 U7(f1142_out1(T113)) -> f1151_out1(zero(T113)) 18.82/5.79 f1151_in -> U8(f1151_in) 18.82/5.79 U8(f1151_out1(T118)) -> f1151_out1(one(T118)) 18.82/5.79 f1256_in -> U9(f1256_in) 18.82/5.79 U9(f1256_out1(T157, T158, X180)) -> f1256_out1(zero(T157), zero(T158), zero(X180)) 18.82/5.79 f1256_in -> U10(f1151_in) 18.82/5.79 U10(f1151_out1(T179)) -> f1256_out1(zero(one(T179)), one(b), one(one(T179))) 18.82/5.79 f1256_in -> U11(f1142_in) 18.82/5.79 U11(f1142_out1(T185)) -> f1256_out1(zero(zero(T185)), one(b), one(zero(T185))) 18.82/5.79 f1256_in -> U12(f1256_in) 18.82/5.79 U12(f1256_out1(T197, T198, X232)) -> f1256_out1(zero(T197), one(T198), one(X232)) 18.82/5.79 f1256_in -> U13(f1592_in) 18.82/5.79 U13(f1592_out1(T211, T212, X256)) -> f1256_out1(one(T211), zero(T212), one(X256)) 18.82/5.79 f1256_in -> U14(f1650_in) 18.82/5.79 U14(f1650_out1(T247, T248, X300)) -> f1256_out1(one(T247), one(T248), zero(X300)) 18.82/5.79 f1696_in -> f1696_out1(b, one(b)) 18.82/5.79 f1696_in -> U15(f1142_in) 18.82/5.79 U15(f1142_out1(T272)) -> f1696_out1(zero(T272), one(T272)) 18.82/5.79 f1696_in -> U16(f1696_in) 18.82/5.79 U16(f1696_out1(T277, X346)) -> f1696_out1(one(T277), zero(X346)) 18.82/5.79 f1677_in -> U17(f1142_in) 18.82/5.79 U17(f1142_out1(T261)) -> f1677_out1(zero(T261), one(T261)) 18.82/5.79 f1677_in -> U18(f1696_in) 18.82/5.79 U18(f1696_out1(T266, X331)) -> f1677_out1(one(T266), zero(X331)) 18.82/5.79 f1733_in -> U19(f1256_in) 18.82/5.79 U19(f1256_out1(T309, T310, X402)) -> f1733_out1(zero(T309), zero(T310), one(X402)) 18.82/5.79 f1733_in -> U20(f1142_in) 18.82/5.79 U20(f1142_out1(T331)) -> f1733_out1(zero(zero(T331)), one(b), zero(one(T331))) 18.82/5.79 f1733_in -> U21(f1696_in) 18.82/5.79 U21(f1696_out1(T338, X448)) -> f1733_out1(zero(one(T338)), one(b), zero(zero(X448))) 18.82/5.79 f1733_in -> U22(f1733_in) 18.82/5.79 U22(f1733_out1(T349, T350, X464)) -> f1733_out1(zero(T349), one(T350), zero(X464)) 18.82/5.79 f1733_in -> U23(f1142_in) 18.82/5.79 U23(f1142_out1(T371)) -> f1733_out1(one(b), zero(zero(T371)), zero(one(T371))) 18.82/5.79 f1733_in -> U24(f1696_in) 18.82/5.79 U24(f1696_out1(T378, X510)) -> f1733_out1(one(b), zero(one(T378)), zero(zero(X510))) 18.82/5.79 f1733_in -> U25(f1733_in) 18.82/5.79 U25(f1733_out1(T389, T390, X526)) -> f1733_out1(one(T389), zero(T390), zero(X526)) 18.82/5.79 f1733_in -> U26(f1650_in) 18.82/5.79 U26(f1650_out1(T399, T400, X542)) -> f1733_out1(one(T399), one(T400), one(X542)) 18.82/5.79 f1650_in -> f1650_out1(b, b, one(b)) 18.82/5.79 f1650_in -> U27(f1677_in) 18.82/5.79 U27(f1677_out1(T254, X315)) -> f1650_out1(T254, b, X315) 18.82/5.79 f1650_in -> U28(f1677_in) 18.82/5.79 U28(f1677_out1(T283, X361)) -> f1650_out1(b, T283, X361) 18.82/5.79 f1650_in -> U29(f1733_in) 18.82/5.79 U29(f1733_out1(T295, T296, X378)) -> f1650_out1(T295, T296, X378) 18.82/5.79 f1592_in -> U30(f1151_in) 18.82/5.79 U30(f1151_out1(T219)) -> f1592_out1(b, one(T219), one(T219)) 18.82/5.79 f1592_in -> U31(f1142_in) 18.82/5.79 U31(f1142_out1(T225)) -> f1592_out1(b, zero(T225), zero(T225)) 18.82/5.79 f1592_in -> U32(f1256_in) 18.82/5.79 U32(f1256_out1(T237, T238, X284)) -> f1592_out1(T237, T238, X284) 18.82/5.79 f2175_in(zero(T435)) -> U33(f2175_in(T435), zero(T435)) 18.82/5.79 U33(f2175_out1, zero(T435)) -> f2175_out1 18.82/5.79 f2175_in(one(T439)) -> U34(f2182_in(T439), one(T439)) 18.82/5.79 U34(f2182_out1, one(T439)) -> f2175_out1 18.82/5.79 f2182_in(b) -> f2182_out1 18.82/5.79 f2182_in(zero(T444)) -> U35(f2175_in(T444), zero(T444)) 18.82/5.79 U35(f2175_out1, zero(T444)) -> f2182_out1 18.82/5.79 f2182_in(one(T448)) -> U36(f2182_in(T448), one(T448)) 18.82/5.79 U36(f2182_out1, one(T448)) -> f2182_out1 18.82/5.79 f2229_in(zero(T502)) -> U37(f2229_in(T502), zero(T502)) 18.82/5.79 U37(f2229_out1(T503, T504), zero(T502)) -> f2229_out1(zero(T503), zero(T504)) 18.82/5.79 f2229_in(one(one(T530))) -> U38(f2182_in(T530), one(one(T530))) 18.82/5.79 U38(f2182_out1, one(one(T530))) -> f2229_out1(zero(one(T530)), one(b)) 18.82/5.79 f2229_in(one(zero(T535))) -> U39(f2175_in(T535), one(zero(T535))) 18.82/5.79 U39(f2175_out1, one(zero(T535))) -> f2229_out1(zero(zero(T535)), one(b)) 18.82/5.79 f2229_in(one(T550)) -> U40(f2229_in(T550), one(T550)) 18.82/5.79 U40(f2229_out1(T551, T552), one(T550)) -> f2229_out1(zero(T551), one(T552)) 18.82/5.79 f2229_in(one(T570)) -> U41(f2300_in(T570), one(T570)) 18.82/5.79 U41(f2300_out1(T571, T572), one(T570)) -> f2229_out1(one(T571), zero(T572)) 18.82/5.79 f2229_in(zero(T612)) -> U42(f2342_in(T612), zero(T612)) 18.82/5.79 U42(f2342_out1(T613, T614), zero(T612)) -> f2229_out1(one(T613), one(T614)) 18.82/5.79 f2393_in(one(b)) -> f2393_out1(b) 18.82/5.79 f2393_in(one(T644)) -> U43(f2175_in(T644), one(T644)) 18.82/5.79 U43(f2175_out1, one(T644)) -> f2393_out1(zero(T644)) 18.82/5.79 f2393_in(zero(T651)) -> U44(f2393_in(T651), zero(T651)) 18.82/5.79 U44(f2393_out1(T652), zero(T651)) -> f2393_out1(one(T652)) 18.82/5.79 f2352_in(one(T631)) -> U45(f2175_in(T631), one(T631)) 18.82/5.79 U45(f2175_out1, one(T631)) -> f2352_out1(zero(T631)) 18.82/5.79 f2352_in(zero(T638)) -> U46(f2393_in(T638), zero(T638)) 18.82/5.79 U46(f2393_out1(T639), zero(T638)) -> f2352_out1(one(T639)) 18.82/5.79 f2435_in(one(T698)) -> U47(f2229_in(T698), one(T698)) 18.82/5.79 U47(f2229_out1(T699, T700), one(T698)) -> f2435_out1(zero(T699), zero(T700)) 18.82/5.79 f2435_in(zero(one(T726))) -> U48(f2175_in(T726), zero(one(T726))) 18.82/5.79 U48(f2175_out1, zero(one(T726))) -> f2435_out1(zero(zero(T726)), one(b)) 18.82/5.79 f2435_in(zero(zero(T737))) -> U49(f2393_in(T737), zero(zero(T737))) 18.82/5.79 U49(f2393_out1(T738), zero(zero(T737))) -> f2435_out1(zero(one(T738)), one(b)) 18.82/5.79 f2435_in(zero(T752)) -> U50(f2435_in(T752), zero(T752)) 18.82/5.79 U50(f2435_out1(T753, T754), zero(T752)) -> f2435_out1(zero(T753), one(T754)) 18.82/5.79 f2435_in(zero(one(T780))) -> U51(f2175_in(T780), zero(one(T780))) 18.82/5.79 U51(f2175_out1, zero(one(T780))) -> f2435_out1(one(b), zero(zero(T780))) 18.82/5.79 f2435_in(zero(zero(T791))) -> U52(f2393_in(T791), zero(zero(T791))) 18.82/5.79 U52(f2393_out1(T792), zero(zero(T791))) -> f2435_out1(one(b), zero(one(T792))) 18.82/5.79 f2435_in(zero(T806)) -> U53(f2435_in(T806), zero(T806)) 18.82/5.79 U53(f2435_out1(T807, T808), zero(T806)) -> f2435_out1(one(T807), zero(T808)) 18.82/5.79 f2435_in(one(T820)) -> U54(f2342_in(T820), one(T820)) 18.82/5.79 U54(f2342_out1(T821, T822), one(T820)) -> f2435_out1(one(T821), one(T822)) 18.82/5.79 f2342_in(one(b)) -> f2342_out1(b, b) 18.82/5.79 f2342_in(T624) -> U55(f2352_in(T624), T624) 18.82/5.79 U55(f2352_out1(T625), T624) -> f2342_out1(T625, b) 18.82/5.79 f2342_in(T662) -> U56(f2352_in(T662), T662) 18.82/5.79 U56(f2352_out1(T663), T662) -> f2342_out1(b, T663) 18.82/5.79 f2342_in(T678) -> U57(f2435_in(T678), T678) 18.82/5.79 U57(f2435_out1(T679, T680), T678) -> f2342_out1(T679, T680) 18.82/5.79 f2300_in(one(T578)) -> U58(f2182_in(T578), one(T578)) 18.82/5.79 U58(f2182_out1, one(T578)) -> f2300_out1(b, one(T578)) 18.82/5.79 f2300_in(zero(T583)) -> U59(f2175_in(T583), zero(T583)) 18.82/5.79 U59(f2175_out1, zero(T583)) -> f2300_out1(b, zero(T583)) 18.82/5.79 f2300_in(T598) -> U60(f2229_in(T598), T598) 18.82/5.79 U60(f2229_out1(T599, T600), T598) -> f2300_out1(T599, T600) 18.82/5.79 f109_in(zero(T429)) -> U61(f2175_in(T429), zero(T429)) 18.82/5.79 U61(f2175_out1, zero(T429)) -> f109_out1(b, T429) 18.82/5.79 f109_in(zero(T482)) -> U62(f2229_in(T482), zero(T482)) 18.82/5.79 U62(f2229_out1(T483, T484), zero(T482)) -> f109_out1(zero(T483), T484) 18.82/5.79 f109_in(one(T838)) -> U63(f2300_in(T838), one(T838)) 18.82/5.79 U63(f2300_out1(T839, T840), one(T838)) -> f109_out1(one(T839), T840) 18.82/5.79 f898_in -> U64(f1142_in) 18.82/5.79 U64(f1142_out1(T95)) -> f898_out1(b, T95, zero(T95)) 18.82/5.79 f898_in -> U65(f1256_in) 18.82/5.79 U65(f1256_out1(T143, T144, X156)) -> f898_out1(zero(T143), T144, zero(X156)) 18.82/5.79 f898_in -> U66(f1592_in) 18.82/5.79 U66(f1592_out1(T412, T413, X565)) -> f898_out1(one(T412), T413, one(X565)) 18.82/5.79 f42_in(T36) -> U67(f104_in, T36) 18.82/5.79 U67(f104_out1(T37), T36) -> U68(f109_in(T36), T36, T37) 18.82/5.79 U68(f109_out1(T42, T41), T36, T37) -> f42_out1(T37, T42, T41) 18.82/5.79 f888_in -> U69(f104_in) 18.82/5.79 U69(f104_out1(T70)) -> U70(f898_in, T70) 18.82/5.79 U70(f898_out1(T75, T74, X78), T70) -> f888_out1(T70, T75, T74, X78) 18.82/5.79 18.82/5.79 Q is empty. 18.82/5.79 We have to consider all minimal (P,Q,R)-chains. 18.82/5.79 ---------------------------------------- 18.82/5.79 18.82/5.79 (119) UsableRulesProof (EQUIVALENT) 18.82/5.79 We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R. 18.82/5.79 ---------------------------------------- 18.82/5.79 18.82/5.79 (120) 18.82/5.79 Obligation: 18.82/5.79 Q DP problem: 18.82/5.79 The TRS P consists of the following rules: 18.82/5.79 18.82/5.79 F1142_IN -> F1151_IN 18.82/5.79 F1151_IN -> F1142_IN 18.82/5.79 F1142_IN -> F1142_IN 18.82/5.79 F1151_IN -> F1151_IN 18.82/5.79 18.82/5.79 R is empty. 18.82/5.79 Q is empty. 18.82/5.79 We have to consider all minimal (P,Q,R)-chains. 18.82/5.79 ---------------------------------------- 18.82/5.79 18.82/5.79 (121) 18.82/5.79 Obligation: 18.82/5.79 Q DP problem: 18.82/5.79 The TRS P consists of the following rules: 18.82/5.79 18.82/5.79 F1696_IN -> F1696_IN 18.82/5.79 18.82/5.79 The TRS R consists of the following rules: 18.82/5.79 18.82/5.79 f3_in(T8) -> f3_out1(one(b), T8) 18.82/5.79 f3_in(zero(T23)) -> U1(f3_in(T23), zero(T23)) 18.82/5.79 U1(f3_out1(T24, T25), zero(T23)) -> f3_out1(zero(T24), T25) 18.82/5.79 f3_in(T36) -> U2(f42_in(T36), T36) 18.82/5.79 U2(f42_out1(T37, T38, X33), T36) -> f3_out1(one(T37), T38) 18.82/5.79 f104_in -> f104_out1(one(b)) 18.82/5.79 f104_in -> U3(f104_in) 18.82/5.79 U3(f104_out1(T60)) -> f104_out1(zero(T60)) 18.82/5.79 f104_in -> U4(f888_in) 18.82/5.79 U4(f888_out1(T70, T71, X77, X78)) -> f104_out1(one(T70)) 18.82/5.79 f1142_in -> U5(f1142_in) 18.82/5.79 U5(f1142_out1(T102)) -> f1142_out1(zero(T102)) 18.82/5.79 f1142_in -> U6(f1151_in) 18.82/5.79 U6(f1151_out1(T107)) -> f1142_out1(one(T107)) 18.82/5.79 f1151_in -> f1151_out1(b) 18.82/5.79 f1151_in -> U7(f1142_in) 18.82/5.79 U7(f1142_out1(T113)) -> f1151_out1(zero(T113)) 18.82/5.79 f1151_in -> U8(f1151_in) 18.82/5.79 U8(f1151_out1(T118)) -> f1151_out1(one(T118)) 18.82/5.79 f1256_in -> U9(f1256_in) 18.82/5.79 U9(f1256_out1(T157, T158, X180)) -> f1256_out1(zero(T157), zero(T158), zero(X180)) 18.82/5.79 f1256_in -> U10(f1151_in) 18.82/5.79 U10(f1151_out1(T179)) -> f1256_out1(zero(one(T179)), one(b), one(one(T179))) 18.82/5.79 f1256_in -> U11(f1142_in) 18.82/5.79 U11(f1142_out1(T185)) -> f1256_out1(zero(zero(T185)), one(b), one(zero(T185))) 18.82/5.79 f1256_in -> U12(f1256_in) 18.82/5.79 U12(f1256_out1(T197, T198, X232)) -> f1256_out1(zero(T197), one(T198), one(X232)) 18.82/5.79 f1256_in -> U13(f1592_in) 18.82/5.79 U13(f1592_out1(T211, T212, X256)) -> f1256_out1(one(T211), zero(T212), one(X256)) 18.82/5.79 f1256_in -> U14(f1650_in) 18.82/5.79 U14(f1650_out1(T247, T248, X300)) -> f1256_out1(one(T247), one(T248), zero(X300)) 18.82/5.79 f1696_in -> f1696_out1(b, one(b)) 18.82/5.79 f1696_in -> U15(f1142_in) 18.82/5.79 U15(f1142_out1(T272)) -> f1696_out1(zero(T272), one(T272)) 18.82/5.79 f1696_in -> U16(f1696_in) 18.82/5.79 U16(f1696_out1(T277, X346)) -> f1696_out1(one(T277), zero(X346)) 18.82/5.79 f1677_in -> U17(f1142_in) 18.82/5.79 U17(f1142_out1(T261)) -> f1677_out1(zero(T261), one(T261)) 18.82/5.79 f1677_in -> U18(f1696_in) 18.82/5.79 U18(f1696_out1(T266, X331)) -> f1677_out1(one(T266), zero(X331)) 18.82/5.79 f1733_in -> U19(f1256_in) 18.82/5.79 U19(f1256_out1(T309, T310, X402)) -> f1733_out1(zero(T309), zero(T310), one(X402)) 18.82/5.79 f1733_in -> U20(f1142_in) 18.82/5.79 U20(f1142_out1(T331)) -> f1733_out1(zero(zero(T331)), one(b), zero(one(T331))) 18.82/5.79 f1733_in -> U21(f1696_in) 18.82/5.79 U21(f1696_out1(T338, X448)) -> f1733_out1(zero(one(T338)), one(b), zero(zero(X448))) 18.82/5.79 f1733_in -> U22(f1733_in) 18.82/5.79 U22(f1733_out1(T349, T350, X464)) -> f1733_out1(zero(T349), one(T350), zero(X464)) 18.82/5.79 f1733_in -> U23(f1142_in) 18.82/5.79 U23(f1142_out1(T371)) -> f1733_out1(one(b), zero(zero(T371)), zero(one(T371))) 18.82/5.79 f1733_in -> U24(f1696_in) 18.82/5.79 U24(f1696_out1(T378, X510)) -> f1733_out1(one(b), zero(one(T378)), zero(zero(X510))) 18.82/5.79 f1733_in -> U25(f1733_in) 18.82/5.79 U25(f1733_out1(T389, T390, X526)) -> f1733_out1(one(T389), zero(T390), zero(X526)) 18.82/5.79 f1733_in -> U26(f1650_in) 18.82/5.79 U26(f1650_out1(T399, T400, X542)) -> f1733_out1(one(T399), one(T400), one(X542)) 18.82/5.79 f1650_in -> f1650_out1(b, b, one(b)) 18.82/5.79 f1650_in -> U27(f1677_in) 18.82/5.79 U27(f1677_out1(T254, X315)) -> f1650_out1(T254, b, X315) 18.82/5.79 f1650_in -> U28(f1677_in) 18.82/5.79 U28(f1677_out1(T283, X361)) -> f1650_out1(b, T283, X361) 18.82/5.79 f1650_in -> U29(f1733_in) 18.82/5.79 U29(f1733_out1(T295, T296, X378)) -> f1650_out1(T295, T296, X378) 18.82/5.79 f1592_in -> U30(f1151_in) 18.82/5.79 U30(f1151_out1(T219)) -> f1592_out1(b, one(T219), one(T219)) 18.82/5.79 f1592_in -> U31(f1142_in) 18.82/5.79 U31(f1142_out1(T225)) -> f1592_out1(b, zero(T225), zero(T225)) 18.82/5.79 f1592_in -> U32(f1256_in) 18.82/5.79 U32(f1256_out1(T237, T238, X284)) -> f1592_out1(T237, T238, X284) 18.82/5.79 f2175_in(zero(T435)) -> U33(f2175_in(T435), zero(T435)) 18.82/5.79 U33(f2175_out1, zero(T435)) -> f2175_out1 18.82/5.79 f2175_in(one(T439)) -> U34(f2182_in(T439), one(T439)) 18.82/5.79 U34(f2182_out1, one(T439)) -> f2175_out1 18.82/5.79 f2182_in(b) -> f2182_out1 18.82/5.79 f2182_in(zero(T444)) -> U35(f2175_in(T444), zero(T444)) 18.82/5.79 U35(f2175_out1, zero(T444)) -> f2182_out1 18.82/5.79 f2182_in(one(T448)) -> U36(f2182_in(T448), one(T448)) 18.82/5.79 U36(f2182_out1, one(T448)) -> f2182_out1 18.82/5.79 f2229_in(zero(T502)) -> U37(f2229_in(T502), zero(T502)) 18.82/5.79 U37(f2229_out1(T503, T504), zero(T502)) -> f2229_out1(zero(T503), zero(T504)) 18.82/5.79 f2229_in(one(one(T530))) -> U38(f2182_in(T530), one(one(T530))) 18.82/5.79 U38(f2182_out1, one(one(T530))) -> f2229_out1(zero(one(T530)), one(b)) 18.82/5.79 f2229_in(one(zero(T535))) -> U39(f2175_in(T535), one(zero(T535))) 18.82/5.79 U39(f2175_out1, one(zero(T535))) -> f2229_out1(zero(zero(T535)), one(b)) 18.82/5.79 f2229_in(one(T550)) -> U40(f2229_in(T550), one(T550)) 18.82/5.79 U40(f2229_out1(T551, T552), one(T550)) -> f2229_out1(zero(T551), one(T552)) 18.82/5.79 f2229_in(one(T570)) -> U41(f2300_in(T570), one(T570)) 18.82/5.79 U41(f2300_out1(T571, T572), one(T570)) -> f2229_out1(one(T571), zero(T572)) 18.82/5.79 f2229_in(zero(T612)) -> U42(f2342_in(T612), zero(T612)) 18.82/5.79 U42(f2342_out1(T613, T614), zero(T612)) -> f2229_out1(one(T613), one(T614)) 18.82/5.79 f2393_in(one(b)) -> f2393_out1(b) 18.82/5.79 f2393_in(one(T644)) -> U43(f2175_in(T644), one(T644)) 18.82/5.79 U43(f2175_out1, one(T644)) -> f2393_out1(zero(T644)) 18.82/5.79 f2393_in(zero(T651)) -> U44(f2393_in(T651), zero(T651)) 18.82/5.79 U44(f2393_out1(T652), zero(T651)) -> f2393_out1(one(T652)) 18.82/5.79 f2352_in(one(T631)) -> U45(f2175_in(T631), one(T631)) 18.82/5.79 U45(f2175_out1, one(T631)) -> f2352_out1(zero(T631)) 18.82/5.79 f2352_in(zero(T638)) -> U46(f2393_in(T638), zero(T638)) 18.82/5.79 U46(f2393_out1(T639), zero(T638)) -> f2352_out1(one(T639)) 18.82/5.79 f2435_in(one(T698)) -> U47(f2229_in(T698), one(T698)) 18.82/5.79 U47(f2229_out1(T699, T700), one(T698)) -> f2435_out1(zero(T699), zero(T700)) 18.82/5.79 f2435_in(zero(one(T726))) -> U48(f2175_in(T726), zero(one(T726))) 18.82/5.79 U48(f2175_out1, zero(one(T726))) -> f2435_out1(zero(zero(T726)), one(b)) 18.82/5.79 f2435_in(zero(zero(T737))) -> U49(f2393_in(T737), zero(zero(T737))) 18.82/5.79 U49(f2393_out1(T738), zero(zero(T737))) -> f2435_out1(zero(one(T738)), one(b)) 18.82/5.79 f2435_in(zero(T752)) -> U50(f2435_in(T752), zero(T752)) 18.82/5.79 U50(f2435_out1(T753, T754), zero(T752)) -> f2435_out1(zero(T753), one(T754)) 18.82/5.79 f2435_in(zero(one(T780))) -> U51(f2175_in(T780), zero(one(T780))) 18.82/5.79 U51(f2175_out1, zero(one(T780))) -> f2435_out1(one(b), zero(zero(T780))) 18.82/5.79 f2435_in(zero(zero(T791))) -> U52(f2393_in(T791), zero(zero(T791))) 18.82/5.79 U52(f2393_out1(T792), zero(zero(T791))) -> f2435_out1(one(b), zero(one(T792))) 18.82/5.79 f2435_in(zero(T806)) -> U53(f2435_in(T806), zero(T806)) 18.82/5.79 U53(f2435_out1(T807, T808), zero(T806)) -> f2435_out1(one(T807), zero(T808)) 18.82/5.79 f2435_in(one(T820)) -> U54(f2342_in(T820), one(T820)) 18.82/5.79 U54(f2342_out1(T821, T822), one(T820)) -> f2435_out1(one(T821), one(T822)) 18.82/5.79 f2342_in(one(b)) -> f2342_out1(b, b) 18.82/5.79 f2342_in(T624) -> U55(f2352_in(T624), T624) 18.82/5.79 U55(f2352_out1(T625), T624) -> f2342_out1(T625, b) 18.82/5.79 f2342_in(T662) -> U56(f2352_in(T662), T662) 18.82/5.79 U56(f2352_out1(T663), T662) -> f2342_out1(b, T663) 18.82/5.79 f2342_in(T678) -> U57(f2435_in(T678), T678) 18.82/5.79 U57(f2435_out1(T679, T680), T678) -> f2342_out1(T679, T680) 18.82/5.79 f2300_in(one(T578)) -> U58(f2182_in(T578), one(T578)) 18.82/5.79 U58(f2182_out1, one(T578)) -> f2300_out1(b, one(T578)) 18.82/5.79 f2300_in(zero(T583)) -> U59(f2175_in(T583), zero(T583)) 18.82/5.79 U59(f2175_out1, zero(T583)) -> f2300_out1(b, zero(T583)) 18.82/5.79 f2300_in(T598) -> U60(f2229_in(T598), T598) 18.82/5.79 U60(f2229_out1(T599, T600), T598) -> f2300_out1(T599, T600) 18.82/5.79 f109_in(zero(T429)) -> U61(f2175_in(T429), zero(T429)) 18.82/5.79 U61(f2175_out1, zero(T429)) -> f109_out1(b, T429) 18.82/5.79 f109_in(zero(T482)) -> U62(f2229_in(T482), zero(T482)) 18.82/5.79 U62(f2229_out1(T483, T484), zero(T482)) -> f109_out1(zero(T483), T484) 18.82/5.79 f109_in(one(T838)) -> U63(f2300_in(T838), one(T838)) 18.82/5.79 U63(f2300_out1(T839, T840), one(T838)) -> f109_out1(one(T839), T840) 18.82/5.79 f898_in -> U64(f1142_in) 18.82/5.79 U64(f1142_out1(T95)) -> f898_out1(b, T95, zero(T95)) 18.82/5.79 f898_in -> U65(f1256_in) 18.82/5.79 U65(f1256_out1(T143, T144, X156)) -> f898_out1(zero(T143), T144, zero(X156)) 18.82/5.79 f898_in -> U66(f1592_in) 18.82/5.79 U66(f1592_out1(T412, T413, X565)) -> f898_out1(one(T412), T413, one(X565)) 18.82/5.79 f42_in(T36) -> U67(f104_in, T36) 18.82/5.79 U67(f104_out1(T37), T36) -> U68(f109_in(T36), T36, T37) 18.82/5.79 U68(f109_out1(T42, T41), T36, T37) -> f42_out1(T37, T42, T41) 18.82/5.79 f888_in -> U69(f104_in) 18.82/5.79 U69(f104_out1(T70)) -> U70(f898_in, T70) 18.82/5.79 U70(f898_out1(T75, T74, X78), T70) -> f888_out1(T70, T75, T74, X78) 18.82/5.79 18.82/5.79 Q is empty. 18.82/5.79 We have to consider all minimal (P,Q,R)-chains. 18.82/5.79 ---------------------------------------- 18.82/5.79 18.82/5.79 (122) UsableRulesProof (EQUIVALENT) 18.82/5.79 We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R. 18.82/5.79 ---------------------------------------- 18.82/5.79 18.82/5.79 (123) 18.82/5.79 Obligation: 18.82/5.79 Q DP problem: 18.82/5.79 The TRS P consists of the following rules: 18.82/5.79 18.82/5.79 F1696_IN -> F1696_IN 18.82/5.79 18.82/5.79 R is empty. 18.82/5.79 Q is empty. 18.82/5.79 We have to consider all minimal (P,Q,R)-chains. 18.82/5.79 ---------------------------------------- 18.82/5.79 18.82/5.79 (124) 18.82/5.79 Obligation: 18.82/5.79 Q DP problem: 18.82/5.79 The TRS P consists of the following rules: 18.82/5.79 18.82/5.79 F1256_IN -> F1592_IN 18.82/5.79 F1592_IN -> F1256_IN 18.82/5.79 F1256_IN -> F1256_IN 18.82/5.79 F1256_IN -> F1650_IN 18.82/5.79 F1650_IN -> F1733_IN 18.82/5.79 F1733_IN -> F1256_IN 18.82/5.79 F1733_IN -> F1733_IN 18.82/5.79 F1733_IN -> F1650_IN 18.82/5.79 18.82/5.79 The TRS R consists of the following rules: 18.82/5.79 18.82/5.79 f3_in(T8) -> f3_out1(one(b), T8) 18.82/5.79 f3_in(zero(T23)) -> U1(f3_in(T23), zero(T23)) 18.82/5.79 U1(f3_out1(T24, T25), zero(T23)) -> f3_out1(zero(T24), T25) 18.82/5.79 f3_in(T36) -> U2(f42_in(T36), T36) 18.82/5.79 U2(f42_out1(T37, T38, X33), T36) -> f3_out1(one(T37), T38) 18.82/5.79 f104_in -> f104_out1(one(b)) 18.82/5.79 f104_in -> U3(f104_in) 18.82/5.79 U3(f104_out1(T60)) -> f104_out1(zero(T60)) 18.82/5.79 f104_in -> U4(f888_in) 18.82/5.79 U4(f888_out1(T70, T71, X77, X78)) -> f104_out1(one(T70)) 18.82/5.79 f1142_in -> U5(f1142_in) 18.82/5.79 U5(f1142_out1(T102)) -> f1142_out1(zero(T102)) 18.82/5.79 f1142_in -> U6(f1151_in) 18.82/5.79 U6(f1151_out1(T107)) -> f1142_out1(one(T107)) 18.82/5.79 f1151_in -> f1151_out1(b) 18.82/5.79 f1151_in -> U7(f1142_in) 18.82/5.79 U7(f1142_out1(T113)) -> f1151_out1(zero(T113)) 18.82/5.79 f1151_in -> U8(f1151_in) 18.82/5.79 U8(f1151_out1(T118)) -> f1151_out1(one(T118)) 18.82/5.79 f1256_in -> U9(f1256_in) 18.82/5.79 U9(f1256_out1(T157, T158, X180)) -> f1256_out1(zero(T157), zero(T158), zero(X180)) 18.82/5.79 f1256_in -> U10(f1151_in) 18.82/5.79 U10(f1151_out1(T179)) -> f1256_out1(zero(one(T179)), one(b), one(one(T179))) 18.82/5.79 f1256_in -> U11(f1142_in) 18.82/5.79 U11(f1142_out1(T185)) -> f1256_out1(zero(zero(T185)), one(b), one(zero(T185))) 18.82/5.79 f1256_in -> U12(f1256_in) 18.82/5.79 U12(f1256_out1(T197, T198, X232)) -> f1256_out1(zero(T197), one(T198), one(X232)) 18.82/5.79 f1256_in -> U13(f1592_in) 18.82/5.79 U13(f1592_out1(T211, T212, X256)) -> f1256_out1(one(T211), zero(T212), one(X256)) 18.82/5.79 f1256_in -> U14(f1650_in) 18.82/5.79 U14(f1650_out1(T247, T248, X300)) -> f1256_out1(one(T247), one(T248), zero(X300)) 18.82/5.79 f1696_in -> f1696_out1(b, one(b)) 18.82/5.79 f1696_in -> U15(f1142_in) 18.82/5.79 U15(f1142_out1(T272)) -> f1696_out1(zero(T272), one(T272)) 18.82/5.79 f1696_in -> U16(f1696_in) 18.82/5.79 U16(f1696_out1(T277, X346)) -> f1696_out1(one(T277), zero(X346)) 18.82/5.79 f1677_in -> U17(f1142_in) 18.82/5.79 U17(f1142_out1(T261)) -> f1677_out1(zero(T261), one(T261)) 18.82/5.79 f1677_in -> U18(f1696_in) 18.82/5.79 U18(f1696_out1(T266, X331)) -> f1677_out1(one(T266), zero(X331)) 18.82/5.79 f1733_in -> U19(f1256_in) 18.82/5.79 U19(f1256_out1(T309, T310, X402)) -> f1733_out1(zero(T309), zero(T310), one(X402)) 18.82/5.79 f1733_in -> U20(f1142_in) 18.82/5.79 U20(f1142_out1(T331)) -> f1733_out1(zero(zero(T331)), one(b), zero(one(T331))) 18.82/5.79 f1733_in -> U21(f1696_in) 18.82/5.79 U21(f1696_out1(T338, X448)) -> f1733_out1(zero(one(T338)), one(b), zero(zero(X448))) 18.82/5.79 f1733_in -> U22(f1733_in) 18.82/5.79 U22(f1733_out1(T349, T350, X464)) -> f1733_out1(zero(T349), one(T350), zero(X464)) 18.82/5.79 f1733_in -> U23(f1142_in) 18.82/5.79 U23(f1142_out1(T371)) -> f1733_out1(one(b), zero(zero(T371)), zero(one(T371))) 18.82/5.79 f1733_in -> U24(f1696_in) 18.82/5.79 U24(f1696_out1(T378, X510)) -> f1733_out1(one(b), zero(one(T378)), zero(zero(X510))) 18.82/5.79 f1733_in -> U25(f1733_in) 18.82/5.79 U25(f1733_out1(T389, T390, X526)) -> f1733_out1(one(T389), zero(T390), zero(X526)) 18.82/5.79 f1733_in -> U26(f1650_in) 18.82/5.79 U26(f1650_out1(T399, T400, X542)) -> f1733_out1(one(T399), one(T400), one(X542)) 18.82/5.79 f1650_in -> f1650_out1(b, b, one(b)) 18.82/5.79 f1650_in -> U27(f1677_in) 18.82/5.79 U27(f1677_out1(T254, X315)) -> f1650_out1(T254, b, X315) 18.82/5.79 f1650_in -> U28(f1677_in) 18.82/5.79 U28(f1677_out1(T283, X361)) -> f1650_out1(b, T283, X361) 18.82/5.79 f1650_in -> U29(f1733_in) 18.82/5.79 U29(f1733_out1(T295, T296, X378)) -> f1650_out1(T295, T296, X378) 18.82/5.79 f1592_in -> U30(f1151_in) 18.82/5.79 U30(f1151_out1(T219)) -> f1592_out1(b, one(T219), one(T219)) 18.82/5.79 f1592_in -> U31(f1142_in) 18.82/5.79 U31(f1142_out1(T225)) -> f1592_out1(b, zero(T225), zero(T225)) 18.82/5.79 f1592_in -> U32(f1256_in) 18.82/5.79 U32(f1256_out1(T237, T238, X284)) -> f1592_out1(T237, T238, X284) 18.82/5.79 f2175_in(zero(T435)) -> U33(f2175_in(T435), zero(T435)) 18.82/5.79 U33(f2175_out1, zero(T435)) -> f2175_out1 18.82/5.79 f2175_in(one(T439)) -> U34(f2182_in(T439), one(T439)) 18.82/5.79 U34(f2182_out1, one(T439)) -> f2175_out1 18.82/5.79 f2182_in(b) -> f2182_out1 18.82/5.79 f2182_in(zero(T444)) -> U35(f2175_in(T444), zero(T444)) 18.82/5.79 U35(f2175_out1, zero(T444)) -> f2182_out1 18.82/5.79 f2182_in(one(T448)) -> U36(f2182_in(T448), one(T448)) 18.82/5.79 U36(f2182_out1, one(T448)) -> f2182_out1 18.82/5.79 f2229_in(zero(T502)) -> U37(f2229_in(T502), zero(T502)) 18.82/5.79 U37(f2229_out1(T503, T504), zero(T502)) -> f2229_out1(zero(T503), zero(T504)) 18.82/5.79 f2229_in(one(one(T530))) -> U38(f2182_in(T530), one(one(T530))) 18.82/5.79 U38(f2182_out1, one(one(T530))) -> f2229_out1(zero(one(T530)), one(b)) 18.82/5.79 f2229_in(one(zero(T535))) -> U39(f2175_in(T535), one(zero(T535))) 18.82/5.79 U39(f2175_out1, one(zero(T535))) -> f2229_out1(zero(zero(T535)), one(b)) 18.82/5.79 f2229_in(one(T550)) -> U40(f2229_in(T550), one(T550)) 18.82/5.79 U40(f2229_out1(T551, T552), one(T550)) -> f2229_out1(zero(T551), one(T552)) 18.82/5.79 f2229_in(one(T570)) -> U41(f2300_in(T570), one(T570)) 18.82/5.79 U41(f2300_out1(T571, T572), one(T570)) -> f2229_out1(one(T571), zero(T572)) 18.82/5.79 f2229_in(zero(T612)) -> U42(f2342_in(T612), zero(T612)) 18.82/5.79 U42(f2342_out1(T613, T614), zero(T612)) -> f2229_out1(one(T613), one(T614)) 18.82/5.79 f2393_in(one(b)) -> f2393_out1(b) 18.82/5.79 f2393_in(one(T644)) -> U43(f2175_in(T644), one(T644)) 18.82/5.79 U43(f2175_out1, one(T644)) -> f2393_out1(zero(T644)) 18.82/5.79 f2393_in(zero(T651)) -> U44(f2393_in(T651), zero(T651)) 18.82/5.79 U44(f2393_out1(T652), zero(T651)) -> f2393_out1(one(T652)) 18.82/5.79 f2352_in(one(T631)) -> U45(f2175_in(T631), one(T631)) 18.82/5.79 U45(f2175_out1, one(T631)) -> f2352_out1(zero(T631)) 18.82/5.79 f2352_in(zero(T638)) -> U46(f2393_in(T638), zero(T638)) 18.82/5.79 U46(f2393_out1(T639), zero(T638)) -> f2352_out1(one(T639)) 18.82/5.79 f2435_in(one(T698)) -> U47(f2229_in(T698), one(T698)) 18.82/5.79 U47(f2229_out1(T699, T700), one(T698)) -> f2435_out1(zero(T699), zero(T700)) 18.82/5.79 f2435_in(zero(one(T726))) -> U48(f2175_in(T726), zero(one(T726))) 18.82/5.79 U48(f2175_out1, zero(one(T726))) -> f2435_out1(zero(zero(T726)), one(b)) 18.82/5.79 f2435_in(zero(zero(T737))) -> U49(f2393_in(T737), zero(zero(T737))) 18.82/5.79 U49(f2393_out1(T738), zero(zero(T737))) -> f2435_out1(zero(one(T738)), one(b)) 18.82/5.79 f2435_in(zero(T752)) -> U50(f2435_in(T752), zero(T752)) 18.82/5.79 U50(f2435_out1(T753, T754), zero(T752)) -> f2435_out1(zero(T753), one(T754)) 18.82/5.79 f2435_in(zero(one(T780))) -> U51(f2175_in(T780), zero(one(T780))) 18.82/5.79 U51(f2175_out1, zero(one(T780))) -> f2435_out1(one(b), zero(zero(T780))) 18.82/5.79 f2435_in(zero(zero(T791))) -> U52(f2393_in(T791), zero(zero(T791))) 18.82/5.79 U52(f2393_out1(T792), zero(zero(T791))) -> f2435_out1(one(b), zero(one(T792))) 18.82/5.79 f2435_in(zero(T806)) -> U53(f2435_in(T806), zero(T806)) 18.82/5.79 U53(f2435_out1(T807, T808), zero(T806)) -> f2435_out1(one(T807), zero(T808)) 18.82/5.79 f2435_in(one(T820)) -> U54(f2342_in(T820), one(T820)) 18.82/5.79 U54(f2342_out1(T821, T822), one(T820)) -> f2435_out1(one(T821), one(T822)) 18.82/5.79 f2342_in(one(b)) -> f2342_out1(b, b) 18.82/5.79 f2342_in(T624) -> U55(f2352_in(T624), T624) 18.82/5.79 U55(f2352_out1(T625), T624) -> f2342_out1(T625, b) 18.82/5.79 f2342_in(T662) -> U56(f2352_in(T662), T662) 18.82/5.79 U56(f2352_out1(T663), T662) -> f2342_out1(b, T663) 18.82/5.79 f2342_in(T678) -> U57(f2435_in(T678), T678) 18.82/5.79 U57(f2435_out1(T679, T680), T678) -> f2342_out1(T679, T680) 18.82/5.79 f2300_in(one(T578)) -> U58(f2182_in(T578), one(T578)) 18.82/5.79 U58(f2182_out1, one(T578)) -> f2300_out1(b, one(T578)) 18.82/5.79 f2300_in(zero(T583)) -> U59(f2175_in(T583), zero(T583)) 18.82/5.79 U59(f2175_out1, zero(T583)) -> f2300_out1(b, zero(T583)) 18.82/5.79 f2300_in(T598) -> U60(f2229_in(T598), T598) 18.82/5.79 U60(f2229_out1(T599, T600), T598) -> f2300_out1(T599, T600) 18.82/5.79 f109_in(zero(T429)) -> U61(f2175_in(T429), zero(T429)) 18.82/5.79 U61(f2175_out1, zero(T429)) -> f109_out1(b, T429) 18.82/5.79 f109_in(zero(T482)) -> U62(f2229_in(T482), zero(T482)) 18.82/5.79 U62(f2229_out1(T483, T484), zero(T482)) -> f109_out1(zero(T483), T484) 18.82/5.79 f109_in(one(T838)) -> U63(f2300_in(T838), one(T838)) 18.82/5.79 U63(f2300_out1(T839, T840), one(T838)) -> f109_out1(one(T839), T840) 18.82/5.79 f898_in -> U64(f1142_in) 18.82/5.79 U64(f1142_out1(T95)) -> f898_out1(b, T95, zero(T95)) 18.82/5.79 f898_in -> U65(f1256_in) 18.82/5.79 U65(f1256_out1(T143, T144, X156)) -> f898_out1(zero(T143), T144, zero(X156)) 18.82/5.79 f898_in -> U66(f1592_in) 18.82/5.79 U66(f1592_out1(T412, T413, X565)) -> f898_out1(one(T412), T413, one(X565)) 18.82/5.79 f42_in(T36) -> U67(f104_in, T36) 18.82/5.79 U67(f104_out1(T37), T36) -> U68(f109_in(T36), T36, T37) 18.82/5.79 U68(f109_out1(T42, T41), T36, T37) -> f42_out1(T37, T42, T41) 18.82/5.79 f888_in -> U69(f104_in) 18.82/5.79 U69(f104_out1(T70)) -> U70(f898_in, T70) 18.82/5.79 U70(f898_out1(T75, T74, X78), T70) -> f888_out1(T70, T75, T74, X78) 18.82/5.79 18.82/5.79 Q is empty. 18.82/5.79 We have to consider all minimal (P,Q,R)-chains. 18.82/5.79 ---------------------------------------- 18.82/5.79 18.82/5.79 (125) UsableRulesProof (EQUIVALENT) 18.82/5.79 We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R. 18.82/5.79 ---------------------------------------- 18.82/5.79 18.82/5.79 (126) 18.82/5.79 Obligation: 18.82/5.79 Q DP problem: 18.82/5.79 The TRS P consists of the following rules: 18.82/5.79 18.82/5.79 F1256_IN -> F1592_IN 18.82/5.79 F1592_IN -> F1256_IN 18.82/5.79 F1256_IN -> F1256_IN 18.82/5.79 F1256_IN -> F1650_IN 18.82/5.79 F1650_IN -> F1733_IN 18.82/5.79 F1733_IN -> F1256_IN 18.82/5.79 F1733_IN -> F1733_IN 18.82/5.79 F1733_IN -> F1650_IN 18.82/5.79 18.82/5.79 R is empty. 18.82/5.79 Q is empty. 18.82/5.79 We have to consider all minimal (P,Q,R)-chains. 18.82/5.79 ---------------------------------------- 18.82/5.79 18.82/5.79 (127) 18.82/5.79 Obligation: 18.82/5.79 Q DP problem: 18.82/5.79 The TRS P consists of the following rules: 18.82/5.79 18.82/5.79 F104_IN -> F888_IN 18.82/5.79 F888_IN -> F104_IN 18.82/5.79 F104_IN -> F104_IN 18.82/5.79 18.82/5.79 The TRS R consists of the following rules: 18.82/5.79 18.82/5.79 f3_in(T8) -> f3_out1(one(b), T8) 18.82/5.79 f3_in(zero(T23)) -> U1(f3_in(T23), zero(T23)) 18.82/5.79 U1(f3_out1(T24, T25), zero(T23)) -> f3_out1(zero(T24), T25) 18.82/5.79 f3_in(T36) -> U2(f42_in(T36), T36) 18.82/5.79 U2(f42_out1(T37, T38, X33), T36) -> f3_out1(one(T37), T38) 18.82/5.79 f104_in -> f104_out1(one(b)) 18.82/5.79 f104_in -> U3(f104_in) 18.82/5.79 U3(f104_out1(T60)) -> f104_out1(zero(T60)) 18.82/5.79 f104_in -> U4(f888_in) 18.82/5.79 U4(f888_out1(T70, T71, X77, X78)) -> f104_out1(one(T70)) 18.82/5.79 f1142_in -> U5(f1142_in) 18.82/5.79 U5(f1142_out1(T102)) -> f1142_out1(zero(T102)) 18.82/5.79 f1142_in -> U6(f1151_in) 18.82/5.79 U6(f1151_out1(T107)) -> f1142_out1(one(T107)) 18.82/5.79 f1151_in -> f1151_out1(b) 18.82/5.79 f1151_in -> U7(f1142_in) 18.82/5.79 U7(f1142_out1(T113)) -> f1151_out1(zero(T113)) 18.82/5.79 f1151_in -> U8(f1151_in) 18.82/5.79 U8(f1151_out1(T118)) -> f1151_out1(one(T118)) 18.82/5.79 f1256_in -> U9(f1256_in) 18.82/5.79 U9(f1256_out1(T157, T158, X180)) -> f1256_out1(zero(T157), zero(T158), zero(X180)) 18.82/5.79 f1256_in -> U10(f1151_in) 18.82/5.79 U10(f1151_out1(T179)) -> f1256_out1(zero(one(T179)), one(b), one(one(T179))) 18.82/5.79 f1256_in -> U11(f1142_in) 18.82/5.79 U11(f1142_out1(T185)) -> f1256_out1(zero(zero(T185)), one(b), one(zero(T185))) 18.82/5.79 f1256_in -> U12(f1256_in) 18.82/5.79 U12(f1256_out1(T197, T198, X232)) -> f1256_out1(zero(T197), one(T198), one(X232)) 18.82/5.79 f1256_in -> U13(f1592_in) 18.82/5.79 U13(f1592_out1(T211, T212, X256)) -> f1256_out1(one(T211), zero(T212), one(X256)) 18.82/5.79 f1256_in -> U14(f1650_in) 18.82/5.79 U14(f1650_out1(T247, T248, X300)) -> f1256_out1(one(T247), one(T248), zero(X300)) 18.82/5.79 f1696_in -> f1696_out1(b, one(b)) 18.82/5.79 f1696_in -> U15(f1142_in) 18.82/5.79 U15(f1142_out1(T272)) -> f1696_out1(zero(T272), one(T272)) 18.82/5.79 f1696_in -> U16(f1696_in) 18.82/5.79 U16(f1696_out1(T277, X346)) -> f1696_out1(one(T277), zero(X346)) 18.82/5.79 f1677_in -> U17(f1142_in) 18.82/5.79 U17(f1142_out1(T261)) -> f1677_out1(zero(T261), one(T261)) 18.82/5.79 f1677_in -> U18(f1696_in) 18.82/5.79 U18(f1696_out1(T266, X331)) -> f1677_out1(one(T266), zero(X331)) 18.82/5.79 f1733_in -> U19(f1256_in) 18.82/5.79 U19(f1256_out1(T309, T310, X402)) -> f1733_out1(zero(T309), zero(T310), one(X402)) 18.82/5.79 f1733_in -> U20(f1142_in) 18.82/5.79 U20(f1142_out1(T331)) -> f1733_out1(zero(zero(T331)), one(b), zero(one(T331))) 18.82/5.79 f1733_in -> U21(f1696_in) 18.82/5.79 U21(f1696_out1(T338, X448)) -> f1733_out1(zero(one(T338)), one(b), zero(zero(X448))) 18.82/5.79 f1733_in -> U22(f1733_in) 18.82/5.79 U22(f1733_out1(T349, T350, X464)) -> f1733_out1(zero(T349), one(T350), zero(X464)) 18.82/5.79 f1733_in -> U23(f1142_in) 18.82/5.79 U23(f1142_out1(T371)) -> f1733_out1(one(b), zero(zero(T371)), zero(one(T371))) 18.82/5.79 f1733_in -> U24(f1696_in) 18.82/5.79 U24(f1696_out1(T378, X510)) -> f1733_out1(one(b), zero(one(T378)), zero(zero(X510))) 18.82/5.79 f1733_in -> U25(f1733_in) 18.82/5.79 U25(f1733_out1(T389, T390, X526)) -> f1733_out1(one(T389), zero(T390), zero(X526)) 18.82/5.79 f1733_in -> U26(f1650_in) 18.82/5.79 U26(f1650_out1(T399, T400, X542)) -> f1733_out1(one(T399), one(T400), one(X542)) 18.82/5.79 f1650_in -> f1650_out1(b, b, one(b)) 18.82/5.79 f1650_in -> U27(f1677_in) 18.82/5.79 U27(f1677_out1(T254, X315)) -> f1650_out1(T254, b, X315) 18.82/5.79 f1650_in -> U28(f1677_in) 18.82/5.79 U28(f1677_out1(T283, X361)) -> f1650_out1(b, T283, X361) 18.82/5.79 f1650_in -> U29(f1733_in) 18.82/5.79 U29(f1733_out1(T295, T296, X378)) -> f1650_out1(T295, T296, X378) 18.82/5.79 f1592_in -> U30(f1151_in) 18.82/5.79 U30(f1151_out1(T219)) -> f1592_out1(b, one(T219), one(T219)) 18.82/5.79 f1592_in -> U31(f1142_in) 18.82/5.79 U31(f1142_out1(T225)) -> f1592_out1(b, zero(T225), zero(T225)) 18.82/5.79 f1592_in -> U32(f1256_in) 18.82/5.79 U32(f1256_out1(T237, T238, X284)) -> f1592_out1(T237, T238, X284) 18.82/5.79 f2175_in(zero(T435)) -> U33(f2175_in(T435), zero(T435)) 18.82/5.79 U33(f2175_out1, zero(T435)) -> f2175_out1 18.82/5.79 f2175_in(one(T439)) -> U34(f2182_in(T439), one(T439)) 18.82/5.79 U34(f2182_out1, one(T439)) -> f2175_out1 18.82/5.79 f2182_in(b) -> f2182_out1 18.82/5.79 f2182_in(zero(T444)) -> U35(f2175_in(T444), zero(T444)) 18.82/5.79 U35(f2175_out1, zero(T444)) -> f2182_out1 18.82/5.79 f2182_in(one(T448)) -> U36(f2182_in(T448), one(T448)) 18.82/5.79 U36(f2182_out1, one(T448)) -> f2182_out1 18.82/5.79 f2229_in(zero(T502)) -> U37(f2229_in(T502), zero(T502)) 18.82/5.79 U37(f2229_out1(T503, T504), zero(T502)) -> f2229_out1(zero(T503), zero(T504)) 18.82/5.79 f2229_in(one(one(T530))) -> U38(f2182_in(T530), one(one(T530))) 18.82/5.79 U38(f2182_out1, one(one(T530))) -> f2229_out1(zero(one(T530)), one(b)) 18.82/5.79 f2229_in(one(zero(T535))) -> U39(f2175_in(T535), one(zero(T535))) 18.82/5.79 U39(f2175_out1, one(zero(T535))) -> f2229_out1(zero(zero(T535)), one(b)) 18.82/5.79 f2229_in(one(T550)) -> U40(f2229_in(T550), one(T550)) 18.82/5.79 U40(f2229_out1(T551, T552), one(T550)) -> f2229_out1(zero(T551), one(T552)) 18.82/5.79 f2229_in(one(T570)) -> U41(f2300_in(T570), one(T570)) 18.82/5.79 U41(f2300_out1(T571, T572), one(T570)) -> f2229_out1(one(T571), zero(T572)) 18.82/5.79 f2229_in(zero(T612)) -> U42(f2342_in(T612), zero(T612)) 18.82/5.79 U42(f2342_out1(T613, T614), zero(T612)) -> f2229_out1(one(T613), one(T614)) 18.82/5.79 f2393_in(one(b)) -> f2393_out1(b) 18.82/5.79 f2393_in(one(T644)) -> U43(f2175_in(T644), one(T644)) 18.82/5.79 U43(f2175_out1, one(T644)) -> f2393_out1(zero(T644)) 18.82/5.79 f2393_in(zero(T651)) -> U44(f2393_in(T651), zero(T651)) 18.82/5.79 U44(f2393_out1(T652), zero(T651)) -> f2393_out1(one(T652)) 18.82/5.79 f2352_in(one(T631)) -> U45(f2175_in(T631), one(T631)) 18.82/5.79 U45(f2175_out1, one(T631)) -> f2352_out1(zero(T631)) 18.82/5.79 f2352_in(zero(T638)) -> U46(f2393_in(T638), zero(T638)) 18.82/5.79 U46(f2393_out1(T639), zero(T638)) -> f2352_out1(one(T639)) 18.82/5.79 f2435_in(one(T698)) -> U47(f2229_in(T698), one(T698)) 18.82/5.79 U47(f2229_out1(T699, T700), one(T698)) -> f2435_out1(zero(T699), zero(T700)) 18.82/5.79 f2435_in(zero(one(T726))) -> U48(f2175_in(T726), zero(one(T726))) 18.82/5.79 U48(f2175_out1, zero(one(T726))) -> f2435_out1(zero(zero(T726)), one(b)) 18.82/5.79 f2435_in(zero(zero(T737))) -> U49(f2393_in(T737), zero(zero(T737))) 18.82/5.79 U49(f2393_out1(T738), zero(zero(T737))) -> f2435_out1(zero(one(T738)), one(b)) 18.82/5.79 f2435_in(zero(T752)) -> U50(f2435_in(T752), zero(T752)) 18.82/5.79 U50(f2435_out1(T753, T754), zero(T752)) -> f2435_out1(zero(T753), one(T754)) 18.82/5.79 f2435_in(zero(one(T780))) -> U51(f2175_in(T780), zero(one(T780))) 18.82/5.79 U51(f2175_out1, zero(one(T780))) -> f2435_out1(one(b), zero(zero(T780))) 18.82/5.79 f2435_in(zero(zero(T791))) -> U52(f2393_in(T791), zero(zero(T791))) 18.82/5.79 U52(f2393_out1(T792), zero(zero(T791))) -> f2435_out1(one(b), zero(one(T792))) 18.82/5.79 f2435_in(zero(T806)) -> U53(f2435_in(T806), zero(T806)) 18.82/5.79 U53(f2435_out1(T807, T808), zero(T806)) -> f2435_out1(one(T807), zero(T808)) 18.82/5.79 f2435_in(one(T820)) -> U54(f2342_in(T820), one(T820)) 18.82/5.79 U54(f2342_out1(T821, T822), one(T820)) -> f2435_out1(one(T821), one(T822)) 18.82/5.79 f2342_in(one(b)) -> f2342_out1(b, b) 18.82/5.79 f2342_in(T624) -> U55(f2352_in(T624), T624) 18.82/5.79 U55(f2352_out1(T625), T624) -> f2342_out1(T625, b) 18.82/5.79 f2342_in(T662) -> U56(f2352_in(T662), T662) 18.82/5.79 U56(f2352_out1(T663), T662) -> f2342_out1(b, T663) 18.82/5.79 f2342_in(T678) -> U57(f2435_in(T678), T678) 18.82/5.79 U57(f2435_out1(T679, T680), T678) -> f2342_out1(T679, T680) 18.82/5.79 f2300_in(one(T578)) -> U58(f2182_in(T578), one(T578)) 18.82/5.79 U58(f2182_out1, one(T578)) -> f2300_out1(b, one(T578)) 18.82/5.79 f2300_in(zero(T583)) -> U59(f2175_in(T583), zero(T583)) 18.82/5.79 U59(f2175_out1, zero(T583)) -> f2300_out1(b, zero(T583)) 18.82/5.79 f2300_in(T598) -> U60(f2229_in(T598), T598) 18.82/5.79 U60(f2229_out1(T599, T600), T598) -> f2300_out1(T599, T600) 18.82/5.79 f109_in(zero(T429)) -> U61(f2175_in(T429), zero(T429)) 18.82/5.79 U61(f2175_out1, zero(T429)) -> f109_out1(b, T429) 18.82/5.79 f109_in(zero(T482)) -> U62(f2229_in(T482), zero(T482)) 18.82/5.79 U62(f2229_out1(T483, T484), zero(T482)) -> f109_out1(zero(T483), T484) 18.82/5.79 f109_in(one(T838)) -> U63(f2300_in(T838), one(T838)) 18.82/5.79 U63(f2300_out1(T839, T840), one(T838)) -> f109_out1(one(T839), T840) 18.82/5.79 f898_in -> U64(f1142_in) 18.82/5.79 U64(f1142_out1(T95)) -> f898_out1(b, T95, zero(T95)) 18.82/5.79 f898_in -> U65(f1256_in) 18.82/5.79 U65(f1256_out1(T143, T144, X156)) -> f898_out1(zero(T143), T144, zero(X156)) 18.82/5.79 f898_in -> U66(f1592_in) 18.82/5.79 U66(f1592_out1(T412, T413, X565)) -> f898_out1(one(T412), T413, one(X565)) 18.82/5.79 f42_in(T36) -> U67(f104_in, T36) 18.82/5.79 U67(f104_out1(T37), T36) -> U68(f109_in(T36), T36, T37) 18.82/5.79 U68(f109_out1(T42, T41), T36, T37) -> f42_out1(T37, T42, T41) 18.82/5.79 f888_in -> U69(f104_in) 18.82/5.79 U69(f104_out1(T70)) -> U70(f898_in, T70) 18.82/5.79 U70(f898_out1(T75, T74, X78), T70) -> f888_out1(T70, T75, T74, X78) 18.82/5.79 18.82/5.79 Q is empty. 18.82/5.79 We have to consider all minimal (P,Q,R)-chains. 18.82/5.79 ---------------------------------------- 18.82/5.79 18.82/5.79 (128) UsableRulesProof (EQUIVALENT) 18.82/5.79 We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R. 18.82/5.79 ---------------------------------------- 18.82/5.79 18.82/5.79 (129) 18.82/5.79 Obligation: 18.82/5.79 Q DP problem: 18.82/5.79 The TRS P consists of the following rules: 18.82/5.79 18.82/5.79 F104_IN -> F888_IN 18.82/5.79 F888_IN -> F104_IN 18.82/5.79 F104_IN -> F104_IN 18.82/5.79 18.82/5.79 R is empty. 18.82/5.79 Q is empty. 18.82/5.79 We have to consider all minimal (P,Q,R)-chains. 18.82/5.79 ---------------------------------------- 18.82/5.79 18.82/5.79 (130) 18.82/5.79 Obligation: 18.82/5.79 Q DP problem: 18.82/5.79 The TRS P consists of the following rules: 18.82/5.79 18.82/5.79 F3_IN(zero(T23)) -> F3_IN(T23) 18.82/5.79 18.82/5.79 The TRS R consists of the following rules: 18.82/5.79 18.82/5.79 f3_in(T8) -> f3_out1(one(b), T8) 18.82/5.79 f3_in(zero(T23)) -> U1(f3_in(T23), zero(T23)) 18.82/5.79 U1(f3_out1(T24, T25), zero(T23)) -> f3_out1(zero(T24), T25) 18.82/5.79 f3_in(T36) -> U2(f42_in(T36), T36) 18.82/5.79 U2(f42_out1(T37, T38, X33), T36) -> f3_out1(one(T37), T38) 18.82/5.79 f104_in -> f104_out1(one(b)) 18.82/5.79 f104_in -> U3(f104_in) 18.82/5.79 U3(f104_out1(T60)) -> f104_out1(zero(T60)) 18.82/5.79 f104_in -> U4(f888_in) 18.82/5.79 U4(f888_out1(T70, T71, X77, X78)) -> f104_out1(one(T70)) 18.82/5.79 f1142_in -> U5(f1142_in) 18.82/5.79 U5(f1142_out1(T102)) -> f1142_out1(zero(T102)) 18.82/5.79 f1142_in -> U6(f1151_in) 18.82/5.79 U6(f1151_out1(T107)) -> f1142_out1(one(T107)) 18.82/5.79 f1151_in -> f1151_out1(b) 18.82/5.79 f1151_in -> U7(f1142_in) 18.82/5.79 U7(f1142_out1(T113)) -> f1151_out1(zero(T113)) 18.82/5.79 f1151_in -> U8(f1151_in) 18.82/5.79 U8(f1151_out1(T118)) -> f1151_out1(one(T118)) 18.82/5.79 f1256_in -> U9(f1256_in) 18.82/5.79 U9(f1256_out1(T157, T158, X180)) -> f1256_out1(zero(T157), zero(T158), zero(X180)) 18.82/5.79 f1256_in -> U10(f1151_in) 18.82/5.79 U10(f1151_out1(T179)) -> f1256_out1(zero(one(T179)), one(b), one(one(T179))) 18.82/5.79 f1256_in -> U11(f1142_in) 18.82/5.79 U11(f1142_out1(T185)) -> f1256_out1(zero(zero(T185)), one(b), one(zero(T185))) 18.82/5.79 f1256_in -> U12(f1256_in) 18.82/5.79 U12(f1256_out1(T197, T198, X232)) -> f1256_out1(zero(T197), one(T198), one(X232)) 18.82/5.79 f1256_in -> U13(f1592_in) 18.82/5.79 U13(f1592_out1(T211, T212, X256)) -> f1256_out1(one(T211), zero(T212), one(X256)) 18.82/5.79 f1256_in -> U14(f1650_in) 18.82/5.79 U14(f1650_out1(T247, T248, X300)) -> f1256_out1(one(T247), one(T248), zero(X300)) 18.82/5.79 f1696_in -> f1696_out1(b, one(b)) 18.82/5.79 f1696_in -> U15(f1142_in) 18.82/5.79 U15(f1142_out1(T272)) -> f1696_out1(zero(T272), one(T272)) 18.82/5.79 f1696_in -> U16(f1696_in) 18.82/5.79 U16(f1696_out1(T277, X346)) -> f1696_out1(one(T277), zero(X346)) 18.82/5.79 f1677_in -> U17(f1142_in) 18.82/5.79 U17(f1142_out1(T261)) -> f1677_out1(zero(T261), one(T261)) 18.82/5.79 f1677_in -> U18(f1696_in) 18.82/5.79 U18(f1696_out1(T266, X331)) -> f1677_out1(one(T266), zero(X331)) 18.82/5.79 f1733_in -> U19(f1256_in) 18.82/5.79 U19(f1256_out1(T309, T310, X402)) -> f1733_out1(zero(T309), zero(T310), one(X402)) 18.82/5.79 f1733_in -> U20(f1142_in) 18.82/5.79 U20(f1142_out1(T331)) -> f1733_out1(zero(zero(T331)), one(b), zero(one(T331))) 18.82/5.79 f1733_in -> U21(f1696_in) 18.82/5.79 U21(f1696_out1(T338, X448)) -> f1733_out1(zero(one(T338)), one(b), zero(zero(X448))) 18.82/5.79 f1733_in -> U22(f1733_in) 18.82/5.79 U22(f1733_out1(T349, T350, X464)) -> f1733_out1(zero(T349), one(T350), zero(X464)) 18.82/5.79 f1733_in -> U23(f1142_in) 18.82/5.79 U23(f1142_out1(T371)) -> f1733_out1(one(b), zero(zero(T371)), zero(one(T371))) 18.82/5.79 f1733_in -> U24(f1696_in) 18.82/5.79 U24(f1696_out1(T378, X510)) -> f1733_out1(one(b), zero(one(T378)), zero(zero(X510))) 18.82/5.79 f1733_in -> U25(f1733_in) 18.82/5.79 U25(f1733_out1(T389, T390, X526)) -> f1733_out1(one(T389), zero(T390), zero(X526)) 18.82/5.79 f1733_in -> U26(f1650_in) 18.82/5.79 U26(f1650_out1(T399, T400, X542)) -> f1733_out1(one(T399), one(T400), one(X542)) 18.82/5.79 f1650_in -> f1650_out1(b, b, one(b)) 18.82/5.79 f1650_in -> U27(f1677_in) 18.82/5.79 U27(f1677_out1(T254, X315)) -> f1650_out1(T254, b, X315) 18.82/5.79 f1650_in -> U28(f1677_in) 18.82/5.79 U28(f1677_out1(T283, X361)) -> f1650_out1(b, T283, X361) 18.82/5.79 f1650_in -> U29(f1733_in) 18.82/5.79 U29(f1733_out1(T295, T296, X378)) -> f1650_out1(T295, T296, X378) 18.82/5.79 f1592_in -> U30(f1151_in) 18.82/5.79 U30(f1151_out1(T219)) -> f1592_out1(b, one(T219), one(T219)) 18.82/5.79 f1592_in -> U31(f1142_in) 18.82/5.79 U31(f1142_out1(T225)) -> f1592_out1(b, zero(T225), zero(T225)) 18.82/5.79 f1592_in -> U32(f1256_in) 18.82/5.79 U32(f1256_out1(T237, T238, X284)) -> f1592_out1(T237, T238, X284) 18.82/5.79 f2175_in(zero(T435)) -> U33(f2175_in(T435), zero(T435)) 18.82/5.79 U33(f2175_out1, zero(T435)) -> f2175_out1 18.82/5.79 f2175_in(one(T439)) -> U34(f2182_in(T439), one(T439)) 18.82/5.79 U34(f2182_out1, one(T439)) -> f2175_out1 18.82/5.79 f2182_in(b) -> f2182_out1 18.82/5.79 f2182_in(zero(T444)) -> U35(f2175_in(T444), zero(T444)) 18.82/5.79 U35(f2175_out1, zero(T444)) -> f2182_out1 18.82/5.79 f2182_in(one(T448)) -> U36(f2182_in(T448), one(T448)) 18.82/5.79 U36(f2182_out1, one(T448)) -> f2182_out1 18.82/5.79 f2229_in(zero(T502)) -> U37(f2229_in(T502), zero(T502)) 18.82/5.79 U37(f2229_out1(T503, T504), zero(T502)) -> f2229_out1(zero(T503), zero(T504)) 18.82/5.79 f2229_in(one(one(T530))) -> U38(f2182_in(T530), one(one(T530))) 18.82/5.79 U38(f2182_out1, one(one(T530))) -> f2229_out1(zero(one(T530)), one(b)) 18.82/5.79 f2229_in(one(zero(T535))) -> U39(f2175_in(T535), one(zero(T535))) 18.82/5.79 U39(f2175_out1, one(zero(T535))) -> f2229_out1(zero(zero(T535)), one(b)) 18.82/5.79 f2229_in(one(T550)) -> U40(f2229_in(T550), one(T550)) 18.82/5.79 U40(f2229_out1(T551, T552), one(T550)) -> f2229_out1(zero(T551), one(T552)) 18.82/5.79 f2229_in(one(T570)) -> U41(f2300_in(T570), one(T570)) 18.82/5.79 U41(f2300_out1(T571, T572), one(T570)) -> f2229_out1(one(T571), zero(T572)) 18.82/5.79 f2229_in(zero(T612)) -> U42(f2342_in(T612), zero(T612)) 18.82/5.79 U42(f2342_out1(T613, T614), zero(T612)) -> f2229_out1(one(T613), one(T614)) 18.82/5.79 f2393_in(one(b)) -> f2393_out1(b) 18.82/5.79 f2393_in(one(T644)) -> U43(f2175_in(T644), one(T644)) 18.82/5.79 U43(f2175_out1, one(T644)) -> f2393_out1(zero(T644)) 18.82/5.79 f2393_in(zero(T651)) -> U44(f2393_in(T651), zero(T651)) 18.82/5.79 U44(f2393_out1(T652), zero(T651)) -> f2393_out1(one(T652)) 18.82/5.79 f2352_in(one(T631)) -> U45(f2175_in(T631), one(T631)) 18.82/5.79 U45(f2175_out1, one(T631)) -> f2352_out1(zero(T631)) 18.82/5.79 f2352_in(zero(T638)) -> U46(f2393_in(T638), zero(T638)) 18.82/5.79 U46(f2393_out1(T639), zero(T638)) -> f2352_out1(one(T639)) 18.82/5.79 f2435_in(one(T698)) -> U47(f2229_in(T698), one(T698)) 18.82/5.79 U47(f2229_out1(T699, T700), one(T698)) -> f2435_out1(zero(T699), zero(T700)) 18.82/5.79 f2435_in(zero(one(T726))) -> U48(f2175_in(T726), zero(one(T726))) 18.82/5.79 U48(f2175_out1, zero(one(T726))) -> f2435_out1(zero(zero(T726)), one(b)) 18.82/5.79 f2435_in(zero(zero(T737))) -> U49(f2393_in(T737), zero(zero(T737))) 18.82/5.79 U49(f2393_out1(T738), zero(zero(T737))) -> f2435_out1(zero(one(T738)), one(b)) 18.82/5.79 f2435_in(zero(T752)) -> U50(f2435_in(T752), zero(T752)) 18.82/5.79 U50(f2435_out1(T753, T754), zero(T752)) -> f2435_out1(zero(T753), one(T754)) 18.82/5.79 f2435_in(zero(one(T780))) -> U51(f2175_in(T780), zero(one(T780))) 18.82/5.79 U51(f2175_out1, zero(one(T780))) -> f2435_out1(one(b), zero(zero(T780))) 18.82/5.79 f2435_in(zero(zero(T791))) -> U52(f2393_in(T791), zero(zero(T791))) 18.82/5.79 U52(f2393_out1(T792), zero(zero(T791))) -> f2435_out1(one(b), zero(one(T792))) 18.82/5.79 f2435_in(zero(T806)) -> U53(f2435_in(T806), zero(T806)) 18.82/5.79 U53(f2435_out1(T807, T808), zero(T806)) -> f2435_out1(one(T807), zero(T808)) 18.82/5.79 f2435_in(one(T820)) -> U54(f2342_in(T820), one(T820)) 18.82/5.79 U54(f2342_out1(T821, T822), one(T820)) -> f2435_out1(one(T821), one(T822)) 18.82/5.79 f2342_in(one(b)) -> f2342_out1(b, b) 18.82/5.79 f2342_in(T624) -> U55(f2352_in(T624), T624) 18.82/5.79 U55(f2352_out1(T625), T624) -> f2342_out1(T625, b) 18.82/5.79 f2342_in(T662) -> U56(f2352_in(T662), T662) 18.82/5.79 U56(f2352_out1(T663), T662) -> f2342_out1(b, T663) 18.82/5.79 f2342_in(T678) -> U57(f2435_in(T678), T678) 18.82/5.79 U57(f2435_out1(T679, T680), T678) -> f2342_out1(T679, T680) 18.82/5.79 f2300_in(one(T578)) -> U58(f2182_in(T578), one(T578)) 18.82/5.79 U58(f2182_out1, one(T578)) -> f2300_out1(b, one(T578)) 18.82/5.79 f2300_in(zero(T583)) -> U59(f2175_in(T583), zero(T583)) 18.82/5.79 U59(f2175_out1, zero(T583)) -> f2300_out1(b, zero(T583)) 18.82/5.79 f2300_in(T598) -> U60(f2229_in(T598), T598) 18.82/5.79 U60(f2229_out1(T599, T600), T598) -> f2300_out1(T599, T600) 18.82/5.79 f109_in(zero(T429)) -> U61(f2175_in(T429), zero(T429)) 18.82/5.79 U61(f2175_out1, zero(T429)) -> f109_out1(b, T429) 18.82/5.79 f109_in(zero(T482)) -> U62(f2229_in(T482), zero(T482)) 18.82/5.79 U62(f2229_out1(T483, T484), zero(T482)) -> f109_out1(zero(T483), T484) 18.82/5.79 f109_in(one(T838)) -> U63(f2300_in(T838), one(T838)) 18.82/5.79 U63(f2300_out1(T839, T840), one(T838)) -> f109_out1(one(T839), T840) 18.82/5.79 f898_in -> U64(f1142_in) 18.82/5.79 U64(f1142_out1(T95)) -> f898_out1(b, T95, zero(T95)) 18.82/5.79 f898_in -> U65(f1256_in) 18.82/5.79 U65(f1256_out1(T143, T144, X156)) -> f898_out1(zero(T143), T144, zero(X156)) 18.82/5.79 f898_in -> U66(f1592_in) 18.82/5.79 U66(f1592_out1(T412, T413, X565)) -> f898_out1(one(T412), T413, one(X565)) 18.82/5.79 f42_in(T36) -> U67(f104_in, T36) 18.82/5.79 U67(f104_out1(T37), T36) -> U68(f109_in(T36), T36, T37) 18.82/5.79 U68(f109_out1(T42, T41), T36, T37) -> f42_out1(T37, T42, T41) 18.82/5.79 f888_in -> U69(f104_in) 18.82/5.79 U69(f104_out1(T70)) -> U70(f898_in, T70) 18.82/5.79 U70(f898_out1(T75, T74, X78), T70) -> f888_out1(T70, T75, T74, X78) 18.82/5.79 18.82/5.79 Q is empty. 18.82/5.79 We have to consider all minimal (P,Q,R)-chains. 18.82/5.79 ---------------------------------------- 18.82/5.79 18.82/5.79 (131) UsableRulesProof (EQUIVALENT) 18.82/5.79 We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R. 18.82/5.79 ---------------------------------------- 18.82/5.79 18.82/5.79 (132) 18.82/5.79 Obligation: 18.82/5.79 Q DP problem: 18.82/5.79 The TRS P consists of the following rules: 18.82/5.79 18.82/5.79 F3_IN(zero(T23)) -> F3_IN(T23) 18.82/5.79 18.82/5.79 R is empty. 18.82/5.79 Q is empty. 18.82/5.79 We have to consider all minimal (P,Q,R)-chains. 18.82/5.79 ---------------------------------------- 18.82/5.79 18.82/5.79 (133) QDPSizeChangeProof (EQUIVALENT) 18.82/5.79 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 18.82/5.79 18.82/5.79 From the DPs we obtained the following set of size-change graphs: 18.82/5.79 *F3_IN(zero(T23)) -> F3_IN(T23) 18.82/5.79 The graph contains the following edges 1 > 1 18.82/5.79 18.82/5.79 18.82/5.79 ---------------------------------------- 18.82/5.79 18.82/5.79 (134) 18.82/5.79 YES 18.82/5.79 18.82/5.79 ---------------------------------------- 18.82/5.79 18.82/5.79 (135) PrologToDTProblemTransformerProof (SOUND) 18.82/5.79 Built DT problem from termination graph DT10. 18.82/5.79 18.82/5.79 { 18.82/5.79 "root": 1, 18.82/5.79 "program": { 18.82/5.79 "directives": [], 18.82/5.79 "clauses": [ 18.82/5.79 [ 18.82/5.79 "(add (b) (b) (b))", 18.82/5.79 null 18.82/5.79 ], 18.82/5.79 [ 18.82/5.79 "(add X (b) X)", 18.82/5.79 "(binaryZ X)" 18.82/5.79 ], 18.82/5.79 [ 18.82/5.79 "(add (b) Y Y)", 18.82/5.79 "(binaryZ Y)" 18.82/5.79 ], 18.82/5.79 [ 18.82/5.79 "(add X Y Z)", 18.82/5.79 "(addz X Y Z)" 18.82/5.79 ], 18.82/5.79 [ 18.82/5.79 "(addx (one X) (b) (one X))", 18.82/5.79 "(binary X)" 18.82/5.79 ], 18.82/5.79 [ 18.82/5.79 "(addx (zero X) (b) (zero X))", 18.82/5.79 "(binaryZ X)" 18.82/5.79 ], 18.82/5.79 [ 18.82/5.79 "(addx X Y Z)", 18.82/5.79 "(addz X Y Z)" 18.82/5.79 ], 18.82/5.79 [ 18.82/5.79 "(addy (b) (one Y) (one Y))", 18.82/5.79 "(binary Y)" 18.82/5.79 ], 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}, 18.82/5.83 "ground": [], 18.82/5.83 "free": [], 18.82/5.83 "exprvars": [] 18.82/5.83 } 18.82/5.83 }, 18.82/5.83 "2413": { 18.82/5.83 "goal": [{ 18.82/5.83 "clause": 14, 18.82/5.83 "scope": 23, 18.82/5.83 "term": "(addc T603 T604 T602)" 18.82/5.83 }], 18.82/5.83 "kb": { 18.82/5.83 "nonunifying": [], 18.82/5.83 "intvars": {}, 18.82/5.83 "arithmetic": { 18.82/5.83 "type": "PlainIntegerRelationState", 18.82/5.83 "relations": [] 18.82/5.83 }, 18.82/5.83 "ground": ["T602"], 18.82/5.83 "free": [], 18.82/5.83 "exprvars": [] 18.82/5.83 } 18.82/5.83 }, 18.82/5.83 "2534": { 18.82/5.83 "goal": [{ 18.82/5.83 "clause": -1, 18.82/5.83 "scope": -1, 18.82/5.83 "term": "(succ T642 T641)" 18.82/5.83 }], 18.82/5.83 "kb": { 18.82/5.83 "nonunifying": [], 18.82/5.83 "intvars": {}, 18.82/5.83 "arithmetic": { 18.82/5.83 "type": "PlainIntegerRelationState", 18.82/5.83 "relations": [] 18.82/5.83 }, 18.82/5.83 "ground": ["T641"], 18.82/5.83 "free": [], 18.82/5.83 "exprvars": [] 18.82/5.83 } 18.82/5.83 }, 18.82/5.83 "2655": { 18.82/5.83 "goal": [], 18.82/5.83 "kb": { 18.82/5.83 "nonunifying": [], 18.82/5.83 "intvars": {}, 18.82/5.83 "arithmetic": { 18.82/5.83 "type": "PlainIntegerRelationState", 18.82/5.83 "relations": [] 18.82/5.83 }, 18.82/5.83 "ground": [], 18.82/5.83 "free": [], 18.82/5.83 "exprvars": [] 18.82/5.83 } 18.82/5.83 }, 18.82/5.83 "2412": { 18.82/5.83 "goal": [ 18.82/5.83 { 18.82/5.83 "clause": 14, 18.82/5.83 "scope": 23, 18.82/5.83 "term": "(addc T603 T604 T602)" 18.82/5.83 }, 18.82/5.83 { 18.82/5.83 "clause": 15, 18.82/5.83 "scope": 23, 18.82/5.83 "term": "(addc T603 T604 T602)" 18.82/5.83 }, 18.82/5.83 { 18.82/5.83 "clause": 16, 18.82/5.83 "scope": 23, 18.82/5.83 "term": "(addc T603 T604 T602)" 18.82/5.83 }, 18.82/5.83 { 18.82/5.83 "clause": 17, 18.82/5.83 "scope": 23, 18.82/5.83 "term": "(addc T603 T604 T602)" 18.82/5.83 } 18.82/5.83 ], 18.82/5.83 "kb": { 18.82/5.83 "nonunifying": [], 18.82/5.83 "intvars": {}, 18.82/5.83 "arithmetic": { 18.82/5.83 "type": "PlainIntegerRelationState", 18.82/5.83 "relations": [] 18.82/5.83 }, 18.82/5.83 "ground": ["T602"], 18.82/5.83 "free": [], 18.82/5.83 "exprvars": [] 18.82/5.83 } 18.82/5.83 }, 18.82/5.83 "2533": { 18.82/5.83 "goal": [], 18.82/5.83 "kb": { 18.82/5.83 "nonunifying": [], 18.82/5.83 "intvars": {}, 18.82/5.83 "arithmetic": { 18.82/5.83 "type": "PlainIntegerRelationState", 18.82/5.83 "relations": [] 18.82/5.83 }, 18.82/5.83 "ground": [], 18.82/5.83 "free": [], 18.82/5.83 "exprvars": [] 18.82/5.83 } 18.82/5.83 }, 18.82/5.83 "2654": { 18.82/5.83 "goal": [{ 18.82/5.83 "clause": -1, 18.82/5.83 "scope": -1, 18.82/5.83 "term": "(add T977 (zero T977) T969)" 18.82/5.83 }], 18.82/5.83 "kb": { 18.82/5.83 "nonunifying": [ 18.82/5.83 [ 18.82/5.83 "(times T1 T2 T969)", 18.82/5.83 "(times (one (b)) X2 X2)" 18.82/5.83 ], 18.82/5.83 [ 18.82/5.83 "(times T1 T2 T969)", 18.82/5.83 "(times (zero X1010) X1011 (zero X1012))" 18.82/5.83 ] 18.82/5.83 ], 18.82/5.83 "intvars": {}, 18.82/5.83 "arithmetic": { 18.82/5.83 "type": "PlainIntegerRelationState", 18.82/5.83 "relations": [] 18.82/5.83 }, 18.82/5.83 "ground": ["T969"], 18.82/5.83 "free": [ 18.82/5.83 "X2", 18.82/5.83 "X1010", 18.82/5.83 "X1011", 18.82/5.83 "X1012" 18.82/5.83 ], 18.82/5.83 "exprvars": [] 18.82/5.83 } 18.82/5.83 }, 18.82/5.83 "2532": { 18.82/5.83 "goal": [{ 18.82/5.83 "clause": -1, 18.82/5.83 "scope": -1, 18.82/5.83 "term": "(binaryZ T634)" 18.82/5.83 }], 18.82/5.83 "kb": { 18.82/5.83 "nonunifying": [], 18.82/5.83 "intvars": {}, 18.82/5.83 "arithmetic": { 18.82/5.83 "type": "PlainIntegerRelationState", 18.82/5.83 "relations": [] 18.82/5.83 }, 18.82/5.83 "ground": ["T634"], 18.82/5.83 "free": [], 18.82/5.83 "exprvars": [] 18.82/5.83 } 18.82/5.83 }, 18.82/5.83 "2653": { 18.82/5.83 "goal": [ 18.82/5.83 { 18.82/5.83 "clause": 39, 18.82/5.83 "scope": 31, 18.82/5.83 "term": "(',' (times T970 T971 X1074) (add T971 (zero X1074) T969))" 18.82/5.83 }, 18.82/5.83 { 18.82/5.83 "clause": 40, 18.82/5.83 "scope": 31, 18.82/5.83 "term": "(',' (times T970 T971 X1074) (add T971 (zero X1074) T969))" 18.82/5.83 } 18.82/5.83 ], 18.82/5.83 "kb": { 18.82/5.83 "nonunifying": [ 18.82/5.83 [ 18.82/5.83 "(times T1 T2 T969)", 18.82/5.83 "(times (one (b)) X2 X2)" 18.82/5.83 ], 18.82/5.83 [ 18.82/5.83 "(times T1 T2 T969)", 18.82/5.83 "(times (zero X1010) X1011 (zero X1012))" 18.82/5.83 ] 18.82/5.83 ], 18.82/5.83 "intvars": {}, 18.82/5.83 "arithmetic": { 18.82/5.83 "type": "PlainIntegerRelationState", 18.82/5.83 "relations": [] 18.82/5.83 }, 18.82/5.83 "ground": ["T969"], 18.82/5.83 "free": [ 18.82/5.83 "X2", 18.82/5.83 "X1010", 18.82/5.83 "X1011", 18.82/5.83 "X1012", 18.82/5.83 "X1074" 18.82/5.83 ], 18.82/5.83 "exprvars": [] 18.82/5.83 } 18.82/5.83 }, 18.82/5.83 "2531": { 18.82/5.83 "goal": [{ 18.82/5.83 "clause": 35, 18.82/5.83 "scope": 25, 18.82/5.83 "term": "(succ T629 T628)" 18.82/5.83 }], 18.82/5.83 "kb": { 18.82/5.83 "nonunifying": [], 18.82/5.83 "intvars": {}, 18.82/5.83 "arithmetic": { 18.82/5.83 "type": "PlainIntegerRelationState", 18.82/5.83 "relations": [] 18.82/5.83 }, 18.82/5.83 "ground": ["T628"], 18.82/5.83 "free": [], 18.82/5.83 "exprvars": [] 18.82/5.83 } 18.82/5.83 }, 18.82/5.83 "2652": { 18.82/5.83 "goal": [{ 18.82/5.83 "clause": 38, 18.82/5.83 "scope": 31, 18.82/5.83 "term": "(',' (times T970 T971 X1074) (add T971 (zero X1074) T969))" 18.82/5.83 }], 18.82/5.83 "kb": { 18.82/5.83 "nonunifying": [ 18.82/5.83 [ 18.82/5.83 "(times T1 T2 T969)", 18.82/5.83 "(times (one (b)) X2 X2)" 18.82/5.83 ], 18.82/5.83 [ 18.82/5.83 "(times T1 T2 T969)", 18.82/5.83 "(times (zero X1010) X1011 (zero X1012))" 18.82/5.83 ] 18.82/5.83 ], 18.82/5.83 "intvars": {}, 18.82/5.83 "arithmetic": { 18.82/5.83 "type": "PlainIntegerRelationState", 18.82/5.83 "relations": [] 18.82/5.83 }, 18.82/5.83 "ground": ["T969"], 18.82/5.83 "free": [ 18.82/5.83 "X2", 18.82/5.83 "X1010", 18.82/5.83 "X1011", 18.82/5.83 "X1012", 18.82/5.83 "X1074" 18.82/5.83 ], 18.82/5.83 "exprvars": [] 18.82/5.83 } 18.82/5.83 }, 18.82/5.83 "2530": { 18.82/5.83 "goal": [{ 18.82/5.83 "clause": 34, 18.82/5.83 "scope": 25, 18.95/5.83 "term": "(succ T629 T628)" 18.95/5.83 }], 18.95/5.83 "kb": { 18.95/5.83 "nonunifying": [], 18.95/5.83 "intvars": {}, 18.95/5.83 "arithmetic": { 18.95/5.83 "type": "PlainIntegerRelationState", 18.95/5.83 "relations": [] 18.95/5.83 }, 18.95/5.83 "ground": ["T628"], 18.95/5.83 "free": [], 18.95/5.83 "exprvars": [] 18.95/5.83 } 18.95/5.83 }, 18.95/5.83 "2651": { 18.95/5.83 "goal": [ 18.95/5.83 { 18.95/5.83 "clause": 38, 18.95/5.83 "scope": 31, 18.95/5.83 "term": "(',' (times T970 T971 X1074) (add T971 (zero X1074) T969))" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "clause": 39, 18.95/5.83 "scope": 31, 18.95/5.83 "term": "(',' (times T970 T971 X1074) (add T971 (zero X1074) T969))" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "clause": 40, 18.95/5.83 "scope": 31, 18.95/5.83 "term": "(',' (times T970 T971 X1074) (add T971 (zero X1074) T969))" 18.95/5.83 } 18.95/5.83 ], 18.95/5.83 "kb": { 18.95/5.83 "nonunifying": [ 18.95/5.83 [ 18.95/5.83 "(times T1 T2 T969)", 18.95/5.83 "(times (one (b)) X2 X2)" 18.95/5.83 ], 18.95/5.83 [ 18.95/5.83 "(times T1 T2 T969)", 18.95/5.83 "(times (zero X1010) X1011 (zero X1012))" 18.95/5.83 ] 18.95/5.83 ], 18.95/5.83 "intvars": {}, 18.95/5.83 "arithmetic": { 18.95/5.83 "type": "PlainIntegerRelationState", 18.95/5.83 "relations": [] 18.95/5.83 }, 18.95/5.83 "ground": ["T969"], 18.95/5.83 "free": [ 18.95/5.83 "X2", 18.95/5.83 "X1010", 18.95/5.83 "X1011", 18.95/5.83 "X1012", 18.95/5.83 "X1074" 18.95/5.83 ], 18.95/5.83 "exprvars": [] 18.95/5.83 } 18.95/5.83 }, 18.95/5.83 "1329": { 18.95/5.83 "goal": [{ 18.95/5.83 "clause": 31, 18.95/5.83 "scope": 6, 18.95/5.83 "term": "(binaryZ T111)" 18.95/5.83 }], 18.95/5.83 "kb": { 18.95/5.83 "nonunifying": [], 18.95/5.83 "intvars": {}, 18.95/5.83 "arithmetic": { 18.95/5.83 "type": "PlainIntegerRelationState", 18.95/5.83 "relations": [] 18.95/5.83 }, 18.95/5.83 "ground": [], 18.95/5.83 "free": [], 18.95/5.83 "exprvars": [] 18.95/5.83 } 18.95/5.83 }, 18.95/5.83 "2539": { 18.95/5.83 "goal": [], 18.95/5.83 "kb": { 18.95/5.83 "nonunifying": [], 18.95/5.83 "intvars": {}, 18.95/5.83 "arithmetic": { 18.95/5.83 "type": "PlainIntegerRelationState", 18.95/5.83 "relations": [] 18.95/5.83 }, 18.95/5.83 "ground": [], 18.95/5.83 "free": [], 18.95/5.83 "exprvars": [] 18.95/5.83 } 18.95/5.83 }, 18.95/5.83 "2417": { 18.95/5.83 "goal": [], 18.95/5.83 "kb": { 18.95/5.83 "nonunifying": [], 18.95/5.83 "intvars": {}, 18.95/5.83 "arithmetic": { 18.95/5.83 "type": "PlainIntegerRelationState", 18.95/5.83 "relations": [] 18.95/5.83 }, 18.95/5.83 "ground": [], 18.95/5.83 "free": [], 18.95/5.83 "exprvars": [] 18.95/5.83 } 18.95/5.83 }, 18.95/5.83 "2538": { 18.95/5.83 "goal": [{ 18.95/5.83 "clause": -1, 18.95/5.83 "scope": -1, 18.95/5.83 "term": "(succZ T653 T652)" 18.95/5.83 }], 18.95/5.83 "kb": { 18.95/5.83 "nonunifying": [], 18.95/5.83 "intvars": {}, 18.95/5.83 "arithmetic": { 18.95/5.83 "type": "PlainIntegerRelationState", 18.95/5.83 "relations": [] 18.95/5.83 }, 18.95/5.83 "ground": ["T652"], 18.95/5.83 "free": [], 18.95/5.83 "exprvars": [] 18.95/5.83 } 18.95/5.83 }, 18.95/5.83 "2659": { 18.95/5.83 "goal": [], 18.95/5.83 "kb": { 18.95/5.83 "nonunifying": [], 18.95/5.83 "intvars": {}, 18.95/5.83 "arithmetic": { 18.95/5.83 "type": "PlainIntegerRelationState", 18.95/5.83 "relations": [] 18.95/5.83 }, 18.95/5.83 "ground": [], 18.95/5.83 "free": [], 18.95/5.83 "exprvars": [] 18.95/5.83 } 18.95/5.83 } 18.95/5.83 }, 18.95/5.83 "edges": [ 18.95/5.83 { 18.95/5.83 "from": 1, 18.95/5.83 "to": 4, 18.95/5.83 "label": "CASE" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 4, 18.95/5.83 "to": 15, 18.95/5.83 "label": "EVAL with clause\ntimes(one(b), X2, X2).\nand substitutionT1 -> one(b),\nT2 -> T5,\nX2 -> T5,\nT3 -> T5" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 4, 18.95/5.83 "to": 16, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 15, 18.95/5.83 "to": 17, 18.95/5.83 "label": "SUCCESS" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 16, 18.95/5.83 "to": 2630, 18.95/5.83 "label": "EVAL with clause\ntimes(zero(X1010), X1011, zero(X1012)) :- times(X1010, X1011, X1012).\nand substitutionX1010 -> T906,\nT1 -> zero(T906),\nT2 -> T907,\nX1011 -> T907,\nX1012 -> T905,\nT3 -> zero(T905),\nT903 -> T906,\nT904 -> T907" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 16, 18.95/5.83 "to": 2631, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 17, 18.95/5.83 "to": 18, 18.95/5.83 "label": "EVAL with clause\ntimes(zero(X6), X7, zero(X8)) :- times(X6, X7, X8).\nand substitutionX6 -> T12,\nT1 -> zero(T12),\nT2 -> T13,\nX7 -> T13,\nX8 -> T11,\nT5 -> zero(T11),\nT9 -> T12,\nT10 -> T13" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 17, 18.95/5.83 "to": 19, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 18, 18.95/5.83 "to": 20, 18.95/5.83 "label": "CASE" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 19, 18.95/5.83 "to": 2611, 18.95/5.83 "label": "EVAL with clause\ntimes(one(X956), X957, X958) :- ','(times(X956, X957, X959), add(X957, zero(X959), X958)).\nand substitutionX956 -> T852,\nT1 -> one(T852),\nT2 -> T853,\nX957 -> T853,\nT5 -> T851,\nX958 -> T851,\nT849 -> T852,\nT850 -> T853" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 19, 18.95/5.83 "to": 2612, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 20, 18.95/5.83 "to": 21, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 20, 18.95/5.83 "to": 22, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 21, 18.95/5.83 "to": 23, 18.95/5.83 "label": "EVAL with clause\ntimes(one(b), X13, X13).\nand substitutionT12 -> one(b),\nT13 -> T18,\nX13 -> T18,\nT11 -> T18" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 21, 18.95/5.83 "to": 24, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 22, 18.95/5.83 "to": 26, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 22, 18.95/5.83 "to": 27, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 23, 18.95/5.83 "to": 25, 18.95/5.83 "label": "SUCCESS" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 26, 18.95/5.83 "to": 30, 18.95/5.83 "label": "EVAL with clause\ntimes(zero(X26), X27, zero(X28)) :- times(X26, X27, X28).\nand substitutionX26 -> T34,\nT12 -> zero(T34),\nT13 -> T35,\nX27 -> T35,\nX28 -> T33,\nT11 -> zero(T33),\nT31 -> T34,\nT32 -> T35" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 26, 18.95/5.83 "to": 31, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 27, 18.95/5.83 "to": 132, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 27, 18.95/5.83 "to": 133, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 30, 18.95/5.83 "to": 1, 18.95/5.83 "label": "INSTANCE with matching:\nT1 -> T34\nT2 -> T35\nT3 -> T33" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 132, 18.95/5.83 "to": 135, 18.95/5.83 "label": "EVAL with clause\ntimes(one(X45), X46, X47) :- ','(times(X45, X46, X48), add(X46, zero(X48), X47)).\nand substitutionX45 -> T53,\nT12 -> one(T53),\nT13 -> T54,\nX46 -> T54,\nT11 -> T52,\nX47 -> T52,\nT50 -> T53,\nT51 -> T54" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 132, 18.95/5.83 "to": 136, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 133, 18.95/5.83 "to": 2608, 18.95/5.83 "label": "FAILURE" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 135, 18.95/5.83 "to": 503, 18.95/5.83 "label": "SPLIT 1" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 135, 18.95/5.83 "to": 504, 18.95/5.83 "label": "SPLIT 2\nnew knowledge:\nT53 is ground\nreplacements:X48 -> T57,\nT54 -> T58" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 503, 18.95/5.83 "to": 505, 18.95/5.83 "label": "CASE" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 504, 18.95/5.83 "to": 2274, 18.95/5.83 "label": "CASE" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 505, 18.95/5.83 "to": 506, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 505, 18.95/5.83 "to": 507, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 506, 18.95/5.83 "to": 516, 18.95/5.83 "label": "EVAL with clause\ntimes(one(b), X57, X57).\nand substitutionT53 -> one(b),\nT54 -> T65,\nX57 -> T65,\nX48 -> T65" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 506, 18.95/5.83 "to": 527, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 507, 18.95/5.83 "to": 591, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 507, 18.95/5.83 "to": 595, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 516, 18.95/5.83 "to": 534, 18.95/5.83 "label": "SUCCESS" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 591, 18.95/5.83 "to": 672, 18.95/5.83 "label": "EVAL with clause\ntimes(zero(X74), X75, zero(X76)) :- times(X74, X75, X76).\nand substitutionX74 -> T76,\nT53 -> zero(T76),\nT54 -> T77,\nX75 -> T77,\nX76 -> X77,\nX48 -> zero(X77),\nT74 -> T76,\nT75 -> T77" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 591, 18.95/5.83 "to": 683, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 595, 18.95/5.83 "to": 1254, 18.95/5.83 "label": "EVAL with clause\ntimes(one(X89), X90, X91) :- ','(times(X89, X90, X92), add(X90, zero(X92), X91)).\nand substitutionX89 -> T86,\nT53 -> one(T86),\nT54 -> T87,\nX90 -> T87,\nX48 -> X93,\nX91 -> X93,\nT84 -> T86,\nT85 -> T87" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 595, 18.95/5.83 "to": 1255, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 672, 18.95/5.83 "to": 503, 18.95/5.83 "label": "INSTANCE with matching:\nT53 -> T76\nT54 -> T77\nX48 -> X77" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1254, 18.95/5.83 "to": 1261, 18.95/5.83 "label": "SPLIT 1" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1254, 18.95/5.83 "to": 1262, 18.95/5.83 "label": "SPLIT 2\nnew knowledge:\nT86 is ground\nreplacements:X92 -> T90,\nT87 -> T91" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1261, 18.95/5.83 "to": 503, 18.95/5.83 "label": "INSTANCE with matching:\nT53 -> T86\nT54 -> T87\nX48 -> X92" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1262, 18.95/5.83 "to": 1271, 18.95/5.83 "label": "CASE" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1271, 18.95/5.83 "to": 1273, 18.95/5.83 "label": "BACKTRACK\nfor clause: add(b, b, b)because of non-unification" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1273, 18.95/5.83 "to": 1277, 18.95/5.83 "label": "BACKTRACK\nfor clause: add(X, b, X) :- binaryZ(X)because of non-unification" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1277, 18.95/5.83 "to": 1283, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1277, 18.95/5.83 "to": 1285, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1283, 18.95/5.83 "to": 1295, 18.95/5.83 "label": "EVAL with clause\nadd(b, X103, X103) :- binaryZ(X103).\nand substitutionT91 -> b,\nT90 -> T100,\nX103 -> zero(T100),\nX93 -> zero(T100),\nT99 -> T100" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1283, 18.95/5.83 "to": 1297, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1285, 18.95/5.83 "to": 1517, 18.95/5.83 "label": "ONLY EVAL with clause\nadd(X144, X145, X146) :- addz(X144, X145, X146).\nand substitutionT91 -> T145,\nX144 -> T145,\nT90 -> T146,\nX145 -> zero(T146),\nX93 -> X147,\nX146 -> X147,\nT143 -> T145,\nT144 -> T146" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1295, 18.95/5.83 "to": 1303, 18.95/5.83 "label": "CASE" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1303, 18.95/5.83 "to": 1309, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1303, 18.95/5.83 "to": 1310, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1309, 18.95/5.83 "to": 1324, 18.95/5.83 "label": "ONLY EVAL with clause\nbinaryZ(zero(X111)) :- binaryZ(X111).\nand substitutionT100 -> T111,\nX111 -> T111,\nT110 -> T111" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1310, 18.95/5.83 "to": 1511, 18.95/5.83 "label": "BACKTRACK\nfor clause: binaryZ(one(X)) :- binary(X)because of non-unification" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1324, 18.95/5.83 "to": 1327, 18.95/5.83 "label": "CASE" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1327, 18.95/5.83 "to": 1329, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1327, 18.95/5.83 "to": 1331, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1329, 18.95/5.83 "to": 1337, 18.95/5.83 "label": "EVAL with clause\nbinaryZ(zero(X117)) :- binaryZ(X117).\nand substitutionX117 -> T118,\nT111 -> zero(T118),\nT117 -> T118" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1329, 18.95/5.83 "to": 1338, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1331, 18.95/5.83 "to": 1493, 18.95/5.83 "label": "EVAL with clause\nbinaryZ(one(X121)) :- binary(X121).\nand substitutionX121 -> T123,\nT111 -> one(T123),\nT122 -> T123" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1331, 18.95/5.83 "to": 1494, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1337, 18.95/5.83 "to": 1324, 18.95/5.83 "label": "INSTANCE with matching:\nT111 -> T118" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1493, 18.95/5.83 "to": 1495, 18.95/5.83 "label": "CASE" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1495, 18.95/5.83 "to": 1496, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1495, 18.95/5.83 "to": 1497, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1496, 18.95/5.83 "to": 1498, 18.95/5.83 "label": "EVAL with clause\nbinary(b).\nand substitutionT123 -> b" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1496, 18.95/5.83 "to": 1500, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1497, 18.95/5.83 "to": 1503, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1497, 18.95/5.83 "to": 1504, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1498, 18.95/5.83 "to": 1502, 18.95/5.83 "label": "SUCCESS" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1503, 18.95/5.83 "to": 1505, 18.95/5.83 "label": "EVAL with clause\nbinary(zero(X126)) :- binaryZ(X126).\nand substitutionX126 -> T129,\nT123 -> zero(T129),\nT128 -> T129" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1503, 18.95/5.83 "to": 1506, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1504, 18.95/5.83 "to": 1509, 18.95/5.83 "label": "EVAL with clause\nbinary(one(X130)) :- binary(X130).\nand substitutionX130 -> T134,\nT123 -> one(T134),\nT133 -> T134" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1504, 18.95/5.83 "to": 1510, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1505, 18.95/5.83 "to": 1324, 18.95/5.83 "label": "INSTANCE with matching:\nT111 -> T129" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1509, 18.95/5.83 "to": 1493, 18.95/5.83 "label": "INSTANCE with matching:\nT123 -> T134" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1517, 18.95/5.83 "to": 1520, 18.95/5.83 "label": "CASE" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1520, 18.95/5.83 "to": 1523, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1520, 18.95/5.83 "to": 1524, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1523, 18.95/5.83 "to": 1527, 18.95/5.83 "label": "EVAL with clause\naddz(zero(X168), zero(X169), zero(X170)) :- addz(X168, X169, X170).\nand substitutionX168 -> T159,\nT145 -> zero(T159),\nT146 -> T160,\nX169 -> T160,\nX170 -> X171,\nX147 -> zero(X171),\nT157 -> T159,\nT158 -> T160" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1523, 18.95/5.83 "to": 1528, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1524, 18.95/5.83 "to": 2261, 18.95/5.83 "label": "BACKTRACK\nfor clause: addz(zero(X), one(Y), one(Z)) :- addx(X, Y, Z)because of non-unification" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1527, 18.95/5.83 "to": 1529, 18.95/5.83 "label": "CASE" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1529, 18.95/5.83 "to": 1641, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1529, 18.95/5.83 "to": 1642, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1641, 18.95/5.83 "to": 1643, 18.95/5.83 "label": "EVAL with clause\naddz(zero(X192), zero(X193), zero(X194)) :- addz(X192, X193, X194).\nand substitutionX192 -> T173,\nT159 -> zero(T173),\nX193 -> T174,\nT160 -> zero(T174),\nX194 -> X195,\nX171 -> zero(X195),\nT171 -> T173,\nT172 -> T174" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1641, 18.95/5.83 "to": 1645, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1642, 18.95/5.83 "to": 1646, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1642, 18.95/5.83 "to": 1647, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1643, 18.95/5.83 "to": 1527, 18.95/5.83 "label": "INSTANCE with matching:\nT159 -> T173\nT160 -> T174\nX171 -> X195" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1646, 18.95/5.83 "to": 1648, 18.95/5.83 "label": "EVAL with clause\naddz(zero(X216), one(X217), one(X218)) :- addx(X216, X217, X218).\nand substitutionX216 -> T187,\nT159 -> zero(T187),\nX217 -> T188,\nT160 -> one(T188),\nX218 -> X219,\nX171 -> one(X219),\nT185 -> T187,\nT186 -> T188" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1646, 18.95/5.83 "to": 1649, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1647, 18.95/5.83 "to": 1714, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1647, 18.95/5.83 "to": 1715, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1648, 18.95/5.83 "to": 1652, 18.95/5.83 "label": "CASE" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1652, 18.95/5.83 "to": 1653, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1652, 18.95/5.83 "to": 1654, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1653, 18.95/5.83 "to": 1655, 18.95/5.83 "label": "EVAL with clause\naddx(one(X225), b, one(X225)) :- binary(X225).\nand substitutionX225 -> T195,\nT187 -> one(T195),\nT188 -> b,\nX219 -> one(T195),\nT194 -> T195" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1653, 18.95/5.83 "to": 1657, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1654, 18.95/5.83 "to": 1663, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1654, 18.95/5.83 "to": 1664, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1655, 18.95/5.83 "to": 1493, 18.95/5.83 "label": "INSTANCE with matching:\nT123 -> T195" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1663, 18.95/5.83 "to": 1667, 18.95/5.83 "label": "EVAL with clause\naddx(zero(X230), b, zero(X230)) :- binaryZ(X230).\nand substitutionX230 -> T201,\nT187 -> zero(T201),\nT188 -> b,\nX219 -> zero(T201),\nT200 -> T201" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1663, 18.95/5.83 "to": 1668, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1664, 18.95/5.83 "to": 1669, 18.95/5.83 "label": "ONLY EVAL with clause\naddx(X244, X245, X246) :- addz(X244, X245, X246).\nand substitutionT187 -> T213,\nX244 -> T213,\nT188 -> T214,\nX245 -> T214,\nX219 -> X247,\nX246 -> X247,\nT211 -> T213,\nT212 -> T214" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1667, 18.95/5.83 "to": 1324, 18.95/5.83 "label": "INSTANCE with matching:\nT111 -> T201" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1669, 18.95/5.83 "to": 1527, 18.95/5.83 "label": "INSTANCE with matching:\nT159 -> T213\nT160 -> T214\nX171 -> X247" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1714, 18.95/5.83 "to": 1718, 18.95/5.83 "label": "EVAL with clause\naddz(one(X268), zero(X269), one(X270)) :- addy(X268, X269, X270).\nand substitutionX268 -> T227,\nT159 -> one(T227),\nX269 -> T228,\nT160 -> zero(T228),\nX270 -> X271,\nX171 -> one(X271),\nT225 -> T227,\nT226 -> T228" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1714, 18.95/5.83 "to": 1719, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1715, 18.95/5.83 "to": 1753, 18.95/5.83 "label": "EVAL with clause\naddz(one(X312), one(X313), zero(X314)) :- addc(X312, X313, X314).\nand substitutionX312 -> T263,\nT159 -> one(T263),\nX313 -> T264,\nT160 -> one(T264),\nX314 -> X315,\nX171 -> zero(X315),\nT261 -> T263,\nT262 -> T264" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1715, 18.95/5.83 "to": 1754, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1718, 18.95/5.83 "to": 1722, 18.95/5.83 "label": "CASE" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1722, 18.95/5.83 "to": 1723, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1722, 18.95/5.83 "to": 1724, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1723, 18.95/5.83 "to": 1727, 18.95/5.83 "label": "EVAL with clause\naddy(b, one(X277), one(X277)) :- binary(X277).\nand substitutionT227 -> b,\nX277 -> T235,\nT228 -> one(T235),\nX271 -> one(T235),\nT234 -> T235" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1723, 18.95/5.83 "to": 1728, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1724, 18.95/5.83 "to": 1729, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1724, 18.95/5.83 "to": 1730, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1727, 18.95/5.83 "to": 1493, 18.95/5.83 "label": "INSTANCE with matching:\nT123 -> T235" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1729, 18.95/5.83 "to": 1731, 18.95/5.83 "label": "EVAL with clause\naddy(b, zero(X282), zero(X282)) :- binaryZ(X282).\nand substitutionT227 -> b,\nX282 -> T241,\nT228 -> zero(T241),\nX271 -> zero(T241),\nT240 -> T241" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1729, 18.95/5.83 "to": 1732, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1730, 18.95/5.83 "to": 1734, 18.95/5.83 "label": "ONLY EVAL with clause\naddy(X296, X297, X298) :- addz(X296, X297, X298).\nand substitutionT227 -> T253,\nX296 -> T253,\nT228 -> T254,\nX297 -> T254,\nX271 -> X299,\nX298 -> X299,\nT251 -> T253,\nT252 -> T254" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1731, 18.95/5.83 "to": 1324, 18.95/5.83 "label": "INSTANCE with matching:\nT111 -> T241" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1734, 18.95/5.83 "to": 1527, 18.95/5.83 "label": "INSTANCE with matching:\nT159 -> T253\nT160 -> T254\nX171 -> X299" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1753, 18.95/5.83 "to": 1755, 18.95/5.83 "label": "CASE" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1755, 18.95/5.83 "to": 1756, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1755, 18.95/5.83 "to": 1757, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1756, 18.95/5.83 "to": 1758, 18.95/5.83 "label": "EVAL with clause\naddc(b, b, one(b)).\nand substitutionT263 -> b,\nT264 -> b,\nX315 -> one(b)" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1756, 18.95/5.83 "to": 1759, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1757, 18.95/5.83 "to": 1761, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1757, 18.95/5.83 "to": 1762, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1758, 18.95/5.83 "to": 1760, 18.95/5.83 "label": "SUCCESS" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1761, 18.95/5.83 "to": 1765, 18.95/5.83 "label": "EVAL with clause\naddc(X328, b, X329) :- succZ(X328, X329).\nand substitutionT263 -> T270,\nX328 -> T270,\nT264 -> b,\nX315 -> X330,\nX329 -> X330,\nT269 -> T270" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1761, 18.95/5.83 "to": 1766, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1762, 18.95/5.83 "to": 2111, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1762, 18.95/5.83 "to": 2112, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1765, 18.95/5.83 "to": 1769, 18.95/5.83 "label": "CASE" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1769, 18.95/5.83 "to": 1770, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1769, 18.95/5.83 "to": 1771, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1770, 18.95/5.83 "to": 1772, 18.95/5.83 "label": "EVAL with clause\nsuccZ(zero(X336), one(X336)) :- binaryZ(X336).\nand substitutionX336 -> T277,\nT270 -> zero(T277),\nX330 -> one(T277),\nT276 -> T277" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1770, 18.95/5.83 "to": 1773, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1771, 18.95/5.83 "to": 1776, 18.95/5.83 "label": "EVAL with clause\nsuccZ(one(X344), zero(X345)) :- succ(X344, X345).\nand substitutionX344 -> T282,\nT270 -> one(T282),\nX345 -> X346,\nX330 -> zero(X346),\nT281 -> T282" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1771, 18.95/5.83 "to": 1777, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1772, 18.95/5.83 "to": 1324, 18.95/5.83 "label": "INSTANCE with matching:\nT111 -> T277" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1776, 18.95/5.83 "to": 1778, 18.95/5.83 "label": "CASE" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1778, 18.95/5.83 "to": 1779, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1778, 18.95/5.83 "to": 1780, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1779, 18.95/5.83 "to": 1932, 18.95/5.83 "label": "EVAL with clause\nsucc(b, one(b)).\nand substitutionT282 -> b,\nX346 -> one(b)" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1779, 18.95/5.83 "to": 1933, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1780, 18.95/5.83 "to": 2085, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1780, 18.95/5.83 "to": 2086, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 1932, 18.95/5.83 "to": 2029, 18.95/5.83 "label": "SUCCESS" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2085, 18.95/5.83 "to": 2087, 18.95/5.83 "label": "EVAL with clause\nsucc(zero(X351), one(X351)) :- binaryZ(X351).\nand substitutionX351 -> T288,\nT282 -> zero(T288),\nX346 -> one(T288),\nT287 -> T288" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2085, 18.95/5.83 "to": 2088, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2086, 18.95/5.83 "to": 2109, 18.95/5.83 "label": "EVAL with clause\nsucc(one(X359), zero(X360)) :- succ(X359, X360).\nand substitutionX359 -> T293,\nT282 -> one(T293),\nX360 -> X361,\nX346 -> zero(X361),\nT292 -> T293" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2086, 18.95/5.83 "to": 2110, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2087, 18.95/5.83 "to": 1324, 18.95/5.83 "label": "INSTANCE with matching:\nT111 -> T288" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2109, 18.95/5.83 "to": 1776, 18.95/5.83 "label": "INSTANCE with matching:\nT282 -> T293\nX346 -> X361" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2111, 18.95/5.83 "to": 2113, 18.95/5.83 "label": "EVAL with clause\naddc(b, X374, X375) :- succZ(X374, X375).\nand substitutionT263 -> b,\nT264 -> T299,\nX374 -> T299,\nX315 -> X376,\nX375 -> X376,\nT298 -> T299" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2111, 18.95/5.83 "to": 2114, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2112, 18.95/5.83 "to": 2117, 18.95/5.83 "label": "ONLY EVAL with clause\naddc(X390, X391, X392) :- addC(X390, X391, X392).\nand substitutionT263 -> T311,\nX390 -> T311,\nT264 -> T312,\nX391 -> T312,\nX315 -> X393,\nX392 -> X393,\nT309 -> T311,\nT310 -> T312" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2113, 18.95/5.83 "to": 1765, 18.95/5.83 "label": "INSTANCE with matching:\nT270 -> T299\nX330 -> X376" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2117, 18.95/5.83 "to": 2130, 18.95/5.83 "label": "CASE" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2130, 18.95/5.83 "to": 2133, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2130, 18.95/5.83 "to": 2134, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2133, 18.95/5.83 "to": 2137, 18.95/5.83 "label": "EVAL with clause\naddC(zero(X414), zero(X415), one(X416)) :- addz(X414, X415, X416).\nand substitutionX414 -> T325,\nT311 -> zero(T325),\nX415 -> T326,\nT312 -> zero(T326),\nX416 -> X417,\nX393 -> one(X417),\nT323 -> T325,\nT324 -> T326" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2133, 18.95/5.83 "to": 2138, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2134, 18.95/5.83 "to": 2142, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2134, 18.95/5.83 "to": 2143, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2137, 18.95/5.83 "to": 1527, 18.95/5.83 "label": "INSTANCE with matching:\nT159 -> T325\nT160 -> T326\nX171 -> X417" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2142, 18.95/5.83 "to": 2146, 18.95/5.83 "label": "EVAL with clause\naddC(zero(X438), one(X439), zero(X440)) :- addX(X438, X439, X440).\nand substitutionX438 -> T339,\nT311 -> zero(T339),\nX439 -> T340,\nT312 -> one(T340),\nX440 -> X441,\nX393 -> zero(X441),\nT337 -> T339,\nT338 -> T340" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2142, 18.95/5.83 "to": 2147, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2143, 18.95/5.83 "to": 2185, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2143, 18.95/5.83 "to": 2186, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2146, 18.95/5.83 "to": 2148, 18.95/5.83 "label": "CASE" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2148, 18.95/5.83 "to": 2150, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2148, 18.95/5.83 "to": 2151, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2150, 18.95/5.83 "to": 2155, 18.95/5.83 "label": "EVAL with clause\naddX(zero(X447), b, one(X447)) :- binaryZ(X447).\nand substitutionX447 -> T347,\nT339 -> zero(T347),\nT340 -> b,\nX441 -> one(T347),\nT346 -> T347" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2150, 18.95/5.83 "to": 2156, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2151, 18.95/5.83 "to": 2159, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2151, 18.95/5.83 "to": 2160, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2155, 18.95/5.83 "to": 1324, 18.95/5.83 "label": "INSTANCE with matching:\nT111 -> T347" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2159, 18.95/5.83 "to": 2165, 18.95/5.83 "label": "EVAL with clause\naddX(one(X461), b, zero(X462)) :- succ(X461, X462).\nand substitutionX461 -> T354,\nT339 -> one(T354),\nT340 -> b,\nX462 -> X463,\nX441 -> zero(X463),\nT353 -> T354" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2159, 18.95/5.83 "to": 2166, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2160, 18.95/5.83 "to": 2179, 18.95/5.83 "label": "ONLY EVAL with clause\naddX(X476, X477, X478) :- addC(X476, X477, X478).\nand substitutionT339 -> T365,\nX476 -> T365,\nT340 -> T366,\nX477 -> T366,\nX441 -> X479,\nX478 -> X479,\nT363 -> T365,\nT364 -> T366" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2165, 18.95/5.83 "to": 1776, 18.95/5.83 "label": "INSTANCE with matching:\nT282 -> T354\nX346 -> X463" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2179, 18.95/5.83 "to": 2117, 18.95/5.83 "label": "INSTANCE with matching:\nT311 -> T365\nT312 -> T366\nX393 -> X479" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2185, 18.95/5.83 "to": 2196, 18.95/5.83 "label": "EVAL with clause\naddC(one(X500), zero(X501), zero(X502)) :- addY(X500, X501, X502).\nand substitutionX500 -> T379,\nT311 -> one(T379),\nX501 -> T380,\nT312 -> zero(T380),\nX502 -> X503,\nX393 -> zero(X503),\nT377 -> T379,\nT378 -> T380" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2185, 18.95/5.83 "to": 2197, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2186, 18.95/5.83 "to": 2259, 18.95/5.83 "label": "EVAL with clause\naddC(one(X554), one(X555), one(X556)) :- addc(X554, X555, X556).\nand substitutionX554 -> T415,\nT311 -> one(T415),\nX555 -> T416,\nT312 -> one(T416),\nX556 -> X557,\nX393 -> one(X557),\nT413 -> T415,\nT414 -> T416" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2186, 18.95/5.83 "to": 2260, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2196, 18.95/5.83 "to": 2198, 18.95/5.83 "label": "CASE" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2198, 18.95/5.83 "to": 2199, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2198, 18.95/5.83 "to": 2200, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2199, 18.95/5.83 "to": 2201, 18.95/5.83 "label": "EVAL with clause\naddY(b, zero(X509), one(X509)) :- binaryZ(X509).\nand substitutionT379 -> b,\nX509 -> T387,\nT380 -> zero(T387),\nX503 -> one(T387),\nT386 -> T387" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2199, 18.95/5.83 "to": 2202, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2200, 18.95/5.83 "to": 2206, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2200, 18.95/5.83 "to": 2207, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2201, 18.95/5.83 "to": 1324, 18.95/5.83 "label": "INSTANCE with matching:\nT111 -> T387" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2206, 18.95/5.83 "to": 2238, 18.95/5.83 "label": "EVAL with clause\naddY(b, one(X523), zero(X524)) :- succ(X523, X524).\nand substitutionT379 -> b,\nX523 -> T394,\nT380 -> one(T394),\nX524 -> X525,\nX503 -> zero(X525),\nT393 -> T394" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2206, 18.95/5.83 "to": 2239, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2207, 18.95/5.83 "to": 2249, 18.95/5.83 "label": "ONLY EVAL with clause\naddY(X538, X539, X540) :- addC(X538, X539, X540).\nand substitutionT379 -> T405,\nX538 -> T405,\nT380 -> T406,\nX539 -> T406,\nX503 -> X541,\nX540 -> X541,\nT403 -> T405,\nT404 -> T406" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2238, 18.95/5.83 "to": 1776, 18.95/5.83 "label": "INSTANCE with matching:\nT282 -> T394\nX346 -> X525" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2249, 18.95/5.83 "to": 2117, 18.95/5.83 "label": "INSTANCE with matching:\nT311 -> T405\nT312 -> T406\nX393 -> X541" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2259, 18.95/5.83 "to": 1753, 18.95/5.83 "label": "INSTANCE with matching:\nT263 -> T415\nT264 -> T416\nX315 -> X557" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2261, 18.95/5.83 "to": 2265, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2261, 18.95/5.83 "to": 2266, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2265, 18.95/5.83 "to": 2267, 18.95/5.83 "label": "EVAL with clause\naddz(one(X577), zero(X578), one(X579)) :- addy(X577, X578, X579).\nand substitutionX577 -> T428,\nT145 -> one(T428),\nT146 -> T429,\nX578 -> T429,\nX579 -> X580,\nX147 -> one(X580),\nT426 -> T428,\nT427 -> T429" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2265, 18.95/5.83 "to": 2268, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2266, 18.95/5.83 "to": 2273, 18.95/5.83 "label": "BACKTRACK\nfor clause: addz(one(X), one(Y), zero(Z)) :- addc(X, Y, Z)because of non-unification" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2267, 18.95/5.83 "to": 1718, 18.95/5.83 "label": "INSTANCE with matching:\nT227 -> T428\nT228 -> T429\nX271 -> X580" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2274, 18.95/5.83 "to": 2275, 18.95/5.83 "label": "BACKTRACK\nfor clause: add(b, b, b)because of non-unification" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2275, 18.95/5.83 "to": 2277, 18.95/5.83 "label": "BACKTRACK\nfor clause: add(X, b, X) :- binaryZ(X)because of non-unification" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2277, 18.95/5.83 "to": 2278, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2277, 18.95/5.83 "to": 2279, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2278, 18.95/5.83 "to": 2282, 18.95/5.83 "label": "EVAL with clause\nadd(b, X590, X590) :- binaryZ(X590).\nand substitutionT58 -> b,\nT57 -> T437,\nX590 -> zero(T437),\nT52 -> zero(T437)" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2278, 18.95/5.83 "to": 2285, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2279, 18.95/5.83 "to": 2309, 18.95/5.83 "label": "ONLY EVAL with clause\nadd(X601, X602, X603) :- addz(X601, X602, X603).\nand substitutionT58 -> T453,\nX601 -> T453,\nT57 -> T454,\nX602 -> zero(T454),\nT52 -> T452,\nX603 -> T452,\nT450 -> T453,\nT451 -> T454" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2282, 18.95/5.83 "to": 1295, 18.95/5.83 "label": "INSTANCE with matching:\nT100 -> T437" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2309, 18.95/5.83 "to": 2313, 18.95/5.83 "label": "CASE" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2313, 18.95/5.83 "to": 2318, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2313, 18.95/5.83 "to": 2319, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2318, 18.95/5.83 "to": 2322, 18.95/5.83 "label": "EVAL with clause\naddz(zero(X619), zero(X620), zero(X621)) :- addz(X619, X620, X621).\nand substitutionX619 -> T473,\nT453 -> zero(T473),\nT454 -> T474,\nX620 -> T474,\nX621 -> T472,\nT452 -> zero(T472),\nT470 -> T473,\nT471 -> T474" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2318, 18.95/5.83 "to": 2323, 18.95/5.83 "label": "EVAL-BACKTRACK" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2319, 18.95/5.83 "to": 2601, 18.95/5.83 "label": "BACKTRACK\nfor clause: addz(zero(X), one(Y), one(Z)) :- addx(X, Y, Z)because of non-unification" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2322, 18.95/5.83 "to": 2326, 18.95/5.83 "label": "CASE" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2326, 18.95/5.83 "to": 2329, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2326, 18.95/5.83 "to": 2330, 18.95/5.83 "label": "PARALLEL" 18.95/5.83 }, 18.95/5.83 { 18.95/5.83 "from": 2329, 18.95/5.83 "to": 2331, 18.95/5.83 "label": "EVAL with clause\naddz(zero(X637), zero(X638), zero(X639)) :- addz(X637, X638, X639).\nand substitutionX637 -> T493,\nT473 -> zero(T493),\nX638 -> T494,\nT474 -> zero(T494),\nX639 -> T492,\nT472 -> zero(T492),\nT490 -> T493,\nT491 -> T494" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2329, 18.95/5.84 "to": 2332, 18.95/5.84 "label": "EVAL-BACKTRACK" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2330, 18.95/5.84 "to": 2357, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2330, 18.95/5.84 "to": 2358, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2331, 18.95/5.84 "to": 2322, 18.95/5.84 "label": "INSTANCE with matching:\nT473 -> T493\nT474 -> T494\nT472 -> T492" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2357, 18.95/5.84 "to": 2362, 18.95/5.84 "label": "EVAL with clause\naddz(zero(X655), one(X656), one(X657)) :- addx(X655, X656, X657).\nand substitutionX655 -> T513,\nT473 -> zero(T513),\nX656 -> T514,\nT474 -> one(T514),\nX657 -> T512,\nT472 -> one(T512),\nT510 -> T513,\nT511 -> T514" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2357, 18.95/5.84 "to": 2363, 18.95/5.84 "label": "EVAL-BACKTRACK" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2358, 18.95/5.84 "to": 2380, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2358, 18.95/5.84 "to": 2381, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2362, 18.95/5.84 "to": 2364, 18.95/5.84 "label": "CASE" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2364, 18.95/5.84 "to": 2367, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2364, 18.95/5.84 "to": 2368, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2367, 18.95/5.84 "to": 2371, 18.95/5.84 "label": "EVAL with clause\naddx(one(X663), b, one(X663)) :- binary(X663).\nand substitutionX663 -> T520,\nT513 -> one(T520),\nT514 -> b,\nT512 -> one(T520)" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2367, 18.95/5.84 "to": 2372, 18.95/5.84 "label": "EVAL-BACKTRACK" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2368, 18.95/5.84 "to": 2373, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2368, 18.95/5.84 "to": 2374, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2371, 18.95/5.84 "to": 1493, 18.95/5.84 "label": "INSTANCE with matching:\nT123 -> T520" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2373, 18.95/5.84 "to": 2375, 18.95/5.84 "label": "EVAL with clause\naddx(zero(X668), b, zero(X668)) :- binaryZ(X668).\nand substitutionX668 -> T525,\nT513 -> zero(T525),\nT514 -> b,\nT512 -> zero(T525)" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2373, 18.95/5.84 "to": 2376, 18.95/5.84 "label": "EVAL-BACKTRACK" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2374, 18.95/5.84 "to": 2379, 18.95/5.84 "label": "ONLY EVAL with clause\naddx(X679, X680, X681) :- addz(X679, X680, X681).\nand substitutionT513 -> T541,\nX679 -> T541,\nT514 -> T542,\nX680 -> T542,\nT512 -> T540,\nX681 -> T540,\nT538 -> T541,\nT539 -> T542" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2375, 18.95/5.84 "to": 1324, 18.95/5.84 "label": "INSTANCE with matching:\nT111 -> T525" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2379, 18.95/5.84 "to": 2322, 18.95/5.84 "label": "INSTANCE with matching:\nT473 -> T541\nT474 -> T542\nT472 -> T540" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2380, 18.95/5.84 "to": 2382, 18.95/5.84 "label": "EVAL with clause\naddz(one(X697), zero(X698), one(X699)) :- addy(X697, X698, X699).\nand substitutionX697 -> T561,\nT473 -> one(T561),\nX698 -> T562,\nT474 -> zero(T562),\nX699 -> T560,\nT472 -> one(T560),\nT558 -> T561,\nT559 -> T562" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2380, 18.95/5.84 "to": 2383, 18.95/5.84 "label": "EVAL-BACKTRACK" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2381, 18.95/5.84 "to": 2408, 18.95/5.84 "label": "EVAL with clause\naddz(one(X733), one(X734), zero(X735)) :- addc(X733, X734, X735).\nand substitutionX733 -> T603,\nT473 -> one(T603),\nX734 -> T604,\nT474 -> one(T604),\nX735 -> T602,\nT472 -> zero(T602),\nT600 -> T603,\nT601 -> T604" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2381, 18.95/5.84 "to": 2409, 18.95/5.84 "label": "EVAL-BACKTRACK" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2382, 18.95/5.84 "to": 2384, 18.95/5.84 "label": "CASE" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2384, 18.95/5.84 "to": 2385, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2384, 18.95/5.84 "to": 2386, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2385, 18.95/5.84 "to": 2387, 18.95/5.84 "label": "EVAL with clause\naddy(b, one(X705), one(X705)) :- binary(X705).\nand substitutionT561 -> b,\nX705 -> T568,\nT562 -> one(T568),\nT560 -> one(T568)" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2385, 18.95/5.84 "to": 2388, 18.95/5.84 "label": "EVAL-BACKTRACK" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2386, 18.95/5.84 "to": 2389, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2386, 18.95/5.84 "to": 2390, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2387, 18.95/5.84 "to": 1493, 18.95/5.84 "label": "INSTANCE with matching:\nT123 -> T568" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2389, 18.95/5.84 "to": 2391, 18.95/5.84 "label": "EVAL with clause\naddy(b, zero(X710), zero(X710)) :- binaryZ(X710).\nand substitutionT561 -> b,\nX710 -> T573,\nT562 -> zero(T573),\nT560 -> zero(T573)" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2389, 18.95/5.84 "to": 2392, 18.95/5.84 "label": "EVAL-BACKTRACK" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2390, 18.95/5.84 "to": 2405, 18.95/5.84 "label": "ONLY EVAL with clause\naddy(X721, X722, X723) :- addz(X721, X722, X723).\nand substitutionT561 -> T589,\nX721 -> T589,\nT562 -> T590,\nX722 -> T590,\nT560 -> T588,\nX723 -> T588,\nT586 -> T589,\nT587 -> T590" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2391, 18.95/5.84 "to": 1324, 18.95/5.84 "label": "INSTANCE with matching:\nT111 -> T573" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2405, 18.95/5.84 "to": 2322, 18.95/5.84 "label": "INSTANCE with matching:\nT473 -> T589\nT474 -> T590\nT472 -> T588" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2408, 18.95/5.84 "to": 2412, 18.95/5.84 "label": "CASE" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2412, 18.95/5.84 "to": 2413, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2412, 18.95/5.84 "to": 2414, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2413, 18.95/5.84 "to": 2415, 18.95/5.84 "label": "EVAL with clause\naddc(b, b, one(b)).\nand substitutionT603 -> b,\nT604 -> b,\nT602 -> one(b)" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2413, 18.95/5.84 "to": 2416, 18.95/5.84 "label": "EVAL-BACKTRACK" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2414, 18.95/5.84 "to": 2420, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2414, 18.95/5.84 "to": 2421, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2415, 18.95/5.84 "to": 2417, 18.95/5.84 "label": "SUCCESS" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2420, 18.95/5.84 "to": 2424, 18.95/5.84 "label": "EVAL with clause\naddc(X744, b, X745) :- succZ(X744, X745).\nand substitutionT603 -> T615,\nX744 -> T615,\nT604 -> b,\nT602 -> T614,\nX745 -> T614,\nT613 -> T615" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2420, 18.95/5.84 "to": 2425, 18.95/5.84 "label": "EVAL-BACKTRACK" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2421, 18.95/5.84 "to": 2536, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2421, 18.95/5.84 "to": 2537, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2424, 18.95/5.84 "to": 2432, 18.95/5.84 "label": "CASE" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2432, 18.95/5.84 "to": 2436, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2432, 18.95/5.84 "to": 2437, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2436, 18.95/5.84 "to": 2440, 18.95/5.84 "label": "EVAL with clause\nsuccZ(zero(X751), one(X751)) :- binaryZ(X751).\nand substitutionX751 -> T621,\nT615 -> zero(T621),\nT614 -> one(T621)" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2436, 18.95/5.84 "to": 2441, 18.95/5.84 "label": "EVAL-BACKTRACK" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2437, 18.95/5.84 "to": 2520, 18.95/5.84 "label": "EVAL with clause\nsuccZ(one(X757), zero(X758)) :- succ(X757, X758).\nand substitutionX757 -> T629,\nT615 -> one(T629),\nX758 -> T628,\nT614 -> zero(T628),\nT627 -> T629" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2437, 18.95/5.84 "to": 2521, 18.95/5.84 "label": "EVAL-BACKTRACK" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2440, 18.95/5.84 "to": 1324, 18.95/5.84 "label": "INSTANCE with matching:\nT111 -> T621" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2520, 18.95/5.84 "to": 2522, 18.95/5.84 "label": "CASE" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2522, 18.95/5.84 "to": 2523, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2522, 18.95/5.84 "to": 2524, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2523, 18.95/5.84 "to": 2527, 18.95/5.84 "label": "EVAL with clause\nsucc(b, one(b)).\nand substitutionT629 -> b,\nT628 -> one(b)" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2523, 18.95/5.84 "to": 2528, 18.95/5.84 "label": "EVAL-BACKTRACK" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2524, 18.95/5.84 "to": 2530, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2524, 18.95/5.84 "to": 2531, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2527, 18.95/5.84 "to": 2529, 18.95/5.84 "label": "SUCCESS" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2530, 18.95/5.84 "to": 2532, 18.95/5.84 "label": "EVAL with clause\nsucc(zero(X763), one(X763)) :- binaryZ(X763).\nand substitutionX763 -> T634,\nT629 -> zero(T634),\nT628 -> one(T634)" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2530, 18.95/5.84 "to": 2533, 18.95/5.84 "label": "EVAL-BACKTRACK" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2531, 18.95/5.84 "to": 2534, 18.95/5.84 "label": "EVAL with clause\nsucc(one(X769), zero(X770)) :- succ(X769, X770).\nand substitutionX769 -> T642,\nT629 -> one(T642),\nX770 -> T641,\nT628 -> zero(T641),\nT640 -> T642" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2531, 18.95/5.84 "to": 2535, 18.95/5.84 "label": "EVAL-BACKTRACK" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2532, 18.95/5.84 "to": 1324, 18.95/5.84 "label": "INSTANCE with matching:\nT111 -> T634" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2534, 18.95/5.84 "to": 2520, 18.95/5.84 "label": "INSTANCE with matching:\nT629 -> T642\nT628 -> T641" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2536, 18.95/5.84 "to": 2538, 18.95/5.84 "label": "EVAL with clause\naddc(b, X779, X780) :- succZ(X779, X780).\nand substitutionT603 -> b,\nT604 -> T653,\nX779 -> T653,\nT602 -> T652,\nX780 -> T652,\nT651 -> T653" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2536, 18.95/5.84 "to": 2539, 18.95/5.84 "label": "EVAL-BACKTRACK" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2537, 18.95/5.84 "to": 2543, 18.95/5.84 "label": "ONLY EVAL with clause\naddc(X791, X792, X793) :- addC(X791, X792, X793).\nand substitutionT603 -> T669,\nX791 -> T669,\nT604 -> T670,\nX792 -> T670,\nT602 -> T668,\nX793 -> T668,\nT666 -> T669,\nT667 -> T670" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2538, 18.95/5.84 "to": 2424, 18.95/5.84 "label": "INSTANCE with matching:\nT615 -> T653\nT614 -> T652" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2543, 18.95/5.84 "to": 2544, 18.95/5.84 "label": "CASE" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2544, 18.95/5.84 "to": 2545, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2544, 18.95/5.84 "to": 2546, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2545, 18.95/5.84 "to": 2547, 18.95/5.84 "label": "EVAL with clause\naddC(zero(X809), zero(X810), one(X811)) :- addz(X809, X810, X811).\nand substitutionX809 -> T689,\nT669 -> zero(T689),\nX810 -> T690,\nT670 -> zero(T690),\nX811 -> T688,\nT668 -> one(T688),\nT686 -> T689,\nT687 -> T690" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2545, 18.95/5.84 "to": 2548, 18.95/5.84 "label": "EVAL-BACKTRACK" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2546, 18.95/5.84 "to": 2549, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2546, 18.95/5.84 "to": 2550, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2547, 18.95/5.84 "to": 2322, 18.95/5.84 "label": "INSTANCE with matching:\nT473 -> T689\nT474 -> T690\nT472 -> T688" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2549, 18.95/5.84 "to": 2551, 18.95/5.84 "label": "EVAL with clause\naddC(zero(X827), one(X828), zero(X829)) :- addX(X827, X828, X829).\nand substitutionX827 -> T709,\nT669 -> zero(T709),\nX828 -> T710,\nT670 -> one(T710),\nX829 -> T708,\nT668 -> zero(T708),\nT706 -> T709,\nT707 -> T710" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2549, 18.95/5.84 "to": 2552, 18.95/5.84 "label": "EVAL-BACKTRACK" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2550, 18.95/5.84 "to": 2571, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2550, 18.95/5.84 "to": 2572, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2551, 18.95/5.84 "to": 2553, 18.95/5.84 "label": "CASE" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2553, 18.95/5.84 "to": 2554, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2553, 18.95/5.84 "to": 2555, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2554, 18.95/5.84 "to": 2556, 18.95/5.84 "label": "EVAL with clause\naddX(zero(X835), b, one(X835)) :- binaryZ(X835).\nand substitutionX835 -> T716,\nT709 -> zero(T716),\nT710 -> b,\nT708 -> one(T716)" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2554, 18.95/5.84 "to": 2557, 18.95/5.84 "label": "EVAL-BACKTRACK" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2555, 18.95/5.84 "to": 2558, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2555, 18.95/5.84 "to": 2559, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2556, 18.95/5.84 "to": 1324, 18.95/5.84 "label": "INSTANCE with matching:\nT111 -> T716" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2558, 18.95/5.84 "to": 2560, 18.95/5.84 "label": "EVAL with clause\naddX(one(X845), b, zero(X846)) :- succ(X845, X846).\nand substitutionX845 -> T728,\nT709 -> one(T728),\nT710 -> b,\nX846 -> T727,\nT708 -> zero(T727),\nT726 -> T728" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2558, 18.95/5.84 "to": 2561, 18.95/5.84 "label": "EVAL-BACKTRACK" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2559, 18.95/5.84 "to": 2562, 18.95/5.84 "label": "ONLY EVAL with clause\naddX(X856, X857, X858) :- addC(X856, X857, X858).\nand substitutionT709 -> T743,\nX856 -> T743,\nT710 -> T744,\nX857 -> T744,\nT708 -> T742,\nX858 -> T742,\nT740 -> T743,\nT741 -> T744" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2560, 18.95/5.84 "to": 2520, 18.95/5.84 "label": "INSTANCE with matching:\nT629 -> T728\nT628 -> T727" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2562, 18.95/5.84 "to": 2543, 18.95/5.84 "label": "INSTANCE with matching:\nT669 -> T743\nT670 -> T744\nT668 -> T742" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2571, 18.95/5.84 "to": 2577, 18.95/5.84 "label": "EVAL with clause\naddC(one(X874), zero(X875), zero(X876)) :- addY(X874, X875, X876).\nand substitutionX874 -> T763,\nT669 -> one(T763),\nX875 -> T764,\nT670 -> zero(T764),\nX876 -> T762,\nT668 -> zero(T762),\nT760 -> T763,\nT761 -> T764" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2571, 18.95/5.84 "to": 2578, 18.95/5.84 "label": "EVAL-BACKTRACK" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2572, 18.95/5.84 "to": 2599, 18.95/5.84 "label": "EVAL with clause\naddC(one(X915), one(X916), one(X917)) :- addc(X915, X916, X917).\nand substitutionX915 -> T811,\nT669 -> one(T811),\nX916 -> T812,\nT670 -> one(T812),\nX917 -> T810,\nT668 -> one(T810),\nT808 -> T811,\nT809 -> T812" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2572, 18.95/5.84 "to": 2600, 18.95/5.84 "label": "EVAL-BACKTRACK" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2577, 18.95/5.84 "to": 2581, 18.95/5.84 "label": "CASE" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2581, 18.95/5.84 "to": 2582, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2581, 18.95/5.84 "to": 2583, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2582, 18.95/5.84 "to": 2584, 18.95/5.84 "label": "EVAL with clause\naddY(b, zero(X882), one(X882)) :- binaryZ(X882).\nand substitutionT763 -> b,\nX882 -> T770,\nT764 -> zero(T770),\nT762 -> one(T770)" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2582, 18.95/5.84 "to": 2585, 18.95/5.84 "label": "EVAL-BACKTRACK" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2583, 18.95/5.84 "to": 2587, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2583, 18.95/5.84 "to": 2588, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2584, 18.95/5.84 "to": 1324, 18.95/5.84 "label": "INSTANCE with matching:\nT111 -> T770" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2587, 18.95/5.84 "to": 2589, 18.95/5.84 "label": "EVAL with clause\naddY(b, one(X892), zero(X893)) :- succ(X892, X893).\nand substitutionT763 -> b,\nX892 -> T782,\nT764 -> one(T782),\nX893 -> T781,\nT762 -> zero(T781),\nT780 -> T782" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2587, 18.95/5.84 "to": 2590, 18.95/5.84 "label": "EVAL-BACKTRACK" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2588, 18.95/5.84 "to": 2594, 18.95/5.84 "label": "ONLY EVAL with clause\naddY(X903, X904, X905) :- addC(X903, X904, X905).\nand substitutionT763 -> T797,\nX903 -> T797,\nT764 -> T798,\nX904 -> T798,\nT762 -> T796,\nX905 -> T796,\nT794 -> T797,\nT795 -> T798" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2589, 18.95/5.84 "to": 2520, 18.95/5.84 "label": "INSTANCE with matching:\nT629 -> T782\nT628 -> T781" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2594, 18.95/5.84 "to": 2543, 18.95/5.84 "label": "INSTANCE with matching:\nT669 -> T797\nT670 -> T798\nT668 -> T796" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2599, 18.95/5.84 "to": 2408, 18.95/5.84 "label": "INSTANCE with matching:\nT603 -> T811\nT604 -> T812\nT602 -> T810" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2601, 18.95/5.84 "to": 2603, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2601, 18.95/5.84 "to": 2604, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2603, 18.95/5.84 "to": 2605, 18.95/5.84 "label": "EVAL with clause\naddz(one(X933), zero(X934), one(X935)) :- addy(X933, X934, X935).\nand substitutionX933 -> T829,\nT453 -> one(T829),\nT454 -> T830,\nX934 -> T830,\nX935 -> T828,\nT452 -> one(T828),\nT826 -> T829,\nT827 -> T830" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2603, 18.95/5.84 "to": 2606, 18.95/5.84 "label": "EVAL-BACKTRACK" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2604, 18.95/5.84 "to": 2607, 18.95/5.84 "label": "BACKTRACK\nfor clause: addz(one(X), one(Y), zero(Z)) :- addc(X, Y, Z)because of non-unification" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2605, 18.95/5.84 "to": 2382, 18.95/5.84 "label": "INSTANCE with matching:\nT561 -> T829\nT562 -> T830\nT560 -> T828" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2608, 18.95/5.84 "to": 2609, 18.95/5.84 "label": "EVAL with clause\ntimes(one(X947), X948, X949) :- ','(times(X947, X948, X950), add(X948, zero(X950), X949)).\nand substitutionX947 -> T842,\nT1 -> one(T842),\nT2 -> T843,\nX948 -> T843,\nT11 -> T841,\nX949 -> zero(T841),\nT839 -> T842,\nT840 -> T843" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2608, 18.95/5.84 "to": 2610, 18.95/5.84 "label": "EVAL-BACKTRACK" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2609, 18.95/5.84 "to": 135, 18.95/5.84 "label": "INSTANCE with matching:\nT53 -> T842\nT54 -> T843\nX48 -> X950\nT52 -> zero(T841)" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2611, 18.95/5.84 "to": 2613, 18.95/5.84 "label": "CASE" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2613, 18.95/5.84 "to": 2614, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2613, 18.95/5.84 "to": 2615, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2614, 18.95/5.84 "to": 2616, 18.95/5.84 "label": "EVAL with clause\ntimes(one(b), X964, X964).\nand substitutionT852 -> one(b),\nT853 -> T859,\nX964 -> T859,\nX959 -> T859,\nT858 -> T859" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2614, 18.95/5.84 "to": 2617, 18.95/5.84 "label": "EVAL-BACKTRACK" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2615, 18.95/5.84 "to": 2618, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2615, 18.95/5.84 "to": 2619, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2616, 18.95/5.84 "to": 504, 18.95/5.84 "label": "INSTANCE with matching:\nT58 -> T859\nT57 -> T859\nT52 -> T851" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2618, 18.95/5.84 "to": 2620, 18.95/5.84 "label": "EVAL with clause\ntimes(zero(X981), X982, zero(X983)) :- times(X981, X982, X983).\nand substitutionX981 -> T870,\nT852 -> zero(T870),\nT853 -> T871,\nX982 -> T871,\nX983 -> X984,\nX959 -> zero(X984),\nT868 -> T870,\nT869 -> T871" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2618, 18.95/5.84 "to": 2621, 18.95/5.84 "label": "EVAL-BACKTRACK" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2619, 18.95/5.84 "to": 2624, 18.95/5.84 "label": "EVAL with clause\ntimes(one(X998), X999, X1000) :- ','(times(X998, X999, X1001), add(X999, zero(X1001), X1000)).\nand substitutionX998 -> T886,\nT852 -> one(T886),\nT853 -> T887,\nX999 -> T887,\nX959 -> X1002,\nX1000 -> X1002,\nT884 -> T886,\nT885 -> T887" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2619, 18.95/5.84 "to": 2625, 18.95/5.84 "label": "EVAL-BACKTRACK" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2620, 18.95/5.84 "to": 2622, 18.95/5.84 "label": "SPLIT 1" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2620, 18.95/5.84 "to": 2623, 18.95/5.84 "label": "SPLIT 2\nnew knowledge:\nT870 is ground\nreplacements:X984 -> T874,\nT871 -> T875,\nT1 -> T876,\nT2 -> T877" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2622, 18.95/5.84 "to": 503, 18.95/5.84 "label": "INSTANCE with matching:\nT53 -> T870\nT54 -> T871\nX48 -> X984" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2623, 18.95/5.84 "to": 504, 18.95/5.84 "label": "INSTANCE with matching:\nT58 -> T875\nT57 -> zero(T874)\nT52 -> T851" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2624, 18.95/5.84 "to": 2626, 18.95/5.84 "label": "SPLIT 1" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2624, 18.95/5.84 "to": 2627, 18.95/5.84 "label": "SPLIT 2\nnew knowledge:\nT886 is ground\nreplacements:X1001 -> T890,\nT887 -> T891,\nT1 -> T892,\nT2 -> T893" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2626, 18.95/5.84 "to": 503, 18.95/5.84 "label": "INSTANCE with matching:\nT53 -> T886\nT54 -> T887\nX48 -> X1001" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2627, 18.95/5.84 "to": 2628, 18.95/5.84 "label": "SPLIT 1" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2627, 18.95/5.84 "to": 2629, 18.95/5.84 "label": "SPLIT 2\nnew knowledge:\nT897 is ground\nT890 is ground\nT896 is ground\nreplacements:X1002 -> T896,\nT891 -> T897,\nT892 -> T898,\nT893 -> T899" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2628, 18.95/5.84 "to": 1262, 18.95/5.84 "label": "INSTANCE with matching:\nT91 -> T891\nT90 -> T890\nX93 -> X1002" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2629, 18.95/5.84 "to": 504, 18.95/5.84 "label": "INSTANCE with matching:\nT58 -> T897\nT57 -> T896\nT52 -> T851" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2630, 18.95/5.84 "to": 2632, 18.95/5.84 "label": "CASE" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2631, 18.95/5.84 "to": 2649, 18.95/5.84 "label": "EVAL with clause\ntimes(one(X1071), X1072, X1073) :- ','(times(X1071, X1072, X1074), add(X1072, zero(X1074), X1073)).\nand substitutionX1071 -> T970,\nT1 -> one(T970),\nT2 -> T971,\nX1072 -> T971,\nT3 -> T969,\nX1073 -> T969,\nT967 -> T970,\nT968 -> T971" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2631, 18.95/5.84 "to": 2650, 18.95/5.84 "label": "EVAL-BACKTRACK" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2632, 18.95/5.84 "to": 2633, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2632, 18.95/5.84 "to": 2634, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2633, 18.95/5.84 "to": 2635, 18.95/5.84 "label": "EVAL with clause\ntimes(one(b), X1017, X1017).\nand substitutionT906 -> one(b),\nT907 -> T912,\nX1017 -> T912,\nT905 -> T912" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2633, 18.95/5.84 "to": 2636, 18.95/5.84 "label": "EVAL-BACKTRACK" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2634, 18.95/5.84 "to": 2638, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2634, 18.95/5.84 "to": 2639, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2635, 18.95/5.84 "to": 2637, 18.95/5.84 "label": "SUCCESS" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2638, 18.95/5.84 "to": 2640, 18.95/5.84 "label": "EVAL with clause\ntimes(zero(X1030), X1031, zero(X1032)) :- times(X1030, X1031, X1032).\nand substitutionX1030 -> T928,\nT906 -> zero(T928),\nT907 -> T929,\nX1031 -> T929,\nX1032 -> T927,\nT905 -> zero(T927),\nT925 -> T928,\nT926 -> T929" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2638, 18.95/5.84 "to": 2641, 18.95/5.84 "label": "EVAL-BACKTRACK" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2639, 18.95/5.84 "to": 2642, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2639, 18.95/5.84 "to": 2643, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2640, 18.95/5.84 "to": 1, 18.95/5.84 "label": "INSTANCE with matching:\nT1 -> T928\nT2 -> T929\nT3 -> T927" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2642, 18.95/5.84 "to": 2644, 18.95/5.84 "label": "EVAL with clause\ntimes(one(X1049), X1050, X1051) :- ','(times(X1049, X1050, X1052), add(X1050, zero(X1052), X1051)).\nand substitutionX1049 -> T947,\nT906 -> one(T947),\nT907 -> T948,\nX1050 -> T948,\nT905 -> T946,\nX1051 -> T946,\nT944 -> T947,\nT945 -> T948" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2642, 18.95/5.84 "to": 2645, 18.95/5.84 "label": "EVAL-BACKTRACK" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2643, 18.95/5.84 "to": 2646, 18.95/5.84 "label": "FAILURE" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2644, 18.95/5.84 "to": 135, 18.95/5.84 "label": "INSTANCE with matching:\nT53 -> T947\nT54 -> T948\nX48 -> X1052\nT52 -> T946" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2646, 18.95/5.84 "to": 2647, 18.95/5.84 "label": "EVAL with clause\ntimes(one(X1062), X1063, X1064) :- ','(times(X1062, X1063, X1065), add(X1063, zero(X1065), X1064)).\nand substitutionX1062 -> T960,\nT1 -> one(T960),\nT2 -> T961,\nX1063 -> T961,\nT905 -> T959,\nX1064 -> zero(T959),\nT957 -> T960,\nT958 -> T961" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2646, 18.95/5.84 "to": 2648, 18.95/5.84 "label": "EVAL-BACKTRACK" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2647, 18.95/5.84 "to": 135, 18.95/5.84 "label": "INSTANCE with matching:\nT53 -> T960\nT54 -> T961\nX48 -> X1065\nT52 -> zero(T959)" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2649, 18.95/5.84 "to": 2651, 18.95/5.84 "label": "CASE" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2651, 18.95/5.84 "to": 2652, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2651, 18.95/5.84 "to": 2653, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2652, 18.95/5.84 "to": 2654, 18.95/5.84 "label": "EVAL with clause\ntimes(one(b), X1079, X1079).\nand substitutionT970 -> one(b),\nT971 -> T977,\nX1079 -> T977,\nX1074 -> T977,\nT976 -> T977" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2652, 18.95/5.84 "to": 2655, 18.95/5.84 "label": "EVAL-BACKTRACK" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2653, 18.95/5.84 "to": 2656, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2653, 18.95/5.84 "to": 2657, 18.95/5.84 "label": "PARALLEL" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2654, 18.95/5.84 "to": 504, 18.95/5.84 "label": "INSTANCE with matching:\nT58 -> T977\nT57 -> T977\nT52 -> T969" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2656, 18.95/5.84 "to": 2658, 18.95/5.84 "label": "EVAL with clause\ntimes(zero(X1096), X1097, zero(X1098)) :- times(X1096, X1097, X1098).\nand substitutionX1096 -> T988,\nT970 -> zero(T988),\nT971 -> T989,\nX1097 -> T989,\nX1098 -> X1099,\nX1074 -> zero(X1099),\nT986 -> T988,\nT987 -> T989" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2656, 18.95/5.84 "to": 2659, 18.95/5.84 "label": "EVAL-BACKTRACK" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2657, 18.95/5.84 "to": 2660, 18.95/5.84 "label": "EVAL with clause\ntimes(one(X1111), X1112, X1113) :- ','(times(X1111, X1112, X1114), add(X1112, zero(X1114), X1113)).\nand substitutionX1111 -> T998,\nT970 -> one(T998),\nT971 -> T999,\nX1112 -> T999,\nX1074 -> X1115,\nX1113 -> X1115,\nT996 -> T998,\nT997 -> T999" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2657, 18.95/5.84 "to": 2661, 18.95/5.84 "label": "EVAL-BACKTRACK" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2658, 18.95/5.84 "to": 2620, 18.95/5.84 "label": "INSTANCE with matching:\nT870 -> T988\nT871 -> T989\nX984 -> X1099\nT851 -> T969\nX6 -> X1010\nX7 -> X1011\nX8 -> X1012" 18.95/5.84 }, 18.95/5.84 { 18.95/5.84 "from": 2660, 18.95/5.84 "to": 2624, 18.95/5.84 "label": "INSTANCE with matching:\nT886 -> T998\nT887 -> T999\nX1001 -> X1114\nX1002 -> X1115\nT851 -> T969\nX6 -> X1010\nX7 -> X1011\nX8 -> X1012" 18.95/5.84 } 18.95/5.84 ], 18.95/5.84 "type": "Graph" 18.95/5.84 } 18.95/5.84 } 18.95/5.84 18.95/5.84 ---------------------------------------- 18.95/5.84 18.95/5.84 (136) 18.95/5.84 Obligation: 18.95/5.84 Triples: 18.95/5.84 18.95/5.84 timesF(zero(X1), X2, zero(X3)) :- timesF(X1, X2, X3). 18.95/5.84 timesF(one(X1), X2, X3) :- timesF(X1, X2, X4). 18.95/5.84 timesF(one(X1), X2, X3) :- ','(timescF(X1, X2, X4), addG(X2, X4, X3)). 18.95/5.84 binaryZH(zero(X1)) :- binaryZH(X1). 18.95/5.84 binaryZH(one(X1)) :- binaryI(X1). 18.95/5.84 binaryI(zero(X1)) :- binaryZH(X1). 18.95/5.84 binaryI(one(X1)) :- binaryI(X1). 18.95/5.84 addzJ(zero(X1), zero(X2), zero(X3)) :- addzJ(X1, X2, X3). 18.95/5.84 addzJ(zero(one(X1)), one(b), one(one(X1))) :- binaryI(X1). 18.95/5.84 addzJ(zero(zero(X1)), one(b), one(zero(X1))) :- binaryZH(X1). 18.95/5.84 addzJ(zero(X1), one(X2), one(X3)) :- addzJ(X1, X2, X3). 18.95/5.84 addzJ(one(X1), zero(X2), one(X3)) :- addyK(X1, X2, X3). 18.95/5.84 addzJ(one(X1), one(X2), zero(X3)) :- addcL(X1, X2, X3). 18.95/5.84 succM(zero(X1), one(X1)) :- binaryZH(X1). 18.95/5.84 succM(one(X1), zero(X2)) :- succM(X1, X2). 18.95/5.84 succZN(zero(X1), one(X1)) :- binaryZH(X1). 18.95/5.84 succZN(one(X1), zero(X2)) :- succM(X1, X2). 18.95/5.84 addCO(zero(X1), zero(X2), one(X3)) :- addzJ(X1, X2, X3). 18.95/5.84 addCO(zero(zero(X1)), one(b), zero(one(X1))) :- binaryZH(X1). 18.95/5.84 addCO(zero(one(X1)), one(b), zero(zero(X2))) :- succM(X1, X2). 18.95/5.84 addCO(zero(X1), one(X2), zero(X3)) :- addCO(X1, X2, X3). 18.95/5.84 addCO(one(b), zero(zero(X1)), zero(one(X1))) :- binaryZH(X1). 18.95/5.84 addCO(one(b), zero(one(X1)), zero(zero(X2))) :- succM(X1, X2). 18.95/5.84 addCO(one(X1), zero(X2), zero(X3)) :- addCO(X1, X2, X3). 18.95/5.84 addCO(one(X1), one(X2), one(X3)) :- addcL(X1, X2, X3). 18.95/5.84 addcL(X1, b, X2) :- succZN(X1, X2). 18.95/5.84 addcL(b, X1, X2) :- succZN(X1, X2). 18.95/5.84 addcL(X1, X2, X3) :- addCO(X1, X2, X3). 18.95/5.84 addyK(b, one(X1), one(X1)) :- binaryI(X1). 18.95/5.84 addyK(b, zero(X1), zero(X1)) :- binaryZH(X1). 18.95/5.84 addyK(X1, X2, X3) :- addzJ(X1, X2, X3). 18.95/5.84 binaryZP(X1) :- binaryZH(X1). 18.95/5.84 addzQ(zero(X1), zero(X2), zero(X3)) :- addzQ(X1, X2, X3). 18.95/5.84 addzQ(zero(one(X1)), one(b), one(one(X1))) :- binaryI(X1). 18.95/5.84 addzQ(zero(zero(X1)), one(b), one(zero(X1))) :- binaryZH(X1). 18.95/5.84 addzQ(zero(X1), one(X2), one(X3)) :- addzQ(X1, X2, X3). 18.95/5.84 addzQ(one(X1), zero(X2), one(X3)) :- addyR(X1, X2, X3). 18.95/5.84 addzQ(one(X1), one(X2), zero(X3)) :- addcS(X1, X2, X3). 18.95/5.84 succT(zero(X1), one(X1)) :- binaryZH(X1). 18.95/5.84 succT(one(X1), zero(X2)) :- succT(X1, X2). 18.95/5.84 succZU(zero(X1), one(X1)) :- binaryZH(X1). 18.95/5.84 succZU(one(X1), zero(X2)) :- succT(X1, X2). 18.95/5.84 addCV(zero(X1), zero(X2), one(X3)) :- addzQ(X1, X2, X3). 18.95/5.84 addCV(zero(zero(X1)), one(b), zero(one(X1))) :- binaryZH(X1). 18.95/5.84 addCV(zero(one(X1)), one(b), zero(zero(X2))) :- succT(X1, X2). 18.95/5.84 addCV(zero(X1), one(X2), zero(X3)) :- addCV(X1, X2, X3). 18.95/5.84 addCV(one(b), zero(zero(X1)), zero(one(X1))) :- binaryZH(X1). 18.95/5.84 addCV(one(b), zero(one(X1)), zero(zero(X2))) :- succT(X1, X2). 18.95/5.84 addCV(one(X1), zero(X2), zero(X3)) :- addCV(X1, X2, X3). 18.95/5.84 addCV(one(X1), one(X2), one(X3)) :- addcS(X1, X2, X3). 18.95/5.84 addcS(X1, b, X2) :- succZU(X1, X2). 18.95/5.84 addcS(b, X1, X2) :- succZU(X1, X2). 18.95/5.84 addcS(X1, X2, X3) :- addCV(X1, X2, X3). 18.95/5.84 addyR(b, one(X1), one(X1)) :- binaryI(X1). 18.95/5.84 addyR(b, zero(X1), zero(X1)) :- binaryZH(X1). 18.95/5.84 addyR(X1, X2, X3) :- addzQ(X1, X2, X3). 18.95/5.84 pB(X1, X2, X3, X4) :- timesF(X1, X2, X3). 18.95/5.84 pB(X1, X2, X3, X4) :- ','(timescF(X1, X2, X3), addC1(X2, X3, X4)). 18.95/5.84 addC1(b, X1, zero(X1)) :- binaryZP(X1). 18.95/5.84 addC1(zero(X1), X2, zero(X3)) :- addzQ(X1, X2, X3). 18.95/5.84 addC1(one(X1), X2, one(X3)) :- addyR(X1, X2, X3). 18.95/5.84 addG(b, X1, zero(X1)) :- binaryZP(X1). 18.95/5.84 addG(zero(X1), X2, zero(X3)) :- addzJ(X1, X2, X3). 18.95/5.84 addG(one(X1), X2, one(X3)) :- addyK(X1, X2, X3). 18.95/5.84 pD(X1, X2, X3, X4) :- timesF(X1, X2, X3). 18.95/5.84 pD(X1, X2, X3, X4) :- ','(timescF(X1, X2, X3), addC1(X2, zero(X3), X4)). 18.95/5.84 pE(X1, X2, X3, X4, X5) :- timesF(X1, X2, X3). 18.95/5.84 pE(X1, X2, X3, X4, X5) :- ','(timescF(X1, X2, X3), addG(X2, X3, X4)). 18.95/5.84 pE(X1, X2, X3, X4, X5) :- ','(timescF(X1, X2, X3), ','(addcG(X2, X3, X4), addC1(X2, X4, X5))). 18.95/5.84 timesA(zero(zero(X1)), X2, zero(zero(X3))) :- timesA(X1, X2, X3). 18.95/5.84 timesA(zero(one(X1)), X2, zero(X3)) :- pB(X1, X2, X4, X3). 18.95/5.84 timesA(one(X1), X2, zero(X3)) :- pB(X1, X2, X4, zero(X3)). 18.95/5.84 timesA(one(one(b)), X1, X2) :- addC1(X1, X1, X2). 18.95/5.84 timesA(one(zero(X1)), X2, X3) :- pD(X1, X2, X4, X3). 18.95/5.84 timesA(one(one(X1)), X2, X3) :- pE(X1, X2, X4, X5, X3). 18.95/5.84 timesA(zero(zero(X1)), X2, zero(zero(X3))) :- timesA(X1, X2, X3). 18.95/5.84 timesA(zero(one(X1)), X2, zero(X3)) :- pB(X1, X2, X4, X3). 18.95/5.84 timesA(one(X1), X2, zero(X3)) :- pB(X1, X2, X4, zero(X3)). 18.95/5.84 timesA(one(one(b)), X1, X2) :- addC1(X1, X1, X2). 18.95/5.84 timesA(one(zero(X1)), X2, X3) :- pD(X1, X2, X4, X3). 18.95/5.84 timesA(one(one(X1)), X2, X3) :- pE(X1, X2, X4, X5, X3). 18.95/5.84 18.95/5.84 Clauses: 18.95/5.84 18.95/5.84 timescA(one(b), X1, X1). 18.95/5.84 timescA(zero(one(b)), X1, zero(X1)). 18.95/5.84 timescA(zero(zero(X1)), X2, zero(zero(X3))) :- timescA(X1, X2, X3). 18.95/5.84 timescA(zero(one(X1)), X2, zero(X3)) :- qcB(X1, X2, X4, X3). 18.95/5.84 timescA(one(X1), X2, zero(X3)) :- qcB(X1, X2, X4, zero(X3)). 18.95/5.84 timescA(one(one(b)), X1, X2) :- addcC(X1, X1, X2). 18.95/5.84 timescA(one(zero(X1)), X2, X3) :- qcD(X1, X2, X4, X3). 18.95/5.84 timescA(one(one(X1)), X2, X3) :- qcE(X1, X2, X4, X5, X3). 18.95/5.84 timescA(zero(one(b)), X1, zero(X1)). 18.95/5.84 timescA(zero(zero(X1)), X2, zero(zero(X3))) :- timescA(X1, X2, X3). 18.95/5.84 timescA(zero(one(X1)), X2, zero(X3)) :- qcB(X1, X2, X4, X3). 18.95/5.84 timescA(one(X1), X2, zero(X3)) :- qcB(X1, X2, X4, zero(X3)). 18.95/5.84 timescA(one(one(b)), X1, X2) :- addcC(X1, X1, X2). 18.95/5.84 timescA(one(zero(X1)), X2, X3) :- qcD(X1, X2, X4, X3). 18.95/5.84 timescA(one(one(X1)), X2, X3) :- qcE(X1, X2, X4, X5, X3). 18.95/5.84 timescF(one(b), X1, X1). 18.95/5.84 timescF(zero(X1), X2, zero(X3)) :- timescF(X1, X2, X3). 18.95/5.84 timescF(one(X1), X2, X3) :- ','(timescF(X1, X2, X4), addcG(X2, X4, X3)). 18.95/5.84 binaryZcH(zero(X1)) :- binaryZcH(X1). 18.95/5.84 binaryZcH(one(X1)) :- binarycI(X1). 18.95/5.84 binarycI(b). 18.95/5.84 binarycI(zero(X1)) :- binaryZcH(X1). 18.95/5.84 binarycI(one(X1)) :- binarycI(X1). 18.95/5.84 addzcJ(zero(X1), zero(X2), zero(X3)) :- addzcJ(X1, X2, X3). 18.95/5.84 addzcJ(zero(one(X1)), one(b), one(one(X1))) :- binarycI(X1). 18.95/5.84 addzcJ(zero(zero(X1)), one(b), one(zero(X1))) :- binaryZcH(X1). 18.95/5.84 addzcJ(zero(X1), one(X2), one(X3)) :- addzcJ(X1, X2, X3). 18.95/5.84 addzcJ(one(X1), zero(X2), one(X3)) :- addycK(X1, X2, X3). 18.95/5.84 addzcJ(one(X1), one(X2), zero(X3)) :- addccL(X1, X2, X3). 18.95/5.84 succcM(b, one(b)). 18.95/5.84 succcM(zero(X1), one(X1)) :- binaryZcH(X1). 18.95/5.84 succcM(one(X1), zero(X2)) :- succcM(X1, X2). 18.95/5.84 succZcN(zero(X1), one(X1)) :- binaryZcH(X1). 18.95/5.84 succZcN(one(X1), zero(X2)) :- succcM(X1, X2). 18.95/5.84 addCcO(zero(X1), zero(X2), one(X3)) :- addzcJ(X1, X2, X3). 18.95/5.84 addCcO(zero(zero(X1)), one(b), zero(one(X1))) :- binaryZcH(X1). 18.95/5.84 addCcO(zero(one(X1)), one(b), zero(zero(X2))) :- succcM(X1, X2). 18.95/5.84 addCcO(zero(X1), one(X2), zero(X3)) :- addCcO(X1, X2, X3). 18.95/5.84 addCcO(one(b), zero(zero(X1)), zero(one(X1))) :- binaryZcH(X1). 18.95/5.84 addCcO(one(b), zero(one(X1)), zero(zero(X2))) :- succcM(X1, X2). 18.95/5.84 addCcO(one(X1), zero(X2), zero(X3)) :- addCcO(X1, X2, X3). 18.95/5.84 addCcO(one(X1), one(X2), one(X3)) :- addccL(X1, X2, X3). 18.95/5.84 addccL(b, b, one(b)). 18.95/5.84 addccL(X1, b, X2) :- succZcN(X1, X2). 18.95/5.84 addccL(b, X1, X2) :- succZcN(X1, X2). 18.95/5.84 addccL(X1, X2, X3) :- addCcO(X1, X2, X3). 18.95/5.84 addycK(b, one(X1), one(X1)) :- binarycI(X1). 18.95/5.84 addycK(b, zero(X1), zero(X1)) :- binaryZcH(X1). 18.95/5.84 addycK(X1, X2, X3) :- addzcJ(X1, X2, X3). 18.95/5.84 binaryZcP(X1) :- binaryZcH(X1). 18.95/5.84 addzcQ(zero(X1), zero(X2), zero(X3)) :- addzcQ(X1, X2, X3). 18.95/5.84 addzcQ(zero(one(X1)), one(b), one(one(X1))) :- binarycI(X1). 18.95/5.84 addzcQ(zero(zero(X1)), one(b), one(zero(X1))) :- binaryZcH(X1). 18.95/5.84 addzcQ(zero(X1), one(X2), one(X3)) :- addzcQ(X1, X2, X3). 18.95/5.84 addzcQ(one(X1), zero(X2), one(X3)) :- addycR(X1, X2, X3). 18.95/5.84 addzcQ(one(X1), one(X2), zero(X3)) :- addccS(X1, X2, X3). 18.95/5.84 succcT(b, one(b)). 18.95/5.84 succcT(zero(X1), one(X1)) :- binaryZcH(X1). 18.95/5.84 succcT(one(X1), zero(X2)) :- succcT(X1, X2). 18.95/5.84 succZcU(zero(X1), one(X1)) :- binaryZcH(X1). 18.95/5.84 succZcU(one(X1), zero(X2)) :- succcT(X1, X2). 18.95/5.84 addCcV(zero(X1), zero(X2), one(X3)) :- addzcQ(X1, X2, X3). 18.95/5.84 addCcV(zero(zero(X1)), one(b), zero(one(X1))) :- binaryZcH(X1). 18.95/5.84 addCcV(zero(one(X1)), one(b), zero(zero(X2))) :- succcT(X1, X2). 18.95/5.84 addCcV(zero(X1), one(X2), zero(X3)) :- addCcV(X1, X2, X3). 18.95/5.84 addCcV(one(b), zero(zero(X1)), zero(one(X1))) :- binaryZcH(X1). 18.95/5.84 addCcV(one(b), zero(one(X1)), zero(zero(X2))) :- succcT(X1, X2). 18.95/5.84 addCcV(one(X1), zero(X2), zero(X3)) :- addCcV(X1, X2, X3). 18.95/5.84 addCcV(one(X1), one(X2), one(X3)) :- addccS(X1, X2, X3). 18.95/5.84 addccS(b, b, one(b)). 18.95/5.84 addccS(X1, b, X2) :- succZcU(X1, X2). 18.95/5.84 addccS(b, X1, X2) :- succZcU(X1, X2). 18.95/5.84 addccS(X1, X2, X3) :- addCcV(X1, X2, X3). 18.95/5.84 addycR(b, one(X1), one(X1)) :- binarycI(X1). 18.95/5.84 addycR(b, zero(X1), zero(X1)) :- binaryZcH(X1). 18.95/5.84 addycR(X1, X2, X3) :- addzcQ(X1, X2, X3). 18.95/5.84 qcB(X1, X2, X3, X4) :- ','(timescF(X1, X2, X3), addcC(X2, X3, X4)). 18.95/5.84 addcC(b, X1, zero(X1)) :- binaryZcP(X1). 18.95/5.84 addcC(zero(X1), X2, zero(X3)) :- addzcQ(X1, X2, X3). 18.95/5.84 addcC(one(X1), X2, one(X3)) :- addycR(X1, X2, X3). 18.95/5.84 addcG(b, X1, zero(X1)) :- binaryZcP(X1). 18.95/5.84 addcG(zero(X1), X2, zero(X3)) :- addzcJ(X1, X2, X3). 18.95/5.84 addcG(one(X1), X2, one(X3)) :- addycK(X1, X2, X3). 18.95/5.84 qcD(X1, X2, X3, X4) :- ','(timescF(X1, X2, X3), addcC(X2, zero(X3), X4)). 18.95/5.84 qcE(X1, X2, X3, X4, X5) :- ','(timescF(X1, X2, X3), ','(addcG(X2, X3, X4), addcC(X2, X4, X5))). 18.95/5.84 18.95/5.84 Afs: 18.95/5.84 18.95/5.84 timesA(x1, x2, x3) = timesA(x3) 18.95/5.84 18.95/5.84 18.95/5.84 ---------------------------------------- 18.95/5.84 18.95/5.84 (137) TriplesToPiDPProof (SOUND) 18.95/5.84 We use the technique of [DT09]. With regard to the inferred argument filtering the predicates were used in the following modes: 18.95/5.84 18.95/5.84 timesA_in_3: (f,f,b) 18.95/5.84 18.95/5.84 pB_in_4: (f,f,f,b) 18.95/5.84 18.95/5.84 timesF_in_3: (f,f,f) 18.95/5.84 18.95/5.84 timescF_in_3: (f,f,f) 18.95/5.84 18.95/5.84 addcG_in_3: (f,f,f) 18.95/5.84 18.95/5.84 binaryZcP_in_1: (f) 18.95/5.84 18.95/5.84 binaryZcH_in_1: (f) 18.95/5.84 18.95/5.84 binarycI_in_1: (f) 18.95/5.84 18.95/5.84 addzcJ_in_3: (f,f,f) 18.95/5.84 18.95/5.84 addycK_in_3: (f,f,f) 18.95/5.84 18.95/5.84 addccL_in_3: (f,f,f) 18.95/5.84 18.95/5.84 succZcN_in_2: (f,f) 18.95/5.84 18.95/5.84 succcM_in_2: (f,f) 18.95/5.84 18.95/5.84 addCcO_in_3: (f,f,f) 18.95/5.84 18.95/5.84 addG_in_3: (f,f,f) 18.95/5.84 18.95/5.84 binaryZP_in_1: (f) (b) 18.95/5.84 18.95/5.84 binaryZH_in_1: (f) (b) 18.95/5.84 18.95/5.84 binaryI_in_1: (f) (b) 18.95/5.84 18.95/5.84 addzJ_in_3: (f,f,f) 18.95/5.84 18.95/5.84 addyK_in_3: (f,f,f) 18.95/5.84 18.95/5.84 addcL_in_3: (f,f,f) 18.95/5.84 18.95/5.84 succZN_in_2: (f,f) 18.95/5.84 18.95/5.84 succM_in_2: (f,f) 18.95/5.84 18.95/5.84 addCO_in_3: (f,f,f) 18.95/5.84 18.95/5.84 addC1_in_3: (f,f,b) (b,b,b) 18.95/5.84 18.95/5.84 addzQ_in_3: (f,f,b) (b,b,b) 18.95/5.84 18.95/5.84 addyR_in_3: (f,f,b) (b,b,b) 18.95/5.84 18.95/5.84 addcS_in_3: (f,f,b) (b,b,b) 18.95/5.84 18.95/5.84 succZU_in_2: (f,b) (b,b) 18.95/5.84 18.95/5.84 succT_in_2: (f,b) (b,b) 18.95/5.84 18.95/5.84 addCV_in_3: (f,f,b) (b,b,b) 18.95/5.84 18.95/5.84 pD_in_4: (f,f,f,b) 18.95/5.84 18.95/5.84 pE_in_5: (f,f,f,f,b) 18.95/5.84 18.95/5.84 Transforming TRIPLES into the following Term Rewriting System: 18.95/5.84 18.95/5.84 Pi DP problem: 18.95/5.84 The TRS P consists of the following rules: 18.95/5.84 18.95/5.84 TIMESA_IN_AAG(zero(zero(X1)), X2, zero(zero(X3))) -> U75_AAG(X1, X2, X3, timesA_in_aag(X1, X2, X3)) 18.95/5.84 TIMESA_IN_AAG(zero(zero(X1)), X2, zero(zero(X3))) -> TIMESA_IN_AAG(X1, X2, X3) 18.95/5.84 TIMESA_IN_AAG(zero(one(X1)), X2, zero(X3)) -> U76_AAG(X1, X2, X3, pB_in_aaag(X1, X2, X4, X3)) 18.95/5.84 TIMESA_IN_AAG(zero(one(X1)), X2, zero(X3)) -> PB_IN_AAAG(X1, X2, X4, X3) 18.95/5.84 PB_IN_AAAG(X1, X2, X3, X4) -> U58_AAAG(X1, X2, X3, X4, timesF_in_aaa(X1, X2, X3)) 18.95/5.84 PB_IN_AAAG(X1, X2, X3, X4) -> TIMESF_IN_AAA(X1, X2, X3) 18.95/5.84 TIMESF_IN_AAA(zero(X1), X2, zero(X3)) -> U1_AAA(X1, X2, X3, timesF_in_aaa(X1, X2, X3)) 18.95/5.84 TIMESF_IN_AAA(zero(X1), X2, zero(X3)) -> TIMESF_IN_AAA(X1, X2, X3) 18.95/5.84 TIMESF_IN_AAA(one(X1), X2, X3) -> U2_AAA(X1, X2, X3, timesF_in_aaa(X1, X2, X4)) 18.95/5.84 TIMESF_IN_AAA(one(X1), X2, X3) -> TIMESF_IN_AAA(X1, X2, X4) 18.95/5.84 TIMESF_IN_AAA(one(X1), X2, X3) -> U3_AAA(X1, X2, X3, timescF_in_aaa(X1, X2, X4)) 18.95/5.84 U3_AAA(X1, X2, X3, timescF_out_aaa(X1, X2, X4)) -> U4_AAA(X1, X2, X3, addG_in_aaa(X2, X4, X3)) 18.95/5.84 U3_AAA(X1, X2, X3, timescF_out_aaa(X1, X2, X4)) -> ADDG_IN_AAA(X2, X4, X3) 18.95/5.84 ADDG_IN_AAA(b, X1, zero(X1)) -> U64_AAA(X1, binaryZP_in_a(X1)) 18.95/5.84 ADDG_IN_AAA(b, X1, zero(X1)) -> BINARYZP_IN_A(X1) 18.95/5.84 BINARYZP_IN_A(X1) -> U33_A(X1, binaryZH_in_a(X1)) 18.95/5.84 BINARYZP_IN_A(X1) -> BINARYZH_IN_A(X1) 18.95/5.84 BINARYZH_IN_A(zero(X1)) -> U5_A(X1, binaryZH_in_a(X1)) 18.95/5.84 BINARYZH_IN_A(zero(X1)) -> BINARYZH_IN_A(X1) 18.95/5.84 BINARYZH_IN_A(one(X1)) -> U6_A(X1, binaryI_in_a(X1)) 18.95/5.84 BINARYZH_IN_A(one(X1)) -> BINARYI_IN_A(X1) 18.95/5.84 BINARYI_IN_A(zero(X1)) -> U7_A(X1, binaryZH_in_a(X1)) 18.95/5.84 BINARYI_IN_A(zero(X1)) -> BINARYZH_IN_A(X1) 18.95/5.84 BINARYI_IN_A(one(X1)) -> U8_A(X1, binaryI_in_a(X1)) 18.95/5.84 BINARYI_IN_A(one(X1)) -> BINARYI_IN_A(X1) 18.95/5.84 ADDG_IN_AAA(zero(X1), X2, zero(X3)) -> U65_AAA(X1, X2, X3, addzJ_in_aaa(X1, X2, X3)) 18.95/5.84 ADDG_IN_AAA(zero(X1), X2, zero(X3)) -> ADDZJ_IN_AAA(X1, X2, X3) 18.95/5.84 ADDZJ_IN_AAA(zero(X1), zero(X2), zero(X3)) -> U9_AAA(X1, X2, X3, addzJ_in_aaa(X1, X2, X3)) 18.95/5.84 ADDZJ_IN_AAA(zero(X1), zero(X2), zero(X3)) -> ADDZJ_IN_AAA(X1, X2, X3) 18.95/5.84 ADDZJ_IN_AAA(zero(one(X1)), one(b), one(one(X1))) -> U10_AAA(X1, binaryI_in_a(X1)) 18.95/5.84 ADDZJ_IN_AAA(zero(one(X1)), one(b), one(one(X1))) -> BINARYI_IN_A(X1) 18.95/5.84 ADDZJ_IN_AAA(zero(zero(X1)), one(b), one(zero(X1))) -> U11_AAA(X1, binaryZH_in_a(X1)) 18.95/5.84 ADDZJ_IN_AAA(zero(zero(X1)), one(b), one(zero(X1))) -> BINARYZH_IN_A(X1) 18.95/5.84 ADDZJ_IN_AAA(zero(X1), one(X2), one(X3)) -> U12_AAA(X1, X2, X3, addzJ_in_aaa(X1, X2, X3)) 18.95/5.84 ADDZJ_IN_AAA(zero(X1), one(X2), one(X3)) -> ADDZJ_IN_AAA(X1, X2, X3) 18.95/5.84 ADDZJ_IN_AAA(one(X1), zero(X2), one(X3)) -> U13_AAA(X1, X2, X3, addyK_in_aaa(X1, X2, X3)) 18.95/5.84 ADDZJ_IN_AAA(one(X1), zero(X2), one(X3)) -> ADDYK_IN_AAA(X1, X2, X3) 18.95/5.84 ADDYK_IN_AAA(b, one(X1), one(X1)) -> U30_AAA(X1, binaryI_in_a(X1)) 18.95/5.84 ADDYK_IN_AAA(b, one(X1), one(X1)) -> BINARYI_IN_A(X1) 18.95/5.84 ADDYK_IN_AAA(b, zero(X1), zero(X1)) -> U31_AAA(X1, binaryZH_in_a(X1)) 18.95/5.84 ADDYK_IN_AAA(b, zero(X1), zero(X1)) -> BINARYZH_IN_A(X1) 18.95/5.84 ADDYK_IN_AAA(X1, X2, X3) -> U32_AAA(X1, X2, X3, addzJ_in_aaa(X1, X2, X3)) 18.95/5.84 ADDYK_IN_AAA(X1, X2, X3) -> ADDZJ_IN_AAA(X1, X2, X3) 18.95/5.84 ADDZJ_IN_AAA(one(X1), one(X2), zero(X3)) -> U14_AAA(X1, X2, X3, addcL_in_aaa(X1, X2, X3)) 18.95/5.84 ADDZJ_IN_AAA(one(X1), one(X2), zero(X3)) -> ADDCL_IN_AAA(X1, X2, X3) 18.95/5.84 ADDCL_IN_AAA(X1, b, X2) -> U27_AAA(X1, X2, succZN_in_aa(X1, X2)) 18.95/5.84 ADDCL_IN_AAA(X1, b, X2) -> SUCCZN_IN_AA(X1, X2) 18.95/5.84 SUCCZN_IN_AA(zero(X1), one(X1)) -> U17_AA(X1, binaryZH_in_a(X1)) 18.95/5.84 SUCCZN_IN_AA(zero(X1), one(X1)) -> BINARYZH_IN_A(X1) 18.95/5.84 SUCCZN_IN_AA(one(X1), zero(X2)) -> U18_AA(X1, X2, succM_in_aa(X1, X2)) 18.95/5.84 SUCCZN_IN_AA(one(X1), zero(X2)) -> SUCCM_IN_AA(X1, X2) 18.95/5.84 SUCCM_IN_AA(zero(X1), one(X1)) -> U15_AA(X1, binaryZH_in_a(X1)) 18.95/5.84 SUCCM_IN_AA(zero(X1), one(X1)) -> BINARYZH_IN_A(X1) 18.95/5.84 SUCCM_IN_AA(one(X1), zero(X2)) -> U16_AA(X1, X2, succM_in_aa(X1, X2)) 18.95/5.84 SUCCM_IN_AA(one(X1), zero(X2)) -> SUCCM_IN_AA(X1, X2) 18.95/5.84 ADDCL_IN_AAA(b, X1, X2) -> U28_AAA(X1, X2, succZN_in_aa(X1, X2)) 18.95/5.84 ADDCL_IN_AAA(b, X1, X2) -> SUCCZN_IN_AA(X1, X2) 18.95/5.84 ADDCL_IN_AAA(X1, X2, X3) -> U29_AAA(X1, X2, X3, addCO_in_aaa(X1, X2, X3)) 18.95/5.84 ADDCL_IN_AAA(X1, X2, X3) -> ADDCO_IN_AAA(X1, X2, X3) 18.95/5.84 ADDCO_IN_AAA(zero(X1), zero(X2), one(X3)) -> U19_AAA(X1, X2, X3, addzJ_in_aaa(X1, X2, X3)) 18.95/5.84 ADDCO_IN_AAA(zero(X1), zero(X2), one(X3)) -> ADDZJ_IN_AAA(X1, X2, X3) 18.95/5.84 ADDCO_IN_AAA(zero(zero(X1)), one(b), zero(one(X1))) -> U20_AAA(X1, binaryZH_in_a(X1)) 18.95/5.84 ADDCO_IN_AAA(zero(zero(X1)), one(b), zero(one(X1))) -> BINARYZH_IN_A(X1) 18.95/5.84 ADDCO_IN_AAA(zero(one(X1)), one(b), zero(zero(X2))) -> U21_AAA(X1, X2, succM_in_aa(X1, X2)) 18.95/5.84 ADDCO_IN_AAA(zero(one(X1)), one(b), zero(zero(X2))) -> SUCCM_IN_AA(X1, X2) 18.95/5.84 ADDCO_IN_AAA(zero(X1), one(X2), zero(X3)) -> U22_AAA(X1, X2, X3, addCO_in_aaa(X1, X2, X3)) 18.95/5.84 ADDCO_IN_AAA(zero(X1), one(X2), zero(X3)) -> ADDCO_IN_AAA(X1, X2, X3) 18.95/5.84 ADDCO_IN_AAA(one(b), zero(zero(X1)), zero(one(X1))) -> U23_AAA(X1, binaryZH_in_a(X1)) 18.95/5.84 ADDCO_IN_AAA(one(b), zero(zero(X1)), zero(one(X1))) -> BINARYZH_IN_A(X1) 18.95/5.84 ADDCO_IN_AAA(one(b), zero(one(X1)), zero(zero(X2))) -> U24_AAA(X1, X2, succM_in_aa(X1, X2)) 18.95/5.84 ADDCO_IN_AAA(one(b), zero(one(X1)), zero(zero(X2))) -> SUCCM_IN_AA(X1, X2) 18.95/5.84 ADDCO_IN_AAA(one(X1), zero(X2), zero(X3)) -> U25_AAA(X1, X2, X3, addCO_in_aaa(X1, X2, X3)) 18.95/5.84 ADDCO_IN_AAA(one(X1), zero(X2), zero(X3)) -> ADDCO_IN_AAA(X1, X2, X3) 18.95/5.84 ADDCO_IN_AAA(one(X1), one(X2), one(X3)) -> U26_AAA(X1, X2, X3, addcL_in_aaa(X1, X2, X3)) 18.95/5.84 ADDCO_IN_AAA(one(X1), one(X2), one(X3)) -> ADDCL_IN_AAA(X1, X2, X3) 18.95/5.84 ADDG_IN_AAA(one(X1), X2, one(X3)) -> U66_AAA(X1, X2, X3, addyK_in_aaa(X1, X2, X3)) 18.95/5.84 ADDG_IN_AAA(one(X1), X2, one(X3)) -> ADDYK_IN_AAA(X1, X2, X3) 18.95/5.84 PB_IN_AAAG(X1, X2, X3, X4) -> U59_AAAG(X1, X2, X3, X4, timescF_in_aaa(X1, X2, X3)) 18.95/5.84 U59_AAAG(X1, X2, X3, X4, timescF_out_aaa(X1, X2, X3)) -> U60_AAAG(X1, X2, X3, X4, addC1_in_aag(X2, X3, X4)) 18.95/5.84 U59_AAAG(X1, X2, X3, X4, timescF_out_aaa(X1, X2, X3)) -> ADDC1_IN_AAG(X2, X3, X4) 18.95/5.84 ADDC1_IN_AAG(b, X1, zero(X1)) -> U61_AAG(X1, binaryZP_in_g(X1)) 18.95/5.84 ADDC1_IN_AAG(b, X1, zero(X1)) -> BINARYZP_IN_G(X1) 18.95/5.84 BINARYZP_IN_G(X1) -> U33_G(X1, binaryZH_in_g(X1)) 18.95/5.84 BINARYZP_IN_G(X1) -> BINARYZH_IN_G(X1) 18.95/5.84 BINARYZH_IN_G(zero(X1)) -> U5_G(X1, binaryZH_in_g(X1)) 18.95/5.84 BINARYZH_IN_G(zero(X1)) -> BINARYZH_IN_G(X1) 18.95/5.84 BINARYZH_IN_G(one(X1)) -> U6_G(X1, binaryI_in_g(X1)) 18.95/5.84 BINARYZH_IN_G(one(X1)) -> BINARYI_IN_G(X1) 18.95/5.84 BINARYI_IN_G(zero(X1)) -> U7_G(X1, binaryZH_in_g(X1)) 18.95/5.84 BINARYI_IN_G(zero(X1)) -> BINARYZH_IN_G(X1) 18.95/5.84 BINARYI_IN_G(one(X1)) -> U8_G(X1, binaryI_in_g(X1)) 18.95/5.84 BINARYI_IN_G(one(X1)) -> BINARYI_IN_G(X1) 18.95/5.84 ADDC1_IN_AAG(zero(X1), X2, zero(X3)) -> U62_AAG(X1, X2, X3, addzQ_in_aag(X1, X2, X3)) 18.95/5.84 ADDC1_IN_AAG(zero(X1), X2, zero(X3)) -> ADDZQ_IN_AAG(X1, X2, X3) 18.95/5.84 ADDZQ_IN_AAG(zero(X1), zero(X2), zero(X3)) -> U34_AAG(X1, X2, X3, addzQ_in_aag(X1, X2, X3)) 18.95/5.84 ADDZQ_IN_AAG(zero(X1), zero(X2), zero(X3)) -> ADDZQ_IN_AAG(X1, X2, X3) 18.95/5.84 ADDZQ_IN_AAG(zero(one(X1)), one(b), one(one(X1))) -> U35_AAG(X1, binaryI_in_g(X1)) 18.95/5.84 ADDZQ_IN_AAG(zero(one(X1)), one(b), one(one(X1))) -> BINARYI_IN_G(X1) 18.95/5.84 ADDZQ_IN_AAG(zero(zero(X1)), one(b), one(zero(X1))) -> U36_AAG(X1, binaryZH_in_g(X1)) 18.95/5.84 ADDZQ_IN_AAG(zero(zero(X1)), one(b), one(zero(X1))) -> BINARYZH_IN_G(X1) 18.95/5.84 ADDZQ_IN_AAG(zero(X1), one(X2), one(X3)) -> U37_AAG(X1, X2, X3, addzQ_in_aag(X1, X2, X3)) 18.95/5.84 ADDZQ_IN_AAG(zero(X1), one(X2), one(X3)) -> ADDZQ_IN_AAG(X1, X2, X3) 18.95/5.84 ADDZQ_IN_AAG(one(X1), zero(X2), one(X3)) -> U38_AAG(X1, X2, X3, addyR_in_aag(X1, X2, X3)) 18.95/5.84 ADDZQ_IN_AAG(one(X1), zero(X2), one(X3)) -> ADDYR_IN_AAG(X1, X2, X3) 18.95/5.84 ADDYR_IN_AAG(b, one(X1), one(X1)) -> U55_AAG(X1, binaryI_in_g(X1)) 18.95/5.84 ADDYR_IN_AAG(b, one(X1), one(X1)) -> BINARYI_IN_G(X1) 18.95/5.84 ADDYR_IN_AAG(b, zero(X1), zero(X1)) -> U56_AAG(X1, binaryZH_in_g(X1)) 18.95/5.84 ADDYR_IN_AAG(b, zero(X1), zero(X1)) -> BINARYZH_IN_G(X1) 18.95/5.84 ADDYR_IN_AAG(X1, X2, X3) -> U57_AAG(X1, X2, X3, addzQ_in_aag(X1, X2, X3)) 18.95/5.84 ADDYR_IN_AAG(X1, X2, X3) -> ADDZQ_IN_AAG(X1, X2, X3) 18.95/5.84 ADDZQ_IN_AAG(one(X1), one(X2), zero(X3)) -> U39_AAG(X1, X2, X3, addcS_in_aag(X1, X2, X3)) 18.95/5.84 ADDZQ_IN_AAG(one(X1), one(X2), zero(X3)) -> ADDCS_IN_AAG(X1, X2, X3) 18.95/5.84 ADDCS_IN_AAG(X1, b, X2) -> U52_AAG(X1, X2, succZU_in_ag(X1, X2)) 18.95/5.84 ADDCS_IN_AAG(X1, b, X2) -> SUCCZU_IN_AG(X1, X2) 18.95/5.84 SUCCZU_IN_AG(zero(X1), one(X1)) -> U42_AG(X1, binaryZH_in_g(X1)) 18.95/5.84 SUCCZU_IN_AG(zero(X1), one(X1)) -> BINARYZH_IN_G(X1) 18.95/5.84 SUCCZU_IN_AG(one(X1), zero(X2)) -> U43_AG(X1, X2, succT_in_ag(X1, X2)) 18.95/5.84 SUCCZU_IN_AG(one(X1), zero(X2)) -> SUCCT_IN_AG(X1, X2) 18.95/5.84 SUCCT_IN_AG(zero(X1), one(X1)) -> U40_AG(X1, binaryZH_in_g(X1)) 18.95/5.84 SUCCT_IN_AG(zero(X1), one(X1)) -> BINARYZH_IN_G(X1) 18.95/5.84 SUCCT_IN_AG(one(X1), zero(X2)) -> U41_AG(X1, X2, succT_in_ag(X1, X2)) 18.95/5.84 SUCCT_IN_AG(one(X1), zero(X2)) -> SUCCT_IN_AG(X1, X2) 18.95/5.84 ADDCS_IN_AAG(b, X1, X2) -> U53_AAG(X1, X2, succZU_in_ag(X1, X2)) 18.95/5.84 ADDCS_IN_AAG(b, X1, X2) -> SUCCZU_IN_AG(X1, X2) 18.95/5.84 ADDCS_IN_AAG(X1, X2, X3) -> U54_AAG(X1, X2, X3, addCV_in_aag(X1, X2, X3)) 18.95/5.84 ADDCS_IN_AAG(X1, X2, X3) -> ADDCV_IN_AAG(X1, X2, X3) 18.95/5.84 ADDCV_IN_AAG(zero(X1), zero(X2), one(X3)) -> U44_AAG(X1, X2, X3, addzQ_in_aag(X1, X2, X3)) 18.95/5.84 ADDCV_IN_AAG(zero(X1), zero(X2), one(X3)) -> ADDZQ_IN_AAG(X1, X2, X3) 18.95/5.84 ADDCV_IN_AAG(zero(zero(X1)), one(b), zero(one(X1))) -> U45_AAG(X1, binaryZH_in_g(X1)) 18.95/5.84 ADDCV_IN_AAG(zero(zero(X1)), one(b), zero(one(X1))) -> BINARYZH_IN_G(X1) 18.95/5.84 ADDCV_IN_AAG(zero(one(X1)), one(b), zero(zero(X2))) -> U46_AAG(X1, X2, succT_in_ag(X1, X2)) 18.95/5.84 ADDCV_IN_AAG(zero(one(X1)), one(b), zero(zero(X2))) -> SUCCT_IN_AG(X1, X2) 18.95/5.84 ADDCV_IN_AAG(zero(X1), one(X2), zero(X3)) -> U47_AAG(X1, X2, X3, addCV_in_aag(X1, X2, X3)) 18.95/5.84 ADDCV_IN_AAG(zero(X1), one(X2), zero(X3)) -> ADDCV_IN_AAG(X1, X2, X3) 18.95/5.84 ADDCV_IN_AAG(one(b), zero(zero(X1)), zero(one(X1))) -> U48_AAG(X1, binaryZH_in_g(X1)) 18.95/5.84 ADDCV_IN_AAG(one(b), zero(zero(X1)), zero(one(X1))) -> BINARYZH_IN_G(X1) 18.95/5.84 ADDCV_IN_AAG(one(b), zero(one(X1)), zero(zero(X2))) -> U49_AAG(X1, X2, succT_in_ag(X1, X2)) 18.95/5.84 ADDCV_IN_AAG(one(b), zero(one(X1)), zero(zero(X2))) -> SUCCT_IN_AG(X1, X2) 18.95/5.84 ADDCV_IN_AAG(one(X1), zero(X2), zero(X3)) -> U50_AAG(X1, X2, X3, addCV_in_aag(X1, X2, X3)) 18.95/5.84 ADDCV_IN_AAG(one(X1), zero(X2), zero(X3)) -> ADDCV_IN_AAG(X1, X2, X3) 18.95/5.84 ADDCV_IN_AAG(one(X1), one(X2), one(X3)) -> U51_AAG(X1, X2, X3, addcS_in_aag(X1, X2, X3)) 18.95/5.84 ADDCV_IN_AAG(one(X1), one(X2), one(X3)) -> ADDCS_IN_AAG(X1, X2, X3) 18.95/5.84 ADDC1_IN_AAG(one(X1), X2, one(X3)) -> U63_AAG(X1, X2, X3, addyR_in_aag(X1, X2, X3)) 18.95/5.84 ADDC1_IN_AAG(one(X1), X2, one(X3)) -> ADDYR_IN_AAG(X1, X2, X3) 18.95/5.84 TIMESA_IN_AAG(one(X1), X2, zero(X3)) -> U77_AAG(X1, X2, X3, pB_in_aaag(X1, X2, X4, zero(X3))) 18.95/5.84 TIMESA_IN_AAG(one(X1), X2, zero(X3)) -> PB_IN_AAAG(X1, X2, X4, zero(X3)) 18.95/5.84 TIMESA_IN_AAG(one(one(b)), X1, X2) -> U78_AAG(X1, X2, addC1_in_aag(X1, X1, X2)) 18.95/5.84 TIMESA_IN_AAG(one(one(b)), X1, X2) -> ADDC1_IN_AAG(X1, X1, X2) 18.95/5.84 TIMESA_IN_AAG(one(zero(X1)), X2, X3) -> U79_AAG(X1, X2, X3, pD_in_aaag(X1, X2, X4, X3)) 18.95/5.84 TIMESA_IN_AAG(one(zero(X1)), X2, X3) -> PD_IN_AAAG(X1, X2, X4, X3) 18.95/5.84 PD_IN_AAAG(X1, X2, X3, X4) -> U67_AAAG(X1, X2, X3, X4, timesF_in_aaa(X1, X2, X3)) 18.95/5.84 PD_IN_AAAG(X1, X2, X3, X4) -> TIMESF_IN_AAA(X1, X2, X3) 18.95/5.84 PD_IN_AAAG(X1, X2, X3, X4) -> U68_AAAG(X1, X2, X3, X4, timescF_in_aaa(X1, X2, X3)) 18.95/5.84 U68_AAAG(X1, X2, X3, X4, timescF_out_aaa(X1, X2, X3)) -> U69_AAAG(X1, X2, X3, X4, addC1_in_aag(X2, zero(X3), X4)) 18.95/5.84 U68_AAAG(X1, X2, X3, X4, timescF_out_aaa(X1, X2, X3)) -> ADDC1_IN_AAG(X2, zero(X3), X4) 18.95/5.84 TIMESA_IN_AAG(one(one(X1)), X2, X3) -> U80_AAG(X1, X2, X3, pE_in_aaaag(X1, X2, X4, X5, X3)) 18.95/5.84 TIMESA_IN_AAG(one(one(X1)), X2, X3) -> PE_IN_AAAAG(X1, X2, X4, X5, X3) 18.95/5.84 PE_IN_AAAAG(X1, X2, X3, X4, X5) -> U70_AAAAG(X1, X2, X3, X4, X5, timesF_in_aaa(X1, X2, X3)) 18.95/5.84 PE_IN_AAAAG(X1, X2, X3, X4, X5) -> TIMESF_IN_AAA(X1, X2, X3) 18.95/5.84 PE_IN_AAAAG(X1, X2, X3, X4, X5) -> U71_AAAAG(X1, X2, X3, X4, X5, timescF_in_aaa(X1, X2, X3)) 18.95/5.84 U71_AAAAG(X1, X2, X3, X4, X5, timescF_out_aaa(X1, X2, X3)) -> U72_AAAAG(X1, X2, X3, X4, X5, addG_in_aaa(X2, X3, X4)) 18.95/5.84 U71_AAAAG(X1, X2, X3, X4, X5, timescF_out_aaa(X1, X2, X3)) -> ADDG_IN_AAA(X2, X3, X4) 18.95/5.84 U71_AAAAG(X1, X2, X3, X4, X5, timescF_out_aaa(X1, X2, X3)) -> U73_AAAAG(X1, X2, X3, X4, X5, addcG_in_aaa(X2, X3, X4)) 18.95/5.84 U73_AAAAG(X1, X2, X3, X4, X5, addcG_out_aaa(X2, X3, X4)) -> U74_AAAAG(X1, X2, X3, X4, X5, addC1_in_ggg(X2, X4, X5)) 18.95/5.84 U73_AAAAG(X1, X2, X3, X4, X5, addcG_out_aaa(X2, X3, X4)) -> ADDC1_IN_GGG(X2, X4, X5) 18.95/5.84 ADDC1_IN_GGG(b, X1, zero(X1)) -> U61_GGG(X1, binaryZP_in_g(X1)) 18.95/5.84 ADDC1_IN_GGG(b, X1, zero(X1)) -> BINARYZP_IN_G(X1) 18.95/5.84 ADDC1_IN_GGG(zero(X1), X2, zero(X3)) -> U62_GGG(X1, X2, X3, addzQ_in_ggg(X1, X2, X3)) 18.95/5.84 ADDC1_IN_GGG(zero(X1), X2, zero(X3)) -> ADDZQ_IN_GGG(X1, X2, X3) 18.95/5.84 ADDZQ_IN_GGG(zero(X1), zero(X2), zero(X3)) -> U34_GGG(X1, X2, X3, addzQ_in_ggg(X1, X2, X3)) 18.95/5.84 ADDZQ_IN_GGG(zero(X1), zero(X2), zero(X3)) -> ADDZQ_IN_GGG(X1, X2, X3) 18.95/5.84 ADDZQ_IN_GGG(zero(one(X1)), one(b), one(one(X1))) -> U35_GGG(X1, binaryI_in_g(X1)) 18.95/5.84 ADDZQ_IN_GGG(zero(one(X1)), one(b), one(one(X1))) -> BINARYI_IN_G(X1) 18.95/5.84 ADDZQ_IN_GGG(zero(zero(X1)), one(b), one(zero(X1))) -> U36_GGG(X1, binaryZH_in_g(X1)) 18.95/5.84 ADDZQ_IN_GGG(zero(zero(X1)), one(b), one(zero(X1))) -> BINARYZH_IN_G(X1) 18.95/5.84 ADDZQ_IN_GGG(zero(X1), one(X2), one(X3)) -> U37_GGG(X1, X2, X3, addzQ_in_ggg(X1, X2, X3)) 18.95/5.84 ADDZQ_IN_GGG(zero(X1), one(X2), one(X3)) -> ADDZQ_IN_GGG(X1, X2, X3) 18.95/5.84 ADDZQ_IN_GGG(one(X1), zero(X2), one(X3)) -> U38_GGG(X1, X2, X3, addyR_in_ggg(X1, X2, X3)) 18.95/5.84 ADDZQ_IN_GGG(one(X1), zero(X2), one(X3)) -> ADDYR_IN_GGG(X1, X2, X3) 18.95/5.84 ADDYR_IN_GGG(b, one(X1), one(X1)) -> U55_GGG(X1, binaryI_in_g(X1)) 18.95/5.84 ADDYR_IN_GGG(b, one(X1), one(X1)) -> BINARYI_IN_G(X1) 18.95/5.84 ADDYR_IN_GGG(b, zero(X1), zero(X1)) -> U56_GGG(X1, binaryZH_in_g(X1)) 18.95/5.84 ADDYR_IN_GGG(b, zero(X1), zero(X1)) -> BINARYZH_IN_G(X1) 18.95/5.84 ADDYR_IN_GGG(X1, X2, X3) -> U57_GGG(X1, X2, X3, addzQ_in_ggg(X1, X2, X3)) 18.95/5.84 ADDYR_IN_GGG(X1, X2, X3) -> ADDZQ_IN_GGG(X1, X2, X3) 18.95/5.84 ADDZQ_IN_GGG(one(X1), one(X2), zero(X3)) -> U39_GGG(X1, X2, X3, addcS_in_ggg(X1, X2, X3)) 18.95/5.84 ADDZQ_IN_GGG(one(X1), one(X2), zero(X3)) -> ADDCS_IN_GGG(X1, X2, X3) 18.95/5.84 ADDCS_IN_GGG(X1, b, X2) -> U52_GGG(X1, X2, succZU_in_gg(X1, X2)) 18.95/5.84 ADDCS_IN_GGG(X1, b, X2) -> SUCCZU_IN_GG(X1, X2) 18.95/5.84 SUCCZU_IN_GG(zero(X1), one(X1)) -> U42_GG(X1, binaryZH_in_g(X1)) 18.95/5.84 SUCCZU_IN_GG(zero(X1), one(X1)) -> BINARYZH_IN_G(X1) 18.95/5.84 SUCCZU_IN_GG(one(X1), zero(X2)) -> U43_GG(X1, X2, succT_in_gg(X1, X2)) 18.95/5.84 SUCCZU_IN_GG(one(X1), zero(X2)) -> SUCCT_IN_GG(X1, X2) 18.95/5.84 SUCCT_IN_GG(zero(X1), one(X1)) -> U40_GG(X1, binaryZH_in_g(X1)) 18.95/5.84 SUCCT_IN_GG(zero(X1), one(X1)) -> BINARYZH_IN_G(X1) 18.95/5.84 SUCCT_IN_GG(one(X1), zero(X2)) -> U41_GG(X1, X2, succT_in_gg(X1, X2)) 18.95/5.84 SUCCT_IN_GG(one(X1), zero(X2)) -> SUCCT_IN_GG(X1, X2) 18.95/5.84 ADDCS_IN_GGG(b, X1, X2) -> U53_GGG(X1, X2, succZU_in_gg(X1, X2)) 18.95/5.84 ADDCS_IN_GGG(b, X1, X2) -> SUCCZU_IN_GG(X1, X2) 18.95/5.84 ADDCS_IN_GGG(X1, X2, X3) -> U54_GGG(X1, X2, X3, addCV_in_ggg(X1, X2, X3)) 18.95/5.84 ADDCS_IN_GGG(X1, X2, X3) -> ADDCV_IN_GGG(X1, X2, X3) 18.95/5.84 ADDCV_IN_GGG(zero(X1), zero(X2), one(X3)) -> U44_GGG(X1, X2, X3, addzQ_in_ggg(X1, X2, X3)) 18.95/5.84 ADDCV_IN_GGG(zero(X1), zero(X2), one(X3)) -> ADDZQ_IN_GGG(X1, X2, X3) 18.95/5.84 ADDCV_IN_GGG(zero(zero(X1)), one(b), zero(one(X1))) -> U45_GGG(X1, binaryZH_in_g(X1)) 18.95/5.84 ADDCV_IN_GGG(zero(zero(X1)), one(b), zero(one(X1))) -> BINARYZH_IN_G(X1) 18.95/5.84 ADDCV_IN_GGG(zero(one(X1)), one(b), zero(zero(X2))) -> U46_GGG(X1, X2, succT_in_gg(X1, X2)) 18.95/5.84 ADDCV_IN_GGG(zero(one(X1)), one(b), zero(zero(X2))) -> SUCCT_IN_GG(X1, X2) 18.95/5.84 ADDCV_IN_GGG(zero(X1), one(X2), zero(X3)) -> U47_GGG(X1, X2, X3, addCV_in_ggg(X1, X2, X3)) 18.95/5.84 ADDCV_IN_GGG(zero(X1), one(X2), zero(X3)) -> ADDCV_IN_GGG(X1, X2, X3) 18.95/5.84 ADDCV_IN_GGG(one(b), zero(zero(X1)), zero(one(X1))) -> U48_GGG(X1, binaryZH_in_g(X1)) 18.95/5.84 ADDCV_IN_GGG(one(b), zero(zero(X1)), zero(one(X1))) -> BINARYZH_IN_G(X1) 18.95/5.84 ADDCV_IN_GGG(one(b), zero(one(X1)), zero(zero(X2))) -> U49_GGG(X1, X2, succT_in_gg(X1, X2)) 18.95/5.84 ADDCV_IN_GGG(one(b), zero(one(X1)), zero(zero(X2))) -> SUCCT_IN_GG(X1, X2) 18.95/5.84 ADDCV_IN_GGG(one(X1), zero(X2), zero(X3)) -> U50_GGG(X1, X2, X3, addCV_in_ggg(X1, X2, X3)) 18.95/5.84 ADDCV_IN_GGG(one(X1), zero(X2), zero(X3)) -> ADDCV_IN_GGG(X1, X2, X3) 18.95/5.84 ADDCV_IN_GGG(one(X1), one(X2), one(X3)) -> U51_GGG(X1, X2, X3, addcS_in_ggg(X1, X2, X3)) 18.95/5.84 ADDCV_IN_GGG(one(X1), one(X2), one(X3)) -> ADDCS_IN_GGG(X1, X2, X3) 18.95/5.84 ADDC1_IN_GGG(one(X1), X2, one(X3)) -> U63_GGG(X1, X2, X3, addyR_in_ggg(X1, X2, X3)) 18.95/5.84 ADDC1_IN_GGG(one(X1), X2, one(X3)) -> ADDYR_IN_GGG(X1, X2, X3) 18.95/5.84 18.95/5.84 The TRS R consists of the following rules: 18.95/5.84 18.95/5.84 timescF_in_aaa(one(b), X1, X1) -> timescF_out_aaa(one(b), X1, X1) 18.95/5.84 timescF_in_aaa(zero(X1), X2, zero(X3)) -> U88_aaa(X1, X2, X3, timescF_in_aaa(X1, X2, X3)) 18.95/5.84 timescF_in_aaa(one(X1), X2, X3) -> U89_aaa(X1, X2, X3, timescF_in_aaa(X1, X2, X4)) 18.95/5.84 U89_aaa(X1, X2, X3, timescF_out_aaa(X1, X2, X4)) -> U90_aaa(X1, X2, X3, addcG_in_aaa(X2, X4, X3)) 18.95/5.84 addcG_in_aaa(b, X1, zero(X1)) -> U149_aaa(X1, binaryZcP_in_a(X1)) 18.95/5.84 binaryZcP_in_a(X1) -> U119_a(X1, binaryZcH_in_a(X1)) 18.95/5.84 binaryZcH_in_a(zero(X1)) -> U91_a(X1, binaryZcH_in_a(X1)) 18.95/5.84 binaryZcH_in_a(one(X1)) -> U92_a(X1, binarycI_in_a(X1)) 18.95/5.84 binarycI_in_a(b) -> binarycI_out_a(b) 18.95/5.84 binarycI_in_a(zero(X1)) -> U93_a(X1, binaryZcH_in_a(X1)) 18.95/5.84 U93_a(X1, binaryZcH_out_a(X1)) -> binarycI_out_a(zero(X1)) 18.95/5.84 binarycI_in_a(one(X1)) -> U94_a(X1, binarycI_in_a(X1)) 18.95/5.84 U94_a(X1, binarycI_out_a(X1)) -> binarycI_out_a(one(X1)) 18.95/5.84 U92_a(X1, binarycI_out_a(X1)) -> binaryZcH_out_a(one(X1)) 18.95/5.84 U91_a(X1, binaryZcH_out_a(X1)) -> binaryZcH_out_a(zero(X1)) 18.95/5.84 U119_a(X1, binaryZcH_out_a(X1)) -> binaryZcP_out_a(X1) 18.95/5.84 U149_aaa(X1, binaryZcP_out_a(X1)) -> addcG_out_aaa(b, X1, zero(X1)) 18.95/5.84 addcG_in_aaa(zero(X1), X2, zero(X3)) -> U150_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.84 addzcJ_in_aaa(zero(X1), zero(X2), zero(X3)) -> U95_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.84 addzcJ_in_aaa(zero(one(X1)), one(b), one(one(X1))) -> U96_aaa(X1, binarycI_in_a(X1)) 18.95/5.84 U96_aaa(X1, binarycI_out_a(X1)) -> addzcJ_out_aaa(zero(one(X1)), one(b), one(one(X1))) 18.95/5.84 addzcJ_in_aaa(zero(zero(X1)), one(b), one(zero(X1))) -> U97_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.84 U97_aaa(X1, binaryZcH_out_a(X1)) -> addzcJ_out_aaa(zero(zero(X1)), one(b), one(zero(X1))) 18.95/5.84 addzcJ_in_aaa(zero(X1), one(X2), one(X3)) -> U98_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.84 addzcJ_in_aaa(one(X1), zero(X2), one(X3)) -> U99_aaa(X1, X2, X3, addycK_in_aaa(X1, X2, X3)) 18.95/5.84 addycK_in_aaa(b, one(X1), one(X1)) -> U116_aaa(X1, binarycI_in_a(X1)) 18.95/5.84 U116_aaa(X1, binarycI_out_a(X1)) -> addycK_out_aaa(b, one(X1), one(X1)) 18.95/5.84 addycK_in_aaa(b, zero(X1), zero(X1)) -> U117_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.84 U117_aaa(X1, binaryZcH_out_a(X1)) -> addycK_out_aaa(b, zero(X1), zero(X1)) 18.95/5.84 addycK_in_aaa(X1, X2, X3) -> U118_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.84 addzcJ_in_aaa(one(X1), one(X2), zero(X3)) -> U100_aaa(X1, X2, X3, addccL_in_aaa(X1, X2, X3)) 18.95/5.84 addccL_in_aaa(b, b, one(b)) -> addccL_out_aaa(b, b, one(b)) 18.95/5.84 addccL_in_aaa(X1, b, X2) -> U113_aaa(X1, X2, succZcN_in_aa(X1, X2)) 18.95/5.84 succZcN_in_aa(zero(X1), one(X1)) -> U103_aa(X1, binaryZcH_in_a(X1)) 18.95/5.84 U103_aa(X1, binaryZcH_out_a(X1)) -> succZcN_out_aa(zero(X1), one(X1)) 18.95/5.84 succZcN_in_aa(one(X1), zero(X2)) -> U104_aa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.84 succcM_in_aa(b, one(b)) -> succcM_out_aa(b, one(b)) 18.95/5.84 succcM_in_aa(zero(X1), one(X1)) -> U101_aa(X1, binaryZcH_in_a(X1)) 18.95/5.84 U101_aa(X1, binaryZcH_out_a(X1)) -> succcM_out_aa(zero(X1), one(X1)) 18.95/5.84 succcM_in_aa(one(X1), zero(X2)) -> U102_aa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.84 U102_aa(X1, X2, succcM_out_aa(X1, X2)) -> succcM_out_aa(one(X1), zero(X2)) 18.95/5.84 U104_aa(X1, X2, succcM_out_aa(X1, X2)) -> succZcN_out_aa(one(X1), zero(X2)) 18.95/5.84 U113_aaa(X1, X2, succZcN_out_aa(X1, X2)) -> addccL_out_aaa(X1, b, X2) 18.95/5.84 addccL_in_aaa(b, X1, X2) -> U114_aaa(X1, X2, succZcN_in_aa(X1, X2)) 18.95/5.84 U114_aaa(X1, X2, succZcN_out_aa(X1, X2)) -> addccL_out_aaa(b, X1, X2) 18.95/5.84 addccL_in_aaa(X1, X2, X3) -> U115_aaa(X1, X2, X3, addCcO_in_aaa(X1, X2, X3)) 18.95/5.84 addCcO_in_aaa(zero(X1), zero(X2), one(X3)) -> U105_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.84 U105_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(zero(X1), zero(X2), one(X3)) 18.95/5.84 addCcO_in_aaa(zero(zero(X1)), one(b), zero(one(X1))) -> U106_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.84 U106_aaa(X1, binaryZcH_out_a(X1)) -> addCcO_out_aaa(zero(zero(X1)), one(b), zero(one(X1))) 18.95/5.84 addCcO_in_aaa(zero(one(X1)), one(b), zero(zero(X2))) -> U107_aaa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.84 U107_aaa(X1, X2, succcM_out_aa(X1, X2)) -> addCcO_out_aaa(zero(one(X1)), one(b), zero(zero(X2))) 18.95/5.84 addCcO_in_aaa(zero(X1), one(X2), zero(X3)) -> U108_aaa(X1, X2, X3, addCcO_in_aaa(X1, X2, X3)) 18.95/5.84 addCcO_in_aaa(one(b), zero(zero(X1)), zero(one(X1))) -> U109_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.84 U109_aaa(X1, binaryZcH_out_a(X1)) -> addCcO_out_aaa(one(b), zero(zero(X1)), zero(one(X1))) 18.95/5.84 addCcO_in_aaa(one(b), zero(one(X1)), zero(zero(X2))) -> U110_aaa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.84 U110_aaa(X1, X2, succcM_out_aa(X1, X2)) -> addCcO_out_aaa(one(b), zero(one(X1)), zero(zero(X2))) 18.95/5.84 addCcO_in_aaa(one(X1), zero(X2), zero(X3)) -> U111_aaa(X1, X2, X3, addCcO_in_aaa(X1, X2, X3)) 18.95/5.84 addCcO_in_aaa(one(X1), one(X2), one(X3)) -> U112_aaa(X1, X2, X3, addccL_in_aaa(X1, X2, X3)) 18.95/5.84 U112_aaa(X1, X2, X3, addccL_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(one(X1), one(X2), one(X3)) 18.95/5.84 U111_aaa(X1, X2, X3, addCcO_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(one(X1), zero(X2), zero(X3)) 18.95/5.84 U108_aaa(X1, X2, X3, addCcO_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(zero(X1), one(X2), zero(X3)) 18.95/5.84 U115_aaa(X1, X2, X3, addCcO_out_aaa(X1, X2, X3)) -> addccL_out_aaa(X1, X2, X3) 18.95/5.84 U100_aaa(X1, X2, X3, addccL_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(one(X1), one(X2), zero(X3)) 18.95/5.84 U118_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addycK_out_aaa(X1, X2, X3) 18.95/5.84 U99_aaa(X1, X2, X3, addycK_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(one(X1), zero(X2), one(X3)) 18.95/5.84 U98_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(zero(X1), one(X2), one(X3)) 18.95/5.84 U95_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(zero(X1), zero(X2), zero(X3)) 18.95/5.84 U150_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addcG_out_aaa(zero(X1), X2, zero(X3)) 18.95/5.84 addcG_in_aaa(one(X1), X2, one(X3)) -> U151_aaa(X1, X2, X3, addycK_in_aaa(X1, X2, X3)) 18.95/5.84 U151_aaa(X1, X2, X3, addycK_out_aaa(X1, X2, X3)) -> addcG_out_aaa(one(X1), X2, one(X3)) 18.95/5.84 U90_aaa(X1, X2, X3, addcG_out_aaa(X2, X4, X3)) -> timescF_out_aaa(one(X1), X2, X3) 18.95/5.84 U88_aaa(X1, X2, X3, timescF_out_aaa(X1, X2, X3)) -> timescF_out_aaa(zero(X1), X2, zero(X3)) 18.95/5.84 18.95/5.84 The argument filtering Pi contains the following mapping: 18.95/5.84 timesA_in_aag(x1, x2, x3) = timesA_in_aag(x3) 18.95/5.84 18.95/5.84 zero(x1) = zero(x1) 18.95/5.84 18.95/5.84 pB_in_aaag(x1, x2, x3, x4) = pB_in_aaag(x4) 18.95/5.84 18.95/5.84 timesF_in_aaa(x1, x2, x3) = timesF_in_aaa 18.95/5.84 18.95/5.84 timescF_in_aaa(x1, x2, x3) = timescF_in_aaa 18.95/5.84 18.95/5.84 timescF_out_aaa(x1, x2, x3) = timescF_out_aaa(x1) 18.95/5.84 18.95/5.84 U88_aaa(x1, x2, x3, x4) = U88_aaa(x4) 18.95/5.84 18.95/5.84 U89_aaa(x1, x2, x3, x4) = U89_aaa(x4) 18.95/5.84 18.95/5.84 U90_aaa(x1, x2, x3, x4) = U90_aaa(x1, x4) 18.95/5.84 18.95/5.84 addcG_in_aaa(x1, x2, x3) = addcG_in_aaa 18.95/5.84 18.95/5.84 U149_aaa(x1, x2) = U149_aaa(x2) 18.95/5.84 18.95/5.84 binaryZcP_in_a(x1) = binaryZcP_in_a 18.95/5.84 18.95/5.84 U119_a(x1, x2) = U119_a(x2) 18.95/5.84 18.95/5.84 binaryZcH_in_a(x1) = binaryZcH_in_a 18.95/5.84 18.95/5.84 U91_a(x1, x2) = U91_a(x2) 18.95/5.84 18.95/5.84 U92_a(x1, x2) = U92_a(x2) 18.95/5.84 18.95/5.84 binarycI_in_a(x1) = binarycI_in_a 18.95/5.84 18.95/5.84 binarycI_out_a(x1) = binarycI_out_a(x1) 18.95/5.84 18.95/5.84 U93_a(x1, x2) = U93_a(x2) 18.95/5.84 18.95/5.84 binaryZcH_out_a(x1) = binaryZcH_out_a(x1) 18.95/5.84 18.95/5.84 U94_a(x1, x2) = U94_a(x2) 18.95/5.84 18.95/5.84 binaryZcP_out_a(x1) = binaryZcP_out_a(x1) 18.95/5.84 18.95/5.84 addcG_out_aaa(x1, x2, x3) = addcG_out_aaa(x1, x2, x3) 18.95/5.84 18.95/5.84 U150_aaa(x1, x2, x3, x4) = U150_aaa(x4) 18.95/5.84 18.95/5.84 addzcJ_in_aaa(x1, x2, x3) = addzcJ_in_aaa 18.95/5.84 18.95/5.84 U95_aaa(x1, x2, x3, x4) = U95_aaa(x4) 18.95/5.84 18.95/5.84 U96_aaa(x1, x2) = U96_aaa(x2) 18.95/5.84 18.95/5.84 addzcJ_out_aaa(x1, x2, x3) = addzcJ_out_aaa(x1, x2, x3) 18.95/5.84 18.95/5.84 U97_aaa(x1, x2) = U97_aaa(x2) 18.95/5.84 18.95/5.84 U98_aaa(x1, x2, x3, x4) = U98_aaa(x4) 18.95/5.84 18.95/5.84 U99_aaa(x1, x2, x3, x4) = U99_aaa(x4) 18.95/5.84 18.95/5.84 addycK_in_aaa(x1, x2, x3) = addycK_in_aaa 18.95/5.84 18.95/5.84 U116_aaa(x1, x2) = U116_aaa(x2) 18.95/5.84 18.95/5.84 addycK_out_aaa(x1, x2, x3) = addycK_out_aaa(x1, x2, x3) 18.95/5.84 18.95/5.84 U117_aaa(x1, x2) = U117_aaa(x2) 18.95/5.84 18.95/5.84 U118_aaa(x1, x2, x3, x4) = U118_aaa(x4) 18.95/5.84 18.95/5.84 U100_aaa(x1, x2, x3, x4) = U100_aaa(x4) 18.95/5.84 18.95/5.84 addccL_in_aaa(x1, x2, x3) = addccL_in_aaa 18.95/5.84 18.95/5.84 addccL_out_aaa(x1, x2, x3) = addccL_out_aaa(x1, x2, x3) 18.95/5.84 18.95/5.84 U113_aaa(x1, x2, x3) = U113_aaa(x3) 18.95/5.84 18.95/5.84 succZcN_in_aa(x1, x2) = succZcN_in_aa 18.95/5.84 18.95/5.84 U103_aa(x1, x2) = U103_aa(x2) 18.95/5.84 18.95/5.84 succZcN_out_aa(x1, x2) = succZcN_out_aa(x1, x2) 18.95/5.84 18.95/5.84 U104_aa(x1, x2, x3) = U104_aa(x3) 18.95/5.84 18.95/5.84 succcM_in_aa(x1, x2) = succcM_in_aa 18.95/5.84 18.95/5.84 succcM_out_aa(x1, x2) = succcM_out_aa(x1, x2) 18.95/5.84 18.95/5.84 U101_aa(x1, x2) = U101_aa(x2) 18.95/5.84 18.95/5.84 U102_aa(x1, x2, x3) = U102_aa(x3) 18.95/5.84 18.95/5.84 U114_aaa(x1, x2, x3) = U114_aaa(x3) 18.95/5.84 18.95/5.84 U115_aaa(x1, x2, x3, x4) = U115_aaa(x4) 18.95/5.84 18.95/5.84 addCcO_in_aaa(x1, x2, x3) = addCcO_in_aaa 18.95/5.84 18.95/5.84 U105_aaa(x1, x2, x3, x4) = U105_aaa(x4) 18.95/5.84 18.95/5.84 addCcO_out_aaa(x1, x2, x3) = addCcO_out_aaa(x1, x2, x3) 18.95/5.84 18.95/5.84 U106_aaa(x1, x2) = U106_aaa(x2) 18.95/5.84 18.95/5.84 U107_aaa(x1, x2, x3) = U107_aaa(x3) 18.95/5.84 18.95/5.84 U108_aaa(x1, x2, x3, x4) = U108_aaa(x4) 18.95/5.84 18.95/5.84 U109_aaa(x1, x2) = U109_aaa(x2) 18.95/5.84 18.95/5.84 U110_aaa(x1, x2, x3) = U110_aaa(x3) 18.95/5.84 18.95/5.84 U111_aaa(x1, x2, x3, x4) = U111_aaa(x4) 18.95/5.84 18.95/5.84 U112_aaa(x1, x2, x3, x4) = U112_aaa(x4) 18.95/5.84 18.95/5.84 U151_aaa(x1, x2, x3, x4) = U151_aaa(x4) 18.95/5.84 18.95/5.84 addG_in_aaa(x1, x2, x3) = addG_in_aaa 18.95/5.84 18.95/5.84 binaryZP_in_a(x1) = binaryZP_in_a 18.95/5.84 18.95/5.84 binaryZH_in_a(x1) = binaryZH_in_a 18.95/5.84 18.95/5.84 binaryI_in_a(x1) = binaryI_in_a 18.95/5.84 18.95/5.84 addzJ_in_aaa(x1, x2, x3) = addzJ_in_aaa 18.95/5.84 18.95/5.84 addyK_in_aaa(x1, x2, x3) = addyK_in_aaa 18.95/5.84 18.95/5.84 addcL_in_aaa(x1, x2, x3) = addcL_in_aaa 18.95/5.84 18.95/5.84 succZN_in_aa(x1, x2) = succZN_in_aa 18.95/5.84 18.95/5.84 succM_in_aa(x1, x2) = succM_in_aa 18.95/5.84 18.95/5.84 addCO_in_aaa(x1, x2, x3) = addCO_in_aaa 18.95/5.84 18.95/5.84 addC1_in_aag(x1, x2, x3) = addC1_in_aag(x3) 18.95/5.84 18.95/5.84 binaryZP_in_g(x1) = binaryZP_in_g(x1) 18.95/5.84 18.95/5.84 binaryZH_in_g(x1) = binaryZH_in_g(x1) 18.95/5.84 18.95/5.84 one(x1) = one(x1) 18.95/5.84 18.95/5.84 binaryI_in_g(x1) = binaryI_in_g(x1) 18.95/5.84 18.95/5.84 addzQ_in_aag(x1, x2, x3) = addzQ_in_aag(x3) 18.95/5.84 18.95/5.84 addyR_in_aag(x1, x2, x3) = addyR_in_aag(x3) 18.95/5.84 18.95/5.84 addcS_in_aag(x1, x2, x3) = addcS_in_aag(x3) 18.95/5.84 18.95/5.84 succZU_in_ag(x1, x2) = succZU_in_ag(x2) 18.95/5.84 18.95/5.84 succT_in_ag(x1, x2) = succT_in_ag(x2) 18.95/5.84 18.95/5.84 addCV_in_aag(x1, x2, x3) = addCV_in_aag(x3) 18.95/5.84 18.95/5.84 pD_in_aaag(x1, x2, x3, x4) = pD_in_aaag(x4) 18.95/5.84 18.95/5.84 pE_in_aaaag(x1, x2, x3, x4, x5) = pE_in_aaaag(x5) 18.95/5.84 18.95/5.84 addC1_in_ggg(x1, x2, x3) = addC1_in_ggg(x1, x2, x3) 18.95/5.84 18.95/5.84 b = b 18.95/5.84 18.95/5.84 addzQ_in_ggg(x1, x2, x3) = addzQ_in_ggg(x1, x2, x3) 18.95/5.84 18.95/5.84 addyR_in_ggg(x1, x2, x3) = addyR_in_ggg(x1, x2, x3) 18.95/5.84 18.95/5.84 addcS_in_ggg(x1, x2, x3) = addcS_in_ggg(x1, x2, x3) 18.95/5.84 18.95/5.84 succZU_in_gg(x1, x2) = succZU_in_gg(x1, x2) 18.95/5.84 18.95/5.84 succT_in_gg(x1, x2) = succT_in_gg(x1, x2) 18.95/5.84 18.95/5.84 addCV_in_ggg(x1, x2, x3) = addCV_in_ggg(x1, x2, x3) 18.95/5.84 18.95/5.84 TIMESA_IN_AAG(x1, x2, x3) = TIMESA_IN_AAG(x3) 18.95/5.84 18.95/5.84 U75_AAG(x1, x2, x3, x4) = U75_AAG(x3, x4) 18.95/5.84 18.95/5.84 U76_AAG(x1, x2, x3, x4) = U76_AAG(x3, x4) 18.95/5.84 18.95/5.84 PB_IN_AAAG(x1, x2, x3, x4) = PB_IN_AAAG(x4) 18.95/5.84 18.95/5.84 U58_AAAG(x1, x2, x3, x4, x5) = U58_AAAG(x4, x5) 18.95/5.84 18.95/5.84 TIMESF_IN_AAA(x1, x2, x3) = TIMESF_IN_AAA 18.95/5.84 18.95/5.84 U1_AAA(x1, x2, x3, x4) = U1_AAA(x4) 18.95/5.84 18.95/5.84 U2_AAA(x1, x2, x3, x4) = U2_AAA(x4) 18.95/5.84 18.95/5.84 U3_AAA(x1, x2, x3, x4) = U3_AAA(x4) 18.95/5.84 18.95/5.84 U4_AAA(x1, x2, x3, x4) = U4_AAA(x1, x4) 18.95/5.84 18.95/5.84 ADDG_IN_AAA(x1, x2, x3) = ADDG_IN_AAA 18.95/5.84 18.95/5.84 U64_AAA(x1, x2) = U64_AAA(x2) 18.95/5.84 18.95/5.84 BINARYZP_IN_A(x1) = BINARYZP_IN_A 18.95/5.84 18.95/5.84 U33_A(x1, x2) = U33_A(x2) 18.95/5.84 18.95/5.84 BINARYZH_IN_A(x1) = BINARYZH_IN_A 18.95/5.84 18.95/5.84 U5_A(x1, x2) = U5_A(x2) 18.95/5.84 18.95/5.84 U6_A(x1, x2) = U6_A(x2) 18.95/5.84 18.95/5.84 BINARYI_IN_A(x1) = BINARYI_IN_A 18.95/5.84 18.95/5.84 U7_A(x1, x2) = U7_A(x2) 18.95/5.84 18.95/5.84 U8_A(x1, x2) = U8_A(x2) 18.95/5.84 18.95/5.84 U65_AAA(x1, x2, x3, x4) = U65_AAA(x4) 18.95/5.84 18.95/5.84 ADDZJ_IN_AAA(x1, x2, x3) = ADDZJ_IN_AAA 18.95/5.84 18.95/5.84 U9_AAA(x1, x2, x3, x4) = U9_AAA(x4) 18.95/5.84 18.95/5.84 U10_AAA(x1, x2) = U10_AAA(x2) 18.95/5.84 18.95/5.84 U11_AAA(x1, x2) = U11_AAA(x2) 18.95/5.84 18.95/5.84 U12_AAA(x1, x2, x3, x4) = U12_AAA(x4) 18.95/5.84 18.95/5.84 U13_AAA(x1, x2, x3, x4) = U13_AAA(x4) 18.95/5.84 18.95/5.84 ADDYK_IN_AAA(x1, x2, x3) = ADDYK_IN_AAA 18.95/5.84 18.95/5.84 U30_AAA(x1, x2) = U30_AAA(x2) 18.95/5.84 18.95/5.84 U31_AAA(x1, x2) = U31_AAA(x2) 18.95/5.84 18.95/5.84 U32_AAA(x1, x2, x3, x4) = U32_AAA(x4) 18.95/5.84 18.95/5.84 U14_AAA(x1, x2, x3, x4) = U14_AAA(x4) 18.95/5.84 18.95/5.84 ADDCL_IN_AAA(x1, x2, x3) = ADDCL_IN_AAA 18.95/5.84 18.95/5.84 U27_AAA(x1, x2, x3) = U27_AAA(x3) 18.95/5.84 18.95/5.84 SUCCZN_IN_AA(x1, x2) = SUCCZN_IN_AA 18.95/5.84 18.95/5.84 U17_AA(x1, x2) = U17_AA(x2) 18.95/5.84 18.95/5.84 U18_AA(x1, x2, x3) = U18_AA(x3) 18.95/5.84 18.95/5.84 SUCCM_IN_AA(x1, x2) = SUCCM_IN_AA 18.95/5.84 18.95/5.84 U15_AA(x1, x2) = U15_AA(x2) 18.95/5.84 18.95/5.84 U16_AA(x1, x2, x3) = U16_AA(x3) 18.95/5.84 18.95/5.84 U28_AAA(x1, x2, x3) = U28_AAA(x3) 18.95/5.84 18.95/5.84 U29_AAA(x1, x2, x3, x4) = U29_AAA(x4) 18.95/5.84 18.95/5.84 ADDCO_IN_AAA(x1, x2, x3) = ADDCO_IN_AAA 18.95/5.84 18.95/5.84 U19_AAA(x1, x2, x3, x4) = U19_AAA(x4) 18.95/5.84 18.95/5.84 U20_AAA(x1, x2) = U20_AAA(x2) 18.95/5.84 18.95/5.84 U21_AAA(x1, x2, x3) = U21_AAA(x3) 18.95/5.84 18.95/5.84 U22_AAA(x1, x2, x3, x4) = U22_AAA(x4) 18.95/5.84 18.95/5.84 U23_AAA(x1, x2) = U23_AAA(x2) 18.95/5.84 18.95/5.84 U24_AAA(x1, x2, x3) = U24_AAA(x3) 18.95/5.84 18.95/5.84 U25_AAA(x1, x2, x3, x4) = U25_AAA(x4) 18.95/5.84 18.95/5.84 U26_AAA(x1, x2, x3, x4) = U26_AAA(x4) 18.95/5.84 18.95/5.84 U66_AAA(x1, x2, x3, x4) = U66_AAA(x4) 18.95/5.84 18.95/5.84 U59_AAAG(x1, x2, x3, x4, x5) = U59_AAAG(x4, x5) 18.95/5.84 18.95/5.84 U60_AAAG(x1, x2, x3, x4, x5) = U60_AAAG(x1, x4, x5) 18.95/5.84 18.95/5.84 ADDC1_IN_AAG(x1, x2, x3) = ADDC1_IN_AAG(x3) 18.95/5.84 18.95/5.84 U61_AAG(x1, x2) = U61_AAG(x1, x2) 18.95/5.84 18.95/5.84 BINARYZP_IN_G(x1) = BINARYZP_IN_G(x1) 18.95/5.84 18.95/5.84 U33_G(x1, x2) = U33_G(x1, x2) 18.95/5.84 18.95/5.84 BINARYZH_IN_G(x1) = BINARYZH_IN_G(x1) 18.95/5.84 18.95/5.84 U5_G(x1, x2) = U5_G(x1, x2) 18.95/5.84 18.95/5.84 U6_G(x1, x2) = U6_G(x1, x2) 18.95/5.84 18.95/5.84 BINARYI_IN_G(x1) = BINARYI_IN_G(x1) 18.95/5.84 18.95/5.84 U7_G(x1, x2) = U7_G(x1, x2) 18.95/5.84 18.95/5.84 U8_G(x1, x2) = U8_G(x1, x2) 18.95/5.84 18.95/5.84 U62_AAG(x1, x2, x3, x4) = U62_AAG(x3, x4) 18.95/5.84 18.95/5.84 ADDZQ_IN_AAG(x1, x2, x3) = ADDZQ_IN_AAG(x3) 18.95/5.84 18.95/5.84 U34_AAG(x1, x2, x3, x4) = U34_AAG(x3, x4) 18.95/5.84 18.95/5.84 U35_AAG(x1, x2) = U35_AAG(x1, x2) 18.95/5.84 18.95/5.84 U36_AAG(x1, x2) = U36_AAG(x1, x2) 18.95/5.84 18.95/5.84 U37_AAG(x1, x2, x3, x4) = U37_AAG(x3, x4) 18.95/5.84 18.95/5.84 U38_AAG(x1, x2, x3, x4) = U38_AAG(x3, x4) 18.95/5.84 18.95/5.84 ADDYR_IN_AAG(x1, x2, x3) = ADDYR_IN_AAG(x3) 18.95/5.84 18.95/5.84 U55_AAG(x1, x2) = U55_AAG(x1, x2) 18.95/5.84 18.95/5.84 U56_AAG(x1, x2) = U56_AAG(x1, x2) 18.95/5.84 18.95/5.84 U57_AAG(x1, x2, x3, x4) = U57_AAG(x3, x4) 18.95/5.84 18.95/5.84 U39_AAG(x1, x2, x3, x4) = U39_AAG(x3, x4) 18.95/5.84 18.95/5.84 ADDCS_IN_AAG(x1, x2, x3) = ADDCS_IN_AAG(x3) 18.95/5.84 18.95/5.84 U52_AAG(x1, x2, x3) = U52_AAG(x2, x3) 18.95/5.84 18.95/5.84 SUCCZU_IN_AG(x1, x2) = SUCCZU_IN_AG(x2) 18.95/5.84 18.95/5.84 U42_AG(x1, x2) = U42_AG(x1, x2) 18.95/5.84 18.95/5.84 U43_AG(x1, x2, x3) = U43_AG(x2, x3) 18.95/5.84 18.95/5.84 SUCCT_IN_AG(x1, x2) = SUCCT_IN_AG(x2) 18.95/5.84 18.95/5.84 U40_AG(x1, x2) = U40_AG(x1, x2) 18.95/5.84 18.95/5.84 U41_AG(x1, x2, x3) = U41_AG(x2, x3) 18.95/5.84 18.95/5.84 U53_AAG(x1, x2, x3) = U53_AAG(x2, x3) 18.95/5.84 18.95/5.84 U54_AAG(x1, x2, x3, x4) = U54_AAG(x3, x4) 18.95/5.84 18.95/5.84 ADDCV_IN_AAG(x1, x2, x3) = ADDCV_IN_AAG(x3) 18.95/5.84 18.95/5.84 U44_AAG(x1, x2, x3, x4) = U44_AAG(x3, x4) 18.95/5.84 18.95/5.84 U45_AAG(x1, x2) = U45_AAG(x1, x2) 18.95/5.84 18.95/5.84 U46_AAG(x1, x2, x3) = U46_AAG(x2, x3) 18.95/5.84 18.95/5.84 U47_AAG(x1, x2, x3, x4) = U47_AAG(x3, x4) 18.95/5.84 18.95/5.84 U48_AAG(x1, x2) = U48_AAG(x1, x2) 18.95/5.84 18.95/5.84 U49_AAG(x1, x2, x3) = U49_AAG(x2, x3) 18.95/5.84 18.95/5.84 U50_AAG(x1, x2, x3, x4) = U50_AAG(x3, x4) 18.95/5.84 18.95/5.84 U51_AAG(x1, x2, x3, x4) = U51_AAG(x3, x4) 18.95/5.84 18.95/5.84 U63_AAG(x1, x2, x3, x4) = U63_AAG(x3, x4) 18.95/5.84 18.95/5.84 U77_AAG(x1, x2, x3, x4) = U77_AAG(x3, x4) 18.95/5.84 18.95/5.84 U78_AAG(x1, x2, x3) = U78_AAG(x2, x3) 18.95/5.84 18.95/5.84 U79_AAG(x1, x2, x3, x4) = U79_AAG(x3, x4) 18.95/5.84 18.95/5.84 PD_IN_AAAG(x1, x2, x3, x4) = PD_IN_AAAG(x4) 18.95/5.84 18.95/5.84 U67_AAAG(x1, x2, x3, x4, x5) = U67_AAAG(x4, x5) 18.95/5.84 18.95/5.84 U68_AAAG(x1, x2, x3, x4, x5) = U68_AAAG(x4, x5) 18.95/5.84 18.95/5.84 U69_AAAG(x1, x2, x3, x4, x5) = U69_AAAG(x1, x4, x5) 18.95/5.84 18.95/5.84 U80_AAG(x1, x2, x3, x4) = U80_AAG(x3, x4) 18.95/5.84 18.95/5.84 PE_IN_AAAAG(x1, x2, x3, x4, x5) = PE_IN_AAAAG(x5) 18.95/5.84 18.95/5.84 U70_AAAAG(x1, x2, x3, x4, x5, x6) = U70_AAAAG(x5, x6) 18.95/5.84 18.95/5.84 U71_AAAAG(x1, x2, x3, x4, x5, x6) = U71_AAAAG(x5, x6) 18.95/5.84 18.95/5.84 U72_AAAAG(x1, x2, x3, x4, x5, x6) = U72_AAAAG(x1, x5, x6) 18.95/5.84 18.95/5.84 U73_AAAAG(x1, x2, x3, x4, x5, x6) = U73_AAAAG(x1, x5, x6) 18.95/5.84 18.95/5.84 U74_AAAAG(x1, x2, x3, x4, x5, x6) = U74_AAAAG(x1, x2, x5, x6) 18.95/5.84 18.95/5.84 ADDC1_IN_GGG(x1, x2, x3) = ADDC1_IN_GGG(x1, x2, x3) 18.95/5.84 18.95/5.84 U61_GGG(x1, x2) = U61_GGG(x1, x2) 18.95/5.84 18.95/5.84 U62_GGG(x1, x2, x3, x4) = U62_GGG(x1, x2, x3, x4) 18.95/5.84 18.95/5.84 ADDZQ_IN_GGG(x1, x2, x3) = ADDZQ_IN_GGG(x1, x2, x3) 18.95/5.84 18.95/5.84 U34_GGG(x1, x2, x3, x4) = U34_GGG(x1, x2, x3, x4) 18.95/5.84 18.95/5.84 U35_GGG(x1, x2) = U35_GGG(x1, x2) 18.95/5.84 18.95/5.84 U36_GGG(x1, x2) = U36_GGG(x1, x2) 18.95/5.84 18.95/5.84 U37_GGG(x1, x2, x3, x4) = U37_GGG(x1, x2, x3, x4) 18.95/5.84 18.95/5.84 U38_GGG(x1, x2, x3, x4) = U38_GGG(x1, x2, x3, x4) 18.95/5.84 18.95/5.84 ADDYR_IN_GGG(x1, x2, x3) = ADDYR_IN_GGG(x1, x2, x3) 18.95/5.84 18.95/5.84 U55_GGG(x1, x2) = U55_GGG(x1, x2) 18.95/5.84 18.95/5.84 U56_GGG(x1, x2) = U56_GGG(x1, x2) 18.95/5.84 18.95/5.84 U57_GGG(x1, x2, x3, x4) = U57_GGG(x1, x2, x3, x4) 18.95/5.84 18.95/5.84 U39_GGG(x1, x2, x3, x4) = U39_GGG(x1, x2, x3, x4) 18.95/5.84 18.95/5.84 ADDCS_IN_GGG(x1, x2, x3) = ADDCS_IN_GGG(x1, x2, x3) 18.95/5.84 18.95/5.84 U52_GGG(x1, x2, x3) = U52_GGG(x1, x2, x3) 18.95/5.84 18.95/5.84 SUCCZU_IN_GG(x1, x2) = SUCCZU_IN_GG(x1, x2) 18.95/5.84 18.95/5.84 U42_GG(x1, x2) = U42_GG(x1, x2) 18.95/5.84 18.95/5.84 U43_GG(x1, x2, x3) = U43_GG(x1, x2, x3) 18.95/5.84 18.95/5.84 SUCCT_IN_GG(x1, x2) = SUCCT_IN_GG(x1, x2) 18.95/5.84 18.95/5.84 U40_GG(x1, x2) = U40_GG(x1, x2) 18.95/5.84 18.95/5.84 U41_GG(x1, x2, x3) = U41_GG(x1, x2, x3) 18.95/5.84 18.95/5.84 U53_GGG(x1, x2, x3) = U53_GGG(x1, x2, x3) 18.95/5.84 18.95/5.84 U54_GGG(x1, x2, x3, x4) = U54_GGG(x1, x2, x3, x4) 18.95/5.84 18.95/5.84 ADDCV_IN_GGG(x1, x2, x3) = ADDCV_IN_GGG(x1, x2, x3) 18.95/5.84 18.95/5.84 U44_GGG(x1, x2, x3, x4) = U44_GGG(x1, x2, x3, x4) 18.95/5.84 18.95/5.84 U45_GGG(x1, x2) = U45_GGG(x1, x2) 18.95/5.84 18.95/5.84 U46_GGG(x1, x2, x3) = U46_GGG(x1, x2, x3) 18.95/5.84 18.95/5.84 U47_GGG(x1, x2, x3, x4) = U47_GGG(x1, x2, x3, x4) 18.95/5.84 18.95/5.84 U48_GGG(x1, x2) = U48_GGG(x1, x2) 18.95/5.84 18.95/5.84 U49_GGG(x1, x2, x3) = U49_GGG(x1, x2, x3) 18.95/5.84 18.95/5.84 U50_GGG(x1, x2, x3, x4) = U50_GGG(x1, x2, x3, x4) 18.95/5.84 18.95/5.84 U51_GGG(x1, x2, x3, x4) = U51_GGG(x1, x2, x3, x4) 18.95/5.84 18.95/5.84 U63_GGG(x1, x2, x3, x4) = U63_GGG(x1, x2, x3, x4) 18.95/5.84 18.95/5.84 18.95/5.84 We have to consider all (P,R,Pi)-chains 18.95/5.84 18.95/5.84 18.95/5.84 Infinitary Constructor Rewriting Termination of PiDP implies Termination of TRIPLES 18.95/5.84 18.95/5.84 18.95/5.84 18.95/5.84 ---------------------------------------- 18.95/5.84 18.95/5.84 (138) 18.95/5.84 Obligation: 18.95/5.84 Pi DP problem: 18.95/5.84 The TRS P consists of the following rules: 18.95/5.84 18.95/5.84 TIMESA_IN_AAG(zero(zero(X1)), X2, zero(zero(X3))) -> U75_AAG(X1, X2, X3, timesA_in_aag(X1, X2, X3)) 18.95/5.84 TIMESA_IN_AAG(zero(zero(X1)), X2, zero(zero(X3))) -> TIMESA_IN_AAG(X1, X2, X3) 18.95/5.84 TIMESA_IN_AAG(zero(one(X1)), X2, zero(X3)) -> U76_AAG(X1, X2, X3, pB_in_aaag(X1, X2, X4, X3)) 18.95/5.84 TIMESA_IN_AAG(zero(one(X1)), X2, zero(X3)) -> PB_IN_AAAG(X1, X2, X4, X3) 18.95/5.84 PB_IN_AAAG(X1, X2, X3, X4) -> U58_AAAG(X1, X2, X3, X4, timesF_in_aaa(X1, X2, X3)) 18.95/5.84 PB_IN_AAAG(X1, X2, X3, X4) -> TIMESF_IN_AAA(X1, X2, X3) 18.95/5.84 TIMESF_IN_AAA(zero(X1), X2, zero(X3)) -> U1_AAA(X1, X2, X3, timesF_in_aaa(X1, X2, X3)) 18.95/5.84 TIMESF_IN_AAA(zero(X1), X2, zero(X3)) -> TIMESF_IN_AAA(X1, X2, X3) 18.95/5.84 TIMESF_IN_AAA(one(X1), X2, X3) -> U2_AAA(X1, X2, X3, timesF_in_aaa(X1, X2, X4)) 18.95/5.84 TIMESF_IN_AAA(one(X1), X2, X3) -> TIMESF_IN_AAA(X1, X2, X4) 18.95/5.84 TIMESF_IN_AAA(one(X1), X2, X3) -> U3_AAA(X1, X2, X3, timescF_in_aaa(X1, X2, X4)) 18.95/5.84 U3_AAA(X1, X2, X3, timescF_out_aaa(X1, X2, X4)) -> U4_AAA(X1, X2, X3, addG_in_aaa(X2, X4, X3)) 18.95/5.84 U3_AAA(X1, X2, X3, timescF_out_aaa(X1, X2, X4)) -> ADDG_IN_AAA(X2, X4, X3) 18.95/5.84 ADDG_IN_AAA(b, X1, zero(X1)) -> U64_AAA(X1, binaryZP_in_a(X1)) 18.95/5.84 ADDG_IN_AAA(b, X1, zero(X1)) -> BINARYZP_IN_A(X1) 18.95/5.84 BINARYZP_IN_A(X1) -> U33_A(X1, binaryZH_in_a(X1)) 18.95/5.84 BINARYZP_IN_A(X1) -> BINARYZH_IN_A(X1) 18.95/5.84 BINARYZH_IN_A(zero(X1)) -> U5_A(X1, binaryZH_in_a(X1)) 18.95/5.84 BINARYZH_IN_A(zero(X1)) -> BINARYZH_IN_A(X1) 18.95/5.84 BINARYZH_IN_A(one(X1)) -> U6_A(X1, binaryI_in_a(X1)) 18.95/5.84 BINARYZH_IN_A(one(X1)) -> BINARYI_IN_A(X1) 18.95/5.84 BINARYI_IN_A(zero(X1)) -> U7_A(X1, binaryZH_in_a(X1)) 18.95/5.84 BINARYI_IN_A(zero(X1)) -> BINARYZH_IN_A(X1) 18.95/5.84 BINARYI_IN_A(one(X1)) -> U8_A(X1, binaryI_in_a(X1)) 18.95/5.84 BINARYI_IN_A(one(X1)) -> BINARYI_IN_A(X1) 18.95/5.84 ADDG_IN_AAA(zero(X1), X2, zero(X3)) -> U65_AAA(X1, X2, X3, addzJ_in_aaa(X1, X2, X3)) 18.95/5.84 ADDG_IN_AAA(zero(X1), X2, zero(X3)) -> ADDZJ_IN_AAA(X1, X2, X3) 18.95/5.84 ADDZJ_IN_AAA(zero(X1), zero(X2), zero(X3)) -> U9_AAA(X1, X2, X3, addzJ_in_aaa(X1, X2, X3)) 18.95/5.84 ADDZJ_IN_AAA(zero(X1), zero(X2), zero(X3)) -> ADDZJ_IN_AAA(X1, X2, X3) 18.95/5.84 ADDZJ_IN_AAA(zero(one(X1)), one(b), one(one(X1))) -> U10_AAA(X1, binaryI_in_a(X1)) 18.95/5.84 ADDZJ_IN_AAA(zero(one(X1)), one(b), one(one(X1))) -> BINARYI_IN_A(X1) 18.95/5.84 ADDZJ_IN_AAA(zero(zero(X1)), one(b), one(zero(X1))) -> U11_AAA(X1, binaryZH_in_a(X1)) 18.95/5.84 ADDZJ_IN_AAA(zero(zero(X1)), one(b), one(zero(X1))) -> BINARYZH_IN_A(X1) 18.95/5.84 ADDZJ_IN_AAA(zero(X1), one(X2), one(X3)) -> U12_AAA(X1, X2, X3, addzJ_in_aaa(X1, X2, X3)) 18.95/5.84 ADDZJ_IN_AAA(zero(X1), one(X2), one(X3)) -> ADDZJ_IN_AAA(X1, X2, X3) 18.95/5.84 ADDZJ_IN_AAA(one(X1), zero(X2), one(X3)) -> U13_AAA(X1, X2, X3, addyK_in_aaa(X1, X2, X3)) 18.95/5.84 ADDZJ_IN_AAA(one(X1), zero(X2), one(X3)) -> ADDYK_IN_AAA(X1, X2, X3) 18.95/5.84 ADDYK_IN_AAA(b, one(X1), one(X1)) -> U30_AAA(X1, binaryI_in_a(X1)) 18.95/5.84 ADDYK_IN_AAA(b, one(X1), one(X1)) -> BINARYI_IN_A(X1) 18.95/5.84 ADDYK_IN_AAA(b, zero(X1), zero(X1)) -> U31_AAA(X1, binaryZH_in_a(X1)) 18.95/5.84 ADDYK_IN_AAA(b, zero(X1), zero(X1)) -> BINARYZH_IN_A(X1) 18.95/5.84 ADDYK_IN_AAA(X1, X2, X3) -> U32_AAA(X1, X2, X3, addzJ_in_aaa(X1, X2, X3)) 18.95/5.84 ADDYK_IN_AAA(X1, X2, X3) -> ADDZJ_IN_AAA(X1, X2, X3) 18.95/5.84 ADDZJ_IN_AAA(one(X1), one(X2), zero(X3)) -> U14_AAA(X1, X2, X3, addcL_in_aaa(X1, X2, X3)) 18.95/5.84 ADDZJ_IN_AAA(one(X1), one(X2), zero(X3)) -> ADDCL_IN_AAA(X1, X2, X3) 18.95/5.84 ADDCL_IN_AAA(X1, b, X2) -> U27_AAA(X1, X2, succZN_in_aa(X1, X2)) 18.95/5.85 ADDCL_IN_AAA(X1, b, X2) -> SUCCZN_IN_AA(X1, X2) 18.95/5.85 SUCCZN_IN_AA(zero(X1), one(X1)) -> U17_AA(X1, binaryZH_in_a(X1)) 18.95/5.85 SUCCZN_IN_AA(zero(X1), one(X1)) -> BINARYZH_IN_A(X1) 18.95/5.85 SUCCZN_IN_AA(one(X1), zero(X2)) -> U18_AA(X1, X2, succM_in_aa(X1, X2)) 18.95/5.85 SUCCZN_IN_AA(one(X1), zero(X2)) -> SUCCM_IN_AA(X1, X2) 18.95/5.85 SUCCM_IN_AA(zero(X1), one(X1)) -> U15_AA(X1, binaryZH_in_a(X1)) 18.95/5.85 SUCCM_IN_AA(zero(X1), one(X1)) -> BINARYZH_IN_A(X1) 18.95/5.85 SUCCM_IN_AA(one(X1), zero(X2)) -> U16_AA(X1, X2, succM_in_aa(X1, X2)) 18.95/5.85 SUCCM_IN_AA(one(X1), zero(X2)) -> SUCCM_IN_AA(X1, X2) 18.95/5.85 ADDCL_IN_AAA(b, X1, X2) -> U28_AAA(X1, X2, succZN_in_aa(X1, X2)) 18.95/5.85 ADDCL_IN_AAA(b, X1, X2) -> SUCCZN_IN_AA(X1, X2) 18.95/5.85 ADDCL_IN_AAA(X1, X2, X3) -> U29_AAA(X1, X2, X3, addCO_in_aaa(X1, X2, X3)) 18.95/5.85 ADDCL_IN_AAA(X1, X2, X3) -> ADDCO_IN_AAA(X1, X2, X3) 18.95/5.85 ADDCO_IN_AAA(zero(X1), zero(X2), one(X3)) -> U19_AAA(X1, X2, X3, addzJ_in_aaa(X1, X2, X3)) 18.95/5.85 ADDCO_IN_AAA(zero(X1), zero(X2), one(X3)) -> ADDZJ_IN_AAA(X1, X2, X3) 18.95/5.85 ADDCO_IN_AAA(zero(zero(X1)), one(b), zero(one(X1))) -> U20_AAA(X1, binaryZH_in_a(X1)) 18.95/5.85 ADDCO_IN_AAA(zero(zero(X1)), one(b), zero(one(X1))) -> BINARYZH_IN_A(X1) 18.95/5.85 ADDCO_IN_AAA(zero(one(X1)), one(b), zero(zero(X2))) -> U21_AAA(X1, X2, succM_in_aa(X1, X2)) 18.95/5.85 ADDCO_IN_AAA(zero(one(X1)), one(b), zero(zero(X2))) -> SUCCM_IN_AA(X1, X2) 18.95/5.85 ADDCO_IN_AAA(zero(X1), one(X2), zero(X3)) -> U22_AAA(X1, X2, X3, addCO_in_aaa(X1, X2, X3)) 18.95/5.85 ADDCO_IN_AAA(zero(X1), one(X2), zero(X3)) -> ADDCO_IN_AAA(X1, X2, X3) 18.95/5.85 ADDCO_IN_AAA(one(b), zero(zero(X1)), zero(one(X1))) -> U23_AAA(X1, binaryZH_in_a(X1)) 18.95/5.85 ADDCO_IN_AAA(one(b), zero(zero(X1)), zero(one(X1))) -> BINARYZH_IN_A(X1) 18.95/5.85 ADDCO_IN_AAA(one(b), zero(one(X1)), zero(zero(X2))) -> U24_AAA(X1, X2, succM_in_aa(X1, X2)) 18.95/5.85 ADDCO_IN_AAA(one(b), zero(one(X1)), zero(zero(X2))) -> SUCCM_IN_AA(X1, X2) 18.95/5.85 ADDCO_IN_AAA(one(X1), zero(X2), zero(X3)) -> U25_AAA(X1, X2, X3, addCO_in_aaa(X1, X2, X3)) 18.95/5.85 ADDCO_IN_AAA(one(X1), zero(X2), zero(X3)) -> ADDCO_IN_AAA(X1, X2, X3) 18.95/5.85 ADDCO_IN_AAA(one(X1), one(X2), one(X3)) -> U26_AAA(X1, X2, X3, addcL_in_aaa(X1, X2, X3)) 18.95/5.85 ADDCO_IN_AAA(one(X1), one(X2), one(X3)) -> ADDCL_IN_AAA(X1, X2, X3) 18.95/5.85 ADDG_IN_AAA(one(X1), X2, one(X3)) -> U66_AAA(X1, X2, X3, addyK_in_aaa(X1, X2, X3)) 18.95/5.85 ADDG_IN_AAA(one(X1), X2, one(X3)) -> ADDYK_IN_AAA(X1, X2, X3) 18.95/5.85 PB_IN_AAAG(X1, X2, X3, X4) -> U59_AAAG(X1, X2, X3, X4, timescF_in_aaa(X1, X2, X3)) 18.95/5.85 U59_AAAG(X1, X2, X3, X4, timescF_out_aaa(X1, X2, X3)) -> U60_AAAG(X1, X2, X3, X4, addC1_in_aag(X2, X3, X4)) 18.95/5.85 U59_AAAG(X1, X2, X3, X4, timescF_out_aaa(X1, X2, X3)) -> ADDC1_IN_AAG(X2, X3, X4) 18.95/5.85 ADDC1_IN_AAG(b, X1, zero(X1)) -> U61_AAG(X1, binaryZP_in_g(X1)) 18.95/5.85 ADDC1_IN_AAG(b, X1, zero(X1)) -> BINARYZP_IN_G(X1) 18.95/5.85 BINARYZP_IN_G(X1) -> U33_G(X1, binaryZH_in_g(X1)) 18.95/5.85 BINARYZP_IN_G(X1) -> BINARYZH_IN_G(X1) 18.95/5.85 BINARYZH_IN_G(zero(X1)) -> U5_G(X1, binaryZH_in_g(X1)) 18.95/5.85 BINARYZH_IN_G(zero(X1)) -> BINARYZH_IN_G(X1) 18.95/5.85 BINARYZH_IN_G(one(X1)) -> U6_G(X1, binaryI_in_g(X1)) 18.95/5.85 BINARYZH_IN_G(one(X1)) -> BINARYI_IN_G(X1) 18.95/5.85 BINARYI_IN_G(zero(X1)) -> U7_G(X1, binaryZH_in_g(X1)) 18.95/5.85 BINARYI_IN_G(zero(X1)) -> BINARYZH_IN_G(X1) 18.95/5.85 BINARYI_IN_G(one(X1)) -> U8_G(X1, binaryI_in_g(X1)) 18.95/5.85 BINARYI_IN_G(one(X1)) -> BINARYI_IN_G(X1) 18.95/5.85 ADDC1_IN_AAG(zero(X1), X2, zero(X3)) -> U62_AAG(X1, X2, X3, addzQ_in_aag(X1, X2, X3)) 18.95/5.85 ADDC1_IN_AAG(zero(X1), X2, zero(X3)) -> ADDZQ_IN_AAG(X1, X2, X3) 18.95/5.85 ADDZQ_IN_AAG(zero(X1), zero(X2), zero(X3)) -> U34_AAG(X1, X2, X3, addzQ_in_aag(X1, X2, X3)) 18.95/5.85 ADDZQ_IN_AAG(zero(X1), zero(X2), zero(X3)) -> ADDZQ_IN_AAG(X1, X2, X3) 18.95/5.85 ADDZQ_IN_AAG(zero(one(X1)), one(b), one(one(X1))) -> U35_AAG(X1, binaryI_in_g(X1)) 18.95/5.85 ADDZQ_IN_AAG(zero(one(X1)), one(b), one(one(X1))) -> BINARYI_IN_G(X1) 18.95/5.85 ADDZQ_IN_AAG(zero(zero(X1)), one(b), one(zero(X1))) -> U36_AAG(X1, binaryZH_in_g(X1)) 18.95/5.85 ADDZQ_IN_AAG(zero(zero(X1)), one(b), one(zero(X1))) -> BINARYZH_IN_G(X1) 18.95/5.85 ADDZQ_IN_AAG(zero(X1), one(X2), one(X3)) -> U37_AAG(X1, X2, X3, addzQ_in_aag(X1, X2, X3)) 18.95/5.85 ADDZQ_IN_AAG(zero(X1), one(X2), one(X3)) -> ADDZQ_IN_AAG(X1, X2, X3) 18.95/5.85 ADDZQ_IN_AAG(one(X1), zero(X2), one(X3)) -> U38_AAG(X1, X2, X3, addyR_in_aag(X1, X2, X3)) 18.95/5.85 ADDZQ_IN_AAG(one(X1), zero(X2), one(X3)) -> ADDYR_IN_AAG(X1, X2, X3) 18.95/5.85 ADDYR_IN_AAG(b, one(X1), one(X1)) -> U55_AAG(X1, binaryI_in_g(X1)) 18.95/5.85 ADDYR_IN_AAG(b, one(X1), one(X1)) -> BINARYI_IN_G(X1) 18.95/5.85 ADDYR_IN_AAG(b, zero(X1), zero(X1)) -> U56_AAG(X1, binaryZH_in_g(X1)) 18.95/5.85 ADDYR_IN_AAG(b, zero(X1), zero(X1)) -> BINARYZH_IN_G(X1) 18.95/5.85 ADDYR_IN_AAG(X1, X2, X3) -> U57_AAG(X1, X2, X3, addzQ_in_aag(X1, X2, X3)) 18.95/5.85 ADDYR_IN_AAG(X1, X2, X3) -> ADDZQ_IN_AAG(X1, X2, X3) 18.95/5.85 ADDZQ_IN_AAG(one(X1), one(X2), zero(X3)) -> U39_AAG(X1, X2, X3, addcS_in_aag(X1, X2, X3)) 18.95/5.85 ADDZQ_IN_AAG(one(X1), one(X2), zero(X3)) -> ADDCS_IN_AAG(X1, X2, X3) 18.95/5.85 ADDCS_IN_AAG(X1, b, X2) -> U52_AAG(X1, X2, succZU_in_ag(X1, X2)) 18.95/5.85 ADDCS_IN_AAG(X1, b, X2) -> SUCCZU_IN_AG(X1, X2) 18.95/5.85 SUCCZU_IN_AG(zero(X1), one(X1)) -> U42_AG(X1, binaryZH_in_g(X1)) 18.95/5.85 SUCCZU_IN_AG(zero(X1), one(X1)) -> BINARYZH_IN_G(X1) 18.95/5.85 SUCCZU_IN_AG(one(X1), zero(X2)) -> U43_AG(X1, X2, succT_in_ag(X1, X2)) 18.95/5.85 SUCCZU_IN_AG(one(X1), zero(X2)) -> SUCCT_IN_AG(X1, X2) 18.95/5.85 SUCCT_IN_AG(zero(X1), one(X1)) -> U40_AG(X1, binaryZH_in_g(X1)) 18.95/5.85 SUCCT_IN_AG(zero(X1), one(X1)) -> BINARYZH_IN_G(X1) 18.95/5.85 SUCCT_IN_AG(one(X1), zero(X2)) -> U41_AG(X1, X2, succT_in_ag(X1, X2)) 18.95/5.85 SUCCT_IN_AG(one(X1), zero(X2)) -> SUCCT_IN_AG(X1, X2) 18.95/5.85 ADDCS_IN_AAG(b, X1, X2) -> U53_AAG(X1, X2, succZU_in_ag(X1, X2)) 18.95/5.85 ADDCS_IN_AAG(b, X1, X2) -> SUCCZU_IN_AG(X1, X2) 18.95/5.85 ADDCS_IN_AAG(X1, X2, X3) -> U54_AAG(X1, X2, X3, addCV_in_aag(X1, X2, X3)) 18.95/5.85 ADDCS_IN_AAG(X1, X2, X3) -> ADDCV_IN_AAG(X1, X2, X3) 18.95/5.85 ADDCV_IN_AAG(zero(X1), zero(X2), one(X3)) -> U44_AAG(X1, X2, X3, addzQ_in_aag(X1, X2, X3)) 18.95/5.85 ADDCV_IN_AAG(zero(X1), zero(X2), one(X3)) -> ADDZQ_IN_AAG(X1, X2, X3) 18.95/5.85 ADDCV_IN_AAG(zero(zero(X1)), one(b), zero(one(X1))) -> U45_AAG(X1, binaryZH_in_g(X1)) 18.95/5.85 ADDCV_IN_AAG(zero(zero(X1)), one(b), zero(one(X1))) -> BINARYZH_IN_G(X1) 18.95/5.85 ADDCV_IN_AAG(zero(one(X1)), one(b), zero(zero(X2))) -> U46_AAG(X1, X2, succT_in_ag(X1, X2)) 18.95/5.85 ADDCV_IN_AAG(zero(one(X1)), one(b), zero(zero(X2))) -> SUCCT_IN_AG(X1, X2) 18.95/5.85 ADDCV_IN_AAG(zero(X1), one(X2), zero(X3)) -> U47_AAG(X1, X2, X3, addCV_in_aag(X1, X2, X3)) 18.95/5.85 ADDCV_IN_AAG(zero(X1), one(X2), zero(X3)) -> ADDCV_IN_AAG(X1, X2, X3) 18.95/5.85 ADDCV_IN_AAG(one(b), zero(zero(X1)), zero(one(X1))) -> U48_AAG(X1, binaryZH_in_g(X1)) 18.95/5.85 ADDCV_IN_AAG(one(b), zero(zero(X1)), zero(one(X1))) -> BINARYZH_IN_G(X1) 18.95/5.85 ADDCV_IN_AAG(one(b), zero(one(X1)), zero(zero(X2))) -> U49_AAG(X1, X2, succT_in_ag(X1, X2)) 18.95/5.85 ADDCV_IN_AAG(one(b), zero(one(X1)), zero(zero(X2))) -> SUCCT_IN_AG(X1, X2) 18.95/5.85 ADDCV_IN_AAG(one(X1), zero(X2), zero(X3)) -> U50_AAG(X1, X2, X3, addCV_in_aag(X1, X2, X3)) 18.95/5.85 ADDCV_IN_AAG(one(X1), zero(X2), zero(X3)) -> ADDCV_IN_AAG(X1, X2, X3) 18.95/5.85 ADDCV_IN_AAG(one(X1), one(X2), one(X3)) -> U51_AAG(X1, X2, X3, addcS_in_aag(X1, X2, X3)) 18.95/5.85 ADDCV_IN_AAG(one(X1), one(X2), one(X3)) -> ADDCS_IN_AAG(X1, X2, X3) 18.95/5.85 ADDC1_IN_AAG(one(X1), X2, one(X3)) -> U63_AAG(X1, X2, X3, addyR_in_aag(X1, X2, X3)) 18.95/5.85 ADDC1_IN_AAG(one(X1), X2, one(X3)) -> ADDYR_IN_AAG(X1, X2, X3) 18.95/5.85 TIMESA_IN_AAG(one(X1), X2, zero(X3)) -> U77_AAG(X1, X2, X3, pB_in_aaag(X1, X2, X4, zero(X3))) 18.95/5.85 TIMESA_IN_AAG(one(X1), X2, zero(X3)) -> PB_IN_AAAG(X1, X2, X4, zero(X3)) 18.95/5.85 TIMESA_IN_AAG(one(one(b)), X1, X2) -> U78_AAG(X1, X2, addC1_in_aag(X1, X1, X2)) 18.95/5.85 TIMESA_IN_AAG(one(one(b)), X1, X2) -> ADDC1_IN_AAG(X1, X1, X2) 18.95/5.85 TIMESA_IN_AAG(one(zero(X1)), X2, X3) -> U79_AAG(X1, X2, X3, pD_in_aaag(X1, X2, X4, X3)) 18.95/5.85 TIMESA_IN_AAG(one(zero(X1)), X2, X3) -> PD_IN_AAAG(X1, X2, X4, X3) 18.95/5.85 PD_IN_AAAG(X1, X2, X3, X4) -> U67_AAAG(X1, X2, X3, X4, timesF_in_aaa(X1, X2, X3)) 18.95/5.85 PD_IN_AAAG(X1, X2, X3, X4) -> TIMESF_IN_AAA(X1, X2, X3) 18.95/5.85 PD_IN_AAAG(X1, X2, X3, X4) -> U68_AAAG(X1, X2, X3, X4, timescF_in_aaa(X1, X2, X3)) 18.95/5.85 U68_AAAG(X1, X2, X3, X4, timescF_out_aaa(X1, X2, X3)) -> U69_AAAG(X1, X2, X3, X4, addC1_in_aag(X2, zero(X3), X4)) 18.95/5.85 U68_AAAG(X1, X2, X3, X4, timescF_out_aaa(X1, X2, X3)) -> ADDC1_IN_AAG(X2, zero(X3), X4) 18.95/5.85 TIMESA_IN_AAG(one(one(X1)), X2, X3) -> U80_AAG(X1, X2, X3, pE_in_aaaag(X1, X2, X4, X5, X3)) 18.95/5.85 TIMESA_IN_AAG(one(one(X1)), X2, X3) -> PE_IN_AAAAG(X1, X2, X4, X5, X3) 18.95/5.85 PE_IN_AAAAG(X1, X2, X3, X4, X5) -> U70_AAAAG(X1, X2, X3, X4, X5, timesF_in_aaa(X1, X2, X3)) 18.95/5.85 PE_IN_AAAAG(X1, X2, X3, X4, X5) -> TIMESF_IN_AAA(X1, X2, X3) 18.95/5.85 PE_IN_AAAAG(X1, X2, X3, X4, X5) -> U71_AAAAG(X1, X2, X3, X4, X5, timescF_in_aaa(X1, X2, X3)) 18.95/5.85 U71_AAAAG(X1, X2, X3, X4, X5, timescF_out_aaa(X1, X2, X3)) -> U72_AAAAG(X1, X2, X3, X4, X5, addG_in_aaa(X2, X3, X4)) 18.95/5.85 U71_AAAAG(X1, X2, X3, X4, X5, timescF_out_aaa(X1, X2, X3)) -> ADDG_IN_AAA(X2, X3, X4) 18.95/5.85 U71_AAAAG(X1, X2, X3, X4, X5, timescF_out_aaa(X1, X2, X3)) -> U73_AAAAG(X1, X2, X3, X4, X5, addcG_in_aaa(X2, X3, X4)) 18.95/5.85 U73_AAAAG(X1, X2, X3, X4, X5, addcG_out_aaa(X2, X3, X4)) -> U74_AAAAG(X1, X2, X3, X4, X5, addC1_in_ggg(X2, X4, X5)) 18.95/5.85 U73_AAAAG(X1, X2, X3, X4, X5, addcG_out_aaa(X2, X3, X4)) -> ADDC1_IN_GGG(X2, X4, X5) 18.95/5.85 ADDC1_IN_GGG(b, X1, zero(X1)) -> U61_GGG(X1, binaryZP_in_g(X1)) 18.95/5.85 ADDC1_IN_GGG(b, X1, zero(X1)) -> BINARYZP_IN_G(X1) 18.95/5.85 ADDC1_IN_GGG(zero(X1), X2, zero(X3)) -> U62_GGG(X1, X2, X3, addzQ_in_ggg(X1, X2, X3)) 18.95/5.85 ADDC1_IN_GGG(zero(X1), X2, zero(X3)) -> ADDZQ_IN_GGG(X1, X2, X3) 18.95/5.85 ADDZQ_IN_GGG(zero(X1), zero(X2), zero(X3)) -> U34_GGG(X1, X2, X3, addzQ_in_ggg(X1, X2, X3)) 18.95/5.85 ADDZQ_IN_GGG(zero(X1), zero(X2), zero(X3)) -> ADDZQ_IN_GGG(X1, X2, X3) 18.95/5.85 ADDZQ_IN_GGG(zero(one(X1)), one(b), one(one(X1))) -> U35_GGG(X1, binaryI_in_g(X1)) 18.95/5.85 ADDZQ_IN_GGG(zero(one(X1)), one(b), one(one(X1))) -> BINARYI_IN_G(X1) 18.95/5.85 ADDZQ_IN_GGG(zero(zero(X1)), one(b), one(zero(X1))) -> U36_GGG(X1, binaryZH_in_g(X1)) 18.95/5.85 ADDZQ_IN_GGG(zero(zero(X1)), one(b), one(zero(X1))) -> BINARYZH_IN_G(X1) 18.95/5.85 ADDZQ_IN_GGG(zero(X1), one(X2), one(X3)) -> U37_GGG(X1, X2, X3, addzQ_in_ggg(X1, X2, X3)) 18.95/5.85 ADDZQ_IN_GGG(zero(X1), one(X2), one(X3)) -> ADDZQ_IN_GGG(X1, X2, X3) 18.95/5.85 ADDZQ_IN_GGG(one(X1), zero(X2), one(X3)) -> U38_GGG(X1, X2, X3, addyR_in_ggg(X1, X2, X3)) 18.95/5.85 ADDZQ_IN_GGG(one(X1), zero(X2), one(X3)) -> ADDYR_IN_GGG(X1, X2, X3) 18.95/5.85 ADDYR_IN_GGG(b, one(X1), one(X1)) -> U55_GGG(X1, binaryI_in_g(X1)) 18.95/5.85 ADDYR_IN_GGG(b, one(X1), one(X1)) -> BINARYI_IN_G(X1) 18.95/5.85 ADDYR_IN_GGG(b, zero(X1), zero(X1)) -> U56_GGG(X1, binaryZH_in_g(X1)) 18.95/5.85 ADDYR_IN_GGG(b, zero(X1), zero(X1)) -> BINARYZH_IN_G(X1) 18.95/5.85 ADDYR_IN_GGG(X1, X2, X3) -> U57_GGG(X1, X2, X3, addzQ_in_ggg(X1, X2, X3)) 18.95/5.85 ADDYR_IN_GGG(X1, X2, X3) -> ADDZQ_IN_GGG(X1, X2, X3) 18.95/5.85 ADDZQ_IN_GGG(one(X1), one(X2), zero(X3)) -> U39_GGG(X1, X2, X3, addcS_in_ggg(X1, X2, X3)) 18.95/5.85 ADDZQ_IN_GGG(one(X1), one(X2), zero(X3)) -> ADDCS_IN_GGG(X1, X2, X3) 18.95/5.85 ADDCS_IN_GGG(X1, b, X2) -> U52_GGG(X1, X2, succZU_in_gg(X1, X2)) 18.95/5.85 ADDCS_IN_GGG(X1, b, X2) -> SUCCZU_IN_GG(X1, X2) 18.95/5.85 SUCCZU_IN_GG(zero(X1), one(X1)) -> U42_GG(X1, binaryZH_in_g(X1)) 18.95/5.85 SUCCZU_IN_GG(zero(X1), one(X1)) -> BINARYZH_IN_G(X1) 18.95/5.85 SUCCZU_IN_GG(one(X1), zero(X2)) -> U43_GG(X1, X2, succT_in_gg(X1, X2)) 18.95/5.85 SUCCZU_IN_GG(one(X1), zero(X2)) -> SUCCT_IN_GG(X1, X2) 18.95/5.85 SUCCT_IN_GG(zero(X1), one(X1)) -> U40_GG(X1, binaryZH_in_g(X1)) 18.95/5.85 SUCCT_IN_GG(zero(X1), one(X1)) -> BINARYZH_IN_G(X1) 18.95/5.85 SUCCT_IN_GG(one(X1), zero(X2)) -> U41_GG(X1, X2, succT_in_gg(X1, X2)) 18.95/5.85 SUCCT_IN_GG(one(X1), zero(X2)) -> SUCCT_IN_GG(X1, X2) 18.95/5.85 ADDCS_IN_GGG(b, X1, X2) -> U53_GGG(X1, X2, succZU_in_gg(X1, X2)) 18.95/5.85 ADDCS_IN_GGG(b, X1, X2) -> SUCCZU_IN_GG(X1, X2) 18.95/5.85 ADDCS_IN_GGG(X1, X2, X3) -> U54_GGG(X1, X2, X3, addCV_in_ggg(X1, X2, X3)) 18.95/5.85 ADDCS_IN_GGG(X1, X2, X3) -> ADDCV_IN_GGG(X1, X2, X3) 18.95/5.85 ADDCV_IN_GGG(zero(X1), zero(X2), one(X3)) -> U44_GGG(X1, X2, X3, addzQ_in_ggg(X1, X2, X3)) 18.95/5.85 ADDCV_IN_GGG(zero(X1), zero(X2), one(X3)) -> ADDZQ_IN_GGG(X1, X2, X3) 18.95/5.85 ADDCV_IN_GGG(zero(zero(X1)), one(b), zero(one(X1))) -> U45_GGG(X1, binaryZH_in_g(X1)) 18.95/5.85 ADDCV_IN_GGG(zero(zero(X1)), one(b), zero(one(X1))) -> BINARYZH_IN_G(X1) 18.95/5.85 ADDCV_IN_GGG(zero(one(X1)), one(b), zero(zero(X2))) -> U46_GGG(X1, X2, succT_in_gg(X1, X2)) 18.95/5.85 ADDCV_IN_GGG(zero(one(X1)), one(b), zero(zero(X2))) -> SUCCT_IN_GG(X1, X2) 18.95/5.85 ADDCV_IN_GGG(zero(X1), one(X2), zero(X3)) -> U47_GGG(X1, X2, X3, addCV_in_ggg(X1, X2, X3)) 18.95/5.85 ADDCV_IN_GGG(zero(X1), one(X2), zero(X3)) -> ADDCV_IN_GGG(X1, X2, X3) 18.95/5.85 ADDCV_IN_GGG(one(b), zero(zero(X1)), zero(one(X1))) -> U48_GGG(X1, binaryZH_in_g(X1)) 18.95/5.85 ADDCV_IN_GGG(one(b), zero(zero(X1)), zero(one(X1))) -> BINARYZH_IN_G(X1) 18.95/5.85 ADDCV_IN_GGG(one(b), zero(one(X1)), zero(zero(X2))) -> U49_GGG(X1, X2, succT_in_gg(X1, X2)) 18.95/5.85 ADDCV_IN_GGG(one(b), zero(one(X1)), zero(zero(X2))) -> SUCCT_IN_GG(X1, X2) 18.95/5.85 ADDCV_IN_GGG(one(X1), zero(X2), zero(X3)) -> U50_GGG(X1, X2, X3, addCV_in_ggg(X1, X2, X3)) 18.95/5.85 ADDCV_IN_GGG(one(X1), zero(X2), zero(X3)) -> ADDCV_IN_GGG(X1, X2, X3) 18.95/5.85 ADDCV_IN_GGG(one(X1), one(X2), one(X3)) -> U51_GGG(X1, X2, X3, addcS_in_ggg(X1, X2, X3)) 18.95/5.85 ADDCV_IN_GGG(one(X1), one(X2), one(X3)) -> ADDCS_IN_GGG(X1, X2, X3) 18.95/5.85 ADDC1_IN_GGG(one(X1), X2, one(X3)) -> U63_GGG(X1, X2, X3, addyR_in_ggg(X1, X2, X3)) 18.95/5.85 ADDC1_IN_GGG(one(X1), X2, one(X3)) -> ADDYR_IN_GGG(X1, X2, X3) 18.95/5.85 18.95/5.85 The TRS R consists of the following rules: 18.95/5.85 18.95/5.85 timescF_in_aaa(one(b), X1, X1) -> timescF_out_aaa(one(b), X1, X1) 18.95/5.85 timescF_in_aaa(zero(X1), X2, zero(X3)) -> U88_aaa(X1, X2, X3, timescF_in_aaa(X1, X2, X3)) 18.95/5.85 timescF_in_aaa(one(X1), X2, X3) -> U89_aaa(X1, X2, X3, timescF_in_aaa(X1, X2, X4)) 18.95/5.85 U89_aaa(X1, X2, X3, timescF_out_aaa(X1, X2, X4)) -> U90_aaa(X1, X2, X3, addcG_in_aaa(X2, X4, X3)) 18.95/5.85 addcG_in_aaa(b, X1, zero(X1)) -> U149_aaa(X1, binaryZcP_in_a(X1)) 18.95/5.85 binaryZcP_in_a(X1) -> U119_a(X1, binaryZcH_in_a(X1)) 18.95/5.85 binaryZcH_in_a(zero(X1)) -> U91_a(X1, binaryZcH_in_a(X1)) 18.95/5.85 binaryZcH_in_a(one(X1)) -> U92_a(X1, binarycI_in_a(X1)) 18.95/5.85 binarycI_in_a(b) -> binarycI_out_a(b) 18.95/5.85 binarycI_in_a(zero(X1)) -> U93_a(X1, binaryZcH_in_a(X1)) 18.95/5.85 U93_a(X1, binaryZcH_out_a(X1)) -> binarycI_out_a(zero(X1)) 18.95/5.85 binarycI_in_a(one(X1)) -> U94_a(X1, binarycI_in_a(X1)) 18.95/5.85 U94_a(X1, binarycI_out_a(X1)) -> binarycI_out_a(one(X1)) 18.95/5.85 U92_a(X1, binarycI_out_a(X1)) -> binaryZcH_out_a(one(X1)) 18.95/5.85 U91_a(X1, binaryZcH_out_a(X1)) -> binaryZcH_out_a(zero(X1)) 18.95/5.85 U119_a(X1, binaryZcH_out_a(X1)) -> binaryZcP_out_a(X1) 18.95/5.85 U149_aaa(X1, binaryZcP_out_a(X1)) -> addcG_out_aaa(b, X1, zero(X1)) 18.95/5.85 addcG_in_aaa(zero(X1), X2, zero(X3)) -> U150_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.85 addzcJ_in_aaa(zero(X1), zero(X2), zero(X3)) -> U95_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.85 addzcJ_in_aaa(zero(one(X1)), one(b), one(one(X1))) -> U96_aaa(X1, binarycI_in_a(X1)) 18.95/5.85 U96_aaa(X1, binarycI_out_a(X1)) -> addzcJ_out_aaa(zero(one(X1)), one(b), one(one(X1))) 18.95/5.85 addzcJ_in_aaa(zero(zero(X1)), one(b), one(zero(X1))) -> U97_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.85 U97_aaa(X1, binaryZcH_out_a(X1)) -> addzcJ_out_aaa(zero(zero(X1)), one(b), one(zero(X1))) 18.95/5.85 addzcJ_in_aaa(zero(X1), one(X2), one(X3)) -> U98_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.85 addzcJ_in_aaa(one(X1), zero(X2), one(X3)) -> U99_aaa(X1, X2, X3, addycK_in_aaa(X1, X2, X3)) 18.95/5.85 addycK_in_aaa(b, one(X1), one(X1)) -> U116_aaa(X1, binarycI_in_a(X1)) 18.95/5.85 U116_aaa(X1, binarycI_out_a(X1)) -> addycK_out_aaa(b, one(X1), one(X1)) 18.95/5.85 addycK_in_aaa(b, zero(X1), zero(X1)) -> U117_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.85 U117_aaa(X1, binaryZcH_out_a(X1)) -> addycK_out_aaa(b, zero(X1), zero(X1)) 18.95/5.85 addycK_in_aaa(X1, X2, X3) -> U118_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.85 addzcJ_in_aaa(one(X1), one(X2), zero(X3)) -> U100_aaa(X1, X2, X3, addccL_in_aaa(X1, X2, X3)) 18.95/5.85 addccL_in_aaa(b, b, one(b)) -> addccL_out_aaa(b, b, one(b)) 18.95/5.85 addccL_in_aaa(X1, b, X2) -> U113_aaa(X1, X2, succZcN_in_aa(X1, X2)) 18.95/5.85 succZcN_in_aa(zero(X1), one(X1)) -> U103_aa(X1, binaryZcH_in_a(X1)) 18.95/5.85 U103_aa(X1, binaryZcH_out_a(X1)) -> succZcN_out_aa(zero(X1), one(X1)) 18.95/5.85 succZcN_in_aa(one(X1), zero(X2)) -> U104_aa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.85 succcM_in_aa(b, one(b)) -> succcM_out_aa(b, one(b)) 18.95/5.85 succcM_in_aa(zero(X1), one(X1)) -> U101_aa(X1, binaryZcH_in_a(X1)) 18.95/5.85 U101_aa(X1, binaryZcH_out_a(X1)) -> succcM_out_aa(zero(X1), one(X1)) 18.95/5.85 succcM_in_aa(one(X1), zero(X2)) -> U102_aa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.85 U102_aa(X1, X2, succcM_out_aa(X1, X2)) -> succcM_out_aa(one(X1), zero(X2)) 18.95/5.85 U104_aa(X1, X2, succcM_out_aa(X1, X2)) -> succZcN_out_aa(one(X1), zero(X2)) 18.95/5.85 U113_aaa(X1, X2, succZcN_out_aa(X1, X2)) -> addccL_out_aaa(X1, b, X2) 18.95/5.85 addccL_in_aaa(b, X1, X2) -> U114_aaa(X1, X2, succZcN_in_aa(X1, X2)) 18.95/5.85 U114_aaa(X1, X2, succZcN_out_aa(X1, X2)) -> addccL_out_aaa(b, X1, X2) 18.95/5.85 addccL_in_aaa(X1, X2, X3) -> U115_aaa(X1, X2, X3, addCcO_in_aaa(X1, X2, X3)) 18.95/5.85 addCcO_in_aaa(zero(X1), zero(X2), one(X3)) -> U105_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.85 U105_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(zero(X1), zero(X2), one(X3)) 18.95/5.85 addCcO_in_aaa(zero(zero(X1)), one(b), zero(one(X1))) -> U106_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.85 U106_aaa(X1, binaryZcH_out_a(X1)) -> addCcO_out_aaa(zero(zero(X1)), one(b), zero(one(X1))) 18.95/5.85 addCcO_in_aaa(zero(one(X1)), one(b), zero(zero(X2))) -> U107_aaa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.85 U107_aaa(X1, X2, succcM_out_aa(X1, X2)) -> addCcO_out_aaa(zero(one(X1)), one(b), zero(zero(X2))) 18.95/5.85 addCcO_in_aaa(zero(X1), one(X2), zero(X3)) -> U108_aaa(X1, X2, X3, addCcO_in_aaa(X1, X2, X3)) 18.95/5.85 addCcO_in_aaa(one(b), zero(zero(X1)), zero(one(X1))) -> U109_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.85 U109_aaa(X1, binaryZcH_out_a(X1)) -> addCcO_out_aaa(one(b), zero(zero(X1)), zero(one(X1))) 18.95/5.85 addCcO_in_aaa(one(b), zero(one(X1)), zero(zero(X2))) -> U110_aaa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.85 U110_aaa(X1, X2, succcM_out_aa(X1, X2)) -> addCcO_out_aaa(one(b), zero(one(X1)), zero(zero(X2))) 18.95/5.85 addCcO_in_aaa(one(X1), zero(X2), zero(X3)) -> U111_aaa(X1, X2, X3, addCcO_in_aaa(X1, X2, X3)) 18.95/5.85 addCcO_in_aaa(one(X1), one(X2), one(X3)) -> U112_aaa(X1, X2, X3, addccL_in_aaa(X1, X2, X3)) 18.95/5.85 U112_aaa(X1, X2, X3, addccL_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(one(X1), one(X2), one(X3)) 18.95/5.85 U111_aaa(X1, X2, X3, addCcO_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(one(X1), zero(X2), zero(X3)) 18.95/5.85 U108_aaa(X1, X2, X3, addCcO_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(zero(X1), one(X2), zero(X3)) 18.95/5.85 U115_aaa(X1, X2, X3, addCcO_out_aaa(X1, X2, X3)) -> addccL_out_aaa(X1, X2, X3) 18.95/5.85 U100_aaa(X1, X2, X3, addccL_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(one(X1), one(X2), zero(X3)) 18.95/5.85 U118_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addycK_out_aaa(X1, X2, X3) 18.95/5.85 U99_aaa(X1, X2, X3, addycK_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(one(X1), zero(X2), one(X3)) 18.95/5.85 U98_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(zero(X1), one(X2), one(X3)) 18.95/5.85 U95_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(zero(X1), zero(X2), zero(X3)) 18.95/5.85 U150_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addcG_out_aaa(zero(X1), X2, zero(X3)) 18.95/5.85 addcG_in_aaa(one(X1), X2, one(X3)) -> U151_aaa(X1, X2, X3, addycK_in_aaa(X1, X2, X3)) 18.95/5.85 U151_aaa(X1, X2, X3, addycK_out_aaa(X1, X2, X3)) -> addcG_out_aaa(one(X1), X2, one(X3)) 18.95/5.85 U90_aaa(X1, X2, X3, addcG_out_aaa(X2, X4, X3)) -> timescF_out_aaa(one(X1), X2, X3) 18.95/5.85 U88_aaa(X1, X2, X3, timescF_out_aaa(X1, X2, X3)) -> timescF_out_aaa(zero(X1), X2, zero(X3)) 18.95/5.85 18.95/5.85 The argument filtering Pi contains the following mapping: 18.95/5.85 timesA_in_aag(x1, x2, x3) = timesA_in_aag(x3) 18.95/5.85 18.95/5.85 zero(x1) = zero(x1) 18.95/5.85 18.95/5.85 pB_in_aaag(x1, x2, x3, x4) = pB_in_aaag(x4) 18.95/5.85 18.95/5.85 timesF_in_aaa(x1, x2, x3) = timesF_in_aaa 18.95/5.85 18.95/5.85 timescF_in_aaa(x1, x2, x3) = timescF_in_aaa 18.95/5.85 18.95/5.85 timescF_out_aaa(x1, x2, x3) = timescF_out_aaa(x1) 18.95/5.85 18.95/5.85 U88_aaa(x1, x2, x3, x4) = U88_aaa(x4) 18.95/5.85 18.95/5.85 U89_aaa(x1, x2, x3, x4) = U89_aaa(x4) 18.95/5.85 18.95/5.85 U90_aaa(x1, x2, x3, x4) = U90_aaa(x1, x4) 18.95/5.85 18.95/5.85 addcG_in_aaa(x1, x2, x3) = addcG_in_aaa 18.95/5.85 18.95/5.85 U149_aaa(x1, x2) = U149_aaa(x2) 18.95/5.85 18.95/5.85 binaryZcP_in_a(x1) = binaryZcP_in_a 18.95/5.85 18.95/5.85 U119_a(x1, x2) = U119_a(x2) 18.95/5.85 18.95/5.85 binaryZcH_in_a(x1) = binaryZcH_in_a 18.95/5.85 18.95/5.85 U91_a(x1, x2) = U91_a(x2) 18.95/5.85 18.95/5.85 U92_a(x1, x2) = U92_a(x2) 18.95/5.85 18.95/5.85 binarycI_in_a(x1) = binarycI_in_a 18.95/5.85 18.95/5.85 binarycI_out_a(x1) = binarycI_out_a(x1) 18.95/5.85 18.95/5.85 U93_a(x1, x2) = U93_a(x2) 18.95/5.85 18.95/5.85 binaryZcH_out_a(x1) = binaryZcH_out_a(x1) 18.95/5.85 18.95/5.85 U94_a(x1, x2) = U94_a(x2) 18.95/5.85 18.95/5.85 binaryZcP_out_a(x1) = binaryZcP_out_a(x1) 18.95/5.85 18.95/5.85 addcG_out_aaa(x1, x2, x3) = addcG_out_aaa(x1, x2, x3) 18.95/5.85 18.95/5.85 U150_aaa(x1, x2, x3, x4) = U150_aaa(x4) 18.95/5.85 18.95/5.85 addzcJ_in_aaa(x1, x2, x3) = addzcJ_in_aaa 18.95/5.85 18.95/5.85 U95_aaa(x1, x2, x3, x4) = U95_aaa(x4) 18.95/5.85 18.95/5.85 U96_aaa(x1, x2) = U96_aaa(x2) 18.95/5.85 18.95/5.85 addzcJ_out_aaa(x1, x2, x3) = addzcJ_out_aaa(x1, x2, x3) 18.95/5.85 18.95/5.85 U97_aaa(x1, x2) = U97_aaa(x2) 18.95/5.85 18.95/5.85 U98_aaa(x1, x2, x3, x4) = U98_aaa(x4) 18.95/5.85 18.95/5.85 U99_aaa(x1, x2, x3, x4) = U99_aaa(x4) 18.95/5.85 18.95/5.85 addycK_in_aaa(x1, x2, x3) = addycK_in_aaa 18.95/5.85 18.95/5.85 U116_aaa(x1, x2) = U116_aaa(x2) 18.95/5.85 18.95/5.85 addycK_out_aaa(x1, x2, x3) = addycK_out_aaa(x1, x2, x3) 18.95/5.85 18.95/5.85 U117_aaa(x1, x2) = U117_aaa(x2) 18.95/5.85 18.95/5.85 U118_aaa(x1, x2, x3, x4) = U118_aaa(x4) 18.95/5.85 18.95/5.85 U100_aaa(x1, x2, x3, x4) = U100_aaa(x4) 18.95/5.85 18.95/5.85 addccL_in_aaa(x1, x2, x3) = addccL_in_aaa 18.95/5.85 18.95/5.85 addccL_out_aaa(x1, x2, x3) = addccL_out_aaa(x1, x2, x3) 18.95/5.85 18.95/5.85 U113_aaa(x1, x2, x3) = U113_aaa(x3) 18.95/5.85 18.95/5.85 succZcN_in_aa(x1, x2) = succZcN_in_aa 18.95/5.85 18.95/5.85 U103_aa(x1, x2) = U103_aa(x2) 18.95/5.85 18.95/5.85 succZcN_out_aa(x1, x2) = succZcN_out_aa(x1, x2) 18.95/5.85 18.95/5.85 U104_aa(x1, x2, x3) = U104_aa(x3) 18.95/5.85 18.95/5.85 succcM_in_aa(x1, x2) = succcM_in_aa 18.95/5.85 18.95/5.85 succcM_out_aa(x1, x2) = succcM_out_aa(x1, x2) 18.95/5.85 18.95/5.85 U101_aa(x1, x2) = U101_aa(x2) 18.95/5.85 18.95/5.85 U102_aa(x1, x2, x3) = U102_aa(x3) 18.95/5.85 18.95/5.85 U114_aaa(x1, x2, x3) = U114_aaa(x3) 18.95/5.85 18.95/5.85 U115_aaa(x1, x2, x3, x4) = U115_aaa(x4) 18.95/5.85 18.95/5.85 addCcO_in_aaa(x1, x2, x3) = addCcO_in_aaa 18.95/5.85 18.95/5.85 U105_aaa(x1, x2, x3, x4) = U105_aaa(x4) 18.95/5.85 18.95/5.85 addCcO_out_aaa(x1, x2, x3) = addCcO_out_aaa(x1, x2, x3) 18.95/5.85 18.95/5.85 U106_aaa(x1, x2) = U106_aaa(x2) 18.95/5.85 18.95/5.85 U107_aaa(x1, x2, x3) = U107_aaa(x3) 18.95/5.85 18.95/5.85 U108_aaa(x1, x2, x3, x4) = U108_aaa(x4) 18.95/5.85 18.95/5.85 U109_aaa(x1, x2) = U109_aaa(x2) 18.95/5.85 18.95/5.85 U110_aaa(x1, x2, x3) = U110_aaa(x3) 18.95/5.85 18.95/5.85 U111_aaa(x1, x2, x3, x4) = U111_aaa(x4) 18.95/5.85 18.95/5.85 U112_aaa(x1, x2, x3, x4) = U112_aaa(x4) 18.95/5.85 18.95/5.85 U151_aaa(x1, x2, x3, x4) = U151_aaa(x4) 18.95/5.85 18.95/5.85 addG_in_aaa(x1, x2, x3) = addG_in_aaa 18.95/5.85 18.95/5.85 binaryZP_in_a(x1) = binaryZP_in_a 18.95/5.85 18.95/5.85 binaryZH_in_a(x1) = binaryZH_in_a 18.95/5.85 18.95/5.85 binaryI_in_a(x1) = binaryI_in_a 18.95/5.85 18.95/5.85 addzJ_in_aaa(x1, x2, x3) = addzJ_in_aaa 18.95/5.85 18.95/5.85 addyK_in_aaa(x1, x2, x3) = addyK_in_aaa 18.95/5.85 18.95/5.85 addcL_in_aaa(x1, x2, x3) = addcL_in_aaa 18.95/5.85 18.95/5.85 succZN_in_aa(x1, x2) = succZN_in_aa 18.95/5.85 18.95/5.85 succM_in_aa(x1, x2) = succM_in_aa 18.95/5.85 18.95/5.85 addCO_in_aaa(x1, x2, x3) = addCO_in_aaa 18.95/5.85 18.95/5.85 addC1_in_aag(x1, x2, x3) = addC1_in_aag(x3) 18.95/5.85 18.95/5.85 binaryZP_in_g(x1) = binaryZP_in_g(x1) 18.95/5.85 18.95/5.85 binaryZH_in_g(x1) = binaryZH_in_g(x1) 18.95/5.85 18.95/5.85 one(x1) = one(x1) 18.95/5.85 18.95/5.85 binaryI_in_g(x1) = binaryI_in_g(x1) 18.95/5.85 18.95/5.85 addzQ_in_aag(x1, x2, x3) = addzQ_in_aag(x3) 18.95/5.85 18.95/5.85 addyR_in_aag(x1, x2, x3) = addyR_in_aag(x3) 18.95/5.85 18.95/5.85 addcS_in_aag(x1, x2, x3) = addcS_in_aag(x3) 18.95/5.85 18.95/5.85 succZU_in_ag(x1, x2) = succZU_in_ag(x2) 18.95/5.85 18.95/5.85 succT_in_ag(x1, x2) = succT_in_ag(x2) 18.95/5.85 18.95/5.85 addCV_in_aag(x1, x2, x3) = addCV_in_aag(x3) 18.95/5.85 18.95/5.85 pD_in_aaag(x1, x2, x3, x4) = pD_in_aaag(x4) 18.95/5.85 18.95/5.85 pE_in_aaaag(x1, x2, x3, x4, x5) = pE_in_aaaag(x5) 18.95/5.85 18.95/5.85 addC1_in_ggg(x1, x2, x3) = addC1_in_ggg(x1, x2, x3) 18.95/5.85 18.95/5.85 b = b 18.95/5.85 18.95/5.85 addzQ_in_ggg(x1, x2, x3) = addzQ_in_ggg(x1, x2, x3) 18.95/5.85 18.95/5.85 addyR_in_ggg(x1, x2, x3) = addyR_in_ggg(x1, x2, x3) 18.95/5.85 18.95/5.85 addcS_in_ggg(x1, x2, x3) = addcS_in_ggg(x1, x2, x3) 18.95/5.85 18.95/5.85 succZU_in_gg(x1, x2) = succZU_in_gg(x1, x2) 18.95/5.85 18.95/5.85 succT_in_gg(x1, x2) = succT_in_gg(x1, x2) 18.95/5.85 18.95/5.85 addCV_in_ggg(x1, x2, x3) = addCV_in_ggg(x1, x2, x3) 18.95/5.85 18.95/5.85 TIMESA_IN_AAG(x1, x2, x3) = TIMESA_IN_AAG(x3) 18.95/5.85 18.95/5.85 U75_AAG(x1, x2, x3, x4) = U75_AAG(x3, x4) 18.95/5.85 18.95/5.85 U76_AAG(x1, x2, x3, x4) = U76_AAG(x3, x4) 18.95/5.85 18.95/5.85 PB_IN_AAAG(x1, x2, x3, x4) = PB_IN_AAAG(x4) 18.95/5.85 18.95/5.85 U58_AAAG(x1, x2, x3, x4, x5) = U58_AAAG(x4, x5) 18.95/5.85 18.95/5.85 TIMESF_IN_AAA(x1, x2, x3) = TIMESF_IN_AAA 18.95/5.85 18.95/5.85 U1_AAA(x1, x2, x3, x4) = U1_AAA(x4) 18.95/5.85 18.95/5.85 U2_AAA(x1, x2, x3, x4) = U2_AAA(x4) 18.95/5.85 18.95/5.85 U3_AAA(x1, x2, x3, x4) = U3_AAA(x4) 18.95/5.85 18.95/5.85 U4_AAA(x1, x2, x3, x4) = U4_AAA(x1, x4) 18.95/5.85 18.95/5.85 ADDG_IN_AAA(x1, x2, x3) = ADDG_IN_AAA 18.95/5.85 18.95/5.85 U64_AAA(x1, x2) = U64_AAA(x2) 18.95/5.85 18.95/5.85 BINARYZP_IN_A(x1) = BINARYZP_IN_A 18.95/5.85 18.95/5.85 U33_A(x1, x2) = U33_A(x2) 18.95/5.85 18.95/5.85 BINARYZH_IN_A(x1) = BINARYZH_IN_A 18.95/5.85 18.95/5.85 U5_A(x1, x2) = U5_A(x2) 18.95/5.85 18.95/5.85 U6_A(x1, x2) = U6_A(x2) 18.95/5.85 18.95/5.85 BINARYI_IN_A(x1) = BINARYI_IN_A 18.95/5.85 18.95/5.85 U7_A(x1, x2) = U7_A(x2) 18.95/5.85 18.95/5.85 U8_A(x1, x2) = U8_A(x2) 18.95/5.85 18.95/5.85 U65_AAA(x1, x2, x3, x4) = U65_AAA(x4) 18.95/5.85 18.95/5.85 ADDZJ_IN_AAA(x1, x2, x3) = ADDZJ_IN_AAA 18.95/5.85 18.95/5.85 U9_AAA(x1, x2, x3, x4) = U9_AAA(x4) 18.95/5.85 18.95/5.85 U10_AAA(x1, x2) = U10_AAA(x2) 18.95/5.85 18.95/5.85 U11_AAA(x1, x2) = U11_AAA(x2) 18.95/5.85 18.95/5.85 U12_AAA(x1, x2, x3, x4) = U12_AAA(x4) 18.95/5.85 18.95/5.85 U13_AAA(x1, x2, x3, x4) = U13_AAA(x4) 18.95/5.85 18.95/5.85 ADDYK_IN_AAA(x1, x2, x3) = ADDYK_IN_AAA 18.95/5.85 18.95/5.85 U30_AAA(x1, x2) = U30_AAA(x2) 18.95/5.85 18.95/5.85 U31_AAA(x1, x2) = U31_AAA(x2) 18.95/5.85 18.95/5.85 U32_AAA(x1, x2, x3, x4) = U32_AAA(x4) 18.95/5.85 18.95/5.85 U14_AAA(x1, x2, x3, x4) = U14_AAA(x4) 18.95/5.85 18.95/5.85 ADDCL_IN_AAA(x1, x2, x3) = ADDCL_IN_AAA 18.95/5.85 18.95/5.85 U27_AAA(x1, x2, x3) = U27_AAA(x3) 18.95/5.85 18.95/5.85 SUCCZN_IN_AA(x1, x2) = SUCCZN_IN_AA 18.95/5.85 18.95/5.85 U17_AA(x1, x2) = U17_AA(x2) 18.95/5.85 18.95/5.85 U18_AA(x1, x2, x3) = U18_AA(x3) 18.95/5.85 18.95/5.85 SUCCM_IN_AA(x1, x2) = SUCCM_IN_AA 18.95/5.85 18.95/5.85 U15_AA(x1, x2) = U15_AA(x2) 18.95/5.85 18.95/5.85 U16_AA(x1, x2, x3) = U16_AA(x3) 18.95/5.85 18.95/5.85 U28_AAA(x1, x2, x3) = U28_AAA(x3) 18.95/5.85 18.95/5.85 U29_AAA(x1, x2, x3, x4) = U29_AAA(x4) 18.95/5.85 18.95/5.85 ADDCO_IN_AAA(x1, x2, x3) = ADDCO_IN_AAA 18.95/5.85 18.95/5.85 U19_AAA(x1, x2, x3, x4) = U19_AAA(x4) 18.95/5.85 18.95/5.85 U20_AAA(x1, x2) = U20_AAA(x2) 18.95/5.85 18.95/5.85 U21_AAA(x1, x2, x3) = U21_AAA(x3) 18.95/5.85 18.95/5.85 U22_AAA(x1, x2, x3, x4) = U22_AAA(x4) 18.95/5.85 18.95/5.85 U23_AAA(x1, x2) = U23_AAA(x2) 18.95/5.85 18.95/5.85 U24_AAA(x1, x2, x3) = U24_AAA(x3) 18.95/5.85 18.95/5.85 U25_AAA(x1, x2, x3, x4) = U25_AAA(x4) 18.95/5.85 18.95/5.85 U26_AAA(x1, x2, x3, x4) = U26_AAA(x4) 18.95/5.85 18.95/5.85 U66_AAA(x1, x2, x3, x4) = U66_AAA(x4) 18.95/5.85 18.95/5.85 U59_AAAG(x1, x2, x3, x4, x5) = U59_AAAG(x4, x5) 18.95/5.85 18.95/5.85 U60_AAAG(x1, x2, x3, x4, x5) = U60_AAAG(x1, x4, x5) 18.95/5.85 18.95/5.85 ADDC1_IN_AAG(x1, x2, x3) = ADDC1_IN_AAG(x3) 18.95/5.85 18.95/5.85 U61_AAG(x1, x2) = U61_AAG(x1, x2) 18.95/5.85 18.95/5.85 BINARYZP_IN_G(x1) = BINARYZP_IN_G(x1) 18.95/5.85 18.95/5.85 U33_G(x1, x2) = U33_G(x1, x2) 18.95/5.85 18.95/5.85 BINARYZH_IN_G(x1) = BINARYZH_IN_G(x1) 18.95/5.85 18.95/5.85 U5_G(x1, x2) = U5_G(x1, x2) 18.95/5.85 18.95/5.85 U6_G(x1, x2) = U6_G(x1, x2) 18.95/5.85 18.95/5.85 BINARYI_IN_G(x1) = BINARYI_IN_G(x1) 18.95/5.85 18.95/5.85 U7_G(x1, x2) = U7_G(x1, x2) 18.95/5.85 18.95/5.85 U8_G(x1, x2) = U8_G(x1, x2) 18.95/5.85 18.95/5.85 U62_AAG(x1, x2, x3, x4) = U62_AAG(x3, x4) 18.95/5.85 18.95/5.85 ADDZQ_IN_AAG(x1, x2, x3) = ADDZQ_IN_AAG(x3) 18.95/5.85 18.95/5.85 U34_AAG(x1, x2, x3, x4) = U34_AAG(x3, x4) 18.95/5.85 18.95/5.85 U35_AAG(x1, x2) = U35_AAG(x1, x2) 18.95/5.85 18.95/5.85 U36_AAG(x1, x2) = U36_AAG(x1, x2) 18.95/5.85 18.95/5.85 U37_AAG(x1, x2, x3, x4) = U37_AAG(x3, x4) 18.95/5.85 18.95/5.85 U38_AAG(x1, x2, x3, x4) = U38_AAG(x3, x4) 18.95/5.85 18.95/5.85 ADDYR_IN_AAG(x1, x2, x3) = ADDYR_IN_AAG(x3) 18.95/5.85 18.95/5.85 U55_AAG(x1, x2) = U55_AAG(x1, x2) 18.95/5.85 18.95/5.85 U56_AAG(x1, x2) = U56_AAG(x1, x2) 18.95/5.85 18.95/5.85 U57_AAG(x1, x2, x3, x4) = U57_AAG(x3, x4) 18.95/5.85 18.95/5.85 U39_AAG(x1, x2, x3, x4) = U39_AAG(x3, x4) 18.95/5.85 18.95/5.85 ADDCS_IN_AAG(x1, x2, x3) = ADDCS_IN_AAG(x3) 18.95/5.85 18.95/5.85 U52_AAG(x1, x2, x3) = U52_AAG(x2, x3) 18.95/5.85 18.95/5.85 SUCCZU_IN_AG(x1, x2) = SUCCZU_IN_AG(x2) 18.95/5.85 18.95/5.85 U42_AG(x1, x2) = U42_AG(x1, x2) 18.95/5.85 18.95/5.85 U43_AG(x1, x2, x3) = U43_AG(x2, x3) 18.95/5.85 18.95/5.85 SUCCT_IN_AG(x1, x2) = SUCCT_IN_AG(x2) 18.95/5.85 18.95/5.85 U40_AG(x1, x2) = U40_AG(x1, x2) 18.95/5.85 18.95/5.85 U41_AG(x1, x2, x3) = U41_AG(x2, x3) 18.95/5.85 18.95/5.85 U53_AAG(x1, x2, x3) = U53_AAG(x2, x3) 18.95/5.85 18.95/5.85 U54_AAG(x1, x2, x3, x4) = U54_AAG(x3, x4) 18.95/5.85 18.95/5.85 ADDCV_IN_AAG(x1, x2, x3) = ADDCV_IN_AAG(x3) 18.95/5.85 18.95/5.85 U44_AAG(x1, x2, x3, x4) = U44_AAG(x3, x4) 18.95/5.85 18.95/5.85 U45_AAG(x1, x2) = U45_AAG(x1, x2) 18.95/5.85 18.95/5.85 U46_AAG(x1, x2, x3) = U46_AAG(x2, x3) 18.95/5.85 18.95/5.85 U47_AAG(x1, x2, x3, x4) = U47_AAG(x3, x4) 18.95/5.85 18.95/5.85 U48_AAG(x1, x2) = U48_AAG(x1, x2) 18.95/5.85 18.95/5.85 U49_AAG(x1, x2, x3) = U49_AAG(x2, x3) 18.95/5.85 18.95/5.85 U50_AAG(x1, x2, x3, x4) = U50_AAG(x3, x4) 18.95/5.85 18.95/5.85 U51_AAG(x1, x2, x3, x4) = U51_AAG(x3, x4) 18.95/5.85 18.95/5.85 U63_AAG(x1, x2, x3, x4) = U63_AAG(x3, x4) 18.95/5.85 18.95/5.85 U77_AAG(x1, x2, x3, x4) = U77_AAG(x3, x4) 18.95/5.85 18.95/5.85 U78_AAG(x1, x2, x3) = U78_AAG(x2, x3) 18.95/5.85 18.95/5.85 U79_AAG(x1, x2, x3, x4) = U79_AAG(x3, x4) 18.95/5.85 18.95/5.85 PD_IN_AAAG(x1, x2, x3, x4) = PD_IN_AAAG(x4) 18.95/5.85 18.95/5.85 U67_AAAG(x1, x2, x3, x4, x5) = U67_AAAG(x4, x5) 18.95/5.85 18.95/5.85 U68_AAAG(x1, x2, x3, x4, x5) = U68_AAAG(x4, x5) 18.95/5.85 18.95/5.85 U69_AAAG(x1, x2, x3, x4, x5) = U69_AAAG(x1, x4, x5) 18.95/5.85 18.95/5.85 U80_AAG(x1, x2, x3, x4) = U80_AAG(x3, x4) 18.95/5.85 18.95/5.85 PE_IN_AAAAG(x1, x2, x3, x4, x5) = PE_IN_AAAAG(x5) 18.95/5.85 18.95/5.85 U70_AAAAG(x1, x2, x3, x4, x5, x6) = U70_AAAAG(x5, x6) 18.95/5.85 18.95/5.85 U71_AAAAG(x1, x2, x3, x4, x5, x6) = U71_AAAAG(x5, x6) 18.95/5.85 18.95/5.85 U72_AAAAG(x1, x2, x3, x4, x5, x6) = U72_AAAAG(x1, x5, x6) 18.95/5.85 18.95/5.85 U73_AAAAG(x1, x2, x3, x4, x5, x6) = U73_AAAAG(x1, x5, x6) 18.95/5.85 18.95/5.85 U74_AAAAG(x1, x2, x3, x4, x5, x6) = U74_AAAAG(x1, x2, x5, x6) 18.95/5.85 18.95/5.85 ADDC1_IN_GGG(x1, x2, x3) = ADDC1_IN_GGG(x1, x2, x3) 18.95/5.85 18.95/5.85 U61_GGG(x1, x2) = U61_GGG(x1, x2) 18.95/5.85 18.95/5.85 U62_GGG(x1, x2, x3, x4) = U62_GGG(x1, x2, x3, x4) 18.95/5.85 18.95/5.85 ADDZQ_IN_GGG(x1, x2, x3) = ADDZQ_IN_GGG(x1, x2, x3) 18.95/5.85 18.95/5.85 U34_GGG(x1, x2, x3, x4) = U34_GGG(x1, x2, x3, x4) 18.95/5.85 18.95/5.85 U35_GGG(x1, x2) = U35_GGG(x1, x2) 18.95/5.85 18.95/5.85 U36_GGG(x1, x2) = U36_GGG(x1, x2) 18.95/5.85 18.95/5.85 U37_GGG(x1, x2, x3, x4) = U37_GGG(x1, x2, x3, x4) 18.95/5.85 18.95/5.85 U38_GGG(x1, x2, x3, x4) = U38_GGG(x1, x2, x3, x4) 18.95/5.85 18.95/5.85 ADDYR_IN_GGG(x1, x2, x3) = ADDYR_IN_GGG(x1, x2, x3) 18.95/5.85 18.95/5.85 U55_GGG(x1, x2) = U55_GGG(x1, x2) 18.95/5.85 18.95/5.85 U56_GGG(x1, x2) = U56_GGG(x1, x2) 18.95/5.85 18.95/5.85 U57_GGG(x1, x2, x3, x4) = U57_GGG(x1, x2, x3, x4) 18.95/5.85 18.95/5.85 U39_GGG(x1, x2, x3, x4) = U39_GGG(x1, x2, x3, x4) 18.95/5.85 18.95/5.85 ADDCS_IN_GGG(x1, x2, x3) = ADDCS_IN_GGG(x1, x2, x3) 18.95/5.85 18.95/5.85 U52_GGG(x1, x2, x3) = U52_GGG(x1, x2, x3) 18.95/5.85 18.95/5.85 SUCCZU_IN_GG(x1, x2) = SUCCZU_IN_GG(x1, x2) 18.95/5.85 18.95/5.85 U42_GG(x1, x2) = U42_GG(x1, x2) 18.95/5.85 18.95/5.85 U43_GG(x1, x2, x3) = U43_GG(x1, x2, x3) 18.95/5.85 18.95/5.85 SUCCT_IN_GG(x1, x2) = SUCCT_IN_GG(x1, x2) 18.95/5.85 18.95/5.85 U40_GG(x1, x2) = U40_GG(x1, x2) 18.95/5.85 18.95/5.85 U41_GG(x1, x2, x3) = U41_GG(x1, x2, x3) 18.95/5.85 18.95/5.85 U53_GGG(x1, x2, x3) = U53_GGG(x1, x2, x3) 18.95/5.85 18.95/5.85 U54_GGG(x1, x2, x3, x4) = U54_GGG(x1, x2, x3, x4) 18.95/5.85 18.95/5.85 ADDCV_IN_GGG(x1, x2, x3) = ADDCV_IN_GGG(x1, x2, x3) 18.95/5.85 18.95/5.85 U44_GGG(x1, x2, x3, x4) = U44_GGG(x1, x2, x3, x4) 18.95/5.85 18.95/5.85 U45_GGG(x1, x2) = U45_GGG(x1, x2) 18.95/5.85 18.95/5.85 U46_GGG(x1, x2, x3) = U46_GGG(x1, x2, x3) 18.95/5.85 18.95/5.85 U47_GGG(x1, x2, x3, x4) = U47_GGG(x1, x2, x3, x4) 18.95/5.85 18.95/5.85 U48_GGG(x1, x2) = U48_GGG(x1, x2) 18.95/5.85 18.95/5.85 U49_GGG(x1, x2, x3) = U49_GGG(x1, x2, x3) 18.95/5.85 18.95/5.85 U50_GGG(x1, x2, x3, x4) = U50_GGG(x1, x2, x3, x4) 18.95/5.85 18.95/5.85 U51_GGG(x1, x2, x3, x4) = U51_GGG(x1, x2, x3, x4) 18.95/5.85 18.95/5.85 U63_GGG(x1, x2, x3, x4) = U63_GGG(x1, x2, x3, x4) 18.95/5.85 18.95/5.85 18.95/5.85 We have to consider all (P,R,Pi)-chains 18.95/5.85 ---------------------------------------- 18.95/5.85 18.95/5.85 (139) DependencyGraphProof (EQUIVALENT) 18.95/5.85 The approximation of the Dependency Graph [LOPSTR] contains 10 SCCs with 175 less nodes. 18.95/5.85 ---------------------------------------- 18.95/5.85 18.95/5.85 (140) 18.95/5.85 Complex Obligation (AND) 18.95/5.85 18.95/5.85 ---------------------------------------- 18.95/5.85 18.95/5.85 (141) 18.95/5.85 Obligation: 18.95/5.85 Pi DP problem: 18.95/5.85 The TRS P consists of the following rules: 18.95/5.85 18.95/5.85 BINARYZH_IN_G(one(X1)) -> BINARYI_IN_G(X1) 18.95/5.85 BINARYI_IN_G(zero(X1)) -> BINARYZH_IN_G(X1) 18.95/5.85 BINARYZH_IN_G(zero(X1)) -> BINARYZH_IN_G(X1) 18.95/5.85 BINARYI_IN_G(one(X1)) -> BINARYI_IN_G(X1) 18.95/5.85 18.95/5.85 The TRS R consists of the following rules: 18.95/5.85 18.95/5.85 timescF_in_aaa(one(b), X1, X1) -> timescF_out_aaa(one(b), X1, X1) 18.95/5.85 timescF_in_aaa(zero(X1), X2, zero(X3)) -> U88_aaa(X1, X2, X3, timescF_in_aaa(X1, X2, X3)) 18.95/5.85 timescF_in_aaa(one(X1), X2, X3) -> U89_aaa(X1, X2, X3, timescF_in_aaa(X1, X2, X4)) 18.95/5.85 U89_aaa(X1, X2, X3, timescF_out_aaa(X1, X2, X4)) -> U90_aaa(X1, X2, X3, addcG_in_aaa(X2, X4, X3)) 18.95/5.85 addcG_in_aaa(b, X1, zero(X1)) -> U149_aaa(X1, binaryZcP_in_a(X1)) 18.95/5.85 binaryZcP_in_a(X1) -> U119_a(X1, binaryZcH_in_a(X1)) 18.95/5.85 binaryZcH_in_a(zero(X1)) -> U91_a(X1, binaryZcH_in_a(X1)) 18.95/5.85 binaryZcH_in_a(one(X1)) -> U92_a(X1, binarycI_in_a(X1)) 18.95/5.85 binarycI_in_a(b) -> binarycI_out_a(b) 18.95/5.85 binarycI_in_a(zero(X1)) -> U93_a(X1, binaryZcH_in_a(X1)) 18.95/5.85 U93_a(X1, binaryZcH_out_a(X1)) -> binarycI_out_a(zero(X1)) 18.95/5.85 binarycI_in_a(one(X1)) -> U94_a(X1, binarycI_in_a(X1)) 18.95/5.85 U94_a(X1, binarycI_out_a(X1)) -> binarycI_out_a(one(X1)) 18.95/5.85 U92_a(X1, binarycI_out_a(X1)) -> binaryZcH_out_a(one(X1)) 18.95/5.85 U91_a(X1, binaryZcH_out_a(X1)) -> binaryZcH_out_a(zero(X1)) 18.95/5.85 U119_a(X1, binaryZcH_out_a(X1)) -> binaryZcP_out_a(X1) 18.95/5.85 U149_aaa(X1, binaryZcP_out_a(X1)) -> addcG_out_aaa(b, X1, zero(X1)) 18.95/5.85 addcG_in_aaa(zero(X1), X2, zero(X3)) -> U150_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.85 addzcJ_in_aaa(zero(X1), zero(X2), zero(X3)) -> U95_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.85 addzcJ_in_aaa(zero(one(X1)), one(b), one(one(X1))) -> U96_aaa(X1, binarycI_in_a(X1)) 18.95/5.85 U96_aaa(X1, binarycI_out_a(X1)) -> addzcJ_out_aaa(zero(one(X1)), one(b), one(one(X1))) 18.95/5.85 addzcJ_in_aaa(zero(zero(X1)), one(b), one(zero(X1))) -> U97_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.85 U97_aaa(X1, binaryZcH_out_a(X1)) -> addzcJ_out_aaa(zero(zero(X1)), one(b), one(zero(X1))) 18.95/5.85 addzcJ_in_aaa(zero(X1), one(X2), one(X3)) -> U98_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.85 addzcJ_in_aaa(one(X1), zero(X2), one(X3)) -> U99_aaa(X1, X2, X3, addycK_in_aaa(X1, X2, X3)) 18.95/5.85 addycK_in_aaa(b, one(X1), one(X1)) -> U116_aaa(X1, binarycI_in_a(X1)) 18.95/5.85 U116_aaa(X1, binarycI_out_a(X1)) -> addycK_out_aaa(b, one(X1), one(X1)) 18.95/5.85 addycK_in_aaa(b, zero(X1), zero(X1)) -> U117_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.85 U117_aaa(X1, binaryZcH_out_a(X1)) -> addycK_out_aaa(b, zero(X1), zero(X1)) 18.95/5.85 addycK_in_aaa(X1, X2, X3) -> U118_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.85 addzcJ_in_aaa(one(X1), one(X2), zero(X3)) -> U100_aaa(X1, X2, X3, addccL_in_aaa(X1, X2, X3)) 18.95/5.85 addccL_in_aaa(b, b, one(b)) -> addccL_out_aaa(b, b, one(b)) 18.95/5.85 addccL_in_aaa(X1, b, X2) -> U113_aaa(X1, X2, succZcN_in_aa(X1, X2)) 18.95/5.85 succZcN_in_aa(zero(X1), one(X1)) -> U103_aa(X1, binaryZcH_in_a(X1)) 18.95/5.85 U103_aa(X1, binaryZcH_out_a(X1)) -> succZcN_out_aa(zero(X1), one(X1)) 18.95/5.85 succZcN_in_aa(one(X1), zero(X2)) -> U104_aa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.85 succcM_in_aa(b, one(b)) -> succcM_out_aa(b, one(b)) 18.95/5.85 succcM_in_aa(zero(X1), one(X1)) -> U101_aa(X1, binaryZcH_in_a(X1)) 18.95/5.85 U101_aa(X1, binaryZcH_out_a(X1)) -> succcM_out_aa(zero(X1), one(X1)) 18.95/5.85 succcM_in_aa(one(X1), zero(X2)) -> U102_aa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.85 U102_aa(X1, X2, succcM_out_aa(X1, X2)) -> succcM_out_aa(one(X1), zero(X2)) 18.95/5.85 U104_aa(X1, X2, succcM_out_aa(X1, X2)) -> succZcN_out_aa(one(X1), zero(X2)) 18.95/5.85 U113_aaa(X1, X2, succZcN_out_aa(X1, X2)) -> addccL_out_aaa(X1, b, X2) 18.95/5.85 addccL_in_aaa(b, X1, X2) -> U114_aaa(X1, X2, succZcN_in_aa(X1, X2)) 18.95/5.85 U114_aaa(X1, X2, succZcN_out_aa(X1, X2)) -> addccL_out_aaa(b, X1, X2) 18.95/5.85 addccL_in_aaa(X1, X2, X3) -> U115_aaa(X1, X2, X3, addCcO_in_aaa(X1, X2, X3)) 18.95/5.85 addCcO_in_aaa(zero(X1), zero(X2), one(X3)) -> U105_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.85 U105_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(zero(X1), zero(X2), one(X3)) 18.95/5.85 addCcO_in_aaa(zero(zero(X1)), one(b), zero(one(X1))) -> U106_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.85 U106_aaa(X1, binaryZcH_out_a(X1)) -> addCcO_out_aaa(zero(zero(X1)), one(b), zero(one(X1))) 18.95/5.85 addCcO_in_aaa(zero(one(X1)), one(b), zero(zero(X2))) -> U107_aaa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.85 U107_aaa(X1, X2, succcM_out_aa(X1, X2)) -> addCcO_out_aaa(zero(one(X1)), one(b), zero(zero(X2))) 18.95/5.85 addCcO_in_aaa(zero(X1), one(X2), zero(X3)) -> U108_aaa(X1, X2, X3, addCcO_in_aaa(X1, X2, X3)) 18.95/5.85 addCcO_in_aaa(one(b), zero(zero(X1)), zero(one(X1))) -> U109_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.85 U109_aaa(X1, binaryZcH_out_a(X1)) -> addCcO_out_aaa(one(b), zero(zero(X1)), zero(one(X1))) 18.95/5.85 addCcO_in_aaa(one(b), zero(one(X1)), zero(zero(X2))) -> U110_aaa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.85 U110_aaa(X1, X2, succcM_out_aa(X1, X2)) -> addCcO_out_aaa(one(b), zero(one(X1)), zero(zero(X2))) 18.95/5.85 addCcO_in_aaa(one(X1), zero(X2), zero(X3)) -> U111_aaa(X1, X2, X3, addCcO_in_aaa(X1, X2, X3)) 18.95/5.85 addCcO_in_aaa(one(X1), one(X2), one(X3)) -> U112_aaa(X1, X2, X3, addccL_in_aaa(X1, X2, X3)) 18.95/5.85 U112_aaa(X1, X2, X3, addccL_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(one(X1), one(X2), one(X3)) 18.95/5.85 U111_aaa(X1, X2, X3, addCcO_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(one(X1), zero(X2), zero(X3)) 18.95/5.85 U108_aaa(X1, X2, X3, addCcO_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(zero(X1), one(X2), zero(X3)) 18.95/5.85 U115_aaa(X1, X2, X3, addCcO_out_aaa(X1, X2, X3)) -> addccL_out_aaa(X1, X2, X3) 18.95/5.85 U100_aaa(X1, X2, X3, addccL_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(one(X1), one(X2), zero(X3)) 18.95/5.85 U118_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addycK_out_aaa(X1, X2, X3) 18.95/5.85 U99_aaa(X1, X2, X3, addycK_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(one(X1), zero(X2), one(X3)) 18.95/5.85 U98_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(zero(X1), one(X2), one(X3)) 18.95/5.85 U95_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(zero(X1), zero(X2), zero(X3)) 18.95/5.85 U150_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addcG_out_aaa(zero(X1), X2, zero(X3)) 18.95/5.85 addcG_in_aaa(one(X1), X2, one(X3)) -> U151_aaa(X1, X2, X3, addycK_in_aaa(X1, X2, X3)) 18.95/5.85 U151_aaa(X1, X2, X3, addycK_out_aaa(X1, X2, X3)) -> addcG_out_aaa(one(X1), X2, one(X3)) 18.95/5.85 U90_aaa(X1, X2, X3, addcG_out_aaa(X2, X4, X3)) -> timescF_out_aaa(one(X1), X2, X3) 18.95/5.85 U88_aaa(X1, X2, X3, timescF_out_aaa(X1, X2, X3)) -> timescF_out_aaa(zero(X1), X2, zero(X3)) 18.95/5.85 18.95/5.85 The argument filtering Pi contains the following mapping: 18.95/5.85 zero(x1) = zero(x1) 18.95/5.85 18.95/5.85 timescF_in_aaa(x1, x2, x3) = timescF_in_aaa 18.95/5.85 18.95/5.85 timescF_out_aaa(x1, x2, x3) = timescF_out_aaa(x1) 18.95/5.85 18.95/5.85 U88_aaa(x1, x2, x3, x4) = U88_aaa(x4) 18.95/5.85 18.95/5.85 U89_aaa(x1, x2, x3, x4) = U89_aaa(x4) 18.95/5.85 18.95/5.85 U90_aaa(x1, x2, x3, x4) = U90_aaa(x1, x4) 18.95/5.85 18.95/5.85 addcG_in_aaa(x1, x2, x3) = addcG_in_aaa 18.95/5.85 18.95/5.85 U149_aaa(x1, x2) = U149_aaa(x2) 18.95/5.85 18.95/5.85 binaryZcP_in_a(x1) = binaryZcP_in_a 18.95/5.85 18.95/5.85 U119_a(x1, x2) = U119_a(x2) 18.95/5.85 18.95/5.85 binaryZcH_in_a(x1) = binaryZcH_in_a 18.95/5.85 18.95/5.85 U91_a(x1, x2) = U91_a(x2) 18.95/5.85 18.95/5.85 U92_a(x1, x2) = U92_a(x2) 18.95/5.85 18.95/5.85 binarycI_in_a(x1) = binarycI_in_a 18.95/5.85 18.95/5.85 binarycI_out_a(x1) = binarycI_out_a(x1) 18.95/5.85 18.95/5.85 U93_a(x1, x2) = U93_a(x2) 18.95/5.85 18.95/5.85 binaryZcH_out_a(x1) = binaryZcH_out_a(x1) 18.95/5.85 18.95/5.85 U94_a(x1, x2) = U94_a(x2) 18.95/5.85 18.95/5.85 binaryZcP_out_a(x1) = binaryZcP_out_a(x1) 18.95/5.85 18.95/5.85 addcG_out_aaa(x1, x2, x3) = addcG_out_aaa(x1, x2, x3) 18.95/5.85 18.95/5.85 U150_aaa(x1, x2, x3, x4) = U150_aaa(x4) 18.95/5.85 18.95/5.85 addzcJ_in_aaa(x1, x2, x3) = addzcJ_in_aaa 18.95/5.85 18.95/5.85 U95_aaa(x1, x2, x3, x4) = U95_aaa(x4) 18.95/5.85 18.95/5.85 U96_aaa(x1, x2) = U96_aaa(x2) 18.95/5.85 18.95/5.85 addzcJ_out_aaa(x1, x2, x3) = addzcJ_out_aaa(x1, x2, x3) 18.95/5.85 18.95/5.85 U97_aaa(x1, x2) = U97_aaa(x2) 18.95/5.85 18.95/5.85 U98_aaa(x1, x2, x3, x4) = U98_aaa(x4) 18.95/5.85 18.95/5.85 U99_aaa(x1, x2, x3, x4) = U99_aaa(x4) 18.95/5.85 18.95/5.85 addycK_in_aaa(x1, x2, x3) = addycK_in_aaa 18.95/5.85 18.95/5.85 U116_aaa(x1, x2) = U116_aaa(x2) 18.95/5.85 18.95/5.85 addycK_out_aaa(x1, x2, x3) = addycK_out_aaa(x1, x2, x3) 18.95/5.85 18.95/5.85 U117_aaa(x1, x2) = U117_aaa(x2) 18.95/5.85 18.95/5.85 U118_aaa(x1, x2, x3, x4) = U118_aaa(x4) 18.95/5.85 18.95/5.85 U100_aaa(x1, x2, x3, x4) = U100_aaa(x4) 18.95/5.85 18.95/5.85 addccL_in_aaa(x1, x2, x3) = addccL_in_aaa 18.95/5.85 18.95/5.85 addccL_out_aaa(x1, x2, x3) = addccL_out_aaa(x1, x2, x3) 18.95/5.85 18.95/5.85 U113_aaa(x1, x2, x3) = U113_aaa(x3) 18.95/5.85 18.95/5.85 succZcN_in_aa(x1, x2) = succZcN_in_aa 18.95/5.85 18.95/5.85 U103_aa(x1, x2) = U103_aa(x2) 18.95/5.85 18.95/5.85 succZcN_out_aa(x1, x2) = succZcN_out_aa(x1, x2) 18.95/5.85 18.95/5.85 U104_aa(x1, x2, x3) = U104_aa(x3) 18.95/5.85 18.95/5.85 succcM_in_aa(x1, x2) = succcM_in_aa 18.95/5.85 18.95/5.85 succcM_out_aa(x1, x2) = succcM_out_aa(x1, x2) 18.95/5.85 18.95/5.85 U101_aa(x1, x2) = U101_aa(x2) 18.95/5.85 18.95/5.85 U102_aa(x1, x2, x3) = U102_aa(x3) 18.95/5.85 18.95/5.85 U114_aaa(x1, x2, x3) = U114_aaa(x3) 18.95/5.85 18.95/5.85 U115_aaa(x1, x2, x3, x4) = U115_aaa(x4) 18.95/5.85 18.95/5.85 addCcO_in_aaa(x1, x2, x3) = addCcO_in_aaa 18.95/5.85 18.95/5.85 U105_aaa(x1, x2, x3, x4) = U105_aaa(x4) 18.95/5.85 18.95/5.85 addCcO_out_aaa(x1, x2, x3) = addCcO_out_aaa(x1, x2, x3) 18.95/5.85 18.95/5.85 U106_aaa(x1, x2) = U106_aaa(x2) 18.95/5.85 18.95/5.85 U107_aaa(x1, x2, x3) = U107_aaa(x3) 18.95/5.85 18.95/5.85 U108_aaa(x1, x2, x3, x4) = U108_aaa(x4) 18.95/5.85 18.95/5.85 U109_aaa(x1, x2) = U109_aaa(x2) 18.95/5.85 18.95/5.85 U110_aaa(x1, x2, x3) = U110_aaa(x3) 18.95/5.85 18.95/5.85 U111_aaa(x1, x2, x3, x4) = U111_aaa(x4) 18.95/5.85 18.95/5.85 U112_aaa(x1, x2, x3, x4) = U112_aaa(x4) 18.95/5.85 18.95/5.85 U151_aaa(x1, x2, x3, x4) = U151_aaa(x4) 18.95/5.85 18.95/5.85 one(x1) = one(x1) 18.95/5.85 18.95/5.85 b = b 18.95/5.85 18.95/5.85 BINARYZH_IN_G(x1) = BINARYZH_IN_G(x1) 18.95/5.85 18.95/5.85 BINARYI_IN_G(x1) = BINARYI_IN_G(x1) 18.95/5.85 18.95/5.85 18.95/5.85 We have to consider all (P,R,Pi)-chains 18.95/5.85 ---------------------------------------- 18.95/5.85 18.95/5.85 (142) UsableRulesProof (EQUIVALENT) 18.95/5.85 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 18.95/5.85 ---------------------------------------- 18.95/5.85 18.95/5.85 (143) 18.95/5.85 Obligation: 18.95/5.85 Pi DP problem: 18.95/5.85 The TRS P consists of the following rules: 18.95/5.85 18.95/5.85 BINARYZH_IN_G(one(X1)) -> BINARYI_IN_G(X1) 18.95/5.85 BINARYI_IN_G(zero(X1)) -> BINARYZH_IN_G(X1) 18.95/5.85 BINARYZH_IN_G(zero(X1)) -> BINARYZH_IN_G(X1) 18.95/5.85 BINARYI_IN_G(one(X1)) -> BINARYI_IN_G(X1) 18.95/5.85 18.95/5.85 R is empty. 18.95/5.85 Pi is empty. 18.95/5.85 We have to consider all (P,R,Pi)-chains 18.95/5.85 ---------------------------------------- 18.95/5.85 18.95/5.85 (144) PiDPToQDPProof (EQUIVALENT) 18.95/5.85 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 18.95/5.85 ---------------------------------------- 18.95/5.85 18.95/5.85 (145) 18.95/5.85 Obligation: 18.95/5.85 Q DP problem: 18.95/5.85 The TRS P consists of the following rules: 18.95/5.85 18.95/5.85 BINARYZH_IN_G(one(X1)) -> BINARYI_IN_G(X1) 18.95/5.85 BINARYI_IN_G(zero(X1)) -> BINARYZH_IN_G(X1) 18.95/5.85 BINARYZH_IN_G(zero(X1)) -> BINARYZH_IN_G(X1) 18.95/5.85 BINARYI_IN_G(one(X1)) -> BINARYI_IN_G(X1) 18.95/5.85 18.95/5.85 R is empty. 18.95/5.85 Q is empty. 18.95/5.85 We have to consider all (P,Q,R)-chains. 18.95/5.85 ---------------------------------------- 18.95/5.85 18.95/5.85 (146) QDPSizeChangeProof (EQUIVALENT) 18.95/5.85 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 18.95/5.85 18.95/5.85 From the DPs we obtained the following set of size-change graphs: 18.95/5.85 *BINARYI_IN_G(zero(X1)) -> BINARYZH_IN_G(X1) 18.95/5.85 The graph contains the following edges 1 > 1 18.95/5.85 18.95/5.85 18.95/5.85 *BINARYI_IN_G(one(X1)) -> BINARYI_IN_G(X1) 18.95/5.85 The graph contains the following edges 1 > 1 18.95/5.85 18.95/5.85 18.95/5.85 *BINARYZH_IN_G(zero(X1)) -> BINARYZH_IN_G(X1) 18.95/5.85 The graph contains the following edges 1 > 1 18.95/5.85 18.95/5.85 18.95/5.85 *BINARYZH_IN_G(one(X1)) -> BINARYI_IN_G(X1) 18.95/5.85 The graph contains the following edges 1 > 1 18.95/5.85 18.95/5.85 18.95/5.85 ---------------------------------------- 18.95/5.85 18.95/5.85 (147) 18.95/5.85 YES 18.95/5.85 18.95/5.85 ---------------------------------------- 18.95/5.85 18.95/5.85 (148) 18.95/5.85 Obligation: 18.95/5.85 Pi DP problem: 18.95/5.85 The TRS P consists of the following rules: 18.95/5.85 18.95/5.85 SUCCT_IN_GG(one(X1), zero(X2)) -> SUCCT_IN_GG(X1, X2) 18.95/5.85 18.95/5.85 The TRS R consists of the following rules: 18.95/5.85 18.95/5.85 timescF_in_aaa(one(b), X1, X1) -> timescF_out_aaa(one(b), X1, X1) 18.95/5.85 timescF_in_aaa(zero(X1), X2, zero(X3)) -> U88_aaa(X1, X2, X3, timescF_in_aaa(X1, X2, X3)) 18.95/5.85 timescF_in_aaa(one(X1), X2, X3) -> U89_aaa(X1, X2, X3, timescF_in_aaa(X1, X2, X4)) 18.95/5.85 U89_aaa(X1, X2, X3, timescF_out_aaa(X1, X2, X4)) -> U90_aaa(X1, X2, X3, addcG_in_aaa(X2, X4, X3)) 18.95/5.85 addcG_in_aaa(b, X1, zero(X1)) -> U149_aaa(X1, binaryZcP_in_a(X1)) 18.95/5.85 binaryZcP_in_a(X1) -> U119_a(X1, binaryZcH_in_a(X1)) 18.95/5.85 binaryZcH_in_a(zero(X1)) -> U91_a(X1, binaryZcH_in_a(X1)) 18.95/5.85 binaryZcH_in_a(one(X1)) -> U92_a(X1, binarycI_in_a(X1)) 18.95/5.85 binarycI_in_a(b) -> binarycI_out_a(b) 18.95/5.85 binarycI_in_a(zero(X1)) -> U93_a(X1, binaryZcH_in_a(X1)) 18.95/5.85 U93_a(X1, binaryZcH_out_a(X1)) -> binarycI_out_a(zero(X1)) 18.95/5.85 binarycI_in_a(one(X1)) -> U94_a(X1, binarycI_in_a(X1)) 18.95/5.85 U94_a(X1, binarycI_out_a(X1)) -> binarycI_out_a(one(X1)) 18.95/5.85 U92_a(X1, binarycI_out_a(X1)) -> binaryZcH_out_a(one(X1)) 18.95/5.85 U91_a(X1, binaryZcH_out_a(X1)) -> binaryZcH_out_a(zero(X1)) 18.95/5.85 U119_a(X1, binaryZcH_out_a(X1)) -> binaryZcP_out_a(X1) 18.95/5.85 U149_aaa(X1, binaryZcP_out_a(X1)) -> addcG_out_aaa(b, X1, zero(X1)) 18.95/5.85 addcG_in_aaa(zero(X1), X2, zero(X3)) -> U150_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.85 addzcJ_in_aaa(zero(X1), zero(X2), zero(X3)) -> U95_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.85 addzcJ_in_aaa(zero(one(X1)), one(b), one(one(X1))) -> U96_aaa(X1, binarycI_in_a(X1)) 18.95/5.85 U96_aaa(X1, binarycI_out_a(X1)) -> addzcJ_out_aaa(zero(one(X1)), one(b), one(one(X1))) 18.95/5.85 addzcJ_in_aaa(zero(zero(X1)), one(b), one(zero(X1))) -> U97_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.85 U97_aaa(X1, binaryZcH_out_a(X1)) -> addzcJ_out_aaa(zero(zero(X1)), one(b), one(zero(X1))) 18.95/5.85 addzcJ_in_aaa(zero(X1), one(X2), one(X3)) -> U98_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.85 addzcJ_in_aaa(one(X1), zero(X2), one(X3)) -> U99_aaa(X1, X2, X3, addycK_in_aaa(X1, X2, X3)) 18.95/5.85 addycK_in_aaa(b, one(X1), one(X1)) -> U116_aaa(X1, binarycI_in_a(X1)) 18.95/5.85 U116_aaa(X1, binarycI_out_a(X1)) -> addycK_out_aaa(b, one(X1), one(X1)) 18.95/5.85 addycK_in_aaa(b, zero(X1), zero(X1)) -> U117_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.85 U117_aaa(X1, binaryZcH_out_a(X1)) -> addycK_out_aaa(b, zero(X1), zero(X1)) 18.95/5.85 addycK_in_aaa(X1, X2, X3) -> U118_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.85 addzcJ_in_aaa(one(X1), one(X2), zero(X3)) -> U100_aaa(X1, X2, X3, addccL_in_aaa(X1, X2, X3)) 18.95/5.85 addccL_in_aaa(b, b, one(b)) -> addccL_out_aaa(b, b, one(b)) 18.95/5.85 addccL_in_aaa(X1, b, X2) -> U113_aaa(X1, X2, succZcN_in_aa(X1, X2)) 18.95/5.85 succZcN_in_aa(zero(X1), one(X1)) -> U103_aa(X1, binaryZcH_in_a(X1)) 18.95/5.85 U103_aa(X1, binaryZcH_out_a(X1)) -> succZcN_out_aa(zero(X1), one(X1)) 18.95/5.85 succZcN_in_aa(one(X1), zero(X2)) -> U104_aa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.85 succcM_in_aa(b, one(b)) -> succcM_out_aa(b, one(b)) 18.95/5.85 succcM_in_aa(zero(X1), one(X1)) -> U101_aa(X1, binaryZcH_in_a(X1)) 18.95/5.85 U101_aa(X1, binaryZcH_out_a(X1)) -> succcM_out_aa(zero(X1), one(X1)) 18.95/5.85 succcM_in_aa(one(X1), zero(X2)) -> U102_aa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.85 U102_aa(X1, X2, succcM_out_aa(X1, X2)) -> succcM_out_aa(one(X1), zero(X2)) 18.95/5.85 U104_aa(X1, X2, succcM_out_aa(X1, X2)) -> succZcN_out_aa(one(X1), zero(X2)) 18.95/5.85 U113_aaa(X1, X2, succZcN_out_aa(X1, X2)) -> addccL_out_aaa(X1, b, X2) 18.95/5.85 addccL_in_aaa(b, X1, X2) -> U114_aaa(X1, X2, succZcN_in_aa(X1, X2)) 18.95/5.85 U114_aaa(X1, X2, succZcN_out_aa(X1, X2)) -> addccL_out_aaa(b, X1, X2) 18.95/5.85 addccL_in_aaa(X1, X2, X3) -> U115_aaa(X1, X2, X3, addCcO_in_aaa(X1, X2, X3)) 18.95/5.85 addCcO_in_aaa(zero(X1), zero(X2), one(X3)) -> U105_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.85 U105_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(zero(X1), zero(X2), one(X3)) 18.95/5.85 addCcO_in_aaa(zero(zero(X1)), one(b), zero(one(X1))) -> U106_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.85 U106_aaa(X1, binaryZcH_out_a(X1)) -> addCcO_out_aaa(zero(zero(X1)), one(b), zero(one(X1))) 18.95/5.85 addCcO_in_aaa(zero(one(X1)), one(b), zero(zero(X2))) -> U107_aaa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.85 U107_aaa(X1, X2, succcM_out_aa(X1, X2)) -> addCcO_out_aaa(zero(one(X1)), one(b), zero(zero(X2))) 18.95/5.85 addCcO_in_aaa(zero(X1), one(X2), zero(X3)) -> U108_aaa(X1, X2, X3, addCcO_in_aaa(X1, X2, X3)) 18.95/5.85 addCcO_in_aaa(one(b), zero(zero(X1)), zero(one(X1))) -> U109_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.85 U109_aaa(X1, binaryZcH_out_a(X1)) -> addCcO_out_aaa(one(b), zero(zero(X1)), zero(one(X1))) 18.95/5.85 addCcO_in_aaa(one(b), zero(one(X1)), zero(zero(X2))) -> U110_aaa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.85 U110_aaa(X1, X2, succcM_out_aa(X1, X2)) -> addCcO_out_aaa(one(b), zero(one(X1)), zero(zero(X2))) 18.95/5.85 addCcO_in_aaa(one(X1), zero(X2), zero(X3)) -> U111_aaa(X1, X2, X3, addCcO_in_aaa(X1, X2, X3)) 18.95/5.85 addCcO_in_aaa(one(X1), one(X2), one(X3)) -> U112_aaa(X1, X2, X3, addccL_in_aaa(X1, X2, X3)) 18.95/5.85 U112_aaa(X1, X2, X3, addccL_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(one(X1), one(X2), one(X3)) 18.95/5.85 U111_aaa(X1, X2, X3, addCcO_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(one(X1), zero(X2), zero(X3)) 18.95/5.85 U108_aaa(X1, X2, X3, addCcO_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(zero(X1), one(X2), zero(X3)) 18.95/5.85 U115_aaa(X1, X2, X3, addCcO_out_aaa(X1, X2, X3)) -> addccL_out_aaa(X1, X2, X3) 18.95/5.85 U100_aaa(X1, X2, X3, addccL_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(one(X1), one(X2), zero(X3)) 18.95/5.85 U118_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addycK_out_aaa(X1, X2, X3) 18.95/5.85 U99_aaa(X1, X2, X3, addycK_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(one(X1), zero(X2), one(X3)) 18.95/5.85 U98_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(zero(X1), one(X2), one(X3)) 18.95/5.85 U95_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(zero(X1), zero(X2), zero(X3)) 18.95/5.85 U150_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addcG_out_aaa(zero(X1), X2, zero(X3)) 18.95/5.85 addcG_in_aaa(one(X1), X2, one(X3)) -> U151_aaa(X1, X2, X3, addycK_in_aaa(X1, X2, X3)) 18.95/5.85 U151_aaa(X1, X2, X3, addycK_out_aaa(X1, X2, X3)) -> addcG_out_aaa(one(X1), X2, one(X3)) 18.95/5.85 U90_aaa(X1, X2, X3, addcG_out_aaa(X2, X4, X3)) -> timescF_out_aaa(one(X1), X2, X3) 18.95/5.85 U88_aaa(X1, X2, X3, timescF_out_aaa(X1, X2, X3)) -> timescF_out_aaa(zero(X1), X2, zero(X3)) 18.95/5.85 18.95/5.85 The argument filtering Pi contains the following mapping: 18.95/5.85 zero(x1) = zero(x1) 18.95/5.85 18.95/5.85 timescF_in_aaa(x1, x2, x3) = timescF_in_aaa 18.95/5.85 18.95/5.85 timescF_out_aaa(x1, x2, x3) = timescF_out_aaa(x1) 18.95/5.85 18.95/5.85 U88_aaa(x1, x2, x3, x4) = U88_aaa(x4) 18.95/5.85 18.95/5.85 U89_aaa(x1, x2, x3, x4) = U89_aaa(x4) 18.95/5.85 18.95/5.85 U90_aaa(x1, x2, x3, x4) = U90_aaa(x1, x4) 18.95/5.85 18.95/5.85 addcG_in_aaa(x1, x2, x3) = addcG_in_aaa 18.95/5.85 18.95/5.85 U149_aaa(x1, x2) = U149_aaa(x2) 18.95/5.85 18.95/5.85 binaryZcP_in_a(x1) = binaryZcP_in_a 18.95/5.85 18.95/5.85 U119_a(x1, x2) = U119_a(x2) 18.95/5.85 18.95/5.85 binaryZcH_in_a(x1) = binaryZcH_in_a 18.95/5.85 18.95/5.85 U91_a(x1, x2) = U91_a(x2) 18.95/5.85 18.95/5.85 U92_a(x1, x2) = U92_a(x2) 18.95/5.85 18.95/5.85 binarycI_in_a(x1) = binarycI_in_a 18.95/5.85 18.95/5.85 binarycI_out_a(x1) = binarycI_out_a(x1) 18.95/5.85 18.95/5.85 U93_a(x1, x2) = U93_a(x2) 18.95/5.85 18.95/5.85 binaryZcH_out_a(x1) = binaryZcH_out_a(x1) 18.95/5.85 18.95/5.85 U94_a(x1, x2) = U94_a(x2) 18.95/5.85 18.95/5.85 binaryZcP_out_a(x1) = binaryZcP_out_a(x1) 18.95/5.85 18.95/5.85 addcG_out_aaa(x1, x2, x3) = addcG_out_aaa(x1, x2, x3) 18.95/5.85 18.95/5.85 U150_aaa(x1, x2, x3, x4) = U150_aaa(x4) 18.95/5.85 18.95/5.85 addzcJ_in_aaa(x1, x2, x3) = addzcJ_in_aaa 18.95/5.85 18.95/5.85 U95_aaa(x1, x2, x3, x4) = U95_aaa(x4) 18.95/5.85 18.95/5.85 U96_aaa(x1, x2) = U96_aaa(x2) 18.95/5.85 18.95/5.85 addzcJ_out_aaa(x1, x2, x3) = addzcJ_out_aaa(x1, x2, x3) 18.95/5.85 18.95/5.85 U97_aaa(x1, x2) = U97_aaa(x2) 18.95/5.85 18.95/5.85 U98_aaa(x1, x2, x3, x4) = U98_aaa(x4) 18.95/5.85 18.95/5.85 U99_aaa(x1, x2, x3, x4) = U99_aaa(x4) 18.95/5.85 18.95/5.85 addycK_in_aaa(x1, x2, x3) = addycK_in_aaa 18.95/5.85 18.95/5.85 U116_aaa(x1, x2) = U116_aaa(x2) 18.95/5.85 18.95/5.85 addycK_out_aaa(x1, x2, x3) = addycK_out_aaa(x1, x2, x3) 18.95/5.85 18.95/5.85 U117_aaa(x1, x2) = U117_aaa(x2) 18.95/5.85 18.95/5.85 U118_aaa(x1, x2, x3, x4) = U118_aaa(x4) 18.95/5.85 18.95/5.85 U100_aaa(x1, x2, x3, x4) = U100_aaa(x4) 18.95/5.85 18.95/5.85 addccL_in_aaa(x1, x2, x3) = addccL_in_aaa 18.95/5.85 18.95/5.85 addccL_out_aaa(x1, x2, x3) = addccL_out_aaa(x1, x2, x3) 18.95/5.85 18.95/5.85 U113_aaa(x1, x2, x3) = U113_aaa(x3) 18.95/5.85 18.95/5.85 succZcN_in_aa(x1, x2) = succZcN_in_aa 18.95/5.85 18.95/5.85 U103_aa(x1, x2) = U103_aa(x2) 18.95/5.85 18.95/5.85 succZcN_out_aa(x1, x2) = succZcN_out_aa(x1, x2) 18.95/5.85 18.95/5.85 U104_aa(x1, x2, x3) = U104_aa(x3) 18.95/5.85 18.95/5.85 succcM_in_aa(x1, x2) = succcM_in_aa 18.95/5.85 18.95/5.85 succcM_out_aa(x1, x2) = succcM_out_aa(x1, x2) 18.95/5.85 18.95/5.85 U101_aa(x1, x2) = U101_aa(x2) 18.95/5.85 18.95/5.85 U102_aa(x1, x2, x3) = U102_aa(x3) 18.95/5.85 18.95/5.85 U114_aaa(x1, x2, x3) = U114_aaa(x3) 18.95/5.85 18.95/5.85 U115_aaa(x1, x2, x3, x4) = U115_aaa(x4) 18.95/5.85 18.95/5.85 addCcO_in_aaa(x1, x2, x3) = addCcO_in_aaa 18.95/5.85 18.95/5.85 U105_aaa(x1, x2, x3, x4) = U105_aaa(x4) 18.95/5.85 18.95/5.85 addCcO_out_aaa(x1, x2, x3) = addCcO_out_aaa(x1, x2, x3) 18.95/5.85 18.95/5.85 U106_aaa(x1, x2) = U106_aaa(x2) 18.95/5.85 18.95/5.85 U107_aaa(x1, x2, x3) = U107_aaa(x3) 18.95/5.85 18.95/5.85 U108_aaa(x1, x2, x3, x4) = U108_aaa(x4) 18.95/5.85 18.95/5.85 U109_aaa(x1, x2) = U109_aaa(x2) 18.95/5.85 18.95/5.85 U110_aaa(x1, x2, x3) = U110_aaa(x3) 18.95/5.85 18.95/5.85 U111_aaa(x1, x2, x3, x4) = U111_aaa(x4) 18.95/5.85 18.95/5.85 U112_aaa(x1, x2, x3, x4) = U112_aaa(x4) 18.95/5.85 18.95/5.85 U151_aaa(x1, x2, x3, x4) = U151_aaa(x4) 18.95/5.85 18.95/5.85 one(x1) = one(x1) 18.95/5.85 18.95/5.85 b = b 18.95/5.85 18.95/5.85 SUCCT_IN_GG(x1, x2) = SUCCT_IN_GG(x1, x2) 18.95/5.85 18.95/5.85 18.95/5.85 We have to consider all (P,R,Pi)-chains 18.95/5.85 ---------------------------------------- 18.95/5.85 18.95/5.85 (149) UsableRulesProof (EQUIVALENT) 18.95/5.85 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 18.95/5.85 ---------------------------------------- 18.95/5.85 18.95/5.85 (150) 18.95/5.85 Obligation: 18.95/5.85 Pi DP problem: 18.95/5.85 The TRS P consists of the following rules: 18.95/5.85 18.95/5.85 SUCCT_IN_GG(one(X1), zero(X2)) -> SUCCT_IN_GG(X1, X2) 18.95/5.85 18.95/5.85 R is empty. 18.95/5.85 Pi is empty. 18.95/5.85 We have to consider all (P,R,Pi)-chains 18.95/5.85 ---------------------------------------- 18.95/5.85 18.95/5.85 (151) PiDPToQDPProof (EQUIVALENT) 18.95/5.85 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 18.95/5.85 ---------------------------------------- 18.95/5.85 18.95/5.85 (152) 18.95/5.85 Obligation: 18.95/5.85 Q DP problem: 18.95/5.85 The TRS P consists of the following rules: 18.95/5.85 18.95/5.85 SUCCT_IN_GG(one(X1), zero(X2)) -> SUCCT_IN_GG(X1, X2) 18.95/5.85 18.95/5.85 R is empty. 18.95/5.85 Q is empty. 18.95/5.85 We have to consider all (P,Q,R)-chains. 18.95/5.85 ---------------------------------------- 18.95/5.85 18.95/5.85 (153) QDPSizeChangeProof (EQUIVALENT) 18.95/5.85 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 18.95/5.85 18.95/5.85 From the DPs we obtained the following set of size-change graphs: 18.95/5.85 *SUCCT_IN_GG(one(X1), zero(X2)) -> SUCCT_IN_GG(X1, X2) 18.95/5.85 The graph contains the following edges 1 > 1, 2 > 2 18.95/5.85 18.95/5.85 18.95/5.85 ---------------------------------------- 18.95/5.85 18.95/5.85 (154) 18.95/5.85 YES 18.95/5.85 18.95/5.85 ---------------------------------------- 18.95/5.85 18.95/5.85 (155) 18.95/5.85 Obligation: 18.95/5.85 Pi DP problem: 18.95/5.85 The TRS P consists of the following rules: 18.95/5.85 18.95/5.85 ADDZQ_IN_GGG(zero(X1), one(X2), one(X3)) -> ADDZQ_IN_GGG(X1, X2, X3) 18.95/5.85 ADDZQ_IN_GGG(zero(X1), zero(X2), zero(X3)) -> ADDZQ_IN_GGG(X1, X2, X3) 18.95/5.85 ADDZQ_IN_GGG(one(X1), zero(X2), one(X3)) -> ADDYR_IN_GGG(X1, X2, X3) 18.95/5.85 ADDYR_IN_GGG(X1, X2, X3) -> ADDZQ_IN_GGG(X1, X2, X3) 18.95/5.85 ADDZQ_IN_GGG(one(X1), one(X2), zero(X3)) -> ADDCS_IN_GGG(X1, X2, X3) 18.95/5.85 ADDCS_IN_GGG(X1, X2, X3) -> ADDCV_IN_GGG(X1, X2, X3) 18.95/5.85 ADDCV_IN_GGG(zero(X1), zero(X2), one(X3)) -> ADDZQ_IN_GGG(X1, X2, X3) 18.95/5.85 ADDCV_IN_GGG(zero(X1), one(X2), zero(X3)) -> ADDCV_IN_GGG(X1, X2, X3) 18.95/5.85 ADDCV_IN_GGG(one(X1), zero(X2), zero(X3)) -> ADDCV_IN_GGG(X1, X2, X3) 18.95/5.85 ADDCV_IN_GGG(one(X1), one(X2), one(X3)) -> ADDCS_IN_GGG(X1, X2, X3) 18.95/5.85 18.95/5.85 The TRS R consists of the following rules: 18.95/5.85 18.95/5.85 timescF_in_aaa(one(b), X1, X1) -> timescF_out_aaa(one(b), X1, X1) 18.95/5.85 timescF_in_aaa(zero(X1), X2, zero(X3)) -> U88_aaa(X1, X2, X3, timescF_in_aaa(X1, X2, X3)) 18.95/5.85 timescF_in_aaa(one(X1), X2, X3) -> U89_aaa(X1, X2, X3, timescF_in_aaa(X1, X2, X4)) 18.95/5.85 U89_aaa(X1, X2, X3, timescF_out_aaa(X1, X2, X4)) -> U90_aaa(X1, X2, X3, addcG_in_aaa(X2, X4, X3)) 18.95/5.85 addcG_in_aaa(b, X1, zero(X1)) -> U149_aaa(X1, binaryZcP_in_a(X1)) 18.95/5.85 binaryZcP_in_a(X1) -> U119_a(X1, binaryZcH_in_a(X1)) 18.95/5.85 binaryZcH_in_a(zero(X1)) -> U91_a(X1, binaryZcH_in_a(X1)) 18.95/5.85 binaryZcH_in_a(one(X1)) -> U92_a(X1, binarycI_in_a(X1)) 18.95/5.85 binarycI_in_a(b) -> binarycI_out_a(b) 18.95/5.85 binarycI_in_a(zero(X1)) -> U93_a(X1, binaryZcH_in_a(X1)) 18.95/5.85 U93_a(X1, binaryZcH_out_a(X1)) -> binarycI_out_a(zero(X1)) 18.95/5.85 binarycI_in_a(one(X1)) -> U94_a(X1, binarycI_in_a(X1)) 18.95/5.85 U94_a(X1, binarycI_out_a(X1)) -> binarycI_out_a(one(X1)) 18.95/5.85 U92_a(X1, binarycI_out_a(X1)) -> binaryZcH_out_a(one(X1)) 18.95/5.85 U91_a(X1, binaryZcH_out_a(X1)) -> binaryZcH_out_a(zero(X1)) 18.95/5.85 U119_a(X1, binaryZcH_out_a(X1)) -> binaryZcP_out_a(X1) 18.95/5.85 U149_aaa(X1, binaryZcP_out_a(X1)) -> addcG_out_aaa(b, X1, zero(X1)) 18.95/5.85 addcG_in_aaa(zero(X1), X2, zero(X3)) -> U150_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.85 addzcJ_in_aaa(zero(X1), zero(X2), zero(X3)) -> U95_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.85 addzcJ_in_aaa(zero(one(X1)), one(b), one(one(X1))) -> U96_aaa(X1, binarycI_in_a(X1)) 18.95/5.85 U96_aaa(X1, binarycI_out_a(X1)) -> addzcJ_out_aaa(zero(one(X1)), one(b), one(one(X1))) 18.95/5.85 addzcJ_in_aaa(zero(zero(X1)), one(b), one(zero(X1))) -> U97_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.85 U97_aaa(X1, binaryZcH_out_a(X1)) -> addzcJ_out_aaa(zero(zero(X1)), one(b), one(zero(X1))) 18.95/5.85 addzcJ_in_aaa(zero(X1), one(X2), one(X3)) -> U98_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.85 addzcJ_in_aaa(one(X1), zero(X2), one(X3)) -> U99_aaa(X1, X2, X3, addycK_in_aaa(X1, X2, X3)) 18.95/5.85 addycK_in_aaa(b, one(X1), one(X1)) -> U116_aaa(X1, binarycI_in_a(X1)) 18.95/5.85 U116_aaa(X1, binarycI_out_a(X1)) -> addycK_out_aaa(b, one(X1), one(X1)) 18.95/5.85 addycK_in_aaa(b, zero(X1), zero(X1)) -> U117_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.85 U117_aaa(X1, binaryZcH_out_a(X1)) -> addycK_out_aaa(b, zero(X1), zero(X1)) 18.95/5.85 addycK_in_aaa(X1, X2, X3) -> U118_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.85 addzcJ_in_aaa(one(X1), one(X2), zero(X3)) -> U100_aaa(X1, X2, X3, addccL_in_aaa(X1, X2, X3)) 18.95/5.85 addccL_in_aaa(b, b, one(b)) -> addccL_out_aaa(b, b, one(b)) 18.95/5.85 addccL_in_aaa(X1, b, X2) -> U113_aaa(X1, X2, succZcN_in_aa(X1, X2)) 18.95/5.85 succZcN_in_aa(zero(X1), one(X1)) -> U103_aa(X1, binaryZcH_in_a(X1)) 18.95/5.85 U103_aa(X1, binaryZcH_out_a(X1)) -> succZcN_out_aa(zero(X1), one(X1)) 18.95/5.85 succZcN_in_aa(one(X1), zero(X2)) -> U104_aa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.85 succcM_in_aa(b, one(b)) -> succcM_out_aa(b, one(b)) 18.95/5.85 succcM_in_aa(zero(X1), one(X1)) -> U101_aa(X1, binaryZcH_in_a(X1)) 18.95/5.85 U101_aa(X1, binaryZcH_out_a(X1)) -> succcM_out_aa(zero(X1), one(X1)) 18.95/5.85 succcM_in_aa(one(X1), zero(X2)) -> U102_aa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.85 U102_aa(X1, X2, succcM_out_aa(X1, X2)) -> succcM_out_aa(one(X1), zero(X2)) 18.95/5.85 U104_aa(X1, X2, succcM_out_aa(X1, X2)) -> succZcN_out_aa(one(X1), zero(X2)) 18.95/5.85 U113_aaa(X1, X2, succZcN_out_aa(X1, X2)) -> addccL_out_aaa(X1, b, X2) 18.95/5.85 addccL_in_aaa(b, X1, X2) -> U114_aaa(X1, X2, succZcN_in_aa(X1, X2)) 18.95/5.85 U114_aaa(X1, X2, succZcN_out_aa(X1, X2)) -> addccL_out_aaa(b, X1, X2) 18.95/5.85 addccL_in_aaa(X1, X2, X3) -> U115_aaa(X1, X2, X3, addCcO_in_aaa(X1, X2, X3)) 18.95/5.85 addCcO_in_aaa(zero(X1), zero(X2), one(X3)) -> U105_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.85 U105_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(zero(X1), zero(X2), one(X3)) 18.95/5.85 addCcO_in_aaa(zero(zero(X1)), one(b), zero(one(X1))) -> U106_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.85 U106_aaa(X1, binaryZcH_out_a(X1)) -> addCcO_out_aaa(zero(zero(X1)), one(b), zero(one(X1))) 18.95/5.85 addCcO_in_aaa(zero(one(X1)), one(b), zero(zero(X2))) -> U107_aaa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.85 U107_aaa(X1, X2, succcM_out_aa(X1, X2)) -> addCcO_out_aaa(zero(one(X1)), one(b), zero(zero(X2))) 18.95/5.85 addCcO_in_aaa(zero(X1), one(X2), zero(X3)) -> U108_aaa(X1, X2, X3, addCcO_in_aaa(X1, X2, X3)) 18.95/5.85 addCcO_in_aaa(one(b), zero(zero(X1)), zero(one(X1))) -> U109_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.85 U109_aaa(X1, binaryZcH_out_a(X1)) -> addCcO_out_aaa(one(b), zero(zero(X1)), zero(one(X1))) 18.95/5.85 addCcO_in_aaa(one(b), zero(one(X1)), zero(zero(X2))) -> U110_aaa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.85 U110_aaa(X1, X2, succcM_out_aa(X1, X2)) -> addCcO_out_aaa(one(b), zero(one(X1)), zero(zero(X2))) 18.95/5.85 addCcO_in_aaa(one(X1), zero(X2), zero(X3)) -> U111_aaa(X1, X2, X3, addCcO_in_aaa(X1, X2, X3)) 18.95/5.85 addCcO_in_aaa(one(X1), one(X2), one(X3)) -> U112_aaa(X1, X2, X3, addccL_in_aaa(X1, X2, X3)) 18.95/5.85 U112_aaa(X1, X2, X3, addccL_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(one(X1), one(X2), one(X3)) 18.95/5.85 U111_aaa(X1, X2, X3, addCcO_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(one(X1), zero(X2), zero(X3)) 18.95/5.85 U108_aaa(X1, X2, X3, addCcO_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(zero(X1), one(X2), zero(X3)) 18.95/5.85 U115_aaa(X1, X2, X3, addCcO_out_aaa(X1, X2, X3)) -> addccL_out_aaa(X1, X2, X3) 18.95/5.85 U100_aaa(X1, X2, X3, addccL_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(one(X1), one(X2), zero(X3)) 18.95/5.85 U118_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addycK_out_aaa(X1, X2, X3) 18.95/5.85 U99_aaa(X1, X2, X3, addycK_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(one(X1), zero(X2), one(X3)) 18.95/5.85 U98_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(zero(X1), one(X2), one(X3)) 18.95/5.85 U95_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(zero(X1), zero(X2), zero(X3)) 18.95/5.85 U150_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addcG_out_aaa(zero(X1), X2, zero(X3)) 18.95/5.85 addcG_in_aaa(one(X1), X2, one(X3)) -> U151_aaa(X1, X2, X3, addycK_in_aaa(X1, X2, X3)) 18.95/5.85 U151_aaa(X1, X2, X3, addycK_out_aaa(X1, X2, X3)) -> addcG_out_aaa(one(X1), X2, one(X3)) 18.95/5.85 U90_aaa(X1, X2, X3, addcG_out_aaa(X2, X4, X3)) -> timescF_out_aaa(one(X1), X2, X3) 18.95/5.85 U88_aaa(X1, X2, X3, timescF_out_aaa(X1, X2, X3)) -> timescF_out_aaa(zero(X1), X2, zero(X3)) 18.95/5.85 18.95/5.85 The argument filtering Pi contains the following mapping: 18.95/5.85 zero(x1) = zero(x1) 18.95/5.85 18.95/5.85 timescF_in_aaa(x1, x2, x3) = timescF_in_aaa 18.95/5.85 18.95/5.85 timescF_out_aaa(x1, x2, x3) = timescF_out_aaa(x1) 18.95/5.85 18.95/5.85 U88_aaa(x1, x2, x3, x4) = U88_aaa(x4) 18.95/5.85 18.95/5.85 U89_aaa(x1, x2, x3, x4) = U89_aaa(x4) 18.95/5.85 18.95/5.85 U90_aaa(x1, x2, x3, x4) = U90_aaa(x1, x4) 18.95/5.85 18.95/5.85 addcG_in_aaa(x1, x2, x3) = addcG_in_aaa 18.95/5.85 18.95/5.85 U149_aaa(x1, x2) = U149_aaa(x2) 18.95/5.85 18.95/5.85 binaryZcP_in_a(x1) = binaryZcP_in_a 18.95/5.85 18.95/5.85 U119_a(x1, x2) = U119_a(x2) 18.95/5.85 18.95/5.85 binaryZcH_in_a(x1) = binaryZcH_in_a 18.95/5.85 18.95/5.85 U91_a(x1, x2) = U91_a(x2) 18.95/5.85 18.95/5.85 U92_a(x1, x2) = U92_a(x2) 18.95/5.85 18.95/5.85 binarycI_in_a(x1) = binarycI_in_a 18.95/5.85 18.95/5.85 binarycI_out_a(x1) = binarycI_out_a(x1) 18.95/5.85 18.95/5.85 U93_a(x1, x2) = U93_a(x2) 18.95/5.85 18.95/5.85 binaryZcH_out_a(x1) = binaryZcH_out_a(x1) 18.95/5.85 18.95/5.85 U94_a(x1, x2) = U94_a(x2) 18.95/5.85 18.95/5.85 binaryZcP_out_a(x1) = binaryZcP_out_a(x1) 18.95/5.85 18.95/5.85 addcG_out_aaa(x1, x2, x3) = addcG_out_aaa(x1, x2, x3) 18.95/5.85 18.95/5.85 U150_aaa(x1, x2, x3, x4) = U150_aaa(x4) 18.95/5.85 18.95/5.85 addzcJ_in_aaa(x1, x2, x3) = addzcJ_in_aaa 18.95/5.85 18.95/5.85 U95_aaa(x1, x2, x3, x4) = U95_aaa(x4) 18.95/5.85 18.95/5.85 U96_aaa(x1, x2) = U96_aaa(x2) 18.95/5.85 18.95/5.85 addzcJ_out_aaa(x1, x2, x3) = addzcJ_out_aaa(x1, x2, x3) 18.95/5.85 18.95/5.85 U97_aaa(x1, x2) = U97_aaa(x2) 18.95/5.85 18.95/5.85 U98_aaa(x1, x2, x3, x4) = U98_aaa(x4) 18.95/5.85 18.95/5.85 U99_aaa(x1, x2, x3, x4) = U99_aaa(x4) 18.95/5.85 18.95/5.85 addycK_in_aaa(x1, x2, x3) = addycK_in_aaa 18.95/5.85 18.95/5.85 U116_aaa(x1, x2) = U116_aaa(x2) 18.95/5.85 18.95/5.85 addycK_out_aaa(x1, x2, x3) = addycK_out_aaa(x1, x2, x3) 18.95/5.85 18.95/5.85 U117_aaa(x1, x2) = U117_aaa(x2) 18.95/5.85 18.95/5.85 U118_aaa(x1, x2, x3, x4) = U118_aaa(x4) 18.95/5.85 18.95/5.85 U100_aaa(x1, x2, x3, x4) = U100_aaa(x4) 18.95/5.85 18.95/5.85 addccL_in_aaa(x1, x2, x3) = addccL_in_aaa 18.95/5.85 18.95/5.85 addccL_out_aaa(x1, x2, x3) = addccL_out_aaa(x1, x2, x3) 18.95/5.85 18.95/5.85 U113_aaa(x1, x2, x3) = U113_aaa(x3) 18.95/5.85 18.95/5.85 succZcN_in_aa(x1, x2) = succZcN_in_aa 18.95/5.85 18.95/5.85 U103_aa(x1, x2) = U103_aa(x2) 18.95/5.85 18.95/5.85 succZcN_out_aa(x1, x2) = succZcN_out_aa(x1, x2) 18.95/5.85 18.95/5.85 U104_aa(x1, x2, x3) = U104_aa(x3) 18.95/5.85 18.95/5.85 succcM_in_aa(x1, x2) = succcM_in_aa 18.95/5.85 18.95/5.85 succcM_out_aa(x1, x2) = succcM_out_aa(x1, x2) 18.95/5.85 18.95/5.85 U101_aa(x1, x2) = U101_aa(x2) 18.95/5.85 18.95/5.85 U102_aa(x1, x2, x3) = U102_aa(x3) 18.95/5.85 18.95/5.85 U114_aaa(x1, x2, x3) = U114_aaa(x3) 18.95/5.85 18.95/5.85 U115_aaa(x1, x2, x3, x4) = U115_aaa(x4) 18.95/5.85 18.95/5.85 addCcO_in_aaa(x1, x2, x3) = addCcO_in_aaa 18.95/5.85 18.95/5.85 U105_aaa(x1, x2, x3, x4) = U105_aaa(x4) 18.95/5.85 18.95/5.85 addCcO_out_aaa(x1, x2, x3) = addCcO_out_aaa(x1, x2, x3) 18.95/5.85 18.95/5.85 U106_aaa(x1, x2) = U106_aaa(x2) 18.95/5.85 18.95/5.85 U107_aaa(x1, x2, x3) = U107_aaa(x3) 18.95/5.85 18.95/5.85 U108_aaa(x1, x2, x3, x4) = U108_aaa(x4) 18.95/5.85 18.95/5.85 U109_aaa(x1, x2) = U109_aaa(x2) 18.95/5.85 18.95/5.85 U110_aaa(x1, x2, x3) = U110_aaa(x3) 18.95/5.85 18.95/5.85 U111_aaa(x1, x2, x3, x4) = U111_aaa(x4) 18.95/5.85 18.95/5.85 U112_aaa(x1, x2, x3, x4) = U112_aaa(x4) 18.95/5.85 18.95/5.85 U151_aaa(x1, x2, x3, x4) = U151_aaa(x4) 18.95/5.85 18.95/5.85 one(x1) = one(x1) 18.95/5.85 18.95/5.85 b = b 18.95/5.85 18.95/5.85 ADDZQ_IN_GGG(x1, x2, x3) = ADDZQ_IN_GGG(x1, x2, x3) 18.95/5.85 18.95/5.85 ADDYR_IN_GGG(x1, x2, x3) = ADDYR_IN_GGG(x1, x2, x3) 18.95/5.85 18.95/5.85 ADDCS_IN_GGG(x1, x2, x3) = ADDCS_IN_GGG(x1, x2, x3) 18.95/5.85 18.95/5.85 ADDCV_IN_GGG(x1, x2, x3) = ADDCV_IN_GGG(x1, x2, x3) 18.95/5.85 18.95/5.85 18.95/5.85 We have to consider all (P,R,Pi)-chains 18.95/5.85 ---------------------------------------- 18.95/5.85 18.95/5.85 (156) UsableRulesProof (EQUIVALENT) 18.95/5.85 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 18.95/5.85 ---------------------------------------- 18.95/5.85 18.95/5.85 (157) 18.95/5.85 Obligation: 18.95/5.85 Pi DP problem: 18.95/5.85 The TRS P consists of the following rules: 18.95/5.85 18.95/5.85 ADDZQ_IN_GGG(zero(X1), one(X2), one(X3)) -> ADDZQ_IN_GGG(X1, X2, X3) 18.95/5.85 ADDZQ_IN_GGG(zero(X1), zero(X2), zero(X3)) -> ADDZQ_IN_GGG(X1, X2, X3) 18.95/5.85 ADDZQ_IN_GGG(one(X1), zero(X2), one(X3)) -> ADDYR_IN_GGG(X1, X2, X3) 18.95/5.85 ADDYR_IN_GGG(X1, X2, X3) -> ADDZQ_IN_GGG(X1, X2, X3) 18.95/5.85 ADDZQ_IN_GGG(one(X1), one(X2), zero(X3)) -> ADDCS_IN_GGG(X1, X2, X3) 18.95/5.85 ADDCS_IN_GGG(X1, X2, X3) -> ADDCV_IN_GGG(X1, X2, X3) 18.95/5.85 ADDCV_IN_GGG(zero(X1), zero(X2), one(X3)) -> ADDZQ_IN_GGG(X1, X2, X3) 18.95/5.85 ADDCV_IN_GGG(zero(X1), one(X2), zero(X3)) -> ADDCV_IN_GGG(X1, X2, X3) 18.95/5.85 ADDCV_IN_GGG(one(X1), zero(X2), zero(X3)) -> ADDCV_IN_GGG(X1, X2, X3) 18.95/5.85 ADDCV_IN_GGG(one(X1), one(X2), one(X3)) -> ADDCS_IN_GGG(X1, X2, X3) 18.95/5.85 18.95/5.85 R is empty. 18.95/5.85 Pi is empty. 18.95/5.85 We have to consider all (P,R,Pi)-chains 18.95/5.85 ---------------------------------------- 18.95/5.85 18.95/5.85 (158) PiDPToQDPProof (EQUIVALENT) 18.95/5.85 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 18.95/5.85 ---------------------------------------- 18.95/5.85 18.95/5.85 (159) 18.95/5.85 Obligation: 18.95/5.85 Q DP problem: 18.95/5.85 The TRS P consists of the following rules: 18.95/5.85 18.95/5.85 ADDZQ_IN_GGG(zero(X1), one(X2), one(X3)) -> ADDZQ_IN_GGG(X1, X2, X3) 18.95/5.85 ADDZQ_IN_GGG(zero(X1), zero(X2), zero(X3)) -> ADDZQ_IN_GGG(X1, X2, X3) 18.95/5.85 ADDZQ_IN_GGG(one(X1), zero(X2), one(X3)) -> ADDYR_IN_GGG(X1, X2, X3) 18.95/5.85 ADDYR_IN_GGG(X1, X2, X3) -> ADDZQ_IN_GGG(X1, X2, X3) 18.95/5.85 ADDZQ_IN_GGG(one(X1), one(X2), zero(X3)) -> ADDCS_IN_GGG(X1, X2, X3) 18.95/5.85 ADDCS_IN_GGG(X1, X2, X3) -> ADDCV_IN_GGG(X1, X2, X3) 18.95/5.85 ADDCV_IN_GGG(zero(X1), zero(X2), one(X3)) -> ADDZQ_IN_GGG(X1, X2, X3) 18.95/5.85 ADDCV_IN_GGG(zero(X1), one(X2), zero(X3)) -> ADDCV_IN_GGG(X1, X2, X3) 18.95/5.85 ADDCV_IN_GGG(one(X1), zero(X2), zero(X3)) -> ADDCV_IN_GGG(X1, X2, X3) 18.95/5.85 ADDCV_IN_GGG(one(X1), one(X2), one(X3)) -> ADDCS_IN_GGG(X1, X2, X3) 18.95/5.85 18.95/5.85 R is empty. 18.95/5.85 Q is empty. 18.95/5.85 We have to consider all (P,Q,R)-chains. 18.95/5.85 ---------------------------------------- 18.95/5.85 18.95/5.85 (160) QDPSizeChangeProof (EQUIVALENT) 18.95/5.85 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 18.95/5.85 18.95/5.85 From the DPs we obtained the following set of size-change graphs: 18.95/5.85 *ADDYR_IN_GGG(X1, X2, X3) -> ADDZQ_IN_GGG(X1, X2, X3) 18.95/5.85 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3 18.95/5.85 18.95/5.85 18.95/5.85 *ADDCV_IN_GGG(zero(X1), zero(X2), one(X3)) -> ADDZQ_IN_GGG(X1, X2, X3) 18.95/5.85 The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 18.95/5.85 18.95/5.85 18.95/5.85 *ADDZQ_IN_GGG(one(X1), zero(X2), one(X3)) -> ADDYR_IN_GGG(X1, X2, X3) 18.95/5.85 The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 18.95/5.85 18.95/5.85 18.95/5.85 *ADDZQ_IN_GGG(one(X1), one(X2), zero(X3)) -> ADDCS_IN_GGG(X1, X2, X3) 18.95/5.85 The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 18.95/5.85 18.95/5.85 18.95/5.85 *ADDCS_IN_GGG(X1, X2, X3) -> ADDCV_IN_GGG(X1, X2, X3) 18.95/5.85 The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3 18.95/5.85 18.95/5.85 18.95/5.85 *ADDCV_IN_GGG(one(X1), one(X2), one(X3)) -> ADDCS_IN_GGG(X1, X2, X3) 18.95/5.85 The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 18.95/5.85 18.95/5.85 18.95/5.85 *ADDZQ_IN_GGG(zero(X1), one(X2), one(X3)) -> ADDZQ_IN_GGG(X1, X2, X3) 18.95/5.85 The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 18.95/5.85 18.95/5.85 18.95/5.85 *ADDZQ_IN_GGG(zero(X1), zero(X2), zero(X3)) -> ADDZQ_IN_GGG(X1, X2, X3) 18.95/5.85 The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 18.95/5.85 18.95/5.85 18.95/5.85 *ADDCV_IN_GGG(zero(X1), one(X2), zero(X3)) -> ADDCV_IN_GGG(X1, X2, X3) 18.95/5.85 The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 18.95/5.85 18.95/5.85 18.95/5.85 *ADDCV_IN_GGG(one(X1), zero(X2), zero(X3)) -> ADDCV_IN_GGG(X1, X2, X3) 18.95/5.85 The graph contains the following edges 1 > 1, 2 > 2, 3 > 3 18.95/5.85 18.95/5.85 18.95/5.85 ---------------------------------------- 18.95/5.85 18.95/5.85 (161) 18.95/5.85 YES 18.95/5.85 18.95/5.85 ---------------------------------------- 18.95/5.85 18.95/5.85 (162) 18.95/5.85 Obligation: 18.95/5.85 Pi DP problem: 18.95/5.85 The TRS P consists of the following rules: 18.95/5.85 18.95/5.85 SUCCT_IN_AG(one(X1), zero(X2)) -> SUCCT_IN_AG(X1, X2) 18.95/5.85 18.95/5.85 The TRS R consists of the following rules: 18.95/5.85 18.95/5.85 timescF_in_aaa(one(b), X1, X1) -> timescF_out_aaa(one(b), X1, X1) 18.95/5.85 timescF_in_aaa(zero(X1), X2, zero(X3)) -> U88_aaa(X1, X2, X3, timescF_in_aaa(X1, X2, X3)) 18.95/5.85 timescF_in_aaa(one(X1), X2, X3) -> U89_aaa(X1, X2, X3, timescF_in_aaa(X1, X2, X4)) 18.95/5.85 U89_aaa(X1, X2, X3, timescF_out_aaa(X1, X2, X4)) -> U90_aaa(X1, X2, X3, addcG_in_aaa(X2, X4, X3)) 18.95/5.85 addcG_in_aaa(b, X1, zero(X1)) -> U149_aaa(X1, binaryZcP_in_a(X1)) 18.95/5.85 binaryZcP_in_a(X1) -> U119_a(X1, binaryZcH_in_a(X1)) 18.95/5.85 binaryZcH_in_a(zero(X1)) -> U91_a(X1, binaryZcH_in_a(X1)) 18.95/5.85 binaryZcH_in_a(one(X1)) -> U92_a(X1, binarycI_in_a(X1)) 18.95/5.85 binarycI_in_a(b) -> binarycI_out_a(b) 18.95/5.85 binarycI_in_a(zero(X1)) -> U93_a(X1, binaryZcH_in_a(X1)) 18.95/5.85 U93_a(X1, binaryZcH_out_a(X1)) -> binarycI_out_a(zero(X1)) 18.95/5.85 binarycI_in_a(one(X1)) -> U94_a(X1, binarycI_in_a(X1)) 18.95/5.85 U94_a(X1, binarycI_out_a(X1)) -> binarycI_out_a(one(X1)) 18.95/5.85 U92_a(X1, binarycI_out_a(X1)) -> binaryZcH_out_a(one(X1)) 18.95/5.85 U91_a(X1, binaryZcH_out_a(X1)) -> binaryZcH_out_a(zero(X1)) 18.95/5.85 U119_a(X1, binaryZcH_out_a(X1)) -> binaryZcP_out_a(X1) 18.95/5.85 U149_aaa(X1, binaryZcP_out_a(X1)) -> addcG_out_aaa(b, X1, zero(X1)) 18.95/5.85 addcG_in_aaa(zero(X1), X2, zero(X3)) -> U150_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.85 addzcJ_in_aaa(zero(X1), zero(X2), zero(X3)) -> U95_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.85 addzcJ_in_aaa(zero(one(X1)), one(b), one(one(X1))) -> U96_aaa(X1, binarycI_in_a(X1)) 18.95/5.85 U96_aaa(X1, binarycI_out_a(X1)) -> addzcJ_out_aaa(zero(one(X1)), one(b), one(one(X1))) 18.95/5.85 addzcJ_in_aaa(zero(zero(X1)), one(b), one(zero(X1))) -> U97_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.85 U97_aaa(X1, binaryZcH_out_a(X1)) -> addzcJ_out_aaa(zero(zero(X1)), one(b), one(zero(X1))) 18.95/5.85 addzcJ_in_aaa(zero(X1), one(X2), one(X3)) -> U98_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.85 addzcJ_in_aaa(one(X1), zero(X2), one(X3)) -> U99_aaa(X1, X2, X3, addycK_in_aaa(X1, X2, X3)) 18.95/5.85 addycK_in_aaa(b, one(X1), one(X1)) -> U116_aaa(X1, binarycI_in_a(X1)) 18.95/5.85 U116_aaa(X1, binarycI_out_a(X1)) -> addycK_out_aaa(b, one(X1), one(X1)) 18.95/5.85 addycK_in_aaa(b, zero(X1), zero(X1)) -> U117_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.85 U117_aaa(X1, binaryZcH_out_a(X1)) -> addycK_out_aaa(b, zero(X1), zero(X1)) 18.95/5.85 addycK_in_aaa(X1, X2, X3) -> U118_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.85 addzcJ_in_aaa(one(X1), one(X2), zero(X3)) -> U100_aaa(X1, X2, X3, addccL_in_aaa(X1, X2, X3)) 18.95/5.85 addccL_in_aaa(b, b, one(b)) -> addccL_out_aaa(b, b, one(b)) 18.95/5.85 addccL_in_aaa(X1, b, X2) -> U113_aaa(X1, X2, succZcN_in_aa(X1, X2)) 18.95/5.85 succZcN_in_aa(zero(X1), one(X1)) -> U103_aa(X1, binaryZcH_in_a(X1)) 18.95/5.85 U103_aa(X1, binaryZcH_out_a(X1)) -> succZcN_out_aa(zero(X1), one(X1)) 18.95/5.85 succZcN_in_aa(one(X1), zero(X2)) -> U104_aa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.85 succcM_in_aa(b, one(b)) -> succcM_out_aa(b, one(b)) 18.95/5.85 succcM_in_aa(zero(X1), one(X1)) -> U101_aa(X1, binaryZcH_in_a(X1)) 18.95/5.85 U101_aa(X1, binaryZcH_out_a(X1)) -> succcM_out_aa(zero(X1), one(X1)) 18.95/5.85 succcM_in_aa(one(X1), zero(X2)) -> U102_aa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.85 U102_aa(X1, X2, succcM_out_aa(X1, X2)) -> succcM_out_aa(one(X1), zero(X2)) 18.95/5.85 U104_aa(X1, X2, succcM_out_aa(X1, X2)) -> succZcN_out_aa(one(X1), zero(X2)) 18.95/5.85 U113_aaa(X1, X2, succZcN_out_aa(X1, X2)) -> addccL_out_aaa(X1, b, X2) 18.95/5.85 addccL_in_aaa(b, X1, X2) -> U114_aaa(X1, X2, succZcN_in_aa(X1, X2)) 18.95/5.85 U114_aaa(X1, X2, succZcN_out_aa(X1, X2)) -> addccL_out_aaa(b, X1, X2) 18.95/5.85 addccL_in_aaa(X1, X2, X3) -> U115_aaa(X1, X2, X3, addCcO_in_aaa(X1, X2, X3)) 18.95/5.85 addCcO_in_aaa(zero(X1), zero(X2), one(X3)) -> U105_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.85 U105_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(zero(X1), zero(X2), one(X3)) 18.95/5.85 addCcO_in_aaa(zero(zero(X1)), one(b), zero(one(X1))) -> U106_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.85 U106_aaa(X1, binaryZcH_out_a(X1)) -> addCcO_out_aaa(zero(zero(X1)), one(b), zero(one(X1))) 18.95/5.85 addCcO_in_aaa(zero(one(X1)), one(b), zero(zero(X2))) -> U107_aaa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.85 U107_aaa(X1, X2, succcM_out_aa(X1, X2)) -> addCcO_out_aaa(zero(one(X1)), one(b), zero(zero(X2))) 18.95/5.85 addCcO_in_aaa(zero(X1), one(X2), zero(X3)) -> U108_aaa(X1, X2, X3, addCcO_in_aaa(X1, X2, X3)) 18.95/5.85 addCcO_in_aaa(one(b), zero(zero(X1)), zero(one(X1))) -> U109_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.85 U109_aaa(X1, binaryZcH_out_a(X1)) -> addCcO_out_aaa(one(b), zero(zero(X1)), zero(one(X1))) 18.95/5.85 addCcO_in_aaa(one(b), zero(one(X1)), zero(zero(X2))) -> U110_aaa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.85 U110_aaa(X1, X2, succcM_out_aa(X1, X2)) -> addCcO_out_aaa(one(b), zero(one(X1)), zero(zero(X2))) 18.95/5.85 addCcO_in_aaa(one(X1), zero(X2), zero(X3)) -> U111_aaa(X1, X2, X3, addCcO_in_aaa(X1, X2, X3)) 18.95/5.85 addCcO_in_aaa(one(X1), one(X2), one(X3)) -> U112_aaa(X1, X2, X3, addccL_in_aaa(X1, X2, X3)) 18.95/5.85 U112_aaa(X1, X2, X3, addccL_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(one(X1), one(X2), one(X3)) 18.95/5.85 U111_aaa(X1, X2, X3, addCcO_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(one(X1), zero(X2), zero(X3)) 18.95/5.85 U108_aaa(X1, X2, X3, addCcO_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(zero(X1), one(X2), zero(X3)) 18.95/5.85 U115_aaa(X1, X2, X3, addCcO_out_aaa(X1, X2, X3)) -> addccL_out_aaa(X1, X2, X3) 18.95/5.85 U100_aaa(X1, X2, X3, addccL_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(one(X1), one(X2), zero(X3)) 18.95/5.85 U118_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addycK_out_aaa(X1, X2, X3) 18.95/5.85 U99_aaa(X1, X2, X3, addycK_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(one(X1), zero(X2), one(X3)) 18.95/5.85 U98_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(zero(X1), one(X2), one(X3)) 18.95/5.85 U95_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(zero(X1), zero(X2), zero(X3)) 18.95/5.85 U150_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addcG_out_aaa(zero(X1), X2, zero(X3)) 18.95/5.85 addcG_in_aaa(one(X1), X2, one(X3)) -> U151_aaa(X1, X2, X3, addycK_in_aaa(X1, X2, X3)) 18.95/5.85 U151_aaa(X1, X2, X3, addycK_out_aaa(X1, X2, X3)) -> addcG_out_aaa(one(X1), X2, one(X3)) 18.95/5.85 U90_aaa(X1, X2, X3, addcG_out_aaa(X2, X4, X3)) -> timescF_out_aaa(one(X1), X2, X3) 18.95/5.85 U88_aaa(X1, X2, X3, timescF_out_aaa(X1, X2, X3)) -> timescF_out_aaa(zero(X1), X2, zero(X3)) 18.95/5.85 18.95/5.85 The argument filtering Pi contains the following mapping: 18.95/5.85 zero(x1) = zero(x1) 18.95/5.85 18.95/5.85 timescF_in_aaa(x1, x2, x3) = timescF_in_aaa 18.95/5.85 18.95/5.85 timescF_out_aaa(x1, x2, x3) = timescF_out_aaa(x1) 18.95/5.85 18.95/5.85 U88_aaa(x1, x2, x3, x4) = U88_aaa(x4) 18.95/5.85 18.95/5.85 U89_aaa(x1, x2, x3, x4) = U89_aaa(x4) 18.95/5.85 18.95/5.85 U90_aaa(x1, x2, x3, x4) = U90_aaa(x1, x4) 18.95/5.85 18.95/5.85 addcG_in_aaa(x1, x2, x3) = addcG_in_aaa 18.95/5.85 18.95/5.85 U149_aaa(x1, x2) = U149_aaa(x2) 18.95/5.85 18.95/5.85 binaryZcP_in_a(x1) = binaryZcP_in_a 18.95/5.85 18.95/5.85 U119_a(x1, x2) = U119_a(x2) 18.95/5.85 18.95/5.85 binaryZcH_in_a(x1) = binaryZcH_in_a 18.95/5.85 18.95/5.85 U91_a(x1, x2) = U91_a(x2) 18.95/5.85 18.95/5.85 U92_a(x1, x2) = U92_a(x2) 18.95/5.85 18.95/5.85 binarycI_in_a(x1) = binarycI_in_a 18.95/5.85 18.95/5.85 binarycI_out_a(x1) = binarycI_out_a(x1) 18.95/5.85 18.95/5.85 U93_a(x1, x2) = U93_a(x2) 18.95/5.85 18.95/5.85 binaryZcH_out_a(x1) = binaryZcH_out_a(x1) 18.95/5.85 18.95/5.85 U94_a(x1, x2) = U94_a(x2) 18.95/5.85 18.95/5.85 binaryZcP_out_a(x1) = binaryZcP_out_a(x1) 18.95/5.85 18.95/5.85 addcG_out_aaa(x1, x2, x3) = addcG_out_aaa(x1, x2, x3) 18.95/5.85 18.95/5.85 U150_aaa(x1, x2, x3, x4) = U150_aaa(x4) 18.95/5.85 18.95/5.85 addzcJ_in_aaa(x1, x2, x3) = addzcJ_in_aaa 18.95/5.85 18.95/5.85 U95_aaa(x1, x2, x3, x4) = U95_aaa(x4) 18.95/5.85 18.95/5.85 U96_aaa(x1, x2) = U96_aaa(x2) 18.95/5.85 18.95/5.85 addzcJ_out_aaa(x1, x2, x3) = addzcJ_out_aaa(x1, x2, x3) 18.95/5.85 18.95/5.85 U97_aaa(x1, x2) = U97_aaa(x2) 18.95/5.85 18.95/5.85 U98_aaa(x1, x2, x3, x4) = U98_aaa(x4) 18.95/5.85 18.95/5.85 U99_aaa(x1, x2, x3, x4) = U99_aaa(x4) 18.95/5.85 18.95/5.85 addycK_in_aaa(x1, x2, x3) = addycK_in_aaa 18.95/5.85 18.95/5.85 U116_aaa(x1, x2) = U116_aaa(x2) 18.95/5.85 18.95/5.85 addycK_out_aaa(x1, x2, x3) = addycK_out_aaa(x1, x2, x3) 18.95/5.85 18.95/5.85 U117_aaa(x1, x2) = U117_aaa(x2) 18.95/5.85 18.95/5.85 U118_aaa(x1, x2, x3, x4) = U118_aaa(x4) 18.95/5.85 18.95/5.85 U100_aaa(x1, x2, x3, x4) = U100_aaa(x4) 18.95/5.85 18.95/5.85 addccL_in_aaa(x1, x2, x3) = addccL_in_aaa 18.95/5.85 18.95/5.85 addccL_out_aaa(x1, x2, x3) = addccL_out_aaa(x1, x2, x3) 18.95/5.85 18.95/5.85 U113_aaa(x1, x2, x3) = U113_aaa(x3) 18.95/5.85 18.95/5.85 succZcN_in_aa(x1, x2) = succZcN_in_aa 18.95/5.85 18.95/5.85 U103_aa(x1, x2) = U103_aa(x2) 18.95/5.85 18.95/5.85 succZcN_out_aa(x1, x2) = succZcN_out_aa(x1, x2) 18.95/5.85 18.95/5.85 U104_aa(x1, x2, x3) = U104_aa(x3) 18.95/5.85 18.95/5.85 succcM_in_aa(x1, x2) = succcM_in_aa 18.95/5.85 18.95/5.85 succcM_out_aa(x1, x2) = succcM_out_aa(x1, x2) 18.95/5.85 18.95/5.85 U101_aa(x1, x2) = U101_aa(x2) 18.95/5.85 18.95/5.85 U102_aa(x1, x2, x3) = U102_aa(x3) 18.95/5.85 18.95/5.85 U114_aaa(x1, x2, x3) = U114_aaa(x3) 18.95/5.85 18.95/5.85 U115_aaa(x1, x2, x3, x4) = U115_aaa(x4) 18.95/5.85 18.95/5.85 addCcO_in_aaa(x1, x2, x3) = addCcO_in_aaa 18.95/5.85 18.95/5.85 U105_aaa(x1, x2, x3, x4) = U105_aaa(x4) 18.95/5.85 18.95/5.85 addCcO_out_aaa(x1, x2, x3) = addCcO_out_aaa(x1, x2, x3) 18.95/5.85 18.95/5.85 U106_aaa(x1, x2) = U106_aaa(x2) 18.95/5.85 18.95/5.85 U107_aaa(x1, x2, x3) = U107_aaa(x3) 18.95/5.85 18.95/5.85 U108_aaa(x1, x2, x3, x4) = U108_aaa(x4) 18.95/5.85 18.95/5.85 U109_aaa(x1, x2) = U109_aaa(x2) 18.95/5.85 18.95/5.85 U110_aaa(x1, x2, x3) = U110_aaa(x3) 18.95/5.85 18.95/5.85 U111_aaa(x1, x2, x3, x4) = U111_aaa(x4) 18.95/5.85 18.95/5.85 U112_aaa(x1, x2, x3, x4) = U112_aaa(x4) 18.95/5.85 18.95/5.85 U151_aaa(x1, x2, x3, x4) = U151_aaa(x4) 18.95/5.85 18.95/5.85 one(x1) = one(x1) 18.95/5.85 18.95/5.85 b = b 18.95/5.85 18.95/5.85 SUCCT_IN_AG(x1, x2) = SUCCT_IN_AG(x2) 18.95/5.85 18.95/5.85 18.95/5.85 We have to consider all (P,R,Pi)-chains 18.95/5.85 ---------------------------------------- 18.95/5.85 18.95/5.85 (163) UsableRulesProof (EQUIVALENT) 18.95/5.85 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 18.95/5.85 ---------------------------------------- 18.95/5.85 18.95/5.85 (164) 18.95/5.85 Obligation: 18.95/5.85 Pi DP problem: 18.95/5.85 The TRS P consists of the following rules: 18.95/5.85 18.95/5.85 SUCCT_IN_AG(one(X1), zero(X2)) -> SUCCT_IN_AG(X1, X2) 18.95/5.85 18.95/5.85 R is empty. 18.95/5.85 The argument filtering Pi contains the following mapping: 18.95/5.85 zero(x1) = zero(x1) 18.95/5.85 18.95/5.85 one(x1) = one(x1) 18.95/5.85 18.95/5.85 SUCCT_IN_AG(x1, x2) = SUCCT_IN_AG(x2) 18.95/5.85 18.95/5.85 18.95/5.85 We have to consider all (P,R,Pi)-chains 18.95/5.85 ---------------------------------------- 18.95/5.85 18.95/5.85 (165) PiDPToQDPProof (SOUND) 18.95/5.85 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 18.95/5.85 ---------------------------------------- 18.95/5.85 18.95/5.85 (166) 18.95/5.85 Obligation: 18.95/5.85 Q DP problem: 18.95/5.85 The TRS P consists of the following rules: 18.95/5.85 18.95/5.85 SUCCT_IN_AG(zero(X2)) -> SUCCT_IN_AG(X2) 18.95/5.85 18.95/5.85 R is empty. 18.95/5.85 Q is empty. 18.95/5.85 We have to consider all (P,Q,R)-chains. 18.95/5.85 ---------------------------------------- 18.95/5.85 18.95/5.85 (167) QDPSizeChangeProof (EQUIVALENT) 18.95/5.85 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 18.95/5.85 18.95/5.85 From the DPs we obtained the following set of size-change graphs: 18.95/5.85 *SUCCT_IN_AG(zero(X2)) -> SUCCT_IN_AG(X2) 18.95/5.85 The graph contains the following edges 1 > 1 18.95/5.85 18.95/5.85 18.95/5.85 ---------------------------------------- 18.95/5.85 18.95/5.85 (168) 18.95/5.85 YES 18.95/5.85 18.95/5.85 ---------------------------------------- 18.95/5.85 18.95/5.85 (169) 18.95/5.85 Obligation: 18.95/5.85 Pi DP problem: 18.95/5.85 The TRS P consists of the following rules: 18.95/5.85 18.95/5.85 ADDZQ_IN_AAG(zero(X1), one(X2), one(X3)) -> ADDZQ_IN_AAG(X1, X2, X3) 18.95/5.85 ADDZQ_IN_AAG(zero(X1), zero(X2), zero(X3)) -> ADDZQ_IN_AAG(X1, X2, X3) 18.95/5.85 ADDZQ_IN_AAG(one(X1), zero(X2), one(X3)) -> ADDYR_IN_AAG(X1, X2, X3) 18.95/5.85 ADDYR_IN_AAG(X1, X2, X3) -> ADDZQ_IN_AAG(X1, X2, X3) 18.95/5.85 ADDZQ_IN_AAG(one(X1), one(X2), zero(X3)) -> ADDCS_IN_AAG(X1, X2, X3) 18.95/5.85 ADDCS_IN_AAG(X1, X2, X3) -> ADDCV_IN_AAG(X1, X2, X3) 18.95/5.85 ADDCV_IN_AAG(zero(X1), zero(X2), one(X3)) -> ADDZQ_IN_AAG(X1, X2, X3) 18.95/5.85 ADDCV_IN_AAG(zero(X1), one(X2), zero(X3)) -> ADDCV_IN_AAG(X1, X2, X3) 18.95/5.85 ADDCV_IN_AAG(one(X1), zero(X2), zero(X3)) -> ADDCV_IN_AAG(X1, X2, X3) 18.95/5.85 ADDCV_IN_AAG(one(X1), one(X2), one(X3)) -> ADDCS_IN_AAG(X1, X2, X3) 18.95/5.85 18.95/5.85 The TRS R consists of the following rules: 18.95/5.85 18.95/5.85 timescF_in_aaa(one(b), X1, X1) -> timescF_out_aaa(one(b), X1, X1) 18.95/5.85 timescF_in_aaa(zero(X1), X2, zero(X3)) -> U88_aaa(X1, X2, X3, timescF_in_aaa(X1, X2, X3)) 18.95/5.85 timescF_in_aaa(one(X1), X2, X3) -> U89_aaa(X1, X2, X3, timescF_in_aaa(X1, X2, X4)) 18.95/5.85 U89_aaa(X1, X2, X3, timescF_out_aaa(X1, X2, X4)) -> U90_aaa(X1, X2, X3, addcG_in_aaa(X2, X4, X3)) 18.95/5.85 addcG_in_aaa(b, X1, zero(X1)) -> U149_aaa(X1, binaryZcP_in_a(X1)) 18.95/5.85 binaryZcP_in_a(X1) -> U119_a(X1, binaryZcH_in_a(X1)) 18.95/5.85 binaryZcH_in_a(zero(X1)) -> U91_a(X1, binaryZcH_in_a(X1)) 18.95/5.85 binaryZcH_in_a(one(X1)) -> U92_a(X1, binarycI_in_a(X1)) 18.95/5.85 binarycI_in_a(b) -> binarycI_out_a(b) 18.95/5.85 binarycI_in_a(zero(X1)) -> U93_a(X1, binaryZcH_in_a(X1)) 18.95/5.85 U93_a(X1, binaryZcH_out_a(X1)) -> binarycI_out_a(zero(X1)) 18.95/5.85 binarycI_in_a(one(X1)) -> U94_a(X1, binarycI_in_a(X1)) 18.95/5.85 U94_a(X1, binarycI_out_a(X1)) -> binarycI_out_a(one(X1)) 18.95/5.85 U92_a(X1, binarycI_out_a(X1)) -> binaryZcH_out_a(one(X1)) 18.95/5.85 U91_a(X1, binaryZcH_out_a(X1)) -> binaryZcH_out_a(zero(X1)) 18.95/5.85 U119_a(X1, binaryZcH_out_a(X1)) -> binaryZcP_out_a(X1) 18.95/5.85 U149_aaa(X1, binaryZcP_out_a(X1)) -> addcG_out_aaa(b, X1, zero(X1)) 18.95/5.85 addcG_in_aaa(zero(X1), X2, zero(X3)) -> U150_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.85 addzcJ_in_aaa(zero(X1), zero(X2), zero(X3)) -> U95_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.85 addzcJ_in_aaa(zero(one(X1)), one(b), one(one(X1))) -> U96_aaa(X1, binarycI_in_a(X1)) 18.95/5.85 U96_aaa(X1, binarycI_out_a(X1)) -> addzcJ_out_aaa(zero(one(X1)), one(b), one(one(X1))) 18.95/5.85 addzcJ_in_aaa(zero(zero(X1)), one(b), one(zero(X1))) -> U97_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.85 U97_aaa(X1, binaryZcH_out_a(X1)) -> addzcJ_out_aaa(zero(zero(X1)), one(b), one(zero(X1))) 18.95/5.85 addzcJ_in_aaa(zero(X1), one(X2), one(X3)) -> U98_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.85 addzcJ_in_aaa(one(X1), zero(X2), one(X3)) -> U99_aaa(X1, X2, X3, addycK_in_aaa(X1, X2, X3)) 18.95/5.85 addycK_in_aaa(b, one(X1), one(X1)) -> U116_aaa(X1, binarycI_in_a(X1)) 18.95/5.85 U116_aaa(X1, binarycI_out_a(X1)) -> addycK_out_aaa(b, one(X1), one(X1)) 18.95/5.85 addycK_in_aaa(b, zero(X1), zero(X1)) -> U117_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.85 U117_aaa(X1, binaryZcH_out_a(X1)) -> addycK_out_aaa(b, zero(X1), zero(X1)) 18.95/5.85 addycK_in_aaa(X1, X2, X3) -> U118_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.85 addzcJ_in_aaa(one(X1), one(X2), zero(X3)) -> U100_aaa(X1, X2, X3, addccL_in_aaa(X1, X2, X3)) 18.95/5.85 addccL_in_aaa(b, b, one(b)) -> addccL_out_aaa(b, b, one(b)) 18.95/5.85 addccL_in_aaa(X1, b, X2) -> U113_aaa(X1, X2, succZcN_in_aa(X1, X2)) 18.95/5.85 succZcN_in_aa(zero(X1), one(X1)) -> U103_aa(X1, binaryZcH_in_a(X1)) 18.95/5.85 U103_aa(X1, binaryZcH_out_a(X1)) -> succZcN_out_aa(zero(X1), one(X1)) 18.95/5.85 succZcN_in_aa(one(X1), zero(X2)) -> U104_aa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.85 succcM_in_aa(b, one(b)) -> succcM_out_aa(b, one(b)) 18.95/5.85 succcM_in_aa(zero(X1), one(X1)) -> U101_aa(X1, binaryZcH_in_a(X1)) 18.95/5.85 U101_aa(X1, binaryZcH_out_a(X1)) -> succcM_out_aa(zero(X1), one(X1)) 18.95/5.85 succcM_in_aa(one(X1), zero(X2)) -> U102_aa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.85 U102_aa(X1, X2, succcM_out_aa(X1, X2)) -> succcM_out_aa(one(X1), zero(X2)) 18.95/5.85 U104_aa(X1, X2, succcM_out_aa(X1, X2)) -> succZcN_out_aa(one(X1), zero(X2)) 18.95/5.85 U113_aaa(X1, X2, succZcN_out_aa(X1, X2)) -> addccL_out_aaa(X1, b, X2) 18.95/5.85 addccL_in_aaa(b, X1, X2) -> U114_aaa(X1, X2, succZcN_in_aa(X1, X2)) 18.95/5.85 U114_aaa(X1, X2, succZcN_out_aa(X1, X2)) -> addccL_out_aaa(b, X1, X2) 18.95/5.85 addccL_in_aaa(X1, X2, X3) -> U115_aaa(X1, X2, X3, addCcO_in_aaa(X1, X2, X3)) 18.95/5.85 addCcO_in_aaa(zero(X1), zero(X2), one(X3)) -> U105_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.85 U105_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(zero(X1), zero(X2), one(X3)) 18.95/5.85 addCcO_in_aaa(zero(zero(X1)), one(b), zero(one(X1))) -> U106_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.85 U106_aaa(X1, binaryZcH_out_a(X1)) -> addCcO_out_aaa(zero(zero(X1)), one(b), zero(one(X1))) 18.95/5.85 addCcO_in_aaa(zero(one(X1)), one(b), zero(zero(X2))) -> U107_aaa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.85 U107_aaa(X1, X2, succcM_out_aa(X1, X2)) -> addCcO_out_aaa(zero(one(X1)), one(b), zero(zero(X2))) 18.95/5.85 addCcO_in_aaa(zero(X1), one(X2), zero(X3)) -> U108_aaa(X1, X2, X3, addCcO_in_aaa(X1, X2, X3)) 18.95/5.85 addCcO_in_aaa(one(b), zero(zero(X1)), zero(one(X1))) -> U109_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.85 U109_aaa(X1, binaryZcH_out_a(X1)) -> addCcO_out_aaa(one(b), zero(zero(X1)), zero(one(X1))) 18.95/5.85 addCcO_in_aaa(one(b), zero(one(X1)), zero(zero(X2))) -> U110_aaa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.85 U110_aaa(X1, X2, succcM_out_aa(X1, X2)) -> addCcO_out_aaa(one(b), zero(one(X1)), zero(zero(X2))) 18.95/5.85 addCcO_in_aaa(one(X1), zero(X2), zero(X3)) -> U111_aaa(X1, X2, X3, addCcO_in_aaa(X1, X2, X3)) 18.95/5.85 addCcO_in_aaa(one(X1), one(X2), one(X3)) -> U112_aaa(X1, X2, X3, addccL_in_aaa(X1, X2, X3)) 18.95/5.85 U112_aaa(X1, X2, X3, addccL_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(one(X1), one(X2), one(X3)) 18.95/5.85 U111_aaa(X1, X2, X3, addCcO_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(one(X1), zero(X2), zero(X3)) 18.95/5.85 U108_aaa(X1, X2, X3, addCcO_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(zero(X1), one(X2), zero(X3)) 18.95/5.85 U115_aaa(X1, X2, X3, addCcO_out_aaa(X1, X2, X3)) -> addccL_out_aaa(X1, X2, X3) 18.95/5.85 U100_aaa(X1, X2, X3, addccL_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(one(X1), one(X2), zero(X3)) 18.95/5.85 U118_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addycK_out_aaa(X1, X2, X3) 18.95/5.85 U99_aaa(X1, X2, X3, addycK_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(one(X1), zero(X2), one(X3)) 18.95/5.85 U98_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(zero(X1), one(X2), one(X3)) 18.95/5.85 U95_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(zero(X1), zero(X2), zero(X3)) 18.95/5.85 U150_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addcG_out_aaa(zero(X1), X2, zero(X3)) 18.95/5.85 addcG_in_aaa(one(X1), X2, one(X3)) -> U151_aaa(X1, X2, X3, addycK_in_aaa(X1, X2, X3)) 18.95/5.85 U151_aaa(X1, X2, X3, addycK_out_aaa(X1, X2, X3)) -> addcG_out_aaa(one(X1), X2, one(X3)) 18.95/5.85 U90_aaa(X1, X2, X3, addcG_out_aaa(X2, X4, X3)) -> timescF_out_aaa(one(X1), X2, X3) 18.95/5.85 U88_aaa(X1, X2, X3, timescF_out_aaa(X1, X2, X3)) -> timescF_out_aaa(zero(X1), X2, zero(X3)) 18.95/5.85 18.95/5.85 The argument filtering Pi contains the following mapping: 18.95/5.85 zero(x1) = zero(x1) 18.95/5.85 18.95/5.85 timescF_in_aaa(x1, x2, x3) = timescF_in_aaa 18.95/5.85 18.95/5.85 timescF_out_aaa(x1, x2, x3) = timescF_out_aaa(x1) 18.95/5.85 18.95/5.85 U88_aaa(x1, x2, x3, x4) = U88_aaa(x4) 18.95/5.85 18.95/5.85 U89_aaa(x1, x2, x3, x4) = U89_aaa(x4) 18.95/5.85 18.95/5.85 U90_aaa(x1, x2, x3, x4) = U90_aaa(x1, x4) 18.95/5.85 18.95/5.85 addcG_in_aaa(x1, x2, x3) = addcG_in_aaa 18.95/5.85 18.95/5.85 U149_aaa(x1, x2) = U149_aaa(x2) 18.95/5.85 18.95/5.85 binaryZcP_in_a(x1) = binaryZcP_in_a 18.95/5.85 18.95/5.85 U119_a(x1, x2) = U119_a(x2) 18.95/5.85 18.95/5.85 binaryZcH_in_a(x1) = binaryZcH_in_a 18.95/5.85 18.95/5.85 U91_a(x1, x2) = U91_a(x2) 18.95/5.85 18.95/5.85 U92_a(x1, x2) = U92_a(x2) 18.95/5.85 18.95/5.85 binarycI_in_a(x1) = binarycI_in_a 18.95/5.85 18.95/5.85 binarycI_out_a(x1) = binarycI_out_a(x1) 18.95/5.85 18.95/5.85 U93_a(x1, x2) = U93_a(x2) 18.95/5.85 18.95/5.85 binaryZcH_out_a(x1) = binaryZcH_out_a(x1) 18.95/5.85 18.95/5.85 U94_a(x1, x2) = U94_a(x2) 18.95/5.85 18.95/5.85 binaryZcP_out_a(x1) = binaryZcP_out_a(x1) 18.95/5.85 18.95/5.85 addcG_out_aaa(x1, x2, x3) = addcG_out_aaa(x1, x2, x3) 18.95/5.85 18.95/5.85 U150_aaa(x1, x2, x3, x4) = U150_aaa(x4) 18.95/5.85 18.95/5.85 addzcJ_in_aaa(x1, x2, x3) = addzcJ_in_aaa 18.95/5.85 18.95/5.85 U95_aaa(x1, x2, x3, x4) = U95_aaa(x4) 18.95/5.85 18.95/5.85 U96_aaa(x1, x2) = U96_aaa(x2) 18.95/5.85 18.95/5.85 addzcJ_out_aaa(x1, x2, x3) = addzcJ_out_aaa(x1, x2, x3) 18.95/5.85 18.95/5.85 U97_aaa(x1, x2) = U97_aaa(x2) 18.95/5.85 18.95/5.85 U98_aaa(x1, x2, x3, x4) = U98_aaa(x4) 18.95/5.85 18.95/5.85 U99_aaa(x1, x2, x3, x4) = U99_aaa(x4) 18.95/5.85 18.95/5.85 addycK_in_aaa(x1, x2, x3) = addycK_in_aaa 18.95/5.85 18.95/5.85 U116_aaa(x1, x2) = U116_aaa(x2) 18.95/5.85 18.95/5.85 addycK_out_aaa(x1, x2, x3) = addycK_out_aaa(x1, x2, x3) 18.95/5.85 18.95/5.85 U117_aaa(x1, x2) = U117_aaa(x2) 18.95/5.85 18.95/5.85 U118_aaa(x1, x2, x3, x4) = U118_aaa(x4) 18.95/5.85 18.95/5.85 U100_aaa(x1, x2, x3, x4) = U100_aaa(x4) 18.95/5.85 18.95/5.85 addccL_in_aaa(x1, x2, x3) = addccL_in_aaa 18.95/5.85 18.95/5.85 addccL_out_aaa(x1, x2, x3) = addccL_out_aaa(x1, x2, x3) 18.95/5.85 18.95/5.85 U113_aaa(x1, x2, x3) = U113_aaa(x3) 18.95/5.85 18.95/5.85 succZcN_in_aa(x1, x2) = succZcN_in_aa 18.95/5.85 18.95/5.85 U103_aa(x1, x2) = U103_aa(x2) 18.95/5.85 18.95/5.85 succZcN_out_aa(x1, x2) = succZcN_out_aa(x1, x2) 18.95/5.85 18.95/5.85 U104_aa(x1, x2, x3) = U104_aa(x3) 18.95/5.85 18.95/5.85 succcM_in_aa(x1, x2) = succcM_in_aa 18.95/5.85 18.95/5.85 succcM_out_aa(x1, x2) = succcM_out_aa(x1, x2) 18.95/5.85 18.95/5.85 U101_aa(x1, x2) = U101_aa(x2) 18.95/5.85 18.95/5.85 U102_aa(x1, x2, x3) = U102_aa(x3) 18.95/5.85 18.95/5.85 U114_aaa(x1, x2, x3) = U114_aaa(x3) 18.95/5.85 18.95/5.85 U115_aaa(x1, x2, x3, x4) = U115_aaa(x4) 18.95/5.85 18.95/5.85 addCcO_in_aaa(x1, x2, x3) = addCcO_in_aaa 18.95/5.85 18.95/5.85 U105_aaa(x1, x2, x3, x4) = U105_aaa(x4) 18.95/5.85 18.95/5.85 addCcO_out_aaa(x1, x2, x3) = addCcO_out_aaa(x1, x2, x3) 18.95/5.85 18.95/5.85 U106_aaa(x1, x2) = U106_aaa(x2) 18.95/5.85 18.95/5.85 U107_aaa(x1, x2, x3) = U107_aaa(x3) 18.95/5.85 18.95/5.85 U108_aaa(x1, x2, x3, x4) = U108_aaa(x4) 18.95/5.86 18.95/5.86 U109_aaa(x1, x2) = U109_aaa(x2) 18.95/5.86 18.95/5.86 U110_aaa(x1, x2, x3) = U110_aaa(x3) 18.95/5.86 18.95/5.86 U111_aaa(x1, x2, x3, x4) = U111_aaa(x4) 18.95/5.86 18.95/5.86 U112_aaa(x1, x2, x3, x4) = U112_aaa(x4) 18.95/5.86 18.95/5.86 U151_aaa(x1, x2, x3, x4) = U151_aaa(x4) 18.95/5.86 18.95/5.86 one(x1) = one(x1) 18.95/5.86 18.95/5.86 b = b 18.95/5.86 18.95/5.86 ADDZQ_IN_AAG(x1, x2, x3) = ADDZQ_IN_AAG(x3) 18.95/5.86 18.95/5.86 ADDYR_IN_AAG(x1, x2, x3) = ADDYR_IN_AAG(x3) 18.95/5.86 18.95/5.86 ADDCS_IN_AAG(x1, x2, x3) = ADDCS_IN_AAG(x3) 18.95/5.86 18.95/5.86 ADDCV_IN_AAG(x1, x2, x3) = ADDCV_IN_AAG(x3) 18.95/5.86 18.95/5.86 18.95/5.86 We have to consider all (P,R,Pi)-chains 18.95/5.86 ---------------------------------------- 18.95/5.86 18.95/5.86 (170) UsableRulesProof (EQUIVALENT) 18.95/5.86 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 18.95/5.86 ---------------------------------------- 18.95/5.86 18.95/5.86 (171) 18.95/5.86 Obligation: 18.95/5.86 Pi DP problem: 18.95/5.86 The TRS P consists of the following rules: 18.95/5.86 18.95/5.86 ADDZQ_IN_AAG(zero(X1), one(X2), one(X3)) -> ADDZQ_IN_AAG(X1, X2, X3) 18.95/5.86 ADDZQ_IN_AAG(zero(X1), zero(X2), zero(X3)) -> ADDZQ_IN_AAG(X1, X2, X3) 18.95/5.86 ADDZQ_IN_AAG(one(X1), zero(X2), one(X3)) -> ADDYR_IN_AAG(X1, X2, X3) 18.95/5.86 ADDYR_IN_AAG(X1, X2, X3) -> ADDZQ_IN_AAG(X1, X2, X3) 18.95/5.86 ADDZQ_IN_AAG(one(X1), one(X2), zero(X3)) -> ADDCS_IN_AAG(X1, X2, X3) 18.95/5.86 ADDCS_IN_AAG(X1, X2, X3) -> ADDCV_IN_AAG(X1, X2, X3) 18.95/5.86 ADDCV_IN_AAG(zero(X1), zero(X2), one(X3)) -> ADDZQ_IN_AAG(X1, X2, X3) 18.95/5.86 ADDCV_IN_AAG(zero(X1), one(X2), zero(X3)) -> ADDCV_IN_AAG(X1, X2, X3) 18.95/5.86 ADDCV_IN_AAG(one(X1), zero(X2), zero(X3)) -> ADDCV_IN_AAG(X1, X2, X3) 18.95/5.86 ADDCV_IN_AAG(one(X1), one(X2), one(X3)) -> ADDCS_IN_AAG(X1, X2, X3) 18.95/5.86 18.95/5.86 R is empty. 18.95/5.86 The argument filtering Pi contains the following mapping: 18.95/5.86 zero(x1) = zero(x1) 18.95/5.86 18.95/5.86 one(x1) = one(x1) 18.95/5.86 18.95/5.86 ADDZQ_IN_AAG(x1, x2, x3) = ADDZQ_IN_AAG(x3) 18.95/5.86 18.95/5.86 ADDYR_IN_AAG(x1, x2, x3) = ADDYR_IN_AAG(x3) 18.95/5.86 18.95/5.86 ADDCS_IN_AAG(x1, x2, x3) = ADDCS_IN_AAG(x3) 18.95/5.86 18.95/5.86 ADDCV_IN_AAG(x1, x2, x3) = ADDCV_IN_AAG(x3) 18.95/5.86 18.95/5.86 18.95/5.86 We have to consider all (P,R,Pi)-chains 18.95/5.86 ---------------------------------------- 18.95/5.86 18.95/5.86 (172) PiDPToQDPProof (SOUND) 18.95/5.86 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 18.95/5.86 ---------------------------------------- 18.95/5.86 18.95/5.86 (173) 18.95/5.86 Obligation: 18.95/5.86 Q DP problem: 18.95/5.86 The TRS P consists of the following rules: 18.95/5.86 18.95/5.86 ADDZQ_IN_AAG(one(X3)) -> ADDZQ_IN_AAG(X3) 18.95/5.86 ADDZQ_IN_AAG(zero(X3)) -> ADDZQ_IN_AAG(X3) 18.95/5.86 ADDZQ_IN_AAG(one(X3)) -> ADDYR_IN_AAG(X3) 18.95/5.86 ADDYR_IN_AAG(X3) -> ADDZQ_IN_AAG(X3) 18.95/5.86 ADDZQ_IN_AAG(zero(X3)) -> ADDCS_IN_AAG(X3) 18.95/5.86 ADDCS_IN_AAG(X3) -> ADDCV_IN_AAG(X3) 18.95/5.86 ADDCV_IN_AAG(one(X3)) -> ADDZQ_IN_AAG(X3) 18.95/5.86 ADDCV_IN_AAG(zero(X3)) -> ADDCV_IN_AAG(X3) 18.95/5.86 ADDCV_IN_AAG(one(X3)) -> ADDCS_IN_AAG(X3) 18.95/5.86 18.95/5.86 R is empty. 18.95/5.86 Q is empty. 18.95/5.86 We have to consider all (P,Q,R)-chains. 18.95/5.86 ---------------------------------------- 18.95/5.86 18.95/5.86 (174) QDPSizeChangeProof (EQUIVALENT) 18.95/5.86 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 18.95/5.86 18.95/5.86 From the DPs we obtained the following set of size-change graphs: 18.95/5.86 *ADDYR_IN_AAG(X3) -> ADDZQ_IN_AAG(X3) 18.95/5.86 The graph contains the following edges 1 >= 1 18.95/5.86 18.95/5.86 18.95/5.86 *ADDCV_IN_AAG(one(X3)) -> ADDZQ_IN_AAG(X3) 18.95/5.86 The graph contains the following edges 1 > 1 18.95/5.86 18.95/5.86 18.95/5.86 *ADDZQ_IN_AAG(one(X3)) -> ADDYR_IN_AAG(X3) 18.95/5.86 The graph contains the following edges 1 > 1 18.95/5.86 18.95/5.86 18.95/5.86 *ADDZQ_IN_AAG(zero(X3)) -> ADDCS_IN_AAG(X3) 18.95/5.86 The graph contains the following edges 1 > 1 18.95/5.86 18.95/5.86 18.95/5.86 *ADDCS_IN_AAG(X3) -> ADDCV_IN_AAG(X3) 18.95/5.86 The graph contains the following edges 1 >= 1 18.95/5.86 18.95/5.86 18.95/5.86 *ADDCV_IN_AAG(one(X3)) -> ADDCS_IN_AAG(X3) 18.95/5.86 The graph contains the following edges 1 > 1 18.95/5.86 18.95/5.86 18.95/5.86 *ADDCV_IN_AAG(zero(X3)) -> ADDCV_IN_AAG(X3) 18.95/5.86 The graph contains the following edges 1 > 1 18.95/5.86 18.95/5.86 18.95/5.86 *ADDZQ_IN_AAG(one(X3)) -> ADDZQ_IN_AAG(X3) 18.95/5.86 The graph contains the following edges 1 > 1 18.95/5.86 18.95/5.86 18.95/5.86 *ADDZQ_IN_AAG(zero(X3)) -> ADDZQ_IN_AAG(X3) 18.95/5.86 The graph contains the following edges 1 > 1 18.95/5.86 18.95/5.86 18.95/5.86 ---------------------------------------- 18.95/5.86 18.95/5.86 (175) 18.95/5.86 YES 18.95/5.86 18.95/5.86 ---------------------------------------- 18.95/5.86 18.95/5.86 (176) 18.95/5.86 Obligation: 18.95/5.86 Pi DP problem: 18.95/5.86 The TRS P consists of the following rules: 18.95/5.86 18.95/5.86 BINARYZH_IN_A(one(X1)) -> BINARYI_IN_A(X1) 18.95/5.86 BINARYI_IN_A(zero(X1)) -> BINARYZH_IN_A(X1) 18.95/5.86 BINARYZH_IN_A(zero(X1)) -> BINARYZH_IN_A(X1) 18.95/5.86 BINARYI_IN_A(one(X1)) -> BINARYI_IN_A(X1) 18.95/5.86 18.95/5.86 The TRS R consists of the following rules: 18.95/5.86 18.95/5.86 timescF_in_aaa(one(b), X1, X1) -> timescF_out_aaa(one(b), X1, X1) 18.95/5.86 timescF_in_aaa(zero(X1), X2, zero(X3)) -> U88_aaa(X1, X2, X3, timescF_in_aaa(X1, X2, X3)) 18.95/5.86 timescF_in_aaa(one(X1), X2, X3) -> U89_aaa(X1, X2, X3, timescF_in_aaa(X1, X2, X4)) 18.95/5.86 U89_aaa(X1, X2, X3, timescF_out_aaa(X1, X2, X4)) -> U90_aaa(X1, X2, X3, addcG_in_aaa(X2, X4, X3)) 18.95/5.86 addcG_in_aaa(b, X1, zero(X1)) -> U149_aaa(X1, binaryZcP_in_a(X1)) 18.95/5.86 binaryZcP_in_a(X1) -> U119_a(X1, binaryZcH_in_a(X1)) 18.95/5.86 binaryZcH_in_a(zero(X1)) -> U91_a(X1, binaryZcH_in_a(X1)) 18.95/5.86 binaryZcH_in_a(one(X1)) -> U92_a(X1, binarycI_in_a(X1)) 18.95/5.86 binarycI_in_a(b) -> binarycI_out_a(b) 18.95/5.86 binarycI_in_a(zero(X1)) -> U93_a(X1, binaryZcH_in_a(X1)) 18.95/5.86 U93_a(X1, binaryZcH_out_a(X1)) -> binarycI_out_a(zero(X1)) 18.95/5.86 binarycI_in_a(one(X1)) -> U94_a(X1, binarycI_in_a(X1)) 18.95/5.86 U94_a(X1, binarycI_out_a(X1)) -> binarycI_out_a(one(X1)) 18.95/5.86 U92_a(X1, binarycI_out_a(X1)) -> binaryZcH_out_a(one(X1)) 18.95/5.86 U91_a(X1, binaryZcH_out_a(X1)) -> binaryZcH_out_a(zero(X1)) 18.95/5.86 U119_a(X1, binaryZcH_out_a(X1)) -> binaryZcP_out_a(X1) 18.95/5.86 U149_aaa(X1, binaryZcP_out_a(X1)) -> addcG_out_aaa(b, X1, zero(X1)) 18.95/5.86 addcG_in_aaa(zero(X1), X2, zero(X3)) -> U150_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.86 addzcJ_in_aaa(zero(X1), zero(X2), zero(X3)) -> U95_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.86 addzcJ_in_aaa(zero(one(X1)), one(b), one(one(X1))) -> U96_aaa(X1, binarycI_in_a(X1)) 18.95/5.86 U96_aaa(X1, binarycI_out_a(X1)) -> addzcJ_out_aaa(zero(one(X1)), one(b), one(one(X1))) 18.95/5.86 addzcJ_in_aaa(zero(zero(X1)), one(b), one(zero(X1))) -> U97_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.86 U97_aaa(X1, binaryZcH_out_a(X1)) -> addzcJ_out_aaa(zero(zero(X1)), one(b), one(zero(X1))) 18.95/5.86 addzcJ_in_aaa(zero(X1), one(X2), one(X3)) -> U98_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.86 addzcJ_in_aaa(one(X1), zero(X2), one(X3)) -> U99_aaa(X1, X2, X3, addycK_in_aaa(X1, X2, X3)) 18.95/5.86 addycK_in_aaa(b, one(X1), one(X1)) -> U116_aaa(X1, binarycI_in_a(X1)) 18.95/5.86 U116_aaa(X1, binarycI_out_a(X1)) -> addycK_out_aaa(b, one(X1), one(X1)) 18.95/5.86 addycK_in_aaa(b, zero(X1), zero(X1)) -> U117_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.86 U117_aaa(X1, binaryZcH_out_a(X1)) -> addycK_out_aaa(b, zero(X1), zero(X1)) 18.95/5.86 addycK_in_aaa(X1, X2, X3) -> U118_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.86 addzcJ_in_aaa(one(X1), one(X2), zero(X3)) -> U100_aaa(X1, X2, X3, addccL_in_aaa(X1, X2, X3)) 18.95/5.86 addccL_in_aaa(b, b, one(b)) -> addccL_out_aaa(b, b, one(b)) 18.95/5.86 addccL_in_aaa(X1, b, X2) -> U113_aaa(X1, X2, succZcN_in_aa(X1, X2)) 18.95/5.86 succZcN_in_aa(zero(X1), one(X1)) -> U103_aa(X1, binaryZcH_in_a(X1)) 18.95/5.86 U103_aa(X1, binaryZcH_out_a(X1)) -> succZcN_out_aa(zero(X1), one(X1)) 18.95/5.86 succZcN_in_aa(one(X1), zero(X2)) -> U104_aa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.86 succcM_in_aa(b, one(b)) -> succcM_out_aa(b, one(b)) 18.95/5.86 succcM_in_aa(zero(X1), one(X1)) -> U101_aa(X1, binaryZcH_in_a(X1)) 18.95/5.86 U101_aa(X1, binaryZcH_out_a(X1)) -> succcM_out_aa(zero(X1), one(X1)) 18.95/5.86 succcM_in_aa(one(X1), zero(X2)) -> U102_aa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.86 U102_aa(X1, X2, succcM_out_aa(X1, X2)) -> succcM_out_aa(one(X1), zero(X2)) 18.95/5.86 U104_aa(X1, X2, succcM_out_aa(X1, X2)) -> succZcN_out_aa(one(X1), zero(X2)) 18.95/5.86 U113_aaa(X1, X2, succZcN_out_aa(X1, X2)) -> addccL_out_aaa(X1, b, X2) 18.95/5.86 addccL_in_aaa(b, X1, X2) -> U114_aaa(X1, X2, succZcN_in_aa(X1, X2)) 18.95/5.86 U114_aaa(X1, X2, succZcN_out_aa(X1, X2)) -> addccL_out_aaa(b, X1, X2) 18.95/5.86 addccL_in_aaa(X1, X2, X3) -> U115_aaa(X1, X2, X3, addCcO_in_aaa(X1, X2, X3)) 18.95/5.86 addCcO_in_aaa(zero(X1), zero(X2), one(X3)) -> U105_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.86 U105_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(zero(X1), zero(X2), one(X3)) 18.95/5.86 addCcO_in_aaa(zero(zero(X1)), one(b), zero(one(X1))) -> U106_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.86 U106_aaa(X1, binaryZcH_out_a(X1)) -> addCcO_out_aaa(zero(zero(X1)), one(b), zero(one(X1))) 18.95/5.86 addCcO_in_aaa(zero(one(X1)), one(b), zero(zero(X2))) -> U107_aaa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.86 U107_aaa(X1, X2, succcM_out_aa(X1, X2)) -> addCcO_out_aaa(zero(one(X1)), one(b), zero(zero(X2))) 18.95/5.86 addCcO_in_aaa(zero(X1), one(X2), zero(X3)) -> U108_aaa(X1, X2, X3, addCcO_in_aaa(X1, X2, X3)) 18.95/5.86 addCcO_in_aaa(one(b), zero(zero(X1)), zero(one(X1))) -> U109_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.86 U109_aaa(X1, binaryZcH_out_a(X1)) -> addCcO_out_aaa(one(b), zero(zero(X1)), zero(one(X1))) 18.95/5.86 addCcO_in_aaa(one(b), zero(one(X1)), zero(zero(X2))) -> U110_aaa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.86 U110_aaa(X1, X2, succcM_out_aa(X1, X2)) -> addCcO_out_aaa(one(b), zero(one(X1)), zero(zero(X2))) 18.95/5.86 addCcO_in_aaa(one(X1), zero(X2), zero(X3)) -> U111_aaa(X1, X2, X3, addCcO_in_aaa(X1, X2, X3)) 18.95/5.86 addCcO_in_aaa(one(X1), one(X2), one(X3)) -> U112_aaa(X1, X2, X3, addccL_in_aaa(X1, X2, X3)) 18.95/5.86 U112_aaa(X1, X2, X3, addccL_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(one(X1), one(X2), one(X3)) 18.95/5.86 U111_aaa(X1, X2, X3, addCcO_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(one(X1), zero(X2), zero(X3)) 18.95/5.86 U108_aaa(X1, X2, X3, addCcO_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(zero(X1), one(X2), zero(X3)) 18.95/5.86 U115_aaa(X1, X2, X3, addCcO_out_aaa(X1, X2, X3)) -> addccL_out_aaa(X1, X2, X3) 18.95/5.86 U100_aaa(X1, X2, X3, addccL_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(one(X1), one(X2), zero(X3)) 18.95/5.86 U118_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addycK_out_aaa(X1, X2, X3) 18.95/5.86 U99_aaa(X1, X2, X3, addycK_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(one(X1), zero(X2), one(X3)) 18.95/5.86 U98_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(zero(X1), one(X2), one(X3)) 18.95/5.86 U95_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(zero(X1), zero(X2), zero(X3)) 18.95/5.86 U150_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addcG_out_aaa(zero(X1), X2, zero(X3)) 18.95/5.86 addcG_in_aaa(one(X1), X2, one(X3)) -> U151_aaa(X1, X2, X3, addycK_in_aaa(X1, X2, X3)) 18.95/5.86 U151_aaa(X1, X2, X3, addycK_out_aaa(X1, X2, X3)) -> addcG_out_aaa(one(X1), X2, one(X3)) 18.95/5.86 U90_aaa(X1, X2, X3, addcG_out_aaa(X2, X4, X3)) -> timescF_out_aaa(one(X1), X2, X3) 18.95/5.86 U88_aaa(X1, X2, X3, timescF_out_aaa(X1, X2, X3)) -> timescF_out_aaa(zero(X1), X2, zero(X3)) 18.95/5.86 18.95/5.86 The argument filtering Pi contains the following mapping: 18.95/5.86 zero(x1) = zero(x1) 18.95/5.86 18.95/5.86 timescF_in_aaa(x1, x2, x3) = timescF_in_aaa 18.95/5.86 18.95/5.86 timescF_out_aaa(x1, x2, x3) = timescF_out_aaa(x1) 18.95/5.86 18.95/5.86 U88_aaa(x1, x2, x3, x4) = U88_aaa(x4) 18.95/5.86 18.95/5.86 U89_aaa(x1, x2, x3, x4) = U89_aaa(x4) 18.95/5.86 18.95/5.86 U90_aaa(x1, x2, x3, x4) = U90_aaa(x1, x4) 18.95/5.86 18.95/5.86 addcG_in_aaa(x1, x2, x3) = addcG_in_aaa 18.95/5.86 18.95/5.86 U149_aaa(x1, x2) = U149_aaa(x2) 18.95/5.86 18.95/5.86 binaryZcP_in_a(x1) = binaryZcP_in_a 18.95/5.86 18.95/5.86 U119_a(x1, x2) = U119_a(x2) 18.95/5.86 18.95/5.86 binaryZcH_in_a(x1) = binaryZcH_in_a 18.95/5.86 18.95/5.86 U91_a(x1, x2) = U91_a(x2) 18.95/5.86 18.95/5.86 U92_a(x1, x2) = U92_a(x2) 18.95/5.86 18.95/5.86 binarycI_in_a(x1) = binarycI_in_a 18.95/5.86 18.95/5.86 binarycI_out_a(x1) = binarycI_out_a(x1) 18.95/5.86 18.95/5.86 U93_a(x1, x2) = U93_a(x2) 18.95/5.86 18.95/5.86 binaryZcH_out_a(x1) = binaryZcH_out_a(x1) 18.95/5.86 18.95/5.86 U94_a(x1, x2) = U94_a(x2) 18.95/5.86 18.95/5.86 binaryZcP_out_a(x1) = binaryZcP_out_a(x1) 18.95/5.86 18.95/5.86 addcG_out_aaa(x1, x2, x3) = addcG_out_aaa(x1, x2, x3) 18.95/5.86 18.95/5.86 U150_aaa(x1, x2, x3, x4) = U150_aaa(x4) 18.95/5.86 18.95/5.86 addzcJ_in_aaa(x1, x2, x3) = addzcJ_in_aaa 18.95/5.86 18.95/5.86 U95_aaa(x1, x2, x3, x4) = U95_aaa(x4) 18.95/5.86 18.95/5.86 U96_aaa(x1, x2) = U96_aaa(x2) 18.95/5.86 18.95/5.86 addzcJ_out_aaa(x1, x2, x3) = addzcJ_out_aaa(x1, x2, x3) 18.95/5.86 18.95/5.86 U97_aaa(x1, x2) = U97_aaa(x2) 18.95/5.86 18.95/5.86 U98_aaa(x1, x2, x3, x4) = U98_aaa(x4) 18.95/5.86 18.95/5.86 U99_aaa(x1, x2, x3, x4) = U99_aaa(x4) 18.95/5.86 18.95/5.86 addycK_in_aaa(x1, x2, x3) = addycK_in_aaa 18.95/5.86 18.95/5.86 U116_aaa(x1, x2) = U116_aaa(x2) 18.95/5.86 18.95/5.86 addycK_out_aaa(x1, x2, x3) = addycK_out_aaa(x1, x2, x3) 18.95/5.86 18.95/5.86 U117_aaa(x1, x2) = U117_aaa(x2) 18.95/5.86 18.95/5.86 U118_aaa(x1, x2, x3, x4) = U118_aaa(x4) 18.95/5.86 18.95/5.86 U100_aaa(x1, x2, x3, x4) = U100_aaa(x4) 18.95/5.86 18.95/5.86 addccL_in_aaa(x1, x2, x3) = addccL_in_aaa 18.95/5.86 18.95/5.86 addccL_out_aaa(x1, x2, x3) = addccL_out_aaa(x1, x2, x3) 18.95/5.86 18.95/5.86 U113_aaa(x1, x2, x3) = U113_aaa(x3) 18.95/5.86 18.95/5.86 succZcN_in_aa(x1, x2) = succZcN_in_aa 18.95/5.86 18.95/5.86 U103_aa(x1, x2) = U103_aa(x2) 18.95/5.86 18.95/5.86 succZcN_out_aa(x1, x2) = succZcN_out_aa(x1, x2) 18.95/5.86 18.95/5.86 U104_aa(x1, x2, x3) = U104_aa(x3) 18.95/5.86 18.95/5.86 succcM_in_aa(x1, x2) = succcM_in_aa 18.95/5.86 18.95/5.86 succcM_out_aa(x1, x2) = succcM_out_aa(x1, x2) 18.95/5.86 18.95/5.86 U101_aa(x1, x2) = U101_aa(x2) 18.95/5.86 18.95/5.86 U102_aa(x1, x2, x3) = U102_aa(x3) 18.95/5.86 18.95/5.86 U114_aaa(x1, x2, x3) = U114_aaa(x3) 18.95/5.86 18.95/5.86 U115_aaa(x1, x2, x3, x4) = U115_aaa(x4) 18.95/5.86 18.95/5.86 addCcO_in_aaa(x1, x2, x3) = addCcO_in_aaa 18.95/5.86 18.95/5.86 U105_aaa(x1, x2, x3, x4) = U105_aaa(x4) 18.95/5.86 18.95/5.86 addCcO_out_aaa(x1, x2, x3) = addCcO_out_aaa(x1, x2, x3) 18.95/5.86 18.95/5.86 U106_aaa(x1, x2) = U106_aaa(x2) 18.95/5.86 18.95/5.86 U107_aaa(x1, x2, x3) = U107_aaa(x3) 18.95/5.86 18.95/5.86 U108_aaa(x1, x2, x3, x4) = U108_aaa(x4) 18.95/5.86 18.95/5.86 U109_aaa(x1, x2) = U109_aaa(x2) 18.95/5.86 18.95/5.86 U110_aaa(x1, x2, x3) = U110_aaa(x3) 18.95/5.86 18.95/5.86 U111_aaa(x1, x2, x3, x4) = U111_aaa(x4) 18.95/5.86 18.95/5.86 U112_aaa(x1, x2, x3, x4) = U112_aaa(x4) 18.95/5.86 18.95/5.86 U151_aaa(x1, x2, x3, x4) = U151_aaa(x4) 18.95/5.86 18.95/5.86 one(x1) = one(x1) 18.95/5.86 18.95/5.86 b = b 18.95/5.86 18.95/5.86 BINARYZH_IN_A(x1) = BINARYZH_IN_A 18.95/5.86 18.95/5.86 BINARYI_IN_A(x1) = BINARYI_IN_A 18.95/5.86 18.95/5.86 18.95/5.86 We have to consider all (P,R,Pi)-chains 18.95/5.86 ---------------------------------------- 18.95/5.86 18.95/5.86 (177) UsableRulesProof (EQUIVALENT) 18.95/5.86 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 18.95/5.86 ---------------------------------------- 18.95/5.86 18.95/5.86 (178) 18.95/5.86 Obligation: 18.95/5.86 Pi DP problem: 18.95/5.86 The TRS P consists of the following rules: 18.95/5.86 18.95/5.86 BINARYZH_IN_A(one(X1)) -> BINARYI_IN_A(X1) 18.95/5.86 BINARYI_IN_A(zero(X1)) -> BINARYZH_IN_A(X1) 18.95/5.86 BINARYZH_IN_A(zero(X1)) -> BINARYZH_IN_A(X1) 18.95/5.86 BINARYI_IN_A(one(X1)) -> BINARYI_IN_A(X1) 18.95/5.86 18.95/5.86 R is empty. 18.95/5.86 The argument filtering Pi contains the following mapping: 18.95/5.86 zero(x1) = zero(x1) 18.95/5.86 18.95/5.86 one(x1) = one(x1) 18.95/5.86 18.95/5.86 BINARYZH_IN_A(x1) = BINARYZH_IN_A 18.95/5.86 18.95/5.86 BINARYI_IN_A(x1) = BINARYI_IN_A 18.95/5.86 18.95/5.86 18.95/5.86 We have to consider all (P,R,Pi)-chains 18.95/5.86 ---------------------------------------- 18.95/5.86 18.95/5.86 (179) PiDPToQDPProof (SOUND) 18.95/5.86 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 18.95/5.86 ---------------------------------------- 18.95/5.86 18.95/5.86 (180) 18.95/5.86 Obligation: 18.95/5.86 Q DP problem: 18.95/5.86 The TRS P consists of the following rules: 18.95/5.86 18.95/5.86 BINARYZH_IN_A -> BINARYI_IN_A 18.95/5.86 BINARYI_IN_A -> BINARYZH_IN_A 18.95/5.86 BINARYZH_IN_A -> BINARYZH_IN_A 18.95/5.86 BINARYI_IN_A -> BINARYI_IN_A 18.95/5.86 18.95/5.86 R is empty. 18.95/5.86 Q is empty. 18.95/5.86 We have to consider all (P,Q,R)-chains. 18.95/5.86 ---------------------------------------- 18.95/5.86 18.95/5.86 (181) NonTerminationLoopProof (COMPLETE) 18.95/5.86 We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. 18.95/5.86 Found a loop by semiunifying a rule from P directly. 18.95/5.86 18.95/5.86 s = BINARYZH_IN_A evaluates to t =BINARYZH_IN_A 18.95/5.86 18.95/5.86 Thus s starts an infinite chain as s semiunifies with t with the following substitutions: 18.95/5.86 * Matcher: [ ] 18.95/5.86 * Semiunifier: [ ] 18.95/5.86 18.95/5.86 -------------------------------------------------------------------------------- 18.95/5.86 Rewriting sequence 18.95/5.86 18.95/5.86 The DP semiunifies directly so there is only one rewrite step from BINARYZH_IN_A to BINARYZH_IN_A. 18.95/5.86 18.95/5.86 18.95/5.86 18.95/5.86 18.95/5.86 ---------------------------------------- 18.95/5.86 18.95/5.86 (182) 18.95/5.86 NO 18.95/5.86 18.95/5.86 ---------------------------------------- 18.95/5.86 18.95/5.86 (183) 18.95/5.86 Obligation: 18.95/5.86 Pi DP problem: 18.95/5.86 The TRS P consists of the following rules: 18.95/5.86 18.95/5.86 SUCCM_IN_AA(one(X1), zero(X2)) -> SUCCM_IN_AA(X1, X2) 18.95/5.86 18.95/5.86 The TRS R consists of the following rules: 18.95/5.86 18.95/5.86 timescF_in_aaa(one(b), X1, X1) -> timescF_out_aaa(one(b), X1, X1) 18.95/5.86 timescF_in_aaa(zero(X1), X2, zero(X3)) -> U88_aaa(X1, X2, X3, timescF_in_aaa(X1, X2, X3)) 18.95/5.86 timescF_in_aaa(one(X1), X2, X3) -> U89_aaa(X1, X2, X3, timescF_in_aaa(X1, X2, X4)) 18.95/5.86 U89_aaa(X1, X2, X3, timescF_out_aaa(X1, X2, X4)) -> U90_aaa(X1, X2, X3, addcG_in_aaa(X2, X4, X3)) 18.95/5.86 addcG_in_aaa(b, X1, zero(X1)) -> U149_aaa(X1, binaryZcP_in_a(X1)) 18.95/5.86 binaryZcP_in_a(X1) -> U119_a(X1, binaryZcH_in_a(X1)) 18.95/5.86 binaryZcH_in_a(zero(X1)) -> U91_a(X1, binaryZcH_in_a(X1)) 18.95/5.86 binaryZcH_in_a(one(X1)) -> U92_a(X1, binarycI_in_a(X1)) 18.95/5.86 binarycI_in_a(b) -> binarycI_out_a(b) 18.95/5.86 binarycI_in_a(zero(X1)) -> U93_a(X1, binaryZcH_in_a(X1)) 18.95/5.86 U93_a(X1, binaryZcH_out_a(X1)) -> binarycI_out_a(zero(X1)) 18.95/5.86 binarycI_in_a(one(X1)) -> U94_a(X1, binarycI_in_a(X1)) 18.95/5.86 U94_a(X1, binarycI_out_a(X1)) -> binarycI_out_a(one(X1)) 18.95/5.86 U92_a(X1, binarycI_out_a(X1)) -> binaryZcH_out_a(one(X1)) 18.95/5.86 U91_a(X1, binaryZcH_out_a(X1)) -> binaryZcH_out_a(zero(X1)) 18.95/5.86 U119_a(X1, binaryZcH_out_a(X1)) -> binaryZcP_out_a(X1) 18.95/5.86 U149_aaa(X1, binaryZcP_out_a(X1)) -> addcG_out_aaa(b, X1, zero(X1)) 18.95/5.86 addcG_in_aaa(zero(X1), X2, zero(X3)) -> U150_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.86 addzcJ_in_aaa(zero(X1), zero(X2), zero(X3)) -> U95_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.86 addzcJ_in_aaa(zero(one(X1)), one(b), one(one(X1))) -> U96_aaa(X1, binarycI_in_a(X1)) 18.95/5.86 U96_aaa(X1, binarycI_out_a(X1)) -> addzcJ_out_aaa(zero(one(X1)), one(b), one(one(X1))) 18.95/5.86 addzcJ_in_aaa(zero(zero(X1)), one(b), one(zero(X1))) -> U97_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.86 U97_aaa(X1, binaryZcH_out_a(X1)) -> addzcJ_out_aaa(zero(zero(X1)), one(b), one(zero(X1))) 18.95/5.86 addzcJ_in_aaa(zero(X1), one(X2), one(X3)) -> U98_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.86 addzcJ_in_aaa(one(X1), zero(X2), one(X3)) -> U99_aaa(X1, X2, X3, addycK_in_aaa(X1, X2, X3)) 18.95/5.86 addycK_in_aaa(b, one(X1), one(X1)) -> U116_aaa(X1, binarycI_in_a(X1)) 18.95/5.86 U116_aaa(X1, binarycI_out_a(X1)) -> addycK_out_aaa(b, one(X1), one(X1)) 18.95/5.86 addycK_in_aaa(b, zero(X1), zero(X1)) -> U117_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.86 U117_aaa(X1, binaryZcH_out_a(X1)) -> addycK_out_aaa(b, zero(X1), zero(X1)) 18.95/5.86 addycK_in_aaa(X1, X2, X3) -> U118_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.86 addzcJ_in_aaa(one(X1), one(X2), zero(X3)) -> U100_aaa(X1, X2, X3, addccL_in_aaa(X1, X2, X3)) 18.95/5.86 addccL_in_aaa(b, b, one(b)) -> addccL_out_aaa(b, b, one(b)) 18.95/5.86 addccL_in_aaa(X1, b, X2) -> U113_aaa(X1, X2, succZcN_in_aa(X1, X2)) 18.95/5.86 succZcN_in_aa(zero(X1), one(X1)) -> U103_aa(X1, binaryZcH_in_a(X1)) 18.95/5.86 U103_aa(X1, binaryZcH_out_a(X1)) -> succZcN_out_aa(zero(X1), one(X1)) 18.95/5.86 succZcN_in_aa(one(X1), zero(X2)) -> U104_aa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.86 succcM_in_aa(b, one(b)) -> succcM_out_aa(b, one(b)) 18.95/5.86 succcM_in_aa(zero(X1), one(X1)) -> U101_aa(X1, binaryZcH_in_a(X1)) 18.95/5.86 U101_aa(X1, binaryZcH_out_a(X1)) -> succcM_out_aa(zero(X1), one(X1)) 18.95/5.86 succcM_in_aa(one(X1), zero(X2)) -> U102_aa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.86 U102_aa(X1, X2, succcM_out_aa(X1, X2)) -> succcM_out_aa(one(X1), zero(X2)) 18.95/5.86 U104_aa(X1, X2, succcM_out_aa(X1, X2)) -> succZcN_out_aa(one(X1), zero(X2)) 18.95/5.86 U113_aaa(X1, X2, succZcN_out_aa(X1, X2)) -> addccL_out_aaa(X1, b, X2) 18.95/5.86 addccL_in_aaa(b, X1, X2) -> U114_aaa(X1, X2, succZcN_in_aa(X1, X2)) 18.95/5.86 U114_aaa(X1, X2, succZcN_out_aa(X1, X2)) -> addccL_out_aaa(b, X1, X2) 18.95/5.86 addccL_in_aaa(X1, X2, X3) -> U115_aaa(X1, X2, X3, addCcO_in_aaa(X1, X2, X3)) 18.95/5.86 addCcO_in_aaa(zero(X1), zero(X2), one(X3)) -> U105_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.86 U105_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(zero(X1), zero(X2), one(X3)) 18.95/5.86 addCcO_in_aaa(zero(zero(X1)), one(b), zero(one(X1))) -> U106_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.86 U106_aaa(X1, binaryZcH_out_a(X1)) -> addCcO_out_aaa(zero(zero(X1)), one(b), zero(one(X1))) 18.95/5.86 addCcO_in_aaa(zero(one(X1)), one(b), zero(zero(X2))) -> U107_aaa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.86 U107_aaa(X1, X2, succcM_out_aa(X1, X2)) -> addCcO_out_aaa(zero(one(X1)), one(b), zero(zero(X2))) 18.95/5.86 addCcO_in_aaa(zero(X1), one(X2), zero(X3)) -> U108_aaa(X1, X2, X3, addCcO_in_aaa(X1, X2, X3)) 18.95/5.86 addCcO_in_aaa(one(b), zero(zero(X1)), zero(one(X1))) -> U109_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.86 U109_aaa(X1, binaryZcH_out_a(X1)) -> addCcO_out_aaa(one(b), zero(zero(X1)), zero(one(X1))) 18.95/5.86 addCcO_in_aaa(one(b), zero(one(X1)), zero(zero(X2))) -> U110_aaa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.86 U110_aaa(X1, X2, succcM_out_aa(X1, X2)) -> addCcO_out_aaa(one(b), zero(one(X1)), zero(zero(X2))) 18.95/5.86 addCcO_in_aaa(one(X1), zero(X2), zero(X3)) -> U111_aaa(X1, X2, X3, addCcO_in_aaa(X1, X2, X3)) 18.95/5.86 addCcO_in_aaa(one(X1), one(X2), one(X3)) -> U112_aaa(X1, X2, X3, addccL_in_aaa(X1, X2, X3)) 18.95/5.86 U112_aaa(X1, X2, X3, addccL_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(one(X1), one(X2), one(X3)) 18.95/5.86 U111_aaa(X1, X2, X3, addCcO_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(one(X1), zero(X2), zero(X3)) 18.95/5.86 U108_aaa(X1, X2, X3, addCcO_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(zero(X1), one(X2), zero(X3)) 18.95/5.86 U115_aaa(X1, X2, X3, addCcO_out_aaa(X1, X2, X3)) -> addccL_out_aaa(X1, X2, X3) 18.95/5.86 U100_aaa(X1, X2, X3, addccL_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(one(X1), one(X2), zero(X3)) 18.95/5.86 U118_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addycK_out_aaa(X1, X2, X3) 18.95/5.86 U99_aaa(X1, X2, X3, addycK_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(one(X1), zero(X2), one(X3)) 18.95/5.86 U98_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(zero(X1), one(X2), one(X3)) 18.95/5.86 U95_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(zero(X1), zero(X2), zero(X3)) 18.95/5.86 U150_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addcG_out_aaa(zero(X1), X2, zero(X3)) 18.95/5.86 addcG_in_aaa(one(X1), X2, one(X3)) -> U151_aaa(X1, X2, X3, addycK_in_aaa(X1, X2, X3)) 18.95/5.86 U151_aaa(X1, X2, X3, addycK_out_aaa(X1, X2, X3)) -> addcG_out_aaa(one(X1), X2, one(X3)) 18.95/5.86 U90_aaa(X1, X2, X3, addcG_out_aaa(X2, X4, X3)) -> timescF_out_aaa(one(X1), X2, X3) 18.95/5.86 U88_aaa(X1, X2, X3, timescF_out_aaa(X1, X2, X3)) -> timescF_out_aaa(zero(X1), X2, zero(X3)) 18.95/5.86 18.95/5.86 The argument filtering Pi contains the following mapping: 18.95/5.86 zero(x1) = zero(x1) 18.95/5.86 18.95/5.86 timescF_in_aaa(x1, x2, x3) = timescF_in_aaa 18.95/5.86 18.95/5.86 timescF_out_aaa(x1, x2, x3) = timescF_out_aaa(x1) 18.95/5.86 18.95/5.86 U88_aaa(x1, x2, x3, x4) = U88_aaa(x4) 18.95/5.86 18.95/5.86 U89_aaa(x1, x2, x3, x4) = U89_aaa(x4) 18.95/5.86 18.95/5.86 U90_aaa(x1, x2, x3, x4) = U90_aaa(x1, x4) 18.95/5.86 18.95/5.86 addcG_in_aaa(x1, x2, x3) = addcG_in_aaa 18.95/5.86 18.95/5.86 U149_aaa(x1, x2) = U149_aaa(x2) 18.95/5.86 18.95/5.86 binaryZcP_in_a(x1) = binaryZcP_in_a 18.95/5.86 18.95/5.86 U119_a(x1, x2) = U119_a(x2) 18.95/5.86 18.95/5.86 binaryZcH_in_a(x1) = binaryZcH_in_a 18.95/5.86 18.95/5.86 U91_a(x1, x2) = U91_a(x2) 18.95/5.86 18.95/5.86 U92_a(x1, x2) = U92_a(x2) 18.95/5.86 18.95/5.86 binarycI_in_a(x1) = binarycI_in_a 18.95/5.86 18.95/5.86 binarycI_out_a(x1) = binarycI_out_a(x1) 18.95/5.86 18.95/5.86 U93_a(x1, x2) = U93_a(x2) 18.95/5.86 18.95/5.86 binaryZcH_out_a(x1) = binaryZcH_out_a(x1) 18.95/5.86 18.95/5.86 U94_a(x1, x2) = U94_a(x2) 18.95/5.86 18.95/5.86 binaryZcP_out_a(x1) = binaryZcP_out_a(x1) 18.95/5.86 18.95/5.86 addcG_out_aaa(x1, x2, x3) = addcG_out_aaa(x1, x2, x3) 18.95/5.86 18.95/5.86 U150_aaa(x1, x2, x3, x4) = U150_aaa(x4) 18.95/5.86 18.95/5.86 addzcJ_in_aaa(x1, x2, x3) = addzcJ_in_aaa 18.95/5.86 18.95/5.86 U95_aaa(x1, x2, x3, x4) = U95_aaa(x4) 18.95/5.86 18.95/5.86 U96_aaa(x1, x2) = U96_aaa(x2) 18.95/5.86 18.95/5.86 addzcJ_out_aaa(x1, x2, x3) = addzcJ_out_aaa(x1, x2, x3) 18.95/5.86 18.95/5.86 U97_aaa(x1, x2) = U97_aaa(x2) 18.95/5.86 18.95/5.86 U98_aaa(x1, x2, x3, x4) = U98_aaa(x4) 18.95/5.86 18.95/5.86 U99_aaa(x1, x2, x3, x4) = U99_aaa(x4) 18.95/5.86 18.95/5.86 addycK_in_aaa(x1, x2, x3) = addycK_in_aaa 18.95/5.86 18.95/5.86 U116_aaa(x1, x2) = U116_aaa(x2) 18.95/5.86 18.95/5.86 addycK_out_aaa(x1, x2, x3) = addycK_out_aaa(x1, x2, x3) 18.95/5.86 18.95/5.86 U117_aaa(x1, x2) = U117_aaa(x2) 18.95/5.86 18.95/5.86 U118_aaa(x1, x2, x3, x4) = U118_aaa(x4) 18.95/5.86 18.95/5.86 U100_aaa(x1, x2, x3, x4) = U100_aaa(x4) 18.95/5.86 18.95/5.86 addccL_in_aaa(x1, x2, x3) = addccL_in_aaa 18.95/5.86 18.95/5.86 addccL_out_aaa(x1, x2, x3) = addccL_out_aaa(x1, x2, x3) 18.95/5.86 18.95/5.86 U113_aaa(x1, x2, x3) = U113_aaa(x3) 18.95/5.86 18.95/5.86 succZcN_in_aa(x1, x2) = succZcN_in_aa 18.95/5.86 18.95/5.86 U103_aa(x1, x2) = U103_aa(x2) 18.95/5.86 18.95/5.86 succZcN_out_aa(x1, x2) = succZcN_out_aa(x1, x2) 18.95/5.86 18.95/5.86 U104_aa(x1, x2, x3) = U104_aa(x3) 18.95/5.86 18.95/5.86 succcM_in_aa(x1, x2) = succcM_in_aa 18.95/5.86 18.95/5.86 succcM_out_aa(x1, x2) = succcM_out_aa(x1, x2) 18.95/5.86 18.95/5.86 U101_aa(x1, x2) = U101_aa(x2) 18.95/5.86 18.95/5.86 U102_aa(x1, x2, x3) = U102_aa(x3) 18.95/5.86 18.95/5.86 U114_aaa(x1, x2, x3) = U114_aaa(x3) 18.95/5.86 18.95/5.86 U115_aaa(x1, x2, x3, x4) = U115_aaa(x4) 18.95/5.86 18.95/5.86 addCcO_in_aaa(x1, x2, x3) = addCcO_in_aaa 18.95/5.86 18.95/5.86 U105_aaa(x1, x2, x3, x4) = U105_aaa(x4) 18.95/5.86 18.95/5.86 addCcO_out_aaa(x1, x2, x3) = addCcO_out_aaa(x1, x2, x3) 18.95/5.86 18.95/5.86 U106_aaa(x1, x2) = U106_aaa(x2) 18.95/5.86 18.95/5.86 U107_aaa(x1, x2, x3) = U107_aaa(x3) 18.95/5.86 18.95/5.86 U108_aaa(x1, x2, x3, x4) = U108_aaa(x4) 18.95/5.86 18.95/5.86 U109_aaa(x1, x2) = U109_aaa(x2) 18.95/5.86 18.95/5.86 U110_aaa(x1, x2, x3) = U110_aaa(x3) 18.95/5.86 18.95/5.86 U111_aaa(x1, x2, x3, x4) = U111_aaa(x4) 18.95/5.86 18.95/5.86 U112_aaa(x1, x2, x3, x4) = U112_aaa(x4) 18.95/5.86 18.95/5.86 U151_aaa(x1, x2, x3, x4) = U151_aaa(x4) 18.95/5.86 18.95/5.86 one(x1) = one(x1) 18.95/5.86 18.95/5.86 b = b 18.95/5.86 18.95/5.86 SUCCM_IN_AA(x1, x2) = SUCCM_IN_AA 18.95/5.86 18.95/5.86 18.95/5.86 We have to consider all (P,R,Pi)-chains 18.95/5.86 ---------------------------------------- 18.95/5.86 18.95/5.86 (184) UsableRulesProof (EQUIVALENT) 18.95/5.86 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 18.95/5.86 ---------------------------------------- 18.95/5.86 18.95/5.86 (185) 18.95/5.86 Obligation: 18.95/5.86 Pi DP problem: 18.95/5.86 The TRS P consists of the following rules: 18.95/5.86 18.95/5.86 SUCCM_IN_AA(one(X1), zero(X2)) -> SUCCM_IN_AA(X1, X2) 18.95/5.86 18.95/5.86 R is empty. 18.95/5.86 The argument filtering Pi contains the following mapping: 18.95/5.86 zero(x1) = zero(x1) 18.95/5.86 18.95/5.86 one(x1) = one(x1) 18.95/5.86 18.95/5.86 SUCCM_IN_AA(x1, x2) = SUCCM_IN_AA 18.95/5.86 18.95/5.86 18.95/5.86 We have to consider all (P,R,Pi)-chains 18.95/5.86 ---------------------------------------- 18.95/5.86 18.95/5.86 (186) 18.95/5.86 Obligation: 18.95/5.86 Pi DP problem: 18.95/5.86 The TRS P consists of the following rules: 18.95/5.86 18.95/5.86 ADDZJ_IN_AAA(zero(X1), one(X2), one(X3)) -> ADDZJ_IN_AAA(X1, X2, X3) 18.95/5.86 ADDZJ_IN_AAA(zero(X1), zero(X2), zero(X3)) -> ADDZJ_IN_AAA(X1, X2, X3) 18.95/5.86 ADDZJ_IN_AAA(one(X1), zero(X2), one(X3)) -> ADDYK_IN_AAA(X1, X2, X3) 18.95/5.86 ADDYK_IN_AAA(X1, X2, X3) -> ADDZJ_IN_AAA(X1, X2, X3) 18.95/5.86 ADDZJ_IN_AAA(one(X1), one(X2), zero(X3)) -> ADDCL_IN_AAA(X1, X2, X3) 18.95/5.86 ADDCL_IN_AAA(X1, X2, X3) -> ADDCO_IN_AAA(X1, X2, X3) 18.95/5.86 ADDCO_IN_AAA(zero(X1), zero(X2), one(X3)) -> ADDZJ_IN_AAA(X1, X2, X3) 18.95/5.86 ADDCO_IN_AAA(zero(X1), one(X2), zero(X3)) -> ADDCO_IN_AAA(X1, X2, X3) 18.95/5.86 ADDCO_IN_AAA(one(X1), zero(X2), zero(X3)) -> ADDCO_IN_AAA(X1, X2, X3) 18.95/5.86 ADDCO_IN_AAA(one(X1), one(X2), one(X3)) -> ADDCL_IN_AAA(X1, X2, X3) 18.95/5.86 18.95/5.86 The TRS R consists of the following rules: 18.95/5.86 18.95/5.86 timescF_in_aaa(one(b), X1, X1) -> timescF_out_aaa(one(b), X1, X1) 18.95/5.86 timescF_in_aaa(zero(X1), X2, zero(X3)) -> U88_aaa(X1, X2, X3, timescF_in_aaa(X1, X2, X3)) 18.95/5.86 timescF_in_aaa(one(X1), X2, X3) -> U89_aaa(X1, X2, X3, timescF_in_aaa(X1, X2, X4)) 18.95/5.86 U89_aaa(X1, X2, X3, timescF_out_aaa(X1, X2, X4)) -> U90_aaa(X1, X2, X3, addcG_in_aaa(X2, X4, X3)) 18.95/5.86 addcG_in_aaa(b, X1, zero(X1)) -> U149_aaa(X1, binaryZcP_in_a(X1)) 18.95/5.86 binaryZcP_in_a(X1) -> U119_a(X1, binaryZcH_in_a(X1)) 18.95/5.86 binaryZcH_in_a(zero(X1)) -> U91_a(X1, binaryZcH_in_a(X1)) 18.95/5.86 binaryZcH_in_a(one(X1)) -> U92_a(X1, binarycI_in_a(X1)) 18.95/5.86 binarycI_in_a(b) -> binarycI_out_a(b) 18.95/5.86 binarycI_in_a(zero(X1)) -> U93_a(X1, binaryZcH_in_a(X1)) 18.95/5.86 U93_a(X1, binaryZcH_out_a(X1)) -> binarycI_out_a(zero(X1)) 18.95/5.86 binarycI_in_a(one(X1)) -> U94_a(X1, binarycI_in_a(X1)) 18.95/5.86 U94_a(X1, binarycI_out_a(X1)) -> binarycI_out_a(one(X1)) 18.95/5.86 U92_a(X1, binarycI_out_a(X1)) -> binaryZcH_out_a(one(X1)) 18.95/5.86 U91_a(X1, binaryZcH_out_a(X1)) -> binaryZcH_out_a(zero(X1)) 18.95/5.86 U119_a(X1, binaryZcH_out_a(X1)) -> binaryZcP_out_a(X1) 18.95/5.86 U149_aaa(X1, binaryZcP_out_a(X1)) -> addcG_out_aaa(b, X1, zero(X1)) 18.95/5.86 addcG_in_aaa(zero(X1), X2, zero(X3)) -> U150_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.86 addzcJ_in_aaa(zero(X1), zero(X2), zero(X3)) -> U95_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.86 addzcJ_in_aaa(zero(one(X1)), one(b), one(one(X1))) -> U96_aaa(X1, binarycI_in_a(X1)) 18.95/5.86 U96_aaa(X1, binarycI_out_a(X1)) -> addzcJ_out_aaa(zero(one(X1)), one(b), one(one(X1))) 18.95/5.86 addzcJ_in_aaa(zero(zero(X1)), one(b), one(zero(X1))) -> U97_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.86 U97_aaa(X1, binaryZcH_out_a(X1)) -> addzcJ_out_aaa(zero(zero(X1)), one(b), one(zero(X1))) 18.95/5.86 addzcJ_in_aaa(zero(X1), one(X2), one(X3)) -> U98_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.86 addzcJ_in_aaa(one(X1), zero(X2), one(X3)) -> U99_aaa(X1, X2, X3, addycK_in_aaa(X1, X2, X3)) 18.95/5.86 addycK_in_aaa(b, one(X1), one(X1)) -> U116_aaa(X1, binarycI_in_a(X1)) 18.95/5.86 U116_aaa(X1, binarycI_out_a(X1)) -> addycK_out_aaa(b, one(X1), one(X1)) 18.95/5.86 addycK_in_aaa(b, zero(X1), zero(X1)) -> U117_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.86 U117_aaa(X1, binaryZcH_out_a(X1)) -> addycK_out_aaa(b, zero(X1), zero(X1)) 18.95/5.86 addycK_in_aaa(X1, X2, X3) -> U118_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.86 addzcJ_in_aaa(one(X1), one(X2), zero(X3)) -> U100_aaa(X1, X2, X3, addccL_in_aaa(X1, X2, X3)) 18.95/5.86 addccL_in_aaa(b, b, one(b)) -> addccL_out_aaa(b, b, one(b)) 18.95/5.86 addccL_in_aaa(X1, b, X2) -> U113_aaa(X1, X2, succZcN_in_aa(X1, X2)) 18.95/5.86 succZcN_in_aa(zero(X1), one(X1)) -> U103_aa(X1, binaryZcH_in_a(X1)) 18.95/5.86 U103_aa(X1, binaryZcH_out_a(X1)) -> succZcN_out_aa(zero(X1), one(X1)) 18.95/5.86 succZcN_in_aa(one(X1), zero(X2)) -> U104_aa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.86 succcM_in_aa(b, one(b)) -> succcM_out_aa(b, one(b)) 18.95/5.86 succcM_in_aa(zero(X1), one(X1)) -> U101_aa(X1, binaryZcH_in_a(X1)) 18.95/5.86 U101_aa(X1, binaryZcH_out_a(X1)) -> succcM_out_aa(zero(X1), one(X1)) 18.95/5.86 succcM_in_aa(one(X1), zero(X2)) -> U102_aa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.86 U102_aa(X1, X2, succcM_out_aa(X1, X2)) -> succcM_out_aa(one(X1), zero(X2)) 18.95/5.86 U104_aa(X1, X2, succcM_out_aa(X1, X2)) -> succZcN_out_aa(one(X1), zero(X2)) 18.95/5.86 U113_aaa(X1, X2, succZcN_out_aa(X1, X2)) -> addccL_out_aaa(X1, b, X2) 18.95/5.86 addccL_in_aaa(b, X1, X2) -> U114_aaa(X1, X2, succZcN_in_aa(X1, X2)) 18.95/5.86 U114_aaa(X1, X2, succZcN_out_aa(X1, X2)) -> addccL_out_aaa(b, X1, X2) 18.95/5.86 addccL_in_aaa(X1, X2, X3) -> U115_aaa(X1, X2, X3, addCcO_in_aaa(X1, X2, X3)) 18.95/5.86 addCcO_in_aaa(zero(X1), zero(X2), one(X3)) -> U105_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.86 U105_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(zero(X1), zero(X2), one(X3)) 18.95/5.86 addCcO_in_aaa(zero(zero(X1)), one(b), zero(one(X1))) -> U106_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.86 U106_aaa(X1, binaryZcH_out_a(X1)) -> addCcO_out_aaa(zero(zero(X1)), one(b), zero(one(X1))) 18.95/5.86 addCcO_in_aaa(zero(one(X1)), one(b), zero(zero(X2))) -> U107_aaa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.86 U107_aaa(X1, X2, succcM_out_aa(X1, X2)) -> addCcO_out_aaa(zero(one(X1)), one(b), zero(zero(X2))) 18.95/5.86 addCcO_in_aaa(zero(X1), one(X2), zero(X3)) -> U108_aaa(X1, X2, X3, addCcO_in_aaa(X1, X2, X3)) 18.95/5.86 addCcO_in_aaa(one(b), zero(zero(X1)), zero(one(X1))) -> U109_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.86 U109_aaa(X1, binaryZcH_out_a(X1)) -> addCcO_out_aaa(one(b), zero(zero(X1)), zero(one(X1))) 18.95/5.86 addCcO_in_aaa(one(b), zero(one(X1)), zero(zero(X2))) -> U110_aaa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.86 U110_aaa(X1, X2, succcM_out_aa(X1, X2)) -> addCcO_out_aaa(one(b), zero(one(X1)), zero(zero(X2))) 18.95/5.86 addCcO_in_aaa(one(X1), zero(X2), zero(X3)) -> U111_aaa(X1, X2, X3, addCcO_in_aaa(X1, X2, X3)) 18.95/5.86 addCcO_in_aaa(one(X1), one(X2), one(X3)) -> U112_aaa(X1, X2, X3, addccL_in_aaa(X1, X2, X3)) 18.95/5.86 U112_aaa(X1, X2, X3, addccL_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(one(X1), one(X2), one(X3)) 18.95/5.86 U111_aaa(X1, X2, X3, addCcO_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(one(X1), zero(X2), zero(X3)) 18.95/5.86 U108_aaa(X1, X2, X3, addCcO_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(zero(X1), one(X2), zero(X3)) 18.95/5.86 U115_aaa(X1, X2, X3, addCcO_out_aaa(X1, X2, X3)) -> addccL_out_aaa(X1, X2, X3) 18.95/5.86 U100_aaa(X1, X2, X3, addccL_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(one(X1), one(X2), zero(X3)) 18.95/5.86 U118_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addycK_out_aaa(X1, X2, X3) 18.95/5.86 U99_aaa(X1, X2, X3, addycK_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(one(X1), zero(X2), one(X3)) 18.95/5.86 U98_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(zero(X1), one(X2), one(X3)) 18.95/5.86 U95_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(zero(X1), zero(X2), zero(X3)) 18.95/5.86 U150_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addcG_out_aaa(zero(X1), X2, zero(X3)) 18.95/5.86 addcG_in_aaa(one(X1), X2, one(X3)) -> U151_aaa(X1, X2, X3, addycK_in_aaa(X1, X2, X3)) 18.95/5.86 U151_aaa(X1, X2, X3, addycK_out_aaa(X1, X2, X3)) -> addcG_out_aaa(one(X1), X2, one(X3)) 18.95/5.86 U90_aaa(X1, X2, X3, addcG_out_aaa(X2, X4, X3)) -> timescF_out_aaa(one(X1), X2, X3) 18.95/5.86 U88_aaa(X1, X2, X3, timescF_out_aaa(X1, X2, X3)) -> timescF_out_aaa(zero(X1), X2, zero(X3)) 18.95/5.86 18.95/5.86 The argument filtering Pi contains the following mapping: 18.95/5.86 zero(x1) = zero(x1) 18.95/5.86 18.95/5.86 timescF_in_aaa(x1, x2, x3) = timescF_in_aaa 18.95/5.86 18.95/5.86 timescF_out_aaa(x1, x2, x3) = timescF_out_aaa(x1) 18.95/5.86 18.95/5.86 U88_aaa(x1, x2, x3, x4) = U88_aaa(x4) 18.95/5.86 18.95/5.86 U89_aaa(x1, x2, x3, x4) = U89_aaa(x4) 18.95/5.86 18.95/5.86 U90_aaa(x1, x2, x3, x4) = U90_aaa(x1, x4) 18.95/5.86 18.95/5.86 addcG_in_aaa(x1, x2, x3) = addcG_in_aaa 18.95/5.86 18.95/5.86 U149_aaa(x1, x2) = U149_aaa(x2) 18.95/5.86 18.95/5.86 binaryZcP_in_a(x1) = binaryZcP_in_a 18.95/5.86 18.95/5.86 U119_a(x1, x2) = U119_a(x2) 18.95/5.86 18.95/5.86 binaryZcH_in_a(x1) = binaryZcH_in_a 18.95/5.86 18.95/5.86 U91_a(x1, x2) = U91_a(x2) 18.95/5.86 18.95/5.86 U92_a(x1, x2) = U92_a(x2) 18.95/5.86 18.95/5.86 binarycI_in_a(x1) = binarycI_in_a 18.95/5.86 18.95/5.86 binarycI_out_a(x1) = binarycI_out_a(x1) 18.95/5.86 18.95/5.86 U93_a(x1, x2) = U93_a(x2) 18.95/5.86 18.95/5.86 binaryZcH_out_a(x1) = binaryZcH_out_a(x1) 18.95/5.86 18.95/5.86 U94_a(x1, x2) = U94_a(x2) 18.95/5.86 18.95/5.86 binaryZcP_out_a(x1) = binaryZcP_out_a(x1) 18.95/5.86 18.95/5.86 addcG_out_aaa(x1, x2, x3) = addcG_out_aaa(x1, x2, x3) 18.95/5.86 18.95/5.86 U150_aaa(x1, x2, x3, x4) = U150_aaa(x4) 18.95/5.86 18.95/5.86 addzcJ_in_aaa(x1, x2, x3) = addzcJ_in_aaa 18.95/5.86 18.95/5.86 U95_aaa(x1, x2, x3, x4) = U95_aaa(x4) 18.95/5.86 18.95/5.86 U96_aaa(x1, x2) = U96_aaa(x2) 18.95/5.86 18.95/5.86 addzcJ_out_aaa(x1, x2, x3) = addzcJ_out_aaa(x1, x2, x3) 18.95/5.86 18.95/5.86 U97_aaa(x1, x2) = U97_aaa(x2) 18.95/5.86 18.95/5.86 U98_aaa(x1, x2, x3, x4) = U98_aaa(x4) 18.95/5.86 18.95/5.86 U99_aaa(x1, x2, x3, x4) = U99_aaa(x4) 18.95/5.86 18.95/5.86 addycK_in_aaa(x1, x2, x3) = addycK_in_aaa 18.95/5.86 18.95/5.86 U116_aaa(x1, x2) = U116_aaa(x2) 18.95/5.86 18.95/5.86 addycK_out_aaa(x1, x2, x3) = addycK_out_aaa(x1, x2, x3) 18.95/5.86 18.95/5.86 U117_aaa(x1, x2) = U117_aaa(x2) 18.95/5.86 18.95/5.86 U118_aaa(x1, x2, x3, x4) = U118_aaa(x4) 18.95/5.86 18.95/5.86 U100_aaa(x1, x2, x3, x4) = U100_aaa(x4) 18.95/5.86 18.95/5.86 addccL_in_aaa(x1, x2, x3) = addccL_in_aaa 18.95/5.86 18.95/5.86 addccL_out_aaa(x1, x2, x3) = addccL_out_aaa(x1, x2, x3) 18.95/5.86 18.95/5.86 U113_aaa(x1, x2, x3) = U113_aaa(x3) 18.95/5.86 18.95/5.86 succZcN_in_aa(x1, x2) = succZcN_in_aa 18.95/5.86 18.95/5.86 U103_aa(x1, x2) = U103_aa(x2) 18.95/5.86 18.95/5.86 succZcN_out_aa(x1, x2) = succZcN_out_aa(x1, x2) 18.95/5.86 18.95/5.86 U104_aa(x1, x2, x3) = U104_aa(x3) 18.95/5.86 18.95/5.86 succcM_in_aa(x1, x2) = succcM_in_aa 18.95/5.86 18.95/5.86 succcM_out_aa(x1, x2) = succcM_out_aa(x1, x2) 18.95/5.86 18.95/5.86 U101_aa(x1, x2) = U101_aa(x2) 18.95/5.86 18.95/5.86 U102_aa(x1, x2, x3) = U102_aa(x3) 18.95/5.86 18.95/5.86 U114_aaa(x1, x2, x3) = U114_aaa(x3) 18.95/5.86 18.95/5.86 U115_aaa(x1, x2, x3, x4) = U115_aaa(x4) 18.95/5.86 18.95/5.86 addCcO_in_aaa(x1, x2, x3) = addCcO_in_aaa 18.95/5.86 18.95/5.86 U105_aaa(x1, x2, x3, x4) = U105_aaa(x4) 18.95/5.86 18.95/5.86 addCcO_out_aaa(x1, x2, x3) = addCcO_out_aaa(x1, x2, x3) 18.95/5.86 18.95/5.86 U106_aaa(x1, x2) = U106_aaa(x2) 18.95/5.86 18.95/5.86 U107_aaa(x1, x2, x3) = U107_aaa(x3) 18.95/5.86 18.95/5.86 U108_aaa(x1, x2, x3, x4) = U108_aaa(x4) 18.95/5.86 18.95/5.86 U109_aaa(x1, x2) = U109_aaa(x2) 18.95/5.86 18.95/5.86 U110_aaa(x1, x2, x3) = U110_aaa(x3) 18.95/5.86 18.95/5.86 U111_aaa(x1, x2, x3, x4) = U111_aaa(x4) 18.95/5.86 18.95/5.86 U112_aaa(x1, x2, x3, x4) = U112_aaa(x4) 18.95/5.86 18.95/5.86 U151_aaa(x1, x2, x3, x4) = U151_aaa(x4) 18.95/5.86 18.95/5.86 one(x1) = one(x1) 18.95/5.86 18.95/5.86 b = b 18.95/5.86 18.95/5.86 ADDZJ_IN_AAA(x1, x2, x3) = ADDZJ_IN_AAA 18.95/5.86 18.95/5.86 ADDYK_IN_AAA(x1, x2, x3) = ADDYK_IN_AAA 18.95/5.86 18.95/5.86 ADDCL_IN_AAA(x1, x2, x3) = ADDCL_IN_AAA 18.95/5.86 18.95/5.86 ADDCO_IN_AAA(x1, x2, x3) = ADDCO_IN_AAA 18.95/5.86 18.95/5.86 18.95/5.86 We have to consider all (P,R,Pi)-chains 18.95/5.86 ---------------------------------------- 18.95/5.86 18.95/5.86 (187) UsableRulesProof (EQUIVALENT) 18.95/5.86 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 18.95/5.86 ---------------------------------------- 18.95/5.86 18.95/5.86 (188) 18.95/5.86 Obligation: 18.95/5.86 Pi DP problem: 18.95/5.86 The TRS P consists of the following rules: 18.95/5.86 18.95/5.86 ADDZJ_IN_AAA(zero(X1), one(X2), one(X3)) -> ADDZJ_IN_AAA(X1, X2, X3) 18.95/5.86 ADDZJ_IN_AAA(zero(X1), zero(X2), zero(X3)) -> ADDZJ_IN_AAA(X1, X2, X3) 18.95/5.86 ADDZJ_IN_AAA(one(X1), zero(X2), one(X3)) -> ADDYK_IN_AAA(X1, X2, X3) 18.95/5.86 ADDYK_IN_AAA(X1, X2, X3) -> ADDZJ_IN_AAA(X1, X2, X3) 18.95/5.86 ADDZJ_IN_AAA(one(X1), one(X2), zero(X3)) -> ADDCL_IN_AAA(X1, X2, X3) 18.95/5.86 ADDCL_IN_AAA(X1, X2, X3) -> ADDCO_IN_AAA(X1, X2, X3) 18.95/5.86 ADDCO_IN_AAA(zero(X1), zero(X2), one(X3)) -> ADDZJ_IN_AAA(X1, X2, X3) 18.95/5.86 ADDCO_IN_AAA(zero(X1), one(X2), zero(X3)) -> ADDCO_IN_AAA(X1, X2, X3) 18.95/5.86 ADDCO_IN_AAA(one(X1), zero(X2), zero(X3)) -> ADDCO_IN_AAA(X1, X2, X3) 18.95/5.86 ADDCO_IN_AAA(one(X1), one(X2), one(X3)) -> ADDCL_IN_AAA(X1, X2, X3) 18.95/5.86 18.95/5.86 R is empty. 18.95/5.86 The argument filtering Pi contains the following mapping: 18.95/5.86 zero(x1) = zero(x1) 18.95/5.86 18.95/5.86 one(x1) = one(x1) 18.95/5.86 18.95/5.86 ADDZJ_IN_AAA(x1, x2, x3) = ADDZJ_IN_AAA 18.95/5.86 18.95/5.86 ADDYK_IN_AAA(x1, x2, x3) = ADDYK_IN_AAA 18.95/5.86 18.95/5.86 ADDCL_IN_AAA(x1, x2, x3) = ADDCL_IN_AAA 18.95/5.86 18.95/5.86 ADDCO_IN_AAA(x1, x2, x3) = ADDCO_IN_AAA 18.95/5.86 18.95/5.86 18.95/5.86 We have to consider all (P,R,Pi)-chains 18.95/5.86 ---------------------------------------- 18.95/5.86 18.95/5.86 (189) 18.95/5.86 Obligation: 18.95/5.86 Pi DP problem: 18.95/5.86 The TRS P consists of the following rules: 18.95/5.86 18.95/5.86 TIMESF_IN_AAA(one(X1), X2, X3) -> TIMESF_IN_AAA(X1, X2, X4) 18.95/5.86 TIMESF_IN_AAA(zero(X1), X2, zero(X3)) -> TIMESF_IN_AAA(X1, X2, X3) 18.95/5.86 18.95/5.86 The TRS R consists of the following rules: 18.95/5.86 18.95/5.86 timescF_in_aaa(one(b), X1, X1) -> timescF_out_aaa(one(b), X1, X1) 18.95/5.86 timescF_in_aaa(zero(X1), X2, zero(X3)) -> U88_aaa(X1, X2, X3, timescF_in_aaa(X1, X2, X3)) 18.95/5.86 timescF_in_aaa(one(X1), X2, X3) -> U89_aaa(X1, X2, X3, timescF_in_aaa(X1, X2, X4)) 18.95/5.86 U89_aaa(X1, X2, X3, timescF_out_aaa(X1, X2, X4)) -> U90_aaa(X1, X2, X3, addcG_in_aaa(X2, X4, X3)) 18.95/5.86 addcG_in_aaa(b, X1, zero(X1)) -> U149_aaa(X1, binaryZcP_in_a(X1)) 18.95/5.86 binaryZcP_in_a(X1) -> U119_a(X1, binaryZcH_in_a(X1)) 18.95/5.86 binaryZcH_in_a(zero(X1)) -> U91_a(X1, binaryZcH_in_a(X1)) 18.95/5.86 binaryZcH_in_a(one(X1)) -> U92_a(X1, binarycI_in_a(X1)) 18.95/5.86 binarycI_in_a(b) -> binarycI_out_a(b) 18.95/5.86 binarycI_in_a(zero(X1)) -> U93_a(X1, binaryZcH_in_a(X1)) 18.95/5.86 U93_a(X1, binaryZcH_out_a(X1)) -> binarycI_out_a(zero(X1)) 18.95/5.86 binarycI_in_a(one(X1)) -> U94_a(X1, binarycI_in_a(X1)) 18.95/5.86 U94_a(X1, binarycI_out_a(X1)) -> binarycI_out_a(one(X1)) 18.95/5.86 U92_a(X1, binarycI_out_a(X1)) -> binaryZcH_out_a(one(X1)) 18.95/5.86 U91_a(X1, binaryZcH_out_a(X1)) -> binaryZcH_out_a(zero(X1)) 18.95/5.86 U119_a(X1, binaryZcH_out_a(X1)) -> binaryZcP_out_a(X1) 18.95/5.86 U149_aaa(X1, binaryZcP_out_a(X1)) -> addcG_out_aaa(b, X1, zero(X1)) 18.95/5.86 addcG_in_aaa(zero(X1), X2, zero(X3)) -> U150_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.86 addzcJ_in_aaa(zero(X1), zero(X2), zero(X3)) -> U95_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.86 addzcJ_in_aaa(zero(one(X1)), one(b), one(one(X1))) -> U96_aaa(X1, binarycI_in_a(X1)) 18.95/5.86 U96_aaa(X1, binarycI_out_a(X1)) -> addzcJ_out_aaa(zero(one(X1)), one(b), one(one(X1))) 18.95/5.86 addzcJ_in_aaa(zero(zero(X1)), one(b), one(zero(X1))) -> U97_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.86 U97_aaa(X1, binaryZcH_out_a(X1)) -> addzcJ_out_aaa(zero(zero(X1)), one(b), one(zero(X1))) 18.95/5.86 addzcJ_in_aaa(zero(X1), one(X2), one(X3)) -> U98_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.86 addzcJ_in_aaa(one(X1), zero(X2), one(X3)) -> U99_aaa(X1, X2, X3, addycK_in_aaa(X1, X2, X3)) 18.95/5.86 addycK_in_aaa(b, one(X1), one(X1)) -> U116_aaa(X1, binarycI_in_a(X1)) 18.95/5.86 U116_aaa(X1, binarycI_out_a(X1)) -> addycK_out_aaa(b, one(X1), one(X1)) 18.95/5.86 addycK_in_aaa(b, zero(X1), zero(X1)) -> U117_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.86 U117_aaa(X1, binaryZcH_out_a(X1)) -> addycK_out_aaa(b, zero(X1), zero(X1)) 18.95/5.86 addycK_in_aaa(X1, X2, X3) -> U118_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.86 addzcJ_in_aaa(one(X1), one(X2), zero(X3)) -> U100_aaa(X1, X2, X3, addccL_in_aaa(X1, X2, X3)) 18.95/5.86 addccL_in_aaa(b, b, one(b)) -> addccL_out_aaa(b, b, one(b)) 18.95/5.86 addccL_in_aaa(X1, b, X2) -> U113_aaa(X1, X2, succZcN_in_aa(X1, X2)) 18.95/5.86 succZcN_in_aa(zero(X1), one(X1)) -> U103_aa(X1, binaryZcH_in_a(X1)) 18.95/5.86 U103_aa(X1, binaryZcH_out_a(X1)) -> succZcN_out_aa(zero(X1), one(X1)) 18.95/5.86 succZcN_in_aa(one(X1), zero(X2)) -> U104_aa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.86 succcM_in_aa(b, one(b)) -> succcM_out_aa(b, one(b)) 18.95/5.86 succcM_in_aa(zero(X1), one(X1)) -> U101_aa(X1, binaryZcH_in_a(X1)) 18.95/5.86 U101_aa(X1, binaryZcH_out_a(X1)) -> succcM_out_aa(zero(X1), one(X1)) 18.95/5.86 succcM_in_aa(one(X1), zero(X2)) -> U102_aa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.86 U102_aa(X1, X2, succcM_out_aa(X1, X2)) -> succcM_out_aa(one(X1), zero(X2)) 18.95/5.86 U104_aa(X1, X2, succcM_out_aa(X1, X2)) -> succZcN_out_aa(one(X1), zero(X2)) 18.95/5.86 U113_aaa(X1, X2, succZcN_out_aa(X1, X2)) -> addccL_out_aaa(X1, b, X2) 18.95/5.86 addccL_in_aaa(b, X1, X2) -> U114_aaa(X1, X2, succZcN_in_aa(X1, X2)) 18.95/5.86 U114_aaa(X1, X2, succZcN_out_aa(X1, X2)) -> addccL_out_aaa(b, X1, X2) 18.95/5.86 addccL_in_aaa(X1, X2, X3) -> U115_aaa(X1, X2, X3, addCcO_in_aaa(X1, X2, X3)) 18.95/5.86 addCcO_in_aaa(zero(X1), zero(X2), one(X3)) -> U105_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.86 U105_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(zero(X1), zero(X2), one(X3)) 18.95/5.86 addCcO_in_aaa(zero(zero(X1)), one(b), zero(one(X1))) -> U106_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.86 U106_aaa(X1, binaryZcH_out_a(X1)) -> addCcO_out_aaa(zero(zero(X1)), one(b), zero(one(X1))) 18.95/5.86 addCcO_in_aaa(zero(one(X1)), one(b), zero(zero(X2))) -> U107_aaa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.86 U107_aaa(X1, X2, succcM_out_aa(X1, X2)) -> addCcO_out_aaa(zero(one(X1)), one(b), zero(zero(X2))) 18.95/5.86 addCcO_in_aaa(zero(X1), one(X2), zero(X3)) -> U108_aaa(X1, X2, X3, addCcO_in_aaa(X1, X2, X3)) 18.95/5.86 addCcO_in_aaa(one(b), zero(zero(X1)), zero(one(X1))) -> U109_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.86 U109_aaa(X1, binaryZcH_out_a(X1)) -> addCcO_out_aaa(one(b), zero(zero(X1)), zero(one(X1))) 18.95/5.86 addCcO_in_aaa(one(b), zero(one(X1)), zero(zero(X2))) -> U110_aaa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.86 U110_aaa(X1, X2, succcM_out_aa(X1, X2)) -> addCcO_out_aaa(one(b), zero(one(X1)), zero(zero(X2))) 18.95/5.86 addCcO_in_aaa(one(X1), zero(X2), zero(X3)) -> U111_aaa(X1, X2, X3, addCcO_in_aaa(X1, X2, X3)) 18.95/5.86 addCcO_in_aaa(one(X1), one(X2), one(X3)) -> U112_aaa(X1, X2, X3, addccL_in_aaa(X1, X2, X3)) 18.95/5.86 U112_aaa(X1, X2, X3, addccL_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(one(X1), one(X2), one(X3)) 18.95/5.86 U111_aaa(X1, X2, X3, addCcO_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(one(X1), zero(X2), zero(X3)) 18.95/5.86 U108_aaa(X1, X2, X3, addCcO_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(zero(X1), one(X2), zero(X3)) 18.95/5.86 U115_aaa(X1, X2, X3, addCcO_out_aaa(X1, X2, X3)) -> addccL_out_aaa(X1, X2, X3) 18.95/5.86 U100_aaa(X1, X2, X3, addccL_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(one(X1), one(X2), zero(X3)) 18.95/5.86 U118_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addycK_out_aaa(X1, X2, X3) 18.95/5.86 U99_aaa(X1, X2, X3, addycK_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(one(X1), zero(X2), one(X3)) 18.95/5.86 U98_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(zero(X1), one(X2), one(X3)) 18.95/5.86 U95_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(zero(X1), zero(X2), zero(X3)) 18.95/5.86 U150_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addcG_out_aaa(zero(X1), X2, zero(X3)) 18.95/5.86 addcG_in_aaa(one(X1), X2, one(X3)) -> U151_aaa(X1, X2, X3, addycK_in_aaa(X1, X2, X3)) 18.95/5.86 U151_aaa(X1, X2, X3, addycK_out_aaa(X1, X2, X3)) -> addcG_out_aaa(one(X1), X2, one(X3)) 18.95/5.86 U90_aaa(X1, X2, X3, addcG_out_aaa(X2, X4, X3)) -> timescF_out_aaa(one(X1), X2, X3) 18.95/5.86 U88_aaa(X1, X2, X3, timescF_out_aaa(X1, X2, X3)) -> timescF_out_aaa(zero(X1), X2, zero(X3)) 18.95/5.86 18.95/5.86 The argument filtering Pi contains the following mapping: 18.95/5.86 zero(x1) = zero(x1) 18.95/5.86 18.95/5.86 timescF_in_aaa(x1, x2, x3) = timescF_in_aaa 18.95/5.86 18.95/5.86 timescF_out_aaa(x1, x2, x3) = timescF_out_aaa(x1) 18.95/5.86 18.95/5.86 U88_aaa(x1, x2, x3, x4) = U88_aaa(x4) 18.95/5.86 18.95/5.86 U89_aaa(x1, x2, x3, x4) = U89_aaa(x4) 18.95/5.86 18.95/5.86 U90_aaa(x1, x2, x3, x4) = U90_aaa(x1, x4) 18.95/5.86 18.95/5.86 addcG_in_aaa(x1, x2, x3) = addcG_in_aaa 18.95/5.86 18.95/5.86 U149_aaa(x1, x2) = U149_aaa(x2) 18.95/5.86 18.95/5.86 binaryZcP_in_a(x1) = binaryZcP_in_a 18.95/5.86 18.95/5.86 U119_a(x1, x2) = U119_a(x2) 18.95/5.86 18.95/5.86 binaryZcH_in_a(x1) = binaryZcH_in_a 18.95/5.86 18.95/5.86 U91_a(x1, x2) = U91_a(x2) 18.95/5.86 18.95/5.86 U92_a(x1, x2) = U92_a(x2) 18.95/5.86 18.95/5.86 binarycI_in_a(x1) = binarycI_in_a 18.95/5.86 18.95/5.86 binarycI_out_a(x1) = binarycI_out_a(x1) 18.95/5.86 18.95/5.86 U93_a(x1, x2) = U93_a(x2) 18.95/5.86 18.95/5.86 binaryZcH_out_a(x1) = binaryZcH_out_a(x1) 18.95/5.86 18.95/5.86 U94_a(x1, x2) = U94_a(x2) 18.95/5.86 18.95/5.86 binaryZcP_out_a(x1) = binaryZcP_out_a(x1) 18.95/5.86 18.95/5.86 addcG_out_aaa(x1, x2, x3) = addcG_out_aaa(x1, x2, x3) 18.95/5.86 18.95/5.86 U150_aaa(x1, x2, x3, x4) = U150_aaa(x4) 18.95/5.86 18.95/5.86 addzcJ_in_aaa(x1, x2, x3) = addzcJ_in_aaa 18.95/5.86 18.95/5.86 U95_aaa(x1, x2, x3, x4) = U95_aaa(x4) 18.95/5.86 18.95/5.86 U96_aaa(x1, x2) = U96_aaa(x2) 18.95/5.86 18.95/5.86 addzcJ_out_aaa(x1, x2, x3) = addzcJ_out_aaa(x1, x2, x3) 18.95/5.86 18.95/5.86 U97_aaa(x1, x2) = U97_aaa(x2) 18.95/5.86 18.95/5.86 U98_aaa(x1, x2, x3, x4) = U98_aaa(x4) 18.95/5.86 18.95/5.86 U99_aaa(x1, x2, x3, x4) = U99_aaa(x4) 18.95/5.86 18.95/5.86 addycK_in_aaa(x1, x2, x3) = addycK_in_aaa 18.95/5.86 18.95/5.86 U116_aaa(x1, x2) = U116_aaa(x2) 18.95/5.86 18.95/5.86 addycK_out_aaa(x1, x2, x3) = addycK_out_aaa(x1, x2, x3) 18.95/5.86 18.95/5.86 U117_aaa(x1, x2) = U117_aaa(x2) 18.95/5.86 18.95/5.86 U118_aaa(x1, x2, x3, x4) = U118_aaa(x4) 18.95/5.86 18.95/5.86 U100_aaa(x1, x2, x3, x4) = U100_aaa(x4) 18.95/5.86 18.95/5.86 addccL_in_aaa(x1, x2, x3) = addccL_in_aaa 18.95/5.86 18.95/5.86 addccL_out_aaa(x1, x2, x3) = addccL_out_aaa(x1, x2, x3) 18.95/5.86 18.95/5.86 U113_aaa(x1, x2, x3) = U113_aaa(x3) 18.95/5.86 18.95/5.86 succZcN_in_aa(x1, x2) = succZcN_in_aa 18.95/5.86 18.95/5.86 U103_aa(x1, x2) = U103_aa(x2) 18.95/5.86 18.95/5.86 succZcN_out_aa(x1, x2) = succZcN_out_aa(x1, x2) 18.95/5.86 18.95/5.86 U104_aa(x1, x2, x3) = U104_aa(x3) 18.95/5.86 18.95/5.86 succcM_in_aa(x1, x2) = succcM_in_aa 18.95/5.86 18.95/5.86 succcM_out_aa(x1, x2) = succcM_out_aa(x1, x2) 18.95/5.86 18.95/5.86 U101_aa(x1, x2) = U101_aa(x2) 18.95/5.86 18.95/5.86 U102_aa(x1, x2, x3) = U102_aa(x3) 18.95/5.86 18.95/5.86 U114_aaa(x1, x2, x3) = U114_aaa(x3) 18.95/5.86 18.95/5.86 U115_aaa(x1, x2, x3, x4) = U115_aaa(x4) 18.95/5.86 18.95/5.86 addCcO_in_aaa(x1, x2, x3) = addCcO_in_aaa 18.95/5.86 18.95/5.86 U105_aaa(x1, x2, x3, x4) = U105_aaa(x4) 18.95/5.86 18.95/5.86 addCcO_out_aaa(x1, x2, x3) = addCcO_out_aaa(x1, x2, x3) 18.95/5.86 18.95/5.86 U106_aaa(x1, x2) = U106_aaa(x2) 18.95/5.86 18.95/5.86 U107_aaa(x1, x2, x3) = U107_aaa(x3) 18.95/5.86 18.95/5.86 U108_aaa(x1, x2, x3, x4) = U108_aaa(x4) 18.95/5.86 18.95/5.86 U109_aaa(x1, x2) = U109_aaa(x2) 18.95/5.86 18.95/5.86 U110_aaa(x1, x2, x3) = U110_aaa(x3) 18.95/5.86 18.95/5.86 U111_aaa(x1, x2, x3, x4) = U111_aaa(x4) 18.95/5.86 18.95/5.86 U112_aaa(x1, x2, x3, x4) = U112_aaa(x4) 18.95/5.86 18.95/5.86 U151_aaa(x1, x2, x3, x4) = U151_aaa(x4) 18.95/5.86 18.95/5.86 one(x1) = one(x1) 18.95/5.86 18.95/5.86 b = b 18.95/5.86 18.95/5.86 TIMESF_IN_AAA(x1, x2, x3) = TIMESF_IN_AAA 18.95/5.86 18.95/5.86 18.95/5.86 We have to consider all (P,R,Pi)-chains 18.95/5.86 ---------------------------------------- 18.95/5.86 18.95/5.86 (190) UsableRulesProof (EQUIVALENT) 18.95/5.86 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 18.95/5.86 ---------------------------------------- 18.95/5.86 18.95/5.86 (191) 18.95/5.86 Obligation: 18.95/5.86 Pi DP problem: 18.95/5.86 The TRS P consists of the following rules: 18.95/5.86 18.95/5.86 TIMESF_IN_AAA(one(X1), X2, X3) -> TIMESF_IN_AAA(X1, X2, X4) 18.95/5.86 TIMESF_IN_AAA(zero(X1), X2, zero(X3)) -> TIMESF_IN_AAA(X1, X2, X3) 18.95/5.86 18.95/5.86 R is empty. 18.95/5.86 The argument filtering Pi contains the following mapping: 18.95/5.86 zero(x1) = zero(x1) 18.95/5.86 18.95/5.86 one(x1) = one(x1) 18.95/5.86 18.95/5.86 TIMESF_IN_AAA(x1, x2, x3) = TIMESF_IN_AAA 18.95/5.86 18.95/5.86 18.95/5.86 We have to consider all (P,R,Pi)-chains 18.95/5.86 ---------------------------------------- 18.95/5.86 18.95/5.86 (192) 18.95/5.86 Obligation: 18.95/5.86 Pi DP problem: 18.95/5.86 The TRS P consists of the following rules: 18.95/5.86 18.95/5.86 TIMESA_IN_AAG(zero(zero(X1)), X2, zero(zero(X3))) -> TIMESA_IN_AAG(X1, X2, X3) 18.95/5.86 18.95/5.86 The TRS R consists of the following rules: 18.95/5.86 18.95/5.86 timescF_in_aaa(one(b), X1, X1) -> timescF_out_aaa(one(b), X1, X1) 18.95/5.86 timescF_in_aaa(zero(X1), X2, zero(X3)) -> U88_aaa(X1, X2, X3, timescF_in_aaa(X1, X2, X3)) 18.95/5.86 timescF_in_aaa(one(X1), X2, X3) -> U89_aaa(X1, X2, X3, timescF_in_aaa(X1, X2, X4)) 18.95/5.86 U89_aaa(X1, X2, X3, timescF_out_aaa(X1, X2, X4)) -> U90_aaa(X1, X2, X3, addcG_in_aaa(X2, X4, X3)) 18.95/5.86 addcG_in_aaa(b, X1, zero(X1)) -> U149_aaa(X1, binaryZcP_in_a(X1)) 18.95/5.86 binaryZcP_in_a(X1) -> U119_a(X1, binaryZcH_in_a(X1)) 18.95/5.86 binaryZcH_in_a(zero(X1)) -> U91_a(X1, binaryZcH_in_a(X1)) 18.95/5.86 binaryZcH_in_a(one(X1)) -> U92_a(X1, binarycI_in_a(X1)) 18.95/5.86 binarycI_in_a(b) -> binarycI_out_a(b) 18.95/5.86 binarycI_in_a(zero(X1)) -> U93_a(X1, binaryZcH_in_a(X1)) 18.95/5.86 U93_a(X1, binaryZcH_out_a(X1)) -> binarycI_out_a(zero(X1)) 18.95/5.86 binarycI_in_a(one(X1)) -> U94_a(X1, binarycI_in_a(X1)) 18.95/5.86 U94_a(X1, binarycI_out_a(X1)) -> binarycI_out_a(one(X1)) 18.95/5.86 U92_a(X1, binarycI_out_a(X1)) -> binaryZcH_out_a(one(X1)) 18.95/5.86 U91_a(X1, binaryZcH_out_a(X1)) -> binaryZcH_out_a(zero(X1)) 18.95/5.86 U119_a(X1, binaryZcH_out_a(X1)) -> binaryZcP_out_a(X1) 18.95/5.86 U149_aaa(X1, binaryZcP_out_a(X1)) -> addcG_out_aaa(b, X1, zero(X1)) 18.95/5.86 addcG_in_aaa(zero(X1), X2, zero(X3)) -> U150_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.86 addzcJ_in_aaa(zero(X1), zero(X2), zero(X3)) -> U95_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.86 addzcJ_in_aaa(zero(one(X1)), one(b), one(one(X1))) -> U96_aaa(X1, binarycI_in_a(X1)) 18.95/5.86 U96_aaa(X1, binarycI_out_a(X1)) -> addzcJ_out_aaa(zero(one(X1)), one(b), one(one(X1))) 18.95/5.86 addzcJ_in_aaa(zero(zero(X1)), one(b), one(zero(X1))) -> U97_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.86 U97_aaa(X1, binaryZcH_out_a(X1)) -> addzcJ_out_aaa(zero(zero(X1)), one(b), one(zero(X1))) 18.95/5.86 addzcJ_in_aaa(zero(X1), one(X2), one(X3)) -> U98_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.86 addzcJ_in_aaa(one(X1), zero(X2), one(X3)) -> U99_aaa(X1, X2, X3, addycK_in_aaa(X1, X2, X3)) 18.95/5.86 addycK_in_aaa(b, one(X1), one(X1)) -> U116_aaa(X1, binarycI_in_a(X1)) 18.95/5.86 U116_aaa(X1, binarycI_out_a(X1)) -> addycK_out_aaa(b, one(X1), one(X1)) 18.95/5.86 addycK_in_aaa(b, zero(X1), zero(X1)) -> U117_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.86 U117_aaa(X1, binaryZcH_out_a(X1)) -> addycK_out_aaa(b, zero(X1), zero(X1)) 18.95/5.86 addycK_in_aaa(X1, X2, X3) -> U118_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.86 addzcJ_in_aaa(one(X1), one(X2), zero(X3)) -> U100_aaa(X1, X2, X3, addccL_in_aaa(X1, X2, X3)) 18.95/5.86 addccL_in_aaa(b, b, one(b)) -> addccL_out_aaa(b, b, one(b)) 18.95/5.86 addccL_in_aaa(X1, b, X2) -> U113_aaa(X1, X2, succZcN_in_aa(X1, X2)) 18.95/5.86 succZcN_in_aa(zero(X1), one(X1)) -> U103_aa(X1, binaryZcH_in_a(X1)) 18.95/5.86 U103_aa(X1, binaryZcH_out_a(X1)) -> succZcN_out_aa(zero(X1), one(X1)) 18.95/5.86 succZcN_in_aa(one(X1), zero(X2)) -> U104_aa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.86 succcM_in_aa(b, one(b)) -> succcM_out_aa(b, one(b)) 18.95/5.86 succcM_in_aa(zero(X1), one(X1)) -> U101_aa(X1, binaryZcH_in_a(X1)) 18.95/5.86 U101_aa(X1, binaryZcH_out_a(X1)) -> succcM_out_aa(zero(X1), one(X1)) 18.95/5.86 succcM_in_aa(one(X1), zero(X2)) -> U102_aa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.86 U102_aa(X1, X2, succcM_out_aa(X1, X2)) -> succcM_out_aa(one(X1), zero(X2)) 18.95/5.86 U104_aa(X1, X2, succcM_out_aa(X1, X2)) -> succZcN_out_aa(one(X1), zero(X2)) 18.95/5.86 U113_aaa(X1, X2, succZcN_out_aa(X1, X2)) -> addccL_out_aaa(X1, b, X2) 18.95/5.86 addccL_in_aaa(b, X1, X2) -> U114_aaa(X1, X2, succZcN_in_aa(X1, X2)) 18.95/5.86 U114_aaa(X1, X2, succZcN_out_aa(X1, X2)) -> addccL_out_aaa(b, X1, X2) 18.95/5.86 addccL_in_aaa(X1, X2, X3) -> U115_aaa(X1, X2, X3, addCcO_in_aaa(X1, X2, X3)) 18.95/5.86 addCcO_in_aaa(zero(X1), zero(X2), one(X3)) -> U105_aaa(X1, X2, X3, addzcJ_in_aaa(X1, X2, X3)) 18.95/5.86 U105_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(zero(X1), zero(X2), one(X3)) 18.95/5.86 addCcO_in_aaa(zero(zero(X1)), one(b), zero(one(X1))) -> U106_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.86 U106_aaa(X1, binaryZcH_out_a(X1)) -> addCcO_out_aaa(zero(zero(X1)), one(b), zero(one(X1))) 18.95/5.86 addCcO_in_aaa(zero(one(X1)), one(b), zero(zero(X2))) -> U107_aaa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.86 U107_aaa(X1, X2, succcM_out_aa(X1, X2)) -> addCcO_out_aaa(zero(one(X1)), one(b), zero(zero(X2))) 18.95/5.86 addCcO_in_aaa(zero(X1), one(X2), zero(X3)) -> U108_aaa(X1, X2, X3, addCcO_in_aaa(X1, X2, X3)) 18.95/5.86 addCcO_in_aaa(one(b), zero(zero(X1)), zero(one(X1))) -> U109_aaa(X1, binaryZcH_in_a(X1)) 18.95/5.86 U109_aaa(X1, binaryZcH_out_a(X1)) -> addCcO_out_aaa(one(b), zero(zero(X1)), zero(one(X1))) 18.95/5.86 addCcO_in_aaa(one(b), zero(one(X1)), zero(zero(X2))) -> U110_aaa(X1, X2, succcM_in_aa(X1, X2)) 18.95/5.86 U110_aaa(X1, X2, succcM_out_aa(X1, X2)) -> addCcO_out_aaa(one(b), zero(one(X1)), zero(zero(X2))) 18.95/5.86 addCcO_in_aaa(one(X1), zero(X2), zero(X3)) -> U111_aaa(X1, X2, X3, addCcO_in_aaa(X1, X2, X3)) 18.95/5.86 addCcO_in_aaa(one(X1), one(X2), one(X3)) -> U112_aaa(X1, X2, X3, addccL_in_aaa(X1, X2, X3)) 18.95/5.86 U112_aaa(X1, X2, X3, addccL_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(one(X1), one(X2), one(X3)) 18.95/5.86 U111_aaa(X1, X2, X3, addCcO_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(one(X1), zero(X2), zero(X3)) 18.95/5.86 U108_aaa(X1, X2, X3, addCcO_out_aaa(X1, X2, X3)) -> addCcO_out_aaa(zero(X1), one(X2), zero(X3)) 18.95/5.86 U115_aaa(X1, X2, X3, addCcO_out_aaa(X1, X2, X3)) -> addccL_out_aaa(X1, X2, X3) 18.95/5.86 U100_aaa(X1, X2, X3, addccL_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(one(X1), one(X2), zero(X3)) 18.95/5.86 U118_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addycK_out_aaa(X1, X2, X3) 18.95/5.86 U99_aaa(X1, X2, X3, addycK_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(one(X1), zero(X2), one(X3)) 18.95/5.86 U98_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(zero(X1), one(X2), one(X3)) 18.95/5.86 U95_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addzcJ_out_aaa(zero(X1), zero(X2), zero(X3)) 18.95/5.86 U150_aaa(X1, X2, X3, addzcJ_out_aaa(X1, X2, X3)) -> addcG_out_aaa(zero(X1), X2, zero(X3)) 18.95/5.86 addcG_in_aaa(one(X1), X2, one(X3)) -> U151_aaa(X1, X2, X3, addycK_in_aaa(X1, X2, X3)) 18.95/5.86 U151_aaa(X1, X2, X3, addycK_out_aaa(X1, X2, X3)) -> addcG_out_aaa(one(X1), X2, one(X3)) 18.95/5.86 U90_aaa(X1, X2, X3, addcG_out_aaa(X2, X4, X3)) -> timescF_out_aaa(one(X1), X2, X3) 18.95/5.86 U88_aaa(X1, X2, X3, timescF_out_aaa(X1, X2, X3)) -> timescF_out_aaa(zero(X1), X2, zero(X3)) 18.95/5.86 18.95/5.86 The argument filtering Pi contains the following mapping: 18.95/5.86 zero(x1) = zero(x1) 18.95/5.86 18.95/5.86 timescF_in_aaa(x1, x2, x3) = timescF_in_aaa 18.95/5.86 18.95/5.86 timescF_out_aaa(x1, x2, x3) = timescF_out_aaa(x1) 18.95/5.86 18.95/5.86 U88_aaa(x1, x2, x3, x4) = U88_aaa(x4) 18.95/5.86 18.95/5.86 U89_aaa(x1, x2, x3, x4) = U89_aaa(x4) 18.95/5.86 18.95/5.86 U90_aaa(x1, x2, x3, x4) = U90_aaa(x1, x4) 18.95/5.86 18.95/5.86 addcG_in_aaa(x1, x2, x3) = addcG_in_aaa 18.95/5.86 18.95/5.86 U149_aaa(x1, x2) = U149_aaa(x2) 18.95/5.86 18.95/5.86 binaryZcP_in_a(x1) = binaryZcP_in_a 18.95/5.86 18.95/5.86 U119_a(x1, x2) = U119_a(x2) 18.95/5.86 18.95/5.86 binaryZcH_in_a(x1) = binaryZcH_in_a 18.95/5.86 18.95/5.86 U91_a(x1, x2) = U91_a(x2) 18.95/5.86 18.95/5.86 U92_a(x1, x2) = U92_a(x2) 18.95/5.86 18.95/5.86 binarycI_in_a(x1) = binarycI_in_a 18.95/5.86 18.95/5.86 binarycI_out_a(x1) = binarycI_out_a(x1) 18.95/5.86 18.95/5.86 U93_a(x1, x2) = U93_a(x2) 18.95/5.86 18.95/5.86 binaryZcH_out_a(x1) = binaryZcH_out_a(x1) 18.95/5.86 18.95/5.86 U94_a(x1, x2) = U94_a(x2) 18.95/5.86 18.95/5.86 binaryZcP_out_a(x1) = binaryZcP_out_a(x1) 18.95/5.86 18.95/5.86 addcG_out_aaa(x1, x2, x3) = addcG_out_aaa(x1, x2, x3) 18.95/5.86 18.95/5.86 U150_aaa(x1, x2, x3, x4) = U150_aaa(x4) 18.95/5.86 18.95/5.86 addzcJ_in_aaa(x1, x2, x3) = addzcJ_in_aaa 18.95/5.86 18.95/5.86 U95_aaa(x1, x2, x3, x4) = U95_aaa(x4) 18.95/5.86 18.95/5.86 U96_aaa(x1, x2) = U96_aaa(x2) 18.95/5.86 18.95/5.86 addzcJ_out_aaa(x1, x2, x3) = addzcJ_out_aaa(x1, x2, x3) 18.95/5.86 18.95/5.86 U97_aaa(x1, x2) = U97_aaa(x2) 18.95/5.86 18.95/5.86 U98_aaa(x1, x2, x3, x4) = U98_aaa(x4) 18.95/5.86 18.95/5.86 U99_aaa(x1, x2, x3, x4) = U99_aaa(x4) 18.95/5.86 18.95/5.86 addycK_in_aaa(x1, x2, x3) = addycK_in_aaa 18.95/5.86 18.95/5.86 U116_aaa(x1, x2) = U116_aaa(x2) 18.95/5.86 18.95/5.86 addycK_out_aaa(x1, x2, x3) = addycK_out_aaa(x1, x2, x3) 18.95/5.86 18.95/5.86 U117_aaa(x1, x2) = U117_aaa(x2) 18.95/5.86 18.95/5.86 U118_aaa(x1, x2, x3, x4) = U118_aaa(x4) 18.95/5.86 18.95/5.86 U100_aaa(x1, x2, x3, x4) = U100_aaa(x4) 18.95/5.86 18.95/5.86 addccL_in_aaa(x1, x2, x3) = addccL_in_aaa 18.95/5.86 18.95/5.86 addccL_out_aaa(x1, x2, x3) = addccL_out_aaa(x1, x2, x3) 18.95/5.86 18.95/5.86 U113_aaa(x1, x2, x3) = U113_aaa(x3) 18.95/5.86 18.95/5.86 succZcN_in_aa(x1, x2) = succZcN_in_aa 18.95/5.86 18.95/5.86 U103_aa(x1, x2) = U103_aa(x2) 18.95/5.86 18.95/5.86 succZcN_out_aa(x1, x2) = succZcN_out_aa(x1, x2) 18.95/5.86 18.95/5.86 U104_aa(x1, x2, x3) = U104_aa(x3) 18.95/5.86 18.95/5.86 succcM_in_aa(x1, x2) = succcM_in_aa 18.95/5.86 18.95/5.86 succcM_out_aa(x1, x2) = succcM_out_aa(x1, x2) 18.95/5.86 18.95/5.86 U101_aa(x1, x2) = U101_aa(x2) 18.95/5.86 18.95/5.86 U102_aa(x1, x2, x3) = U102_aa(x3) 18.95/5.86 18.95/5.86 U114_aaa(x1, x2, x3) = U114_aaa(x3) 18.95/5.86 18.95/5.86 U115_aaa(x1, x2, x3, x4) = U115_aaa(x4) 18.95/5.86 18.95/5.86 addCcO_in_aaa(x1, x2, x3) = addCcO_in_aaa 18.95/5.86 18.95/5.86 U105_aaa(x1, x2, x3, x4) = U105_aaa(x4) 18.95/5.86 18.95/5.86 addCcO_out_aaa(x1, x2, x3) = addCcO_out_aaa(x1, x2, x3) 18.95/5.86 18.95/5.86 U106_aaa(x1, x2) = U106_aaa(x2) 18.95/5.86 18.95/5.86 U107_aaa(x1, x2, x3) = U107_aaa(x3) 18.95/5.86 18.95/5.86 U108_aaa(x1, x2, x3, x4) = U108_aaa(x4) 18.95/5.86 18.95/5.86 U109_aaa(x1, x2) = U109_aaa(x2) 18.95/5.86 18.95/5.86 U110_aaa(x1, x2, x3) = U110_aaa(x3) 18.95/5.86 18.95/5.86 U111_aaa(x1, x2, x3, x4) = U111_aaa(x4) 18.95/5.86 18.95/5.86 U112_aaa(x1, x2, x3, x4) = U112_aaa(x4) 18.95/5.86 18.95/5.86 U151_aaa(x1, x2, x3, x4) = U151_aaa(x4) 18.95/5.86 18.95/5.86 one(x1) = one(x1) 18.95/5.86 18.95/5.86 b = b 18.95/5.86 18.95/5.86 TIMESA_IN_AAG(x1, x2, x3) = TIMESA_IN_AAG(x3) 18.95/5.86 18.95/5.86 18.95/5.86 We have to consider all (P,R,Pi)-chains 18.95/5.86 ---------------------------------------- 18.95/5.86 18.95/5.86 (193) UsableRulesProof (EQUIVALENT) 18.95/5.86 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 18.95/5.86 ---------------------------------------- 18.95/5.86 18.95/5.86 (194) 18.95/5.86 Obligation: 18.95/5.86 Pi DP problem: 18.95/5.86 The TRS P consists of the following rules: 18.95/5.86 18.95/5.86 TIMESA_IN_AAG(zero(zero(X1)), X2, zero(zero(X3))) -> TIMESA_IN_AAG(X1, X2, X3) 18.95/5.86 18.95/5.86 R is empty. 18.95/5.86 The argument filtering Pi contains the following mapping: 18.95/5.86 zero(x1) = zero(x1) 18.95/5.86 18.95/5.86 TIMESA_IN_AAG(x1, x2, x3) = TIMESA_IN_AAG(x3) 18.95/5.86 18.95/5.86 18.95/5.86 We have to consider all (P,R,Pi)-chains 18.95/5.86 ---------------------------------------- 18.95/5.86 18.95/5.86 (195) PrologToIRSwTTransformerProof (SOUND) 18.95/5.86 Transformed Prolog program to IRSwT according to method in Master Thesis of A. Weinert 18.95/5.86 18.95/5.86 { 18.95/5.86 "root": 2, 18.95/5.86 "program": { 18.95/5.86 "directives": [], 18.95/5.86 "clauses": [ 18.95/5.86 [ 18.95/5.86 "(add (b) (b) (b))", 18.95/5.86 null 18.95/5.86 ], 18.95/5.86 [ 18.95/5.86 "(add X (b) X)", 18.95/5.86 "(binaryZ X)" 18.95/5.86 ], 18.95/5.86 [ 18.95/5.86 "(add (b) Y Y)", 18.95/5.86 "(binaryZ Y)" 18.95/5.86 ], 18.95/5.86 [ 18.95/5.86 "(add X Y Z)", 18.95/5.86 "(addz X Y Z)" 18.95/5.86 ], 18.95/5.86 [ 18.95/5.86 "(addx (one X) (b) (one X))", 18.95/5.86 "(binary X)" 18.95/5.86 ], 18.95/5.86 [ 18.95/5.86 "(addx (zero X) (b) (zero X))", 18.95/5.86 "(binaryZ X)" 18.95/5.86 ], 18.95/5.86 [ 18.95/5.86 "(addx X Y Z)", 18.95/5.86 "(addz X Y Z)" 18.95/5.86 ], 18.95/5.86 [ 18.95/5.86 "(addy (b) (one Y) (one Y))", 18.95/5.86 "(binary Y)" 18.95/5.86 ], 18.95/5.86 [ 18.95/5.86 "(addy (b) (zero Y) (zero Y))", 18.95/5.86 "(binaryZ Y)" 18.95/5.86 ], 18.95/5.86 [ 18.95/5.86 "(addy X Y Z)", 18.95/5.86 "(addz X Y Z)" 18.95/5.86 ], 18.95/5.86 [ 18.95/5.86 "(addz (zero X) (zero Y) (zero Z))", 18.95/5.86 "(addz X Y Z)" 18.95/5.86 ], 18.95/5.86 [ 18.95/5.86 "(addz (zero X) (one Y) (one Z))", 18.95/5.86 "(addx X Y Z)" 18.95/5.86 ], 18.95/5.86 [ 18.95/5.86 "(addz (one X) (zero Y) (one Z))", 18.95/5.86 "(addy X Y Z)" 18.95/5.86 ], 18.95/5.86 [ 18.95/5.86 "(addz (one X) (one Y) (zero Z))", 18.95/5.86 "(addc X Y Z)" 18.95/5.86 ], 18.95/5.86 [ 18.95/5.86 "(addc (b) (b) (one (b)))", 18.95/5.86 null 18.95/5.86 ], 18.95/5.86 [ 18.95/5.86 "(addc X (b) Z)", 18.95/5.86 "(succZ X Z)" 18.95/5.86 ], 18.95/5.86 [ 18.95/5.86 "(addc (b) Y Z)", 18.95/5.86 "(succZ Y Z)" 18.95/5.86 ], 18.95/5.86 [ 18.95/5.86 "(addc X Y Z)", 18.95/5.86 "(addC X Y Z)" 18.95/5.86 ], 18.95/5.86 [ 18.95/5.86 "(addX (zero X) (b) (one X))", 18.95/5.86 "(binaryZ X)" 18.95/5.86 ], 18.95/5.86 [ 18.95/5.86 "(addX (one X) (b) (zero Z))", 18.95/5.86 "(succ X Z)" 18.95/5.86 ], 18.95/5.86 [ 18.95/5.86 "(addX X Y Z)", 18.95/5.86 "(addC X Y Z)" 18.95/5.86 ], 18.95/5.86 [ 18.95/5.86 "(addY (b) (zero Y) (one Y))", 18.95/5.86 "(binaryZ Y)" 18.95/5.86 ], 18.95/5.86 [ 18.95/5.86 "(addY (b) (one Y) (zero Z))", 18.95/5.86 "(succ Y Z)" 18.95/5.86 ], 18.95/5.86 [ 18.95/5.86 "(addY X Y Z)", 18.95/5.86 "(addC X Y Z)" 18.95/5.86 ], 18.95/5.86 [ 18.95/5.86 "(addC (zero X) (zero Y) (one Z))", 18.95/5.86 "(addz X Y Z)" 18.95/5.86 ], 18.95/5.86 [ 18.95/5.86 "(addC (zero X) (one Y) (zero Z))", 18.95/5.86 "(addX X Y Z)" 18.95/5.86 ], 18.95/5.86 [ 18.95/5.86 "(addC (one X) (zero Y) (zero Z))", 18.95/5.86 "(addY X Y Z)" 18.95/5.86 ], 18.95/5.86 [ 18.95/5.86 "(addC (one X) (one Y) (one Z))", 18.95/5.86 "(addc X Y Z)" 18.95/5.86 ], 18.95/5.86 [ 18.95/5.86 "(binary (b))", 18.95/5.86 null 18.95/5.86 ], 18.95/5.86 [ 18.95/5.86 "(binary (zero X))", 18.95/5.86 "(binaryZ X)" 18.95/5.86 ], 18.95/5.86 [ 18.95/5.86 "(binary (one X))", 18.95/5.86 "(binary X)" 18.95/5.86 ], 18.95/5.86 [ 18.95/5.86 "(binaryZ (zero X))", 18.95/5.86 "(binaryZ X)" 18.95/5.86 ], 18.95/5.86 [ 18.95/5.86 "(binaryZ (one 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19.00/5.89 "arithmetic": { 19.00/5.89 "type": "PlainIntegerRelationState", 19.00/5.89 "relations": [] 19.00/5.89 }, 19.00/5.89 "ground": [], 19.00/5.89 "free": [], 19.00/5.89 "exprvars": [] 19.00/5.89 } 19.00/5.89 }, 19.00/5.89 "1208": { 19.00/5.89 "goal": [], 19.00/5.89 "kb": { 19.00/5.89 "nonunifying": [], 19.00/5.89 "intvars": {}, 19.00/5.89 "arithmetic": { 19.00/5.89 "type": "PlainIntegerRelationState", 19.00/5.89 "relations": [] 19.00/5.89 }, 19.00/5.89 "ground": [], 19.00/5.89 "free": [], 19.00/5.89 "exprvars": [] 19.00/5.89 } 19.00/5.89 } 19.00/5.89 }, 19.00/5.89 "edges": [ 19.00/5.89 { 19.00/5.89 "from": 2, 19.00/5.89 "to": 32, 19.00/5.89 "label": "CASE" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 32, 19.00/5.89 "to": 33, 19.00/5.89 "label": "PARALLEL" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 32, 19.00/5.89 "to": 34, 19.00/5.89 "label": "PARALLEL" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 33, 19.00/5.89 "to": 35, 19.00/5.89 "label": "EVAL with clause\ntimes(one(b), X5, X5).\nand substitutionT1 -> one(b),\nT2 -> T8,\nX5 -> T8,\nT3 -> T8" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 33, 19.00/5.89 "to": 36, 19.00/5.89 "label": "EVAL-BACKTRACK" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 34, 19.00/5.89 "to": 38, 19.00/5.89 "label": "PARALLEL" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 34, 19.00/5.89 "to": 39, 19.00/5.89 "label": "PARALLEL" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 35, 19.00/5.89 "to": 37, 19.00/5.89 "label": "SUCCESS" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 38, 19.00/5.89 "to": 40, 19.00/5.89 "label": "EVAL with clause\ntimes(zero(X18), X19, zero(X20)) :- times(X18, X19, X20).\nand substitutionX18 -> T24,\nT1 -> zero(T24),\nT2 -> T25,\nX19 -> T25,\nX20 -> T23,\nT3 -> zero(T23),\nT21 -> T24,\nT22 -> T25" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 38, 19.00/5.89 "to": 41, 19.00/5.89 "label": "EVAL-BACKTRACK" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 39, 19.00/5.89 "to": 91, 19.00/5.89 "label": "EVAL with clause\ntimes(one(X30), X31, X32) :- ','(times(X30, X31, X33), add(X31, zero(X33), X32)).\nand substitutionX30 -> T37,\nT1 -> one(T37),\nT2 -> T38,\nX31 -> T38,\nT3 -> T36,\nX32 -> T36,\nT34 -> T37,\nT35 -> T38" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 39, 19.00/5.89 "to": 98, 19.00/5.89 "label": "EVAL-BACKTRACK" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 40, 19.00/5.89 "to": 2, 19.00/5.89 "label": "INSTANCE with matching:\nT1 -> T24\nT2 -> T25\nT3 -> T23" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 91, 19.00/5.89 "to": 130, 19.00/5.89 "label": "SPLIT 1" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 91, 19.00/5.89 "to": 131, 19.00/5.89 "label": "SPLIT 2\nnew knowledge:\nT37 is ground\nreplacements:X33 -> T41,\nT38 -> T42" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 130, 19.00/5.89 "to": 134, 19.00/5.89 "label": "CASE" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 131, 19.00/5.89 "to": 2208, 19.00/5.89 "label": "CASE" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 134, 19.00/5.89 "to": 214, 19.00/5.89 "label": "PARALLEL" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 134, 19.00/5.89 "to": 215, 19.00/5.89 "label": "PARALLEL" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 214, 19.00/5.89 "to": 216, 19.00/5.89 "label": "EVAL with clause\ntimes(one(b), X42, X42).\nand substitutionT37 -> one(b),\nT38 -> T49,\nX42 -> T49,\nX33 -> T49" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 214, 19.00/5.89 "to": 217, 19.00/5.89 "label": "EVAL-BACKTRACK" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 215, 19.00/5.89 "to": 226, 19.00/5.89 "label": "PARALLEL" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 215, 19.00/5.89 "to": 227, 19.00/5.89 "label": "PARALLEL" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 216, 19.00/5.89 "to": 218, 19.00/5.89 "label": "SUCCESS" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 226, 19.00/5.89 "to": 267, 19.00/5.89 "label": "EVAL with clause\ntimes(zero(X59), X60, zero(X61)) :- times(X59, X60, X61).\nand substitutionX59 -> T60,\nT37 -> zero(T60),\nT38 -> T61,\nX60 -> T61,\nX61 -> X62,\nX33 -> zero(X62),\nT58 -> T60,\nT59 -> T61" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 226, 19.00/5.89 "to": 276, 19.00/5.89 "label": "EVAL-BACKTRACK" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 227, 19.00/5.89 "to": 338, 19.00/5.89 "label": "EVAL with clause\ntimes(one(X74), X75, X76) :- ','(times(X74, X75, X77), add(X75, zero(X77), X76)).\nand substitutionX74 -> T70,\nT37 -> one(T70),\nT38 -> T71,\nX75 -> T71,\nX33 -> X78,\nX76 -> X78,\nT68 -> T70,\nT69 -> T71" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 227, 19.00/5.89 "to": 344, 19.00/5.89 "label": "EVAL-BACKTRACK" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 267, 19.00/5.89 "to": 130, 19.00/5.89 "label": "INSTANCE with matching:\nT37 -> T60\nT38 -> T61\nX33 -> X62" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 338, 19.00/5.89 "to": 1002, 19.00/5.89 "label": "SPLIT 1" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 338, 19.00/5.89 "to": 1003, 19.00/5.89 "label": "SPLIT 2\nnew knowledge:\nT70 is ground\nreplacements:X77 -> T74,\nT71 -> T75" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1002, 19.00/5.89 "to": 130, 19.00/5.89 "label": "INSTANCE with matching:\nT37 -> T70\nT38 -> T71\nX33 -> X77" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1003, 19.00/5.89 "to": 1006, 19.00/5.89 "label": "CASE" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1006, 19.00/5.89 "to": 1007, 19.00/5.89 "label": "BACKTRACK\nfor clause: add(b, b, b)because of non-unification" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1007, 19.00/5.89 "to": 1008, 19.00/5.89 "label": "BACKTRACK\nfor clause: add(X, b, X) :- binaryZ(X)because of non-unification" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1008, 19.00/5.89 "to": 1009, 19.00/5.89 "label": "PARALLEL" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1008, 19.00/5.89 "to": 1010, 19.00/5.89 "label": "PARALLEL" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1009, 19.00/5.89 "to": 1011, 19.00/5.89 "label": "EVAL with clause\nadd(b, X88, X88) :- binaryZ(X88).\nand substitutionT75 -> b,\nT74 -> T84,\nX88 -> zero(T84),\nX78 -> zero(T84),\nT83 -> T84" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1009, 19.00/5.89 "to": 1012, 19.00/5.89 "label": "EVAL-BACKTRACK" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1010, 19.00/5.89 "to": 1099, 19.00/5.89 "label": "ONLY EVAL with clause\nadd(X129, X130, X131) :- addz(X129, X130, X131).\nand substitutionT75 -> T129,\nX129 -> T129,\nT74 -> T130,\nX130 -> zero(T130),\nX78 -> X132,\nX131 -> X132,\nT127 -> T129,\nT128 -> T130" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1011, 19.00/5.89 "to": 1013, 19.00/5.89 "label": "CASE" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1013, 19.00/5.89 "to": 1014, 19.00/5.89 "label": "PARALLEL" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1013, 19.00/5.89 "to": 1015, 19.00/5.89 "label": "PARALLEL" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1014, 19.00/5.89 "to": 1016, 19.00/5.89 "label": "ONLY EVAL with clause\nbinaryZ(zero(X96)) :- binaryZ(X96).\nand substitutionT84 -> T95,\nX96 -> T95,\nT94 -> T95" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1015, 19.00/5.89 "to": 1083, 19.00/5.89 "label": "BACKTRACK\nfor clause: binaryZ(one(X)) :- binary(X)because of non-unification" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1016, 19.00/5.89 "to": 1017, 19.00/5.89 "label": "CASE" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1017, 19.00/5.89 "to": 1018, 19.00/5.89 "label": "PARALLEL" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1017, 19.00/5.89 "to": 1019, 19.00/5.89 "label": "PARALLEL" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1018, 19.00/5.89 "to": 1020, 19.00/5.89 "label": "EVAL with clause\nbinaryZ(zero(X102)) :- binaryZ(X102).\nand substitutionX102 -> T102,\nT95 -> zero(T102),\nT101 -> T102" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1018, 19.00/5.89 "to": 1021, 19.00/5.89 "label": "EVAL-BACKTRACK" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1019, 19.00/5.89 "to": 1034, 19.00/5.89 "label": "EVAL with clause\nbinaryZ(one(X106)) :- binary(X106).\nand substitutionX106 -> T107,\nT95 -> one(T107),\nT106 -> T107" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1019, 19.00/5.89 "to": 1036, 19.00/5.89 "label": "EVAL-BACKTRACK" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1020, 19.00/5.89 "to": 1016, 19.00/5.89 "label": "INSTANCE with matching:\nT95 -> T102" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1034, 19.00/5.89 "to": 1041, 19.00/5.89 "label": "CASE" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1041, 19.00/5.89 "to": 1043, 19.00/5.89 "label": "PARALLEL" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1041, 19.00/5.89 "to": 1045, 19.00/5.89 "label": "PARALLEL" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1043, 19.00/5.89 "to": 1048, 19.00/5.89 "label": "EVAL with clause\nbinary(b).\nand substitutionT107 -> b" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1043, 19.00/5.89 "to": 1050, 19.00/5.89 "label": "EVAL-BACKTRACK" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1045, 19.00/5.89 "to": 1055, 19.00/5.89 "label": "PARALLEL" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1045, 19.00/5.89 "to": 1056, 19.00/5.89 "label": "PARALLEL" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1048, 19.00/5.89 "to": 1051, 19.00/5.89 "label": "SUCCESS" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1055, 19.00/5.89 "to": 1060, 19.00/5.89 "label": "EVAL with clause\nbinary(zero(X111)) :- binaryZ(X111).\nand substitutionX111 -> T113,\nT107 -> zero(T113),\nT112 -> T113" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1055, 19.00/5.89 "to": 1062, 19.00/5.89 "label": "EVAL-BACKTRACK" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1056, 19.00/5.89 "to": 1075, 19.00/5.89 "label": "EVAL with clause\nbinary(one(X115)) :- binary(X115).\nand substitutionX115 -> T118,\nT107 -> one(T118),\nT117 -> T118" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1056, 19.00/5.89 "to": 1077, 19.00/5.89 "label": "EVAL-BACKTRACK" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1060, 19.00/5.89 "to": 1016, 19.00/5.89 "label": "INSTANCE with matching:\nT95 -> T113" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1075, 19.00/5.89 "to": 1034, 19.00/5.89 "label": "INSTANCE with matching:\nT107 -> T118" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1099, 19.00/5.89 "to": 1109, 19.00/5.89 "label": "CASE" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1109, 19.00/5.89 "to": 1120, 19.00/5.89 "label": "PARALLEL" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1109, 19.00/5.89 "to": 1121, 19.00/5.89 "label": "PARALLEL" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1120, 19.00/5.89 "to": 1138, 19.00/5.89 "label": "EVAL with clause\naddz(zero(X153), zero(X154), zero(X155)) :- addz(X153, X154, X155).\nand substitutionX153 -> T143,\nT129 -> zero(T143),\nT130 -> T144,\nX154 -> T144,\nX155 -> X156,\nX132 -> zero(X156),\nT141 -> T143,\nT142 -> T144" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1120, 19.00/5.89 "to": 1140, 19.00/5.89 "label": "EVAL-BACKTRACK" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1121, 19.00/5.89 "to": 2170, 19.00/5.89 "label": "BACKTRACK\nfor clause: addz(zero(X), one(Y), one(Z)) :- addx(X, Y, Z)because of non-unification" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1138, 19.00/5.89 "to": 1143, 19.00/5.89 "label": "CASE" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1143, 19.00/5.89 "to": 1149, 19.00/5.89 "label": "PARALLEL" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1143, 19.00/5.89 "to": 1150, 19.00/5.89 "label": "PARALLEL" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1149, 19.00/5.89 "to": 1157, 19.00/5.89 "label": "EVAL with clause\naddz(zero(X177), zero(X178), zero(X179)) :- addz(X177, X178, X179).\nand substitutionX177 -> T157,\nT143 -> zero(T157),\nX178 -> T158,\nT144 -> zero(T158),\nX179 -> X180,\nX156 -> zero(X180),\nT155 -> T157,\nT156 -> T158" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1149, 19.00/5.89 "to": 1160, 19.00/5.89 "label": "EVAL-BACKTRACK" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1150, 19.00/5.89 "to": 1182, 19.00/5.89 "label": "PARALLEL" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1150, 19.00/5.89 "to": 1183, 19.00/5.89 "label": "PARALLEL" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1157, 19.00/5.89 "to": 1138, 19.00/5.89 "label": "INSTANCE with matching:\nT143 -> T157\nT144 -> T158\nX156 -> X180" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1182, 19.00/5.89 "to": 1206, 19.00/5.89 "label": "EVAL with clause\naddz(zero(X201), one(X202), one(X203)) :- addx(X201, X202, X203).\nand substitutionX201 -> T171,\nT143 -> zero(T171),\nX202 -> T172,\nT144 -> one(T172),\nX203 -> X204,\nX156 -> one(X204),\nT169 -> T171,\nT170 -> T172" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1182, 19.00/5.89 "to": 1208, 19.00/5.89 "label": "EVAL-BACKTRACK" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1183, 19.00/5.89 "to": 1315, 19.00/5.89 "label": "PARALLEL" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1183, 19.00/5.89 "to": 1316, 19.00/5.89 "label": "PARALLEL" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1206, 19.00/5.89 "to": 1218, 19.00/5.89 "label": "CASE" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1218, 19.00/5.89 "to": 1226, 19.00/5.89 "label": "PARALLEL" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1218, 19.00/5.89 "to": 1227, 19.00/5.89 "label": "PARALLEL" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1226, 19.00/5.89 "to": 1238, 19.00/5.89 "label": "EVAL with clause\naddx(one(X210), b, one(X210)) :- binary(X210).\nand substitutionX210 -> T179,\nT171 -> one(T179),\nT172 -> b,\nX204 -> one(T179),\nT178 -> T179" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1226, 19.00/5.89 "to": 1241, 19.00/5.89 "label": "EVAL-BACKTRACK" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1227, 19.00/5.89 "to": 1252, 19.00/5.89 "label": "PARALLEL" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1227, 19.00/5.89 "to": 1253, 19.00/5.89 "label": "PARALLEL" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1238, 19.00/5.89 "to": 1034, 19.00/5.89 "label": "INSTANCE with matching:\nT107 -> T179" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1252, 19.00/5.89 "to": 1258, 19.00/5.89 "label": "EVAL with clause\naddx(zero(X215), b, zero(X215)) :- binaryZ(X215).\nand substitutionX215 -> T185,\nT171 -> zero(T185),\nT172 -> b,\nX204 -> zero(T185),\nT184 -> T185" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1252, 19.00/5.89 "to": 1259, 19.00/5.89 "label": "EVAL-BACKTRACK" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1253, 19.00/5.89 "to": 1282, 19.00/5.89 "label": "ONLY EVAL with clause\naddx(X229, X230, X231) :- addz(X229, X230, X231).\nand substitutionT171 -> T197,\nX229 -> T197,\nT172 -> T198,\nX230 -> T198,\nX204 -> X232,\nX231 -> X232,\nT195 -> T197,\nT196 -> T198" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1258, 19.00/5.89 "to": 1016, 19.00/5.89 "label": "INSTANCE with matching:\nT95 -> T185" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1282, 19.00/5.89 "to": 1138, 19.00/5.89 "label": "INSTANCE with matching:\nT143 -> T197\nT144 -> T198\nX156 -> X232" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1315, 19.00/5.89 "to": 1347, 19.00/5.89 "label": "EVAL with clause\naddz(one(X253), zero(X254), one(X255)) :- addy(X253, X254, X255).\nand substitutionX253 -> T211,\nT143 -> one(T211),\nX254 -> T212,\nT144 -> zero(T212),\nX255 -> X256,\nX156 -> one(X256),\nT209 -> T211,\nT210 -> T212" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1315, 19.00/5.89 "to": 1350, 19.00/5.89 "label": "EVAL-BACKTRACK" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1316, 19.00/5.89 "to": 1631, 19.00/5.89 "label": "EVAL with clause\naddz(one(X297), one(X298), zero(X299)) :- addc(X297, X298, X299).\nand substitutionX297 -> T247,\nT143 -> one(T247),\nX298 -> T248,\nT144 -> one(T248),\nX299 -> X300,\nX156 -> zero(X300),\nT245 -> T247,\nT246 -> T248" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1316, 19.00/5.89 "to": 1632, 19.00/5.89 "label": "EVAL-BACKTRACK" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1347, 19.00/5.89 "to": 1596, 19.00/5.89 "label": "CASE" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1596, 19.00/5.89 "to": 1598, 19.00/5.89 "label": "PARALLEL" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1596, 19.00/5.89 "to": 1599, 19.00/5.89 "label": "PARALLEL" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1598, 19.00/5.89 "to": 1603, 19.00/5.89 "label": "EVAL with clause\naddy(b, one(X262), one(X262)) :- binary(X262).\nand substitutionT211 -> b,\nX262 -> T219,\nT212 -> one(T219),\nX256 -> one(T219),\nT218 -> T219" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1598, 19.00/5.89 "to": 1604, 19.00/5.89 "label": "EVAL-BACKTRACK" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1599, 19.00/5.89 "to": 1607, 19.00/5.89 "label": "PARALLEL" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1599, 19.00/5.89 "to": 1608, 19.00/5.89 "label": "PARALLEL" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1603, 19.00/5.89 "to": 1034, 19.00/5.89 "label": "INSTANCE with matching:\nT107 -> T219" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1607, 19.00/5.89 "to": 1611, 19.00/5.89 "label": "EVAL with clause\naddy(b, zero(X267), zero(X267)) :- binaryZ(X267).\nand substitutionT211 -> b,\nX267 -> T225,\nT212 -> zero(T225),\nX256 -> zero(T225),\nT224 -> T225" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1607, 19.00/5.89 "to": 1612, 19.00/5.89 "label": "EVAL-BACKTRACK" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1608, 19.00/5.89 "to": 1615, 19.00/5.89 "label": "ONLY EVAL with clause\naddy(X281, X282, X283) :- addz(X281, X282, X283).\nand substitutionT211 -> T237,\nX281 -> T237,\nT212 -> T238,\nX282 -> T238,\nX256 -> X284,\nX283 -> X284,\nT235 -> T237,\nT236 -> T238" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1611, 19.00/5.89 "to": 1016, 19.00/5.89 "label": "INSTANCE with matching:\nT95 -> T225" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1615, 19.00/5.89 "to": 1138, 19.00/5.89 "label": "INSTANCE with matching:\nT143 -> T237\nT144 -> T238\nX156 -> X284" 19.00/5.89 }, 19.00/5.89 { 19.00/5.89 "from": 1631, 19.00/5.89 "to": 1633, 19.00/5.89 "label": "CASE" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1633, 19.00/5.90 "to": 1634, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1633, 19.00/5.90 "to": 1635, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1634, 19.00/5.90 "to": 1636, 19.00/5.90 "label": "EVAL with clause\naddc(b, b, one(b)).\nand substitutionT247 -> b,\nT248 -> b,\nX300 -> one(b)" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1634, 19.00/5.90 "to": 1637, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1635, 19.00/5.90 "to": 1639, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1635, 19.00/5.90 "to": 1640, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1636, 19.00/5.90 "to": 1638, 19.00/5.90 "label": "SUCCESS" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1639, 19.00/5.90 "to": 1670, 19.00/5.90 "label": "EVAL with clause\naddc(X313, b, X314) :- succZ(X313, X314).\nand substitutionT247 -> T254,\nX313 -> T254,\nT248 -> b,\nX300 -> X315,\nX314 -> X315,\nT253 -> T254" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1639, 19.00/5.90 "to": 1671, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1640, 19.00/5.90 "to": 1708, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1640, 19.00/5.90 "to": 1709, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1670, 19.00/5.90 "to": 1672, 19.00/5.90 "label": "CASE" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1672, 19.00/5.90 "to": 1673, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1672, 19.00/5.90 "to": 1674, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1673, 19.00/5.90 "to": 1675, 19.00/5.90 "label": "EVAL with clause\nsuccZ(zero(X321), one(X321)) :- binaryZ(X321).\nand substitutionX321 -> T261,\nT254 -> zero(T261),\nX315 -> one(T261),\nT260 -> T261" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1673, 19.00/5.90 "to": 1676, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1674, 19.00/5.90 "to": 1682, 19.00/5.90 "label": "EVAL with clause\nsuccZ(one(X329), zero(X330)) :- succ(X329, X330).\nand substitutionX329 -> T266,\nT254 -> one(T266),\nX330 -> X331,\nX315 -> zero(X331),\nT265 -> T266" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1674, 19.00/5.90 "to": 1683, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1675, 19.00/5.90 "to": 1016, 19.00/5.90 "label": "INSTANCE with matching:\nT95 -> T261" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1682, 19.00/5.90 "to": 1684, 19.00/5.90 "label": "CASE" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1684, 19.00/5.90 "to": 1685, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1684, 19.00/5.90 "to": 1686, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1685, 19.00/5.90 "to": 1687, 19.00/5.90 "label": "EVAL with clause\nsucc(b, one(b)).\nand substitutionT266 -> b,\nX331 -> one(b)" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1685, 19.00/5.90 "to": 1688, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1686, 19.00/5.90 "to": 1692, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1686, 19.00/5.90 "to": 1693, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1687, 19.00/5.90 "to": 1689, 19.00/5.90 "label": "SUCCESS" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1692, 19.00/5.90 "to": 1694, 19.00/5.90 "label": "EVAL with clause\nsucc(zero(X336), one(X336)) :- binaryZ(X336).\nand substitutionX336 -> T272,\nT266 -> zero(T272),\nX331 -> one(T272),\nT271 -> T272" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1692, 19.00/5.90 "to": 1695, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1693, 19.00/5.90 "to": 1700, 19.00/5.90 "label": "EVAL with clause\nsucc(one(X344), zero(X345)) :- succ(X344, X345).\nand substitutionX344 -> T277,\nT266 -> one(T277),\nX345 -> X346,\nX331 -> zero(X346),\nT276 -> T277" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1693, 19.00/5.90 "to": 1702, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1694, 19.00/5.90 "to": 1016, 19.00/5.90 "label": "INSTANCE with matching:\nT95 -> T272" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1700, 19.00/5.90 "to": 1682, 19.00/5.90 "label": "INSTANCE with matching:\nT266 -> T277\nX331 -> X346" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1708, 19.00/5.90 "to": 1712, 19.00/5.90 "label": "EVAL with clause\naddc(b, X359, X360) :- succZ(X359, X360).\nand substitutionT247 -> b,\nT248 -> T283,\nX359 -> T283,\nX300 -> X361,\nX360 -> X361,\nT282 -> T283" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1708, 19.00/5.90 "to": 1713, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1709, 19.00/5.90 "to": 1763, 19.00/5.90 "label": "ONLY EVAL with clause\naddc(X375, X376, X377) :- addC(X375, X376, X377).\nand substitutionT247 -> T295,\nX375 -> T295,\nT248 -> T296,\nX376 -> T296,\nX300 -> X378,\nX377 -> X378,\nT293 -> T295,\nT294 -> T296" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1712, 19.00/5.90 "to": 1670, 19.00/5.90 "label": "INSTANCE with matching:\nT254 -> T283\nX315 -> X361" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1763, 19.00/5.90 "to": 1764, 19.00/5.90 "label": "CASE" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1764, 19.00/5.90 "to": 1767, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1764, 19.00/5.90 "to": 1768, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1767, 19.00/5.90 "to": 1774, 19.00/5.90 "label": "EVAL with clause\naddC(zero(X399), zero(X400), one(X401)) :- addz(X399, X400, X401).\nand substitutionX399 -> T309,\nT295 -> zero(T309),\nX400 -> T310,\nT296 -> zero(T310),\nX401 -> X402,\nX378 -> one(X402),\nT307 -> T309,\nT308 -> T310" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1767, 19.00/5.90 "to": 1775, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1768, 19.00/5.90 "to": 1781, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1768, 19.00/5.90 "to": 1782, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1774, 19.00/5.90 "to": 1138, 19.00/5.90 "label": "INSTANCE with matching:\nT143 -> T309\nT144 -> T310\nX156 -> X402" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1781, 19.00/5.90 "to": 2098, 19.00/5.90 "label": "EVAL with clause\naddC(zero(X423), one(X424), zero(X425)) :- addX(X423, X424, X425).\nand substitutionX423 -> T323,\nT295 -> zero(T323),\nX424 -> T324,\nT296 -> one(T324),\nX425 -> X426,\nX378 -> zero(X426),\nT321 -> T323,\nT322 -> T324" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1781, 19.00/5.90 "to": 2099, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1782, 19.00/5.90 "to": 2123, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 1782, 19.00/5.90 "to": 2124, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2098, 19.00/5.90 "to": 2100, 19.00/5.90 "label": "CASE" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2100, 19.00/5.90 "to": 2101, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2100, 19.00/5.90 "to": 2102, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2101, 19.00/5.90 "to": 2103, 19.00/5.90 "label": "EVAL with clause\naddX(zero(X432), b, one(X432)) :- binaryZ(X432).\nand substitutionX432 -> T331,\nT323 -> zero(T331),\nT324 -> b,\nX426 -> one(T331),\nT330 -> T331" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2101, 19.00/5.90 "to": 2104, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2102, 19.00/5.90 "to": 2105, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2102, 19.00/5.90 "to": 2106, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2103, 19.00/5.90 "to": 1016, 19.00/5.90 "label": "INSTANCE with matching:\nT95 -> T331" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2105, 19.00/5.90 "to": 2107, 19.00/5.90 "label": "EVAL with clause\naddX(one(X446), b, zero(X447)) :- succ(X446, X447).\nand substitutionX446 -> T338,\nT323 -> one(T338),\nT324 -> b,\nX447 -> X448,\nX426 -> zero(X448),\nT337 -> T338" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2105, 19.00/5.90 "to": 2108, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2106, 19.00/5.90 "to": 2122, 19.00/5.90 "label": "ONLY EVAL with clause\naddX(X461, X462, X463) :- addC(X461, X462, X463).\nand substitutionT323 -> T349,\nX461 -> T349,\nT324 -> T350,\nX462 -> T350,\nX426 -> X464,\nX463 -> X464,\nT347 -> T349,\nT348 -> T350" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2107, 19.00/5.90 "to": 1682, 19.00/5.90 "label": "INSTANCE with matching:\nT266 -> T338\nX331 -> X448" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2122, 19.00/5.90 "to": 1763, 19.00/5.90 "label": "INSTANCE with matching:\nT295 -> T349\nT296 -> T350\nX378 -> X464" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2123, 19.00/5.90 "to": 2125, 19.00/5.90 "label": "EVAL with clause\naddC(one(X485), zero(X486), zero(X487)) :- addY(X485, X486, X487).\nand substitutionX485 -> T363,\nT295 -> one(T363),\nX486 -> T364,\nT296 -> zero(T364),\nX487 -> X488,\nX378 -> zero(X488),\nT361 -> T363,\nT362 -> T364" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2123, 19.00/5.90 "to": 2126, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2124, 19.00/5.90 "to": 2168, 19.00/5.90 "label": "EVAL with clause\naddC(one(X539), one(X540), one(X541)) :- addc(X539, X540, X541).\nand substitutionX539 -> T399,\nT295 -> one(T399),\nX540 -> T400,\nT296 -> one(T400),\nX541 -> X542,\nX378 -> one(X542),\nT397 -> T399,\nT398 -> T400" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2124, 19.00/5.90 "to": 2169, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2125, 19.00/5.90 "to": 2127, 19.00/5.90 "label": "CASE" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2127, 19.00/5.90 "to": 2128, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2127, 19.00/5.90 "to": 2129, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2128, 19.00/5.90 "to": 2131, 19.00/5.90 "label": "EVAL with clause\naddY(b, zero(X494), one(X494)) :- binaryZ(X494).\nand substitutionT363 -> b,\nX494 -> T371,\nT364 -> zero(T371),\nX488 -> one(T371),\nT370 -> T371" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2128, 19.00/5.90 "to": 2132, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2129, 19.00/5.90 "to": 2135, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2129, 19.00/5.90 "to": 2136, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2131, 19.00/5.90 "to": 1016, 19.00/5.90 "label": "INSTANCE with matching:\nT95 -> T371" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2135, 19.00/5.90 "to": 2139, 19.00/5.90 "label": "EVAL with clause\naddY(b, one(X508), zero(X509)) :- succ(X508, X509).\nand substitutionT363 -> b,\nX508 -> T378,\nT364 -> one(T378),\nX509 -> X510,\nX488 -> zero(X510),\nT377 -> T378" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2135, 19.00/5.90 "to": 2164, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2136, 19.00/5.90 "to": 2167, 19.00/5.90 "label": "ONLY EVAL with clause\naddY(X523, X524, X525) :- addC(X523, X524, X525).\nand substitutionT363 -> T389,\nX523 -> T389,\nT364 -> T390,\nX524 -> T390,\nX488 -> X526,\nX525 -> X526,\nT387 -> T389,\nT388 -> T390" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2139, 19.00/5.90 "to": 1682, 19.00/5.90 "label": "INSTANCE with matching:\nT266 -> T378\nX331 -> X510" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2167, 19.00/5.90 "to": 1763, 19.00/5.90 "label": "INSTANCE with matching:\nT295 -> T389\nT296 -> T390\nX378 -> X526" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2168, 19.00/5.90 "to": 1631, 19.00/5.90 "label": "INSTANCE with matching:\nT247 -> T399\nT248 -> T400\nX300 -> X542" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2170, 19.00/5.90 "to": 2171, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2170, 19.00/5.90 "to": 2172, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2171, 19.00/5.90 "to": 2203, 19.00/5.90 "label": "EVAL with clause\naddz(one(X562), zero(X563), one(X564)) :- addy(X562, X563, X564).\nand substitutionX562 -> T412,\nT129 -> one(T412),\nT130 -> T413,\nX563 -> T413,\nX564 -> X565,\nX132 -> one(X565),\nT410 -> T412,\nT411 -> T413" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2171, 19.00/5.90 "to": 2204, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2172, 19.00/5.90 "to": 2205, 19.00/5.90 "label": "BACKTRACK\nfor clause: addz(one(X), one(Y), zero(Z)) :- addc(X, Y, Z)because of non-unification" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2203, 19.00/5.90 "to": 1347, 19.00/5.90 "label": "INSTANCE with matching:\nT211 -> T412\nT212 -> T413\nX256 -> X565" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2208, 19.00/5.90 "to": 2209, 19.00/5.90 "label": "BACKTRACK\nfor clause: add(b, b, b)because of non-unification" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2209, 19.00/5.90 "to": 2210, 19.00/5.90 "label": "BACKTRACK\nfor clause: add(X, b, X) :- binaryZ(X)because of non-unification" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2210, 19.00/5.90 "to": 2211, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2210, 19.00/5.90 "to": 2212, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2211, 19.00/5.90 "to": 2213, 19.00/5.90 "label": "EVAL with clause\nadd(b, X575, X575) :- binaryZ(X575).\nand substitutionT42 -> b,\nT41 -> T421,\nX575 -> zero(T421),\nT36 -> zero(T421)" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2211, 19.00/5.90 "to": 2214, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2212, 19.00/5.90 "to": 2258, 19.00/5.90 "label": "ONLY EVAL with clause\nadd(X613, X614, X615) :- addz(X613, X614, X615).\nand substitutionT42 -> T463,\nX613 -> T463,\nT41 -> T464,\nX614 -> zero(T464),\nT36 -> T462,\nX615 -> T462,\nT460 -> T463,\nT461 -> T464" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2213, 19.00/5.90 "to": 2215, 19.00/5.90 "label": "CASE" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2215, 19.00/5.90 "to": 2216, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2215, 19.00/5.90 "to": 2217, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2216, 19.00/5.90 "to": 2218, 19.00/5.90 "label": "ONLY EVAL with clause\nbinaryZ(zero(X583)) :- binaryZ(X583).\nand substitutionT421 -> T429,\nX583 -> T429" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2217, 19.00/5.90 "to": 2250, 19.00/5.90 "label": "BACKTRACK\nfor clause: binaryZ(one(X)) :- binary(X)because of non-unification" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2218, 19.00/5.90 "to": 2219, 19.00/5.90 "label": "CASE" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2219, 19.00/5.90 "to": 2220, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2219, 19.00/5.90 "to": 2221, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2220, 19.00/5.90 "to": 2231, 19.00/5.90 "label": "EVAL with clause\nbinaryZ(zero(X589)) :- binaryZ(X589).\nand substitutionX589 -> T435,\nT429 -> zero(T435)" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2220, 19.00/5.90 "to": 2232, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2221, 19.00/5.90 "to": 2233, 19.00/5.90 "label": "EVAL with clause\nbinaryZ(one(X593)) :- binary(X593).\nand substitutionX593 -> T439,\nT429 -> one(T439)" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2221, 19.00/5.90 "to": 2234, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2231, 19.00/5.90 "to": 2218, 19.00/5.90 "label": "INSTANCE with matching:\nT429 -> T435" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2233, 19.00/5.90 "to": 2235, 19.00/5.90 "label": "CASE" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2235, 19.00/5.90 "to": 2236, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2235, 19.00/5.90 "to": 2237, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2236, 19.00/5.90 "to": 2240, 19.00/5.90 "label": "EVAL with clause\nbinary(b).\nand substitutionT439 -> b" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2236, 19.00/5.90 "to": 2241, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2237, 19.00/5.90 "to": 2243, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2237, 19.00/5.90 "to": 2244, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2240, 19.00/5.90 "to": 2242, 19.00/5.90 "label": "SUCCESS" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2243, 19.00/5.90 "to": 2245, 19.00/5.90 "label": "EVAL with clause\nbinary(zero(X598)) :- binaryZ(X598).\nand substitutionX598 -> T444,\nT439 -> zero(T444)" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2243, 19.00/5.90 "to": 2246, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2244, 19.00/5.90 "to": 2247, 19.00/5.90 "label": "EVAL with clause\nbinary(one(X602)) :- binary(X602).\nand substitutionX602 -> T448,\nT439 -> one(T448)" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2244, 19.00/5.90 "to": 2248, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2245, 19.00/5.90 "to": 2218, 19.00/5.90 "label": "INSTANCE with matching:\nT429 -> T444" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2247, 19.00/5.90 "to": 2233, 19.00/5.90 "label": "INSTANCE with matching:\nT439 -> T448" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2258, 19.00/5.90 "to": 2262, 19.00/5.90 "label": "CASE" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2262, 19.00/5.90 "to": 2263, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2262, 19.00/5.90 "to": 2264, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2263, 19.00/5.90 "to": 2269, 19.00/5.90 "label": "EVAL with clause\naddz(zero(X631), zero(X632), zero(X633)) :- addz(X631, X632, X633).\nand substitutionX631 -> T483,\nT463 -> zero(T483),\nT464 -> T484,\nX632 -> T484,\nX633 -> T482,\nT462 -> zero(T482),\nT480 -> T483,\nT481 -> T484" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2263, 19.00/5.90 "to": 2270, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2264, 19.00/5.90 "to": 2593, 19.00/5.90 "label": "BACKTRACK\nfor clause: addz(zero(X), one(Y), one(Z)) :- addx(X, Y, Z)because of non-unification" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2269, 19.00/5.90 "to": 2290, 19.00/5.90 "label": "CASE" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2290, 19.00/5.90 "to": 2291, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2290, 19.00/5.90 "to": 2292, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2291, 19.00/5.90 "to": 2293, 19.00/5.90 "label": "EVAL with clause\naddz(zero(X649), zero(X650), zero(X651)) :- addz(X649, X650, X651).\nand substitutionX649 -> T503,\nT483 -> zero(T503),\nX650 -> T504,\nT484 -> zero(T504),\nX651 -> T502,\nT482 -> zero(T502),\nT500 -> T503,\nT501 -> T504" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2291, 19.00/5.90 "to": 2294, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2292, 19.00/5.90 "to": 2295, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2292, 19.00/5.90 "to": 2296, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2293, 19.00/5.90 "to": 2269, 19.00/5.90 "label": "INSTANCE with matching:\nT483 -> T503\nT484 -> T504\nT482 -> T502" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2295, 19.00/5.90 "to": 2307, 19.00/5.90 "label": "EVAL with clause\naddz(zero(X667), one(X668), one(X669)) :- addx(X667, X668, X669).\nand substitutionX667 -> T523,\nT483 -> zero(T523),\nX668 -> T524,\nT484 -> one(T524),\nX669 -> T522,\nT482 -> one(T522),\nT520 -> T523,\nT521 -> T524" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2295, 19.00/5.90 "to": 2308, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2296, 19.00/5.90 "to": 2335, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2296, 19.00/5.90 "to": 2336, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2307, 19.00/5.90 "to": 2310, 19.00/5.90 "label": "CASE" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2310, 19.00/5.90 "to": 2311, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2310, 19.00/5.90 "to": 2312, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2311, 19.00/5.90 "to": 2314, 19.00/5.90 "label": "EVAL with clause\naddx(one(X675), b, one(X675)) :- binary(X675).\nand substitutionX675 -> T530,\nT523 -> one(T530),\nT524 -> b,\nT522 -> one(T530)" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2311, 19.00/5.90 "to": 2315, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2312, 19.00/5.90 "to": 2316, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2312, 19.00/5.90 "to": 2317, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2314, 19.00/5.90 "to": 2233, 19.00/5.90 "label": "INSTANCE with matching:\nT439 -> T530" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2316, 19.00/5.90 "to": 2320, 19.00/5.90 "label": "EVAL with clause\naddx(zero(X680), b, zero(X680)) :- binaryZ(X680).\nand substitutionX680 -> T535,\nT523 -> zero(T535),\nT524 -> b,\nT522 -> zero(T535)" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2316, 19.00/5.90 "to": 2321, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2317, 19.00/5.90 "to": 2334, 19.00/5.90 "label": "ONLY EVAL with clause\naddx(X691, X692, X693) :- addz(X691, X692, X693).\nand substitutionT523 -> T551,\nX691 -> T551,\nT524 -> T552,\nX692 -> T552,\nT522 -> T550,\nX693 -> T550,\nT548 -> T551,\nT549 -> T552" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2320, 19.00/5.90 "to": 2218, 19.00/5.90 "label": "INSTANCE with matching:\nT429 -> T535" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2334, 19.00/5.90 "to": 2269, 19.00/5.90 "label": "INSTANCE with matching:\nT483 -> T551\nT484 -> T552\nT482 -> T550" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2335, 19.00/5.90 "to": 2337, 19.00/5.90 "label": "EVAL with clause\naddz(one(X709), zero(X710), one(X711)) :- addy(X709, X710, X711).\nand substitutionX709 -> T571,\nT483 -> one(T571),\nX710 -> T572,\nT484 -> zero(T572),\nX711 -> T570,\nT482 -> one(T570),\nT568 -> T571,\nT569 -> T572" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2335, 19.00/5.90 "to": 2338, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2336, 19.00/5.90 "to": 2422, 19.00/5.90 "label": "EVAL with clause\naddz(one(X745), one(X746), zero(X747)) :- addc(X745, X746, X747).\nand substitutionX745 -> T613,\nT483 -> one(T613),\nX746 -> T614,\nT484 -> one(T614),\nX747 -> T612,\nT482 -> zero(T612),\nT610 -> T613,\nT611 -> T614" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2336, 19.00/5.90 "to": 2423, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2337, 19.00/5.90 "to": 2339, 19.00/5.90 "label": "CASE" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2339, 19.00/5.90 "to": 2340, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2339, 19.00/5.90 "to": 2341, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2340, 19.00/5.90 "to": 2360, 19.00/5.90 "label": "EVAL with clause\naddy(b, one(X717), one(X717)) :- binary(X717).\nand substitutionT571 -> b,\nX717 -> T578,\nT572 -> one(T578),\nT570 -> one(T578)" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2340, 19.00/5.90 "to": 2361, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2341, 19.00/5.90 "to": 2365, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2341, 19.00/5.90 "to": 2366, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2360, 19.00/5.90 "to": 2233, 19.00/5.90 "label": "INSTANCE with matching:\nT439 -> T578" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2365, 19.00/5.90 "to": 2369, 19.00/5.90 "label": "EVAL with clause\naddy(b, zero(X722), zero(X722)) :- binaryZ(X722).\nand substitutionT571 -> b,\nX722 -> T583,\nT572 -> zero(T583),\nT570 -> zero(T583)" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2365, 19.00/5.90 "to": 2370, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2366, 19.00/5.90 "to": 2377, 19.00/5.90 "label": "ONLY EVAL with clause\naddy(X733, X734, X735) :- addz(X733, X734, X735).\nand substitutionT571 -> T599,\nX733 -> T599,\nT572 -> T600,\nX734 -> T600,\nT570 -> T598,\nX735 -> T598,\nT596 -> T599,\nT597 -> T600" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2369, 19.00/5.90 "to": 2218, 19.00/5.90 "label": "INSTANCE with matching:\nT429 -> T583" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2377, 19.00/5.90 "to": 2269, 19.00/5.90 "label": "INSTANCE with matching:\nT483 -> T599\nT484 -> T600\nT482 -> T598" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2422, 19.00/5.90 "to": 2426, 19.00/5.90 "label": "CASE" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2426, 19.00/5.90 "to": 2427, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2426, 19.00/5.90 "to": 2428, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2427, 19.00/5.90 "to": 2429, 19.00/5.90 "label": "EVAL with clause\naddc(b, b, one(b)).\nand substitutionT613 -> b,\nT614 -> b,\nT612 -> one(b)" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2427, 19.00/5.90 "to": 2430, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2428, 19.00/5.90 "to": 2433, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2428, 19.00/5.90 "to": 2434, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2429, 19.00/5.90 "to": 2431, 19.00/5.90 "label": "SUCCESS" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2433, 19.00/5.90 "to": 2438, 19.00/5.90 "label": "EVAL with clause\naddc(X756, b, X757) :- succZ(X756, X757).\nand substitutionT613 -> T625,\nX756 -> T625,\nT614 -> b,\nT612 -> T624,\nX757 -> T624,\nT623 -> T625" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2433, 19.00/5.90 "to": 2439, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2434, 19.00/5.90 "to": 2468, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2434, 19.00/5.90 "to": 2469, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2438, 19.00/5.90 "to": 2443, 19.00/5.90 "label": "CASE" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2443, 19.00/5.90 "to": 2444, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2443, 19.00/5.90 "to": 2445, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2444, 19.00/5.90 "to": 2446, 19.00/5.90 "label": "EVAL with clause\nsuccZ(zero(X763), one(X763)) :- binaryZ(X763).\nand substitutionX763 -> T631,\nT625 -> zero(T631),\nT624 -> one(T631)" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2444, 19.00/5.90 "to": 2447, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2445, 19.00/5.90 "to": 2450, 19.00/5.90 "label": "EVAL with clause\nsuccZ(one(X769), zero(X770)) :- succ(X769, X770).\nand substitutionX769 -> T639,\nT625 -> one(T639),\nX770 -> T638,\nT624 -> zero(T638),\nT637 -> T639" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2445, 19.00/5.90 "to": 2451, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2446, 19.00/5.90 "to": 2218, 19.00/5.90 "label": "INSTANCE with matching:\nT429 -> T631" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2450, 19.00/5.90 "to": 2454, 19.00/5.90 "label": "CASE" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2454, 19.00/5.90 "to": 2455, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2454, 19.00/5.90 "to": 2456, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2455, 19.00/5.90 "to": 2457, 19.00/5.90 "label": "EVAL with clause\nsucc(b, one(b)).\nand substitutionT639 -> b,\nT638 -> one(b)" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2455, 19.00/5.90 "to": 2458, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2456, 19.00/5.90 "to": 2460, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2456, 19.00/5.90 "to": 2461, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2457, 19.00/5.90 "to": 2459, 19.00/5.90 "label": "SUCCESS" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2460, 19.00/5.90 "to": 2462, 19.00/5.90 "label": "EVAL with clause\nsucc(zero(X775), one(X775)) :- binaryZ(X775).\nand substitutionX775 -> T644,\nT639 -> zero(T644),\nT638 -> one(T644)" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2460, 19.00/5.90 "to": 2463, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2461, 19.00/5.90 "to": 2464, 19.00/5.90 "label": "EVAL with clause\nsucc(one(X781), zero(X782)) :- succ(X781, X782).\nand substitutionX781 -> T652,\nT639 -> one(T652),\nX782 -> T651,\nT638 -> zero(T651),\nT650 -> T652" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2461, 19.00/5.90 "to": 2465, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2462, 19.00/5.90 "to": 2218, 19.00/5.90 "label": "INSTANCE with matching:\nT429 -> T644" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2464, 19.00/5.90 "to": 2450, 19.00/5.90 "label": "INSTANCE with matching:\nT639 -> T652\nT638 -> T651" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2468, 19.00/5.90 "to": 2470, 19.00/5.90 "label": "EVAL with clause\naddc(b, X791, X792) :- succZ(X791, X792).\nand substitutionT613 -> b,\nT614 -> T663,\nX791 -> T663,\nT612 -> T662,\nX792 -> T662,\nT661 -> T663" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2468, 19.00/5.90 "to": 2471, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2469, 19.00/5.90 "to": 2493, 19.00/5.90 "label": "ONLY EVAL with clause\naddc(X803, X804, X805) :- addC(X803, X804, X805).\nand substitutionT613 -> T679,\nX803 -> T679,\nT614 -> T680,\nX804 -> T680,\nT612 -> T678,\nX805 -> T678,\nT676 -> T679,\nT677 -> T680" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2470, 19.00/5.90 "to": 2438, 19.00/5.90 "label": "INSTANCE with matching:\nT625 -> T663\nT624 -> T662" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2493, 19.00/5.90 "to": 2496, 19.00/5.90 "label": "CASE" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2496, 19.00/5.90 "to": 2499, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2496, 19.00/5.90 "to": 2500, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2499, 19.00/5.90 "to": 2501, 19.00/5.90 "label": "EVAL with clause\naddC(zero(X821), zero(X822), one(X823)) :- addz(X821, X822, X823).\nand substitutionX821 -> T699,\nT679 -> zero(T699),\nX822 -> T700,\nT680 -> zero(T700),\nX823 -> T698,\nT678 -> one(T698),\nT696 -> T699,\nT697 -> T700" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2499, 19.00/5.90 "to": 2502, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2500, 19.00/5.90 "to": 2504, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2500, 19.00/5.90 "to": 2505, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2501, 19.00/5.90 "to": 2269, 19.00/5.90 "label": "INSTANCE with matching:\nT483 -> T699\nT484 -> T700\nT482 -> T698" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2504, 19.00/5.90 "to": 2506, 19.00/5.90 "label": "EVAL with clause\naddC(zero(X839), one(X840), zero(X841)) :- addX(X839, X840, X841).\nand substitutionX839 -> T719,\nT679 -> zero(T719),\nX840 -> T720,\nT680 -> one(T720),\nX841 -> T718,\nT678 -> zero(T718),\nT716 -> T719,\nT717 -> T720" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2504, 19.00/5.90 "to": 2507, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2505, 19.00/5.90 "to": 2563, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2505, 19.00/5.90 "to": 2564, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2506, 19.00/5.90 "to": 2510, 19.00/5.90 "label": "CASE" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2510, 19.00/5.90 "to": 2512, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2510, 19.00/5.90 "to": 2513, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2512, 19.00/5.90 "to": 2514, 19.00/5.90 "label": "EVAL with clause\naddX(zero(X847), b, one(X847)) :- binaryZ(X847).\nand substitutionX847 -> T726,\nT719 -> zero(T726),\nT720 -> b,\nT718 -> one(T726)" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2512, 19.00/5.90 "to": 2515, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2513, 19.00/5.90 "to": 2518, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2513, 19.00/5.90 "to": 2519, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2514, 19.00/5.90 "to": 2218, 19.00/5.90 "label": "INSTANCE with matching:\nT429 -> T726" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2518, 19.00/5.90 "to": 2525, 19.00/5.90 "label": "EVAL with clause\naddX(one(X857), b, zero(X858)) :- succ(X857, X858).\nand substitutionX857 -> T738,\nT719 -> one(T738),\nT720 -> b,\nX858 -> T737,\nT718 -> zero(T737),\nT736 -> T738" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2518, 19.00/5.90 "to": 2526, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2519, 19.00/5.90 "to": 2542, 19.00/5.90 "label": "ONLY EVAL with clause\naddX(X868, X869, X870) :- addC(X868, X869, X870).\nand substitutionT719 -> T753,\nX868 -> T753,\nT720 -> T754,\nX869 -> T754,\nT718 -> T752,\nX870 -> T752,\nT750 -> T753,\nT751 -> T754" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2525, 19.00/5.90 "to": 2450, 19.00/5.90 "label": "INSTANCE with matching:\nT639 -> T738\nT638 -> T737" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2542, 19.00/5.90 "to": 2493, 19.00/5.90 "label": "INSTANCE with matching:\nT679 -> T753\nT680 -> T754\nT678 -> T752" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2563, 19.00/5.90 "to": 2566, 19.00/5.90 "label": "EVAL with clause\naddC(one(X886), zero(X887), zero(X888)) :- addY(X886, X887, X888).\nand substitutionX886 -> T773,\nT679 -> one(T773),\nX887 -> T774,\nT680 -> zero(T774),\nX888 -> T772,\nT678 -> zero(T772),\nT770 -> T773,\nT771 -> T774" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2563, 19.00/5.90 "to": 2567, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2564, 19.00/5.90 "to": 2591, 19.00/5.90 "label": "EVAL with clause\naddC(one(X927), one(X928), one(X929)) :- addc(X927, X928, X929).\nand substitutionX927 -> T821,\nT679 -> one(T821),\nX928 -> T822,\nT680 -> one(T822),\nX929 -> T820,\nT678 -> one(T820),\nT818 -> T821,\nT819 -> T822" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2564, 19.00/5.90 "to": 2592, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2566, 19.00/5.90 "to": 2568, 19.00/5.90 "label": "CASE" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2568, 19.00/5.90 "to": 2569, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2568, 19.00/5.90 "to": 2570, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2569, 19.00/5.90 "to": 2573, 19.00/5.90 "label": "EVAL with clause\naddY(b, zero(X894), one(X894)) :- binaryZ(X894).\nand substitutionT773 -> b,\nX894 -> T780,\nT774 -> zero(T780),\nT772 -> one(T780)" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2569, 19.00/5.90 "to": 2574, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2570, 19.00/5.90 "to": 2575, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2570, 19.00/5.90 "to": 2576, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2573, 19.00/5.90 "to": 2218, 19.00/5.90 "label": "INSTANCE with matching:\nT429 -> T780" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2575, 19.00/5.90 "to": 2579, 19.00/5.90 "label": "EVAL with clause\naddY(b, one(X904), zero(X905)) :- succ(X904, X905).\nand substitutionT773 -> b,\nX904 -> T792,\nT774 -> one(T792),\nX905 -> T791,\nT772 -> zero(T791),\nT790 -> T792" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2575, 19.00/5.90 "to": 2580, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2576, 19.00/5.90 "to": 2586, 19.00/5.90 "label": "ONLY EVAL with clause\naddY(X915, X916, X917) :- addC(X915, X916, X917).\nand substitutionT773 -> T807,\nX915 -> T807,\nT774 -> T808,\nX916 -> T808,\nT772 -> T806,\nX917 -> T806,\nT804 -> T807,\nT805 -> T808" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2579, 19.00/5.90 "to": 2450, 19.00/5.90 "label": "INSTANCE with matching:\nT639 -> T792\nT638 -> T791" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2586, 19.00/5.90 "to": 2493, 19.00/5.90 "label": "INSTANCE with matching:\nT679 -> T807\nT680 -> T808\nT678 -> T806" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2591, 19.00/5.90 "to": 2422, 19.00/5.90 "label": "INSTANCE with matching:\nT613 -> T821\nT614 -> T822\nT612 -> T820" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2593, 19.00/5.90 "to": 2595, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2593, 19.00/5.90 "to": 2596, 19.00/5.90 "label": "PARALLEL" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2595, 19.00/5.90 "to": 2597, 19.00/5.90 "label": "EVAL with clause\naddz(one(X945), zero(X946), one(X947)) :- addy(X945, X946, X947).\nand substitutionX945 -> T839,\nT463 -> one(T839),\nT464 -> T840,\nX946 -> T840,\nX947 -> T838,\nT462 -> one(T838),\nT836 -> T839,\nT837 -> T840" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2595, 19.00/5.90 "to": 2598, 19.00/5.90 "label": "EVAL-BACKTRACK" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2596, 19.00/5.90 "to": 2602, 19.00/5.90 "label": "BACKTRACK\nfor clause: addz(one(X), one(Y), zero(Z)) :- addc(X, Y, Z)because of non-unification" 19.00/5.90 }, 19.00/5.90 { 19.00/5.90 "from": 2597, 19.00/5.90 "to": 2337, 19.00/5.90 "label": "INSTANCE with matching:\nT571 -> T839\nT572 -> T840\nT570 -> T838" 19.00/5.90 } 19.00/5.90 ], 19.00/5.90 "type": "Graph" 19.00/5.90 } 19.00/5.90 } 19.00/5.90 19.00/5.90 ---------------------------------------- 19.00/5.90 19.00/5.90 (196) 19.00/5.90 Complex Obligation (AND) 19.00/5.90 19.00/5.90 ---------------------------------------- 19.00/5.90 19.00/5.90 (197) 19.00/5.90 Obligation: 19.00/5.90 Rules: 19.00/5.90 f2235_out(T439) -> f2233_out(T439) :|: TRUE 19.00/5.90 f2233_in(x) -> f2235_in(x) :|: TRUE 19.00/5.90 f2219_in(T429) -> f2220_in(T429) :|: TRUE 19.00/5.90 f2220_out(x1) -> f2219_out(x1) :|: TRUE 19.00/5.90 f2219_in(x2) -> f2221_in(x2) :|: TRUE 19.00/5.90 f2221_out(x3) -> f2219_out(x3) :|: TRUE 19.00/5.90 f2220_in(zero(T435)) -> f2231_in(T435) :|: TRUE 19.00/5.90 f2231_out(x4) -> f2220_out(zero(x4)) :|: TRUE 19.00/5.90 f2220_in(x5) -> f2232_in :|: TRUE 19.00/5.90 f2232_out -> f2220_out(x6) :|: TRUE 19.00/5.90 f2244_in(x7) -> f2248_in :|: TRUE 19.00/5.90 f2244_in(one(T448)) -> f2247_in(T448) :|: TRUE 19.00/5.90 f2247_out(x8) -> f2244_out(one(x8)) :|: TRUE 19.00/5.90 f2248_out -> f2244_out(x9) :|: TRUE 19.00/5.90 f2221_in(one(x10)) -> f2233_in(x10) :|: TRUE 19.00/5.90 f2234_out -> f2221_out(x11) :|: TRUE 19.00/5.90 f2233_out(x12) -> f2221_out(one(x12)) :|: TRUE 19.00/5.90 f2221_in(x13) -> f2234_in :|: TRUE 19.00/5.90 f2218_out(x14) -> f2231_out(x14) :|: TRUE 19.00/5.90 f2231_in(x15) -> f2218_in(x15) :|: TRUE 19.00/5.90 f2237_in(x16) -> f2243_in(x16) :|: TRUE 19.00/5.90 f2244_out(x17) -> f2237_out(x17) :|: TRUE 19.00/5.90 f2243_out(x18) -> f2237_out(x18) :|: TRUE 19.00/5.90 f2237_in(x19) -> f2244_in(x19) :|: TRUE 19.00/5.90 f2235_in(x20) -> f2236_in(x20) :|: TRUE 19.00/5.90 f2237_out(x21) -> f2235_out(x21) :|: TRUE 19.00/5.90 f2236_out(x22) -> f2235_out(x22) :|: TRUE 19.00/5.90 f2235_in(x23) -> f2237_in(x23) :|: TRUE 19.00/5.90 f2219_out(x24) -> f2218_out(x24) :|: TRUE 19.00/5.90 f2218_in(x25) -> f2219_in(x25) :|: TRUE 19.00/5.90 f2243_in(zero(T444)) -> f2245_in(T444) :|: TRUE 19.00/5.90 f2246_out -> f2243_out(x26) :|: TRUE 19.00/5.90 f2245_out(x27) -> f2243_out(zero(x27)) :|: TRUE 19.00/5.90 f2243_in(x28) -> f2246_in :|: TRUE 19.00/5.90 f2218_out(x29) -> f2245_out(x29) :|: TRUE 19.00/5.90 f2245_in(x30) -> f2218_in(x30) :|: TRUE 19.00/5.90 f2233_out(x31) -> f2247_out(x31) :|: TRUE 19.00/5.90 f2247_in(x32) -> f2233_in(x32) :|: TRUE 19.00/5.90 f2_in(T3) -> f32_in(T3) :|: TRUE 19.00/5.90 f32_out(x33) -> f2_out(x33) :|: TRUE 19.00/5.90 f32_in(x34) -> f34_in(x34) :|: TRUE 19.00/5.90 f33_out(x35) -> f32_out(x35) :|: TRUE 19.00/5.90 f34_out(x36) -> f32_out(x36) :|: TRUE 19.00/5.90 f32_in(x37) -> f33_in(x37) :|: TRUE 19.00/5.90 f38_out(x38) -> f34_out(x38) :|: TRUE 19.00/5.90 f34_in(x39) -> f38_in(x39) :|: TRUE 19.00/5.90 f34_in(x40) -> f39_in(x40) :|: TRUE 19.00/5.90 f39_out(x41) -> f34_out(x41) :|: TRUE 19.00/5.90 f91_out(T36) -> f39_out(T36) :|: TRUE 19.00/5.90 f39_in(x42) -> f98_in :|: TRUE 19.00/5.90 f39_in(x43) -> f91_in(x43) :|: TRUE 19.00/5.90 f98_out -> f39_out(x44) :|: TRUE 19.00/5.90 f91_in(x45) -> f130_in :|: TRUE 19.00/5.90 f130_out -> f131_in(x46) :|: TRUE 19.00/5.90 f131_out(x47) -> f91_out(x47) :|: TRUE 19.00/5.90 f131_in(x48) -> f2208_in(x48) :|: TRUE 19.00/5.90 f2208_out(x49) -> f131_out(x49) :|: TRUE 19.00/5.90 f2209_out(x50) -> f2208_out(x50) :|: TRUE 19.00/5.90 f2208_in(x51) -> f2209_in(x51) :|: TRUE 19.00/5.90 f2209_in(x52) -> f2210_in(x52) :|: TRUE 19.00/5.90 f2210_out(x53) -> f2209_out(x53) :|: TRUE 19.00/5.90 f2210_in(x54) -> f2212_in(x54) :|: TRUE 19.00/5.90 f2210_in(x55) -> f2211_in(x55) :|: TRUE 19.00/5.90 f2212_out(x56) -> f2210_out(x56) :|: TRUE 19.00/5.90 f2211_out(x57) -> f2210_out(x57) :|: TRUE 19.00/5.90 f2212_in(T462) -> f2258_in(T462) :|: TRUE 19.00/5.90 f2258_out(x58) -> f2212_out(x58) :|: TRUE 19.00/5.90 f2262_out(x59) -> f2258_out(x59) :|: TRUE 19.00/5.90 f2258_in(x60) -> f2262_in(x60) :|: TRUE 19.00/5.90 f2262_in(x61) -> f2264_in(x61) :|: TRUE 19.00/5.90 f2263_out(x62) -> f2262_out(x62) :|: TRUE 19.00/5.90 f2262_in(x63) -> f2263_in(x63) :|: TRUE 19.00/5.90 f2264_out(x64) -> f2262_out(x64) :|: TRUE 19.00/5.90 f2270_out -> f2263_out(x65) :|: TRUE 19.00/5.90 f2263_in(x66) -> f2270_in :|: TRUE 19.00/5.90 f2263_in(zero(T482)) -> f2269_in(T482) :|: TRUE 19.00/5.90 f2269_out(x67) -> f2263_out(zero(x67)) :|: TRUE 19.00/5.90 f2290_out(x68) -> f2269_out(x68) :|: TRUE 19.00/5.90 f2269_in(x69) -> f2290_in(x69) :|: TRUE 19.00/5.90 f2290_in(x70) -> f2292_in(x70) :|: TRUE 19.00/5.90 f2292_out(x71) -> f2290_out(x71) :|: TRUE 19.00/5.90 f2291_out(x72) -> f2290_out(x72) :|: TRUE 19.00/5.90 f2290_in(x73) -> f2291_in(x73) :|: TRUE 19.00/5.90 f2292_in(x74) -> f2295_in(x74) :|: TRUE 19.00/5.90 f2292_in(x75) -> f2296_in(x75) :|: TRUE 19.00/5.90 f2296_out(x76) -> f2292_out(x76) :|: TRUE 19.00/5.90 f2295_out(x77) -> f2292_out(x77) :|: TRUE 19.00/5.90 f2296_in(x78) -> f2335_in(x78) :|: TRUE 19.00/5.90 f2335_out(x79) -> f2296_out(x79) :|: TRUE 19.00/5.90 f2296_in(x80) -> f2336_in(x80) :|: TRUE 19.00/5.90 f2336_out(x81) -> f2296_out(x81) :|: TRUE 19.00/5.90 f2336_in(x82) -> f2423_in :|: TRUE 19.00/5.90 f2423_out -> f2336_out(x83) :|: TRUE 19.00/5.90 f2422_out(T612) -> f2336_out(zero(T612)) :|: TRUE 19.00/5.90 f2336_in(zero(x84)) -> f2422_in(x84) :|: TRUE 19.00/5.90 f2422_in(x85) -> f2426_in(x85) :|: TRUE 19.00/5.90 f2426_out(x86) -> f2422_out(x86) :|: TRUE 19.00/5.90 f2426_in(x87) -> f2427_in(x87) :|: TRUE 19.00/5.90 f2427_out(x88) -> f2426_out(x88) :|: TRUE 19.00/5.90 f2426_in(x89) -> f2428_in(x89) :|: TRUE 19.00/5.90 f2428_out(x90) -> f2426_out(x90) :|: TRUE 19.00/5.90 f2428_in(x91) -> f2434_in(x91) :|: TRUE 19.00/5.90 f2433_out(x92) -> f2428_out(x92) :|: TRUE 19.00/5.90 f2428_in(x93) -> f2433_in(x93) :|: TRUE 19.00/5.90 f2434_out(x94) -> f2428_out(x94) :|: TRUE 19.00/5.90 f2468_out(x95) -> f2434_out(x95) :|: TRUE 19.00/5.90 f2434_in(x96) -> f2469_in(x96) :|: TRUE 19.00/5.90 f2469_out(x97) -> f2434_out(x97) :|: TRUE 19.00/5.90 f2434_in(x98) -> f2468_in(x98) :|: TRUE 19.00/5.90 f2470_out(T662) -> f2468_out(T662) :|: TRUE 19.00/5.90 f2468_in(x99) -> f2471_in :|: TRUE 19.00/5.90 f2468_in(x100) -> f2470_in(x100) :|: TRUE 19.00/5.90 f2471_out -> f2468_out(x101) :|: TRUE 19.00/5.90 f2438_out(x102) -> f2470_out(x102) :|: TRUE 19.00/5.90 f2470_in(x103) -> f2438_in(x103) :|: TRUE 19.00/5.90 f2443_out(T624) -> f2438_out(T624) :|: TRUE 19.00/5.90 f2438_in(x104) -> f2443_in(x104) :|: TRUE 19.00/5.90 f2444_out(x105) -> f2443_out(x105) :|: TRUE 19.00/5.90 f2443_in(x106) -> f2445_in(x106) :|: TRUE 19.00/5.90 f2443_in(x107) -> f2444_in(x107) :|: TRUE 19.00/5.90 f2445_out(x108) -> f2443_out(x108) :|: TRUE 19.00/5.90 f2444_in(x109) -> f2447_in :|: TRUE 19.00/5.90 f2446_out(T631) -> f2444_out(one(T631)) :|: TRUE 19.00/5.90 f2444_in(one(x110)) -> f2446_in(x110) :|: TRUE 19.00/5.90 f2447_out -> f2444_out(x111) :|: TRUE 19.00/5.90 f2446_in(x112) -> f2218_in(x112) :|: TRUE 19.00/5.90 f2218_out(x113) -> f2446_out(x113) :|: TRUE 19.00/5.90 f2335_in(x114) -> f2338_in :|: TRUE 19.00/5.90 f2338_out -> f2335_out(x115) :|: TRUE 19.00/5.90 f2335_in(one(T570)) -> f2337_in(T570) :|: TRUE 19.00/5.90 f2337_out(x116) -> f2335_out(one(x116)) :|: TRUE 19.00/5.90 f2339_out(x117) -> f2337_out(x117) :|: TRUE 19.00/5.90 f2337_in(x118) -> f2339_in(x118) :|: TRUE 19.00/5.90 f2340_out(x119) -> f2339_out(x119) :|: TRUE 19.00/5.90 f2339_in(x120) -> f2341_in(x120) :|: TRUE 19.00/5.90 f2339_in(x121) -> f2340_in(x121) :|: TRUE 19.00/5.90 f2341_out(x122) -> f2339_out(x122) :|: TRUE 19.00/5.90 f2366_out(x123) -> f2341_out(x123) :|: TRUE 19.00/5.90 f2341_in(x124) -> f2366_in(x124) :|: TRUE 19.00/5.90 f2341_in(x125) -> f2365_in(x125) :|: TRUE 19.00/5.90 f2365_out(x126) -> f2341_out(x126) :|: TRUE 19.00/5.90 f2365_in(zero(T583)) -> f2369_in(T583) :|: TRUE 19.00/5.90 f2369_out(x127) -> f2365_out(zero(x127)) :|: TRUE 19.00/5.90 f2365_in(x128) -> f2370_in :|: TRUE 19.00/5.90 f2370_out -> f2365_out(x129) :|: TRUE 19.00/5.90 f2369_in(x130) -> f2218_in(x130) :|: TRUE 19.00/5.90 f2218_out(x131) -> f2369_out(x131) :|: TRUE 19.00/5.90 f2264_in(x132) -> f2593_in(x132) :|: TRUE 19.00/5.90 f2593_out(x133) -> f2264_out(x133) :|: TRUE 19.00/5.90 f2593_in(x134) -> f2595_in(x134) :|: TRUE 19.00/5.90 f2596_out(x135) -> f2593_out(x135) :|: TRUE 19.00/5.90 f2593_in(x136) -> f2596_in(x136) :|: TRUE 19.00/5.90 f2595_out(x137) -> f2593_out(x137) :|: TRUE 19.00/5.90 f2595_in(x138) -> f2598_in :|: TRUE 19.00/5.90 f2597_out(T838) -> f2595_out(one(T838)) :|: TRUE 19.00/5.90 f2595_in(one(x139)) -> f2597_in(x139) :|: TRUE 19.00/5.90 f2598_out -> f2595_out(x140) :|: TRUE 19.00/5.90 f2337_out(x141) -> f2597_out(x141) :|: TRUE 19.00/5.90 f2597_in(x142) -> f2337_in(x142) :|: TRUE 19.00/5.90 f2377_out(T598) -> f2366_out(T598) :|: TRUE 19.00/5.90 f2366_in(x143) -> f2377_in(x143) :|: TRUE 19.00/5.90 f2377_in(x144) -> f2269_in(x144) :|: TRUE 19.00/5.90 f2269_out(x145) -> f2377_out(x145) :|: TRUE 19.00/5.90 f2445_in(x146) -> f2451_in :|: TRUE 19.00/5.90 f2451_out -> f2445_out(x147) :|: TRUE 19.00/5.90 f2450_out(T638) -> f2445_out(zero(T638)) :|: TRUE 19.00/5.90 f2445_in(zero(x148)) -> f2450_in(x148) :|: TRUE 19.00/5.90 f2450_in(x149) -> f2454_in(x149) :|: TRUE 19.00/5.90 f2454_out(x150) -> f2450_out(x150) :|: TRUE 19.00/5.90 f2454_in(x151) -> f2455_in(x151) :|: TRUE 19.00/5.90 f2456_out(x152) -> f2454_out(x152) :|: TRUE 19.00/5.90 f2454_in(x153) -> f2456_in(x153) :|: TRUE 19.00/5.90 f2455_out(x154) -> f2454_out(x154) :|: TRUE 19.00/5.90 f2460_out(x155) -> f2456_out(x155) :|: TRUE 19.00/5.90 f2461_out(x156) -> f2456_out(x156) :|: TRUE 19.00/5.90 f2456_in(x157) -> f2461_in(x157) :|: TRUE 19.00/5.90 f2456_in(x158) -> f2460_in(x158) :|: TRUE 19.00/5.90 f2460_in(x159) -> f2463_in :|: TRUE 19.00/5.90 f2463_out -> f2460_out(x160) :|: TRUE 19.00/5.90 f2460_in(one(T644)) -> f2462_in(T644) :|: TRUE 19.00/5.90 f2462_out(x161) -> f2460_out(one(x161)) :|: TRUE 19.00/5.90 f2462_in(x162) -> f2218_in(x162) :|: TRUE 19.00/5.90 f2218_out(x163) -> f2462_out(x163) :|: TRUE 19.00/5.90 f2493_out(T678) -> f2469_out(T678) :|: TRUE 19.00/5.90 f2469_in(x164) -> f2493_in(x164) :|: TRUE 19.00/5.90 f2493_in(x165) -> f2496_in(x165) :|: TRUE 19.00/5.90 f2496_out(x166) -> f2493_out(x166) :|: TRUE 19.00/5.90 f2496_in(x167) -> f2500_in(x167) :|: TRUE 19.00/5.90 f2500_out(x168) -> f2496_out(x168) :|: TRUE 19.00/5.90 f2496_in(x169) -> f2499_in(x169) :|: TRUE 19.00/5.90 f2499_out(x170) -> f2496_out(x170) :|: TRUE 19.00/5.90 f2500_in(x171) -> f2505_in(x171) :|: TRUE 19.00/5.90 f2504_out(x172) -> f2500_out(x172) :|: TRUE 19.00/5.90 f2505_out(x173) -> f2500_out(x173) :|: TRUE 19.00/5.90 f2500_in(x174) -> f2504_in(x174) :|: TRUE 19.00/5.90 f2505_in(x175) -> f2563_in(x175) :|: TRUE 19.00/5.90 f2563_out(x176) -> f2505_out(x176) :|: TRUE 19.00/5.90 f2564_out(x177) -> f2505_out(x177) :|: TRUE 19.00/5.90 f2505_in(x178) -> f2564_in(x178) :|: TRUE 19.00/5.90 f2563_in(zero(T772)) -> f2566_in(T772) :|: TRUE 19.00/5.90 f2566_out(x179) -> f2563_out(zero(x179)) :|: TRUE 19.00/5.90 f2567_out -> f2563_out(x180) :|: TRUE 19.00/5.90 f2563_in(x181) -> f2567_in :|: TRUE 19.00/5.90 f2568_out(x182) -> f2566_out(x182) :|: TRUE 19.00/5.90 f2566_in(x183) -> f2568_in(x183) :|: TRUE 19.00/5.90 f2569_out(x184) -> f2568_out(x184) :|: TRUE 19.00/5.90 f2568_in(x185) -> f2569_in(x185) :|: TRUE 19.00/5.90 f2568_in(x186) -> f2570_in(x186) :|: TRUE 19.00/5.90 f2570_out(x187) -> f2568_out(x187) :|: TRUE 19.00/5.90 f2570_in(x188) -> f2576_in(x188) :|: TRUE 19.00/5.90 f2575_out(x189) -> f2570_out(x189) :|: TRUE 19.00/5.90 f2570_in(x190) -> f2575_in(x190) :|: TRUE 19.00/5.90 f2576_out(x191) -> f2570_out(x191) :|: TRUE 19.00/5.90 f2580_out -> f2575_out(x192) :|: TRUE 19.00/5.90 f2575_in(zero(T791)) -> f2579_in(T791) :|: TRUE 19.00/5.90 f2579_out(x193) -> f2575_out(zero(x193)) :|: TRUE 19.00/5.90 f2575_in(x194) -> f2580_in :|: TRUE 19.00/5.90 f2579_in(x195) -> f2450_in(x195) :|: TRUE 19.00/5.90 f2450_out(x196) -> f2579_out(x196) :|: TRUE 19.00/5.90 f2307_out(T522) -> f2295_out(one(T522)) :|: TRUE 19.00/5.90 f2308_out -> f2295_out(x197) :|: TRUE 19.00/5.90 f2295_in(x198) -> f2308_in :|: TRUE 19.00/5.90 f2295_in(one(x199)) -> f2307_in(x199) :|: TRUE 19.00/5.90 f2310_out(x200) -> f2307_out(x200) :|: TRUE 19.00/5.90 f2307_in(x201) -> f2310_in(x201) :|: TRUE 19.00/5.90 f2310_in(x202) -> f2311_in(x202) :|: TRUE 19.00/5.90 f2312_out(x203) -> f2310_out(x203) :|: TRUE 19.00/5.90 f2310_in(x204) -> f2312_in(x204) :|: TRUE 19.00/5.90 f2311_out(x205) -> f2310_out(x205) :|: TRUE 19.00/5.90 f2312_in(x206) -> f2317_in(x206) :|: TRUE 19.00/5.90 f2312_in(x207) -> f2316_in(x207) :|: TRUE 19.00/5.90 f2316_out(x208) -> f2312_out(x208) :|: TRUE 19.00/5.90 f2317_out(x209) -> f2312_out(x209) :|: TRUE 19.00/5.90 f2316_in(x210) -> f2321_in :|: TRUE 19.00/5.90 f2316_in(zero(T535)) -> f2320_in(T535) :|: TRUE 19.00/5.90 f2321_out -> f2316_out(x211) :|: TRUE 19.00/5.90 f2320_out(x212) -> f2316_out(zero(x212)) :|: TRUE 19.00/5.90 f2320_in(x213) -> f2218_in(x213) :|: TRUE 19.00/5.90 f2218_out(x214) -> f2320_out(x214) :|: TRUE 19.00/5.90 f2311_in(one(T530)) -> f2314_in(T530) :|: TRUE 19.00/5.90 f2315_out -> f2311_out(x215) :|: TRUE 19.00/5.90 f2314_out(x216) -> f2311_out(one(x216)) :|: TRUE 19.00/5.90 f2311_in(x217) -> f2315_in :|: TRUE 19.00/5.90 f2233_out(x218) -> f2314_out(x218) :|: TRUE 19.00/5.90 f2314_in(x219) -> f2233_in(x219) :|: TRUE 19.00/5.90 f2211_in(zero(T421)) -> f2213_in(T421) :|: TRUE 19.00/5.90 f2213_out(x220) -> f2211_out(zero(x220)) :|: TRUE 19.00/5.90 f2214_out -> f2211_out(x221) :|: TRUE 19.00/5.90 f2211_in(x222) -> f2214_in :|: TRUE 19.00/5.90 f2213_in(x223) -> f2215_in(x223) :|: TRUE 19.00/5.90 f2215_out(x224) -> f2213_out(x224) :|: TRUE 19.00/5.90 f2215_in(x225) -> f2217_in(x225) :|: TRUE 19.00/5.90 f2216_out(x226) -> f2215_out(x226) :|: TRUE 19.00/5.90 f2215_in(x227) -> f2216_in(x227) :|: TRUE 19.00/5.90 f2217_out(x228) -> f2215_out(x228) :|: TRUE 19.00/5.90 f2218_out(x229) -> f2216_out(x229) :|: TRUE 19.00/5.90 f2216_in(x230) -> f2218_in(x230) :|: TRUE 19.00/5.90 f2569_in(one(T780)) -> f2573_in(T780) :|: TRUE 19.00/5.90 f2569_in(x231) -> f2574_in :|: TRUE 19.00/5.90 f2573_out(x232) -> f2569_out(one(x232)) :|: TRUE 19.00/5.90 f2574_out -> f2569_out(x233) :|: TRUE 19.00/5.90 f2573_in(x234) -> f2218_in(x234) :|: TRUE 19.00/5.90 f2218_out(x235) -> f2573_out(x235) :|: TRUE 19.00/5.90 f2507_out -> f2504_out(x236) :|: TRUE 19.00/5.90 f2504_in(zero(T718)) -> f2506_in(T718) :|: TRUE 19.00/5.90 f2506_out(x237) -> f2504_out(zero(x237)) :|: TRUE 19.00/5.90 f2504_in(x238) -> f2507_in :|: TRUE 19.00/5.90 f2510_out(x239) -> f2506_out(x239) :|: TRUE 19.00/5.90 f2506_in(x240) -> f2510_in(x240) :|: TRUE 19.00/5.90 f2512_out(x241) -> f2510_out(x241) :|: TRUE 19.00/5.90 f2510_in(x242) -> f2513_in(x242) :|: TRUE 19.00/5.90 f2513_out(x243) -> f2510_out(x243) :|: TRUE 19.00/5.90 f2510_in(x244) -> f2512_in(x244) :|: TRUE 19.00/5.90 f2512_in(one(T726)) -> f2514_in(T726) :|: TRUE 19.00/5.90 f2515_out -> f2512_out(x245) :|: TRUE 19.00/5.90 f2514_out(x246) -> f2512_out(one(x246)) :|: TRUE 19.00/5.90 f2512_in(x247) -> f2515_in :|: TRUE 19.00/5.90 f2514_in(x248) -> f2218_in(x248) :|: TRUE 19.00/5.90 f2218_out(x249) -> f2514_out(x249) :|: TRUE 19.00/5.90 f2433_in(x250) -> f2439_in :|: TRUE 19.00/5.90 f2433_in(x251) -> f2438_in(x251) :|: TRUE 19.00/5.90 f2439_out -> f2433_out(x252) :|: TRUE 19.00/5.90 f2438_out(x253) -> f2433_out(x253) :|: TRUE 19.00/5.90 f2513_in(x254) -> f2519_in(x254) :|: TRUE 19.00/5.90 f2518_out(x255) -> f2513_out(x255) :|: TRUE 19.00/5.90 f2519_out(x256) -> f2513_out(x256) :|: TRUE 19.00/5.90 f2513_in(x257) -> f2518_in(x257) :|: TRUE 19.00/5.90 f2526_out -> f2518_out(x258) :|: TRUE 19.00/5.90 f2525_out(T737) -> f2518_out(zero(T737)) :|: TRUE 19.00/5.90 f2518_in(x259) -> f2526_in :|: TRUE 19.00/5.90 f2518_in(zero(x260)) -> f2525_in(x260) :|: TRUE 19.00/5.90 f2450_out(x261) -> f2525_out(x261) :|: TRUE 19.00/5.90 f2525_in(x262) -> f2450_in(x262) :|: TRUE 19.00/5.90 f2360_out(T578) -> f2340_out(one(T578)) :|: TRUE 19.00/5.90 f2340_in(one(x263)) -> f2360_in(x263) :|: TRUE 19.00/5.90 f2361_out -> f2340_out(x264) :|: TRUE 19.00/5.90 f2340_in(x265) -> f2361_in :|: TRUE 19.00/5.90 f2233_out(x266) -> f2360_out(x266) :|: TRUE 19.00/5.90 f2360_in(x267) -> f2233_in(x267) :|: TRUE 19.00/5.90 Start term: f2_in(T3) 19.00/5.90 19.00/5.90 ---------------------------------------- 19.00/5.90 19.00/5.90 (198) IRSwTSimpleDependencyGraphProof (EQUIVALENT) 19.00/5.90 Constructed simple dependency graph. 19.00/5.90 19.00/5.90 Simplified to the following IRSwTs: 19.00/5.90 19.00/5.90 19.00/5.90 ---------------------------------------- 19.00/5.90 19.00/5.90 (199) 19.00/5.90 TRUE 19.00/5.90 19.00/5.90 ---------------------------------------- 19.00/5.90 19.00/5.90 (200) 19.00/5.90 Obligation: 19.00/5.90 Rules: 19.00/5.90 f2460_out(T638) -> f2456_out(T638) :|: TRUE 19.00/5.90 f2461_out(x) -> f2456_out(x) :|: TRUE 19.00/5.90 f2456_in(x1) -> f2461_in(x1) :|: TRUE 19.00/5.90 f2456_in(x2) -> f2460_in(x2) :|: TRUE 19.00/5.90 f2454_in(x3) -> f2455_in(x3) :|: TRUE 19.00/5.90 f2456_out(x4) -> f2454_out(x4) :|: TRUE 19.00/5.90 f2454_in(x5) -> f2456_in(x5) :|: TRUE 19.00/5.90 f2455_out(x6) -> f2454_out(x6) :|: TRUE 19.00/5.90 f2450_in(x7) -> f2454_in(x7) :|: TRUE 19.00/5.90 f2454_out(x8) -> f2450_out(x8) :|: TRUE 19.00/5.90 f2461_in(zero(T651)) -> f2464_in(T651) :|: TRUE 19.00/5.90 f2464_out(x9) -> f2461_out(zero(x9)) :|: TRUE 19.00/5.90 f2461_in(x10) -> f2465_in :|: TRUE 19.00/5.90 f2465_out -> f2461_out(x11) :|: TRUE 19.00/5.90 f2450_out(x12) -> f2464_out(x12) :|: TRUE 19.00/5.90 f2464_in(x13) -> f2450_in(x13) :|: TRUE 19.00/5.90 f2_in(T3) -> f32_in(T3) :|: TRUE 19.00/5.90 f32_out(x14) -> f2_out(x14) :|: TRUE 19.00/5.90 f32_in(x15) -> f34_in(x15) :|: TRUE 19.00/5.90 f33_out(x16) -> f32_out(x16) :|: TRUE 19.00/5.90 f34_out(x17) -> f32_out(x17) :|: TRUE 19.00/5.90 f32_in(x18) -> f33_in(x18) :|: TRUE 19.00/5.90 f38_out(x19) -> f34_out(x19) :|: TRUE 19.00/5.90 f34_in(x20) -> f38_in(x20) :|: TRUE 19.00/5.90 f34_in(x21) -> f39_in(x21) :|: TRUE 19.00/5.90 f39_out(x22) -> f34_out(x22) :|: TRUE 19.00/5.90 f91_out(T36) -> f39_out(T36) :|: TRUE 19.00/5.90 f39_in(x23) -> f98_in :|: TRUE 19.00/5.90 f39_in(x24) -> f91_in(x24) :|: TRUE 19.00/5.90 f98_out -> f39_out(x25) :|: TRUE 19.00/5.90 f91_in(x26) -> f130_in :|: TRUE 19.00/5.90 f130_out -> f131_in(x27) :|: TRUE 19.00/5.90 f131_out(x28) -> f91_out(x28) :|: TRUE 19.00/5.90 f131_in(x29) -> f2208_in(x29) :|: TRUE 19.00/5.90 f2208_out(x30) -> f131_out(x30) :|: TRUE 19.00/5.90 f2209_out(x31) -> f2208_out(x31) :|: TRUE 19.00/5.90 f2208_in(x32) -> f2209_in(x32) :|: TRUE 19.00/5.90 f2209_in(x33) -> f2210_in(x33) :|: TRUE 19.00/5.90 f2210_out(x34) -> f2209_out(x34) :|: TRUE 19.00/5.90 f2210_in(x35) -> f2212_in(x35) :|: TRUE 19.00/5.90 f2210_in(x36) -> f2211_in(x36) :|: TRUE 19.00/5.90 f2212_out(x37) -> f2210_out(x37) :|: TRUE 19.00/5.90 f2211_out(x38) -> f2210_out(x38) :|: TRUE 19.00/5.90 f2212_in(T462) -> f2258_in(T462) :|: TRUE 19.00/5.90 f2258_out(x39) -> f2212_out(x39) :|: TRUE 19.00/5.90 f2262_out(x40) -> f2258_out(x40) :|: TRUE 19.00/5.90 f2258_in(x41) -> f2262_in(x41) :|: TRUE 19.00/5.90 f2262_in(x42) -> f2264_in(x42) :|: TRUE 19.00/5.90 f2263_out(x43) -> f2262_out(x43) :|: TRUE 19.00/5.90 f2262_in(x44) -> f2263_in(x44) :|: TRUE 19.00/5.90 f2264_out(x45) -> f2262_out(x45) :|: TRUE 19.00/5.90 f2270_out -> f2263_out(x46) :|: TRUE 19.00/5.90 f2263_in(x47) -> f2270_in :|: TRUE 19.00/5.90 f2263_in(zero(T482)) -> f2269_in(T482) :|: TRUE 19.00/5.90 f2269_out(x48) -> f2263_out(zero(x48)) :|: TRUE 19.00/5.90 f2290_out(x49) -> f2269_out(x49) :|: TRUE 19.00/5.90 f2269_in(x50) -> f2290_in(x50) :|: TRUE 19.00/5.90 f2290_in(x51) -> f2292_in(x51) :|: TRUE 19.00/5.90 f2292_out(x52) -> f2290_out(x52) :|: TRUE 19.00/5.90 f2291_out(x53) -> f2290_out(x53) :|: TRUE 19.00/5.90 f2290_in(x54) -> f2291_in(x54) :|: TRUE 19.00/5.90 f2292_in(x55) -> f2295_in(x55) :|: TRUE 19.00/5.90 f2292_in(x56) -> f2296_in(x56) :|: TRUE 19.00/5.90 f2296_out(x57) -> f2292_out(x57) :|: TRUE 19.00/5.90 f2295_out(x58) -> f2292_out(x58) :|: TRUE 19.00/5.90 f2296_in(x59) -> f2335_in(x59) :|: TRUE 19.00/5.90 f2335_out(x60) -> f2296_out(x60) :|: TRUE 19.00/5.90 f2296_in(x61) -> f2336_in(x61) :|: TRUE 19.00/5.90 f2336_out(x62) -> f2296_out(x62) :|: TRUE 19.00/5.90 f2336_in(x63) -> f2423_in :|: TRUE 19.00/5.90 f2423_out -> f2336_out(x64) :|: TRUE 19.00/5.90 f2422_out(T612) -> f2336_out(zero(T612)) :|: TRUE 19.00/5.90 f2336_in(zero(x65)) -> f2422_in(x65) :|: TRUE 19.00/5.90 f2422_in(x66) -> f2426_in(x66) :|: TRUE 19.00/5.90 f2426_out(x67) -> f2422_out(x67) :|: TRUE 19.00/5.90 f2426_in(x68) -> f2427_in(x68) :|: TRUE 19.00/5.90 f2427_out(x69) -> f2426_out(x69) :|: TRUE 19.00/5.90 f2426_in(x70) -> f2428_in(x70) :|: TRUE 19.00/5.90 f2428_out(x71) -> f2426_out(x71) :|: TRUE 19.00/5.90 f2428_in(x72) -> f2434_in(x72) :|: TRUE 19.00/5.90 f2433_out(x73) -> f2428_out(x73) :|: TRUE 19.00/5.90 f2428_in(x74) -> f2433_in(x74) :|: TRUE 19.00/5.90 f2434_out(x75) -> f2428_out(x75) :|: TRUE 19.00/5.90 f2468_out(x76) -> f2434_out(x76) :|: TRUE 19.00/5.90 f2434_in(x77) -> f2469_in(x77) :|: TRUE 19.00/5.90 f2469_out(x78) -> f2434_out(x78) :|: TRUE 19.00/5.90 f2434_in(x79) -> f2468_in(x79) :|: TRUE 19.00/5.90 f2493_out(T678) -> f2469_out(T678) :|: TRUE 19.00/5.90 f2469_in(x80) -> f2493_in(x80) :|: TRUE 19.00/5.90 f2493_in(x81) -> f2496_in(x81) :|: TRUE 19.00/5.90 f2496_out(x82) -> f2493_out(x82) :|: TRUE 19.00/5.90 f2496_in(x83) -> f2500_in(x83) :|: TRUE 19.00/5.90 f2500_out(x84) -> f2496_out(x84) :|: TRUE 19.00/5.90 f2496_in(x85) -> f2499_in(x85) :|: TRUE 19.00/5.90 f2499_out(x86) -> f2496_out(x86) :|: TRUE 19.00/5.90 f2500_in(x87) -> f2505_in(x87) :|: TRUE 19.00/5.90 f2504_out(x88) -> f2500_out(x88) :|: TRUE 19.00/5.90 f2505_out(x89) -> f2500_out(x89) :|: TRUE 19.00/5.90 f2500_in(x90) -> f2504_in(x90) :|: TRUE 19.00/5.90 f2505_in(x91) -> f2563_in(x91) :|: TRUE 19.00/5.90 f2563_out(x92) -> f2505_out(x92) :|: TRUE 19.00/5.90 f2564_out(x93) -> f2505_out(x93) :|: TRUE 19.00/5.90 f2505_in(x94) -> f2564_in(x94) :|: TRUE 19.00/5.90 f2563_in(zero(T772)) -> f2566_in(T772) :|: TRUE 19.00/5.90 f2566_out(x95) -> f2563_out(zero(x95)) :|: TRUE 19.00/5.90 f2567_out -> f2563_out(x96) :|: TRUE 19.00/5.90 f2563_in(x97) -> f2567_in :|: TRUE 19.00/5.90 f2568_out(x98) -> f2566_out(x98) :|: TRUE 19.00/5.90 f2566_in(x99) -> f2568_in(x99) :|: TRUE 19.00/5.90 f2569_out(x100) -> f2568_out(x100) :|: TRUE 19.00/5.90 f2568_in(x101) -> f2569_in(x101) :|: TRUE 19.00/5.90 f2568_in(x102) -> f2570_in(x102) :|: TRUE 19.00/5.90 f2570_out(x103) -> f2568_out(x103) :|: TRUE 19.00/5.90 f2570_in(x104) -> f2576_in(x104) :|: TRUE 19.00/5.90 f2575_out(x105) -> f2570_out(x105) :|: TRUE 19.00/5.90 f2570_in(x106) -> f2575_in(x106) :|: TRUE 19.00/5.90 f2576_out(x107) -> f2570_out(x107) :|: TRUE 19.00/5.90 f2580_out -> f2575_out(x108) :|: TRUE 19.00/5.90 f2575_in(zero(T791)) -> f2579_in(T791) :|: TRUE 19.00/5.90 f2579_out(x109) -> f2575_out(zero(x109)) :|: TRUE 19.00/5.90 f2575_in(x110) -> f2580_in :|: TRUE 19.00/5.90 f2579_in(x111) -> f2450_in(x111) :|: TRUE 19.00/5.90 f2450_out(x112) -> f2579_out(x112) :|: TRUE 19.00/5.90 f2433_in(x113) -> f2439_in :|: TRUE 19.00/5.90 f2433_in(T624) -> f2438_in(T624) :|: TRUE 19.00/5.90 f2439_out -> f2433_out(x114) :|: TRUE 19.00/5.90 f2438_out(x115) -> f2433_out(x115) :|: TRUE 19.00/5.90 f2443_out(x116) -> f2438_out(x116) :|: TRUE 19.00/5.90 f2438_in(x117) -> f2443_in(x117) :|: TRUE 19.00/5.90 f2444_out(x118) -> f2443_out(x118) :|: TRUE 19.00/5.90 f2443_in(x119) -> f2445_in(x119) :|: TRUE 19.00/5.90 f2443_in(x120) -> f2444_in(x120) :|: TRUE 19.00/5.90 f2445_out(x121) -> f2443_out(x121) :|: TRUE 19.00/5.90 f2445_in(x122) -> f2451_in :|: TRUE 19.00/5.90 f2451_out -> f2445_out(x123) :|: TRUE 19.00/5.90 f2450_out(x124) -> f2445_out(zero(x124)) :|: TRUE 19.00/5.90 f2445_in(zero(x125)) -> f2450_in(x125) :|: TRUE 19.00/5.90 f2470_out(T662) -> f2468_out(T662) :|: TRUE 19.00/5.90 f2468_in(x126) -> f2471_in :|: TRUE 19.00/5.90 f2468_in(x127) -> f2470_in(x127) :|: TRUE 19.00/5.90 f2471_out -> f2468_out(x128) :|: TRUE 19.00/5.90 f2438_out(x129) -> f2470_out(x129) :|: TRUE 19.00/5.90 f2470_in(x130) -> f2438_in(x130) :|: TRUE 19.00/5.90 f2264_in(x131) -> f2593_in(x131) :|: TRUE 19.00/5.90 f2593_out(x132) -> f2264_out(x132) :|: TRUE 19.00/5.90 f2593_in(x133) -> f2595_in(x133) :|: TRUE 19.00/5.90 f2596_out(x134) -> f2593_out(x134) :|: TRUE 19.00/5.90 f2593_in(x135) -> f2596_in(x135) :|: TRUE 19.00/5.90 f2595_out(x136) -> f2593_out(x136) :|: TRUE 19.00/5.90 f2595_in(x137) -> f2598_in :|: TRUE 19.00/5.90 f2597_out(T838) -> f2595_out(one(T838)) :|: TRUE 19.00/5.90 f2595_in(one(x138)) -> f2597_in(x138) :|: TRUE 19.00/5.90 f2598_out -> f2595_out(x139) :|: TRUE 19.00/5.90 f2337_out(x140) -> f2597_out(x140) :|: TRUE 19.00/5.90 f2597_in(x141) -> f2337_in(x141) :|: TRUE 19.00/5.90 f2339_out(T570) -> f2337_out(T570) :|: TRUE 19.00/5.90 f2337_in(x142) -> f2339_in(x142) :|: TRUE 19.00/5.90 f2340_out(x143) -> f2339_out(x143) :|: TRUE 19.00/5.90 f2339_in(x144) -> f2341_in(x144) :|: TRUE 19.00/5.90 f2339_in(x145) -> f2340_in(x145) :|: TRUE 19.00/5.90 f2341_out(x146) -> f2339_out(x146) :|: TRUE 19.00/5.90 f2366_out(x147) -> f2341_out(x147) :|: TRUE 19.00/5.90 f2341_in(x148) -> f2366_in(x148) :|: TRUE 19.00/5.90 f2341_in(x149) -> f2365_in(x149) :|: TRUE 19.00/5.90 f2365_out(x150) -> f2341_out(x150) :|: TRUE 19.00/5.90 f2377_out(T598) -> f2366_out(T598) :|: TRUE 19.00/5.90 f2366_in(x151) -> f2377_in(x151) :|: TRUE 19.00/5.90 f2377_in(x152) -> f2269_in(x152) :|: TRUE 19.00/5.90 f2269_out(x153) -> f2377_out(x153) :|: TRUE 19.00/5.90 f2507_out -> f2504_out(x154) :|: TRUE 19.00/5.90 f2504_in(zero(T718)) -> f2506_in(T718) :|: TRUE 19.00/5.90 f2506_out(x155) -> f2504_out(zero(x155)) :|: TRUE 19.00/5.90 f2504_in(x156) -> f2507_in :|: TRUE 19.00/5.90 f2510_out(x157) -> f2506_out(x157) :|: TRUE 19.00/5.90 f2506_in(x158) -> f2510_in(x158) :|: TRUE 19.00/5.90 f2512_out(x159) -> f2510_out(x159) :|: TRUE 19.00/5.90 f2510_in(x160) -> f2513_in(x160) :|: TRUE 19.00/5.90 f2513_out(x161) -> f2510_out(x161) :|: TRUE 19.00/5.90 f2510_in(x162) -> f2512_in(x162) :|: TRUE 19.00/5.90 f2513_in(x163) -> f2519_in(x163) :|: TRUE 19.00/5.90 f2518_out(x164) -> f2513_out(x164) :|: TRUE 19.00/5.90 f2519_out(x165) -> f2513_out(x165) :|: TRUE 19.00/5.90 f2513_in(x166) -> f2518_in(x166) :|: TRUE 19.00/5.90 f2526_out -> f2518_out(x167) :|: TRUE 19.00/5.90 f2525_out(T737) -> f2518_out(zero(T737)) :|: TRUE 19.00/5.90 f2518_in(x168) -> f2526_in :|: TRUE 19.00/5.90 f2518_in(zero(x169)) -> f2525_in(x169) :|: TRUE 19.00/5.90 f2450_out(x170) -> f2525_out(x170) :|: TRUE 19.00/5.90 f2525_in(x171) -> f2450_in(x171) :|: TRUE 19.00/5.90 Start term: f2_in(T3) 19.00/5.90 19.00/5.90 ---------------------------------------- 19.00/5.90 19.00/5.90 (201) IRSwTSimpleDependencyGraphProof (EQUIVALENT) 19.00/5.90 Constructed simple dependency graph. 19.00/5.90 19.00/5.90 Simplified to the following IRSwTs: 19.00/5.90 19.00/5.90 19.00/5.90 ---------------------------------------- 19.00/5.90 19.00/5.90 (202) 19.00/5.90 TRUE 19.00/5.90 19.00/5.90 ---------------------------------------- 19.00/5.90 19.00/5.90 (203) 19.00/5.90 Obligation: 19.00/5.90 Rules: 19.00/5.90 f2505_in(T678) -> f2563_in(T678) :|: TRUE 19.00/5.90 f2563_out(x) -> f2505_out(x) :|: TRUE 19.00/5.90 f2564_out(x1) -> f2505_out(x1) :|: TRUE 19.00/5.90 f2505_in(x2) -> f2564_in(x2) :|: TRUE 19.00/5.90 f2568_out(T772) -> f2566_out(T772) :|: TRUE 19.00/5.90 f2566_in(x3) -> f2568_in(x3) :|: TRUE 19.00/5.90 f2542_out(T752) -> f2519_out(T752) :|: TRUE 19.00/5.90 f2519_in(x4) -> f2542_in(x4) :|: TRUE 19.00/5.90 f2493_out(x5) -> f2469_out(x5) :|: TRUE 19.00/5.90 f2469_in(x6) -> f2493_in(x6) :|: TRUE 19.00/5.90 f2507_out -> f2504_out(x7) :|: TRUE 19.00/5.90 f2504_in(zero(T718)) -> f2506_in(T718) :|: TRUE 19.00/5.90 f2506_out(x8) -> f2504_out(zero(x8)) :|: TRUE 19.00/5.90 f2504_in(x9) -> f2507_in :|: TRUE 19.00/5.90 f2493_out(x10) -> f2542_out(x10) :|: TRUE 19.00/5.90 f2542_in(x11) -> f2493_in(x11) :|: TRUE 19.00/5.90 f2493_out(T806) -> f2586_out(T806) :|: TRUE 19.00/5.90 f2586_in(x12) -> f2493_in(x12) :|: TRUE 19.00/5.90 f2312_in(T522) -> f2317_in(T522) :|: TRUE 19.00/5.90 f2312_in(x13) -> f2316_in(x13) :|: TRUE 19.00/5.90 f2316_out(x14) -> f2312_out(x14) :|: TRUE 19.00/5.90 f2317_out(x15) -> f2312_out(x15) :|: TRUE 19.00/5.90 f2291_in(zero(T502)) -> f2293_in(T502) :|: TRUE 19.00/5.90 f2291_in(T482) -> f2294_in :|: TRUE 19.00/5.90 f2294_out -> f2291_out(x16) :|: TRUE 19.00/5.90 f2293_out(x17) -> f2291_out(zero(x17)) :|: TRUE 19.00/5.90 f2512_out(x18) -> f2510_out(x18) :|: TRUE 19.00/5.90 f2510_in(x19) -> f2513_in(x19) :|: TRUE 19.00/5.90 f2513_out(x20) -> f2510_out(x20) :|: TRUE 19.00/5.90 f2510_in(x21) -> f2512_in(x21) :|: TRUE 19.00/5.90 f2269_out(T550) -> f2334_out(T550) :|: TRUE 19.00/5.90 f2334_in(x22) -> f2269_in(x22) :|: TRUE 19.00/5.90 f2293_in(x23) -> f2269_in(x23) :|: TRUE 19.00/5.90 f2269_out(x24) -> f2293_out(x24) :|: TRUE 19.00/5.90 f2493_in(x25) -> f2496_in(x25) :|: TRUE 19.00/5.90 f2496_out(x26) -> f2493_out(x26) :|: TRUE 19.00/5.90 f2377_out(T598) -> f2366_out(T598) :|: TRUE 19.00/5.90 f2366_in(x27) -> f2377_in(x27) :|: TRUE 19.00/5.90 f2428_in(T612) -> f2434_in(T612) :|: TRUE 19.00/5.90 f2433_out(x28) -> f2428_out(x28) :|: TRUE 19.00/5.90 f2428_in(x29) -> f2433_in(x29) :|: TRUE 19.00/5.90 f2434_out(x30) -> f2428_out(x30) :|: TRUE 19.00/5.90 f2290_in(x31) -> f2292_in(x31) :|: TRUE 19.00/5.90 f2292_out(x32) -> f2290_out(x32) :|: TRUE 19.00/5.90 f2291_out(x33) -> f2290_out(x33) :|: TRUE 19.00/5.90 f2290_in(x34) -> f2291_in(x34) :|: TRUE 19.00/5.90 f2335_in(x35) -> f2338_in :|: TRUE 19.00/5.90 f2338_out -> f2335_out(x36) :|: TRUE 19.00/5.90 f2335_in(one(T570)) -> f2337_in(T570) :|: TRUE 19.00/5.90 f2337_out(x37) -> f2335_out(one(x37)) :|: TRUE 19.00/5.90 f2292_in(x38) -> f2295_in(x38) :|: TRUE 19.00/5.90 f2292_in(x39) -> f2296_in(x39) :|: TRUE 19.00/5.90 f2296_out(x40) -> f2292_out(x40) :|: TRUE 19.00/5.90 f2295_out(x41) -> f2292_out(x41) :|: TRUE 19.00/5.90 f2563_in(zero(x42)) -> f2566_in(x42) :|: TRUE 19.00/5.90 f2566_out(x43) -> f2563_out(zero(x43)) :|: TRUE 19.00/5.90 f2567_out -> f2563_out(x44) :|: TRUE 19.00/5.90 f2563_in(x45) -> f2567_in :|: TRUE 19.00/5.90 f2296_in(x46) -> f2335_in(x46) :|: TRUE 19.00/5.90 f2335_out(x47) -> f2296_out(x47) :|: TRUE 19.00/5.90 f2296_in(x48) -> f2336_in(x48) :|: TRUE 19.00/5.90 f2336_out(x49) -> f2296_out(x49) :|: TRUE 19.00/5.90 f2496_in(x50) -> f2500_in(x50) :|: TRUE 19.00/5.90 f2500_out(x51) -> f2496_out(x51) :|: TRUE 19.00/5.90 f2496_in(x52) -> f2499_in(x52) :|: TRUE 19.00/5.90 f2499_out(x53) -> f2496_out(x53) :|: TRUE 19.00/5.90 f2513_in(x54) -> f2519_in(x54) :|: TRUE 19.00/5.90 f2518_out(x55) -> f2513_out(x55) :|: TRUE 19.00/5.90 f2519_out(x56) -> f2513_out(x56) :|: TRUE 19.00/5.90 f2513_in(x57) -> f2518_in(x57) :|: TRUE 19.00/5.90 f2502_out -> f2499_out(x58) :|: TRUE 19.00/5.90 f2501_out(T698) -> f2499_out(one(T698)) :|: TRUE 19.00/5.90 f2499_in(x59) -> f2502_in :|: TRUE 19.00/5.90 f2499_in(one(x60)) -> f2501_in(x60) :|: TRUE 19.00/5.90 f2570_in(x61) -> f2576_in(x61) :|: TRUE 19.00/5.90 f2575_out(x62) -> f2570_out(x62) :|: TRUE 19.00/5.90 f2570_in(x63) -> f2575_in(x63) :|: TRUE 19.00/5.90 f2576_out(x64) -> f2570_out(x64) :|: TRUE 19.00/5.90 f2339_out(x65) -> f2337_out(x65) :|: TRUE 19.00/5.90 f2337_in(x66) -> f2339_in(x66) :|: TRUE 19.00/5.90 f2336_in(x67) -> f2423_in :|: TRUE 19.00/5.90 f2423_out -> f2336_out(x68) :|: TRUE 19.00/5.90 f2422_out(x69) -> f2336_out(zero(x69)) :|: TRUE 19.00/5.90 f2336_in(zero(x70)) -> f2422_in(x70) :|: TRUE 19.00/5.90 f2310_in(x71) -> f2311_in(x71) :|: TRUE 19.00/5.90 f2312_out(x72) -> f2310_out(x72) :|: TRUE 19.00/5.90 f2310_in(x73) -> f2312_in(x73) :|: TRUE 19.00/5.90 f2311_out(x74) -> f2310_out(x74) :|: TRUE 19.00/5.90 f2310_out(x75) -> f2307_out(x75) :|: TRUE 19.00/5.90 f2307_in(x76) -> f2310_in(x76) :|: TRUE 19.00/5.90 f2377_in(x77) -> f2269_in(x77) :|: TRUE 19.00/5.90 f2269_out(x78) -> f2377_out(x78) :|: TRUE 19.00/5.90 f2422_in(x79) -> f2426_in(x79) :|: TRUE 19.00/5.90 f2426_out(x80) -> f2422_out(x80) :|: TRUE 19.00/5.90 f2500_in(x81) -> f2505_in(x81) :|: TRUE 19.00/5.90 f2504_out(x82) -> f2500_out(x82) :|: TRUE 19.00/5.90 f2505_out(x83) -> f2500_out(x83) :|: TRUE 19.00/5.90 f2500_in(x84) -> f2504_in(x84) :|: TRUE 19.00/5.90 f2269_out(x85) -> f2501_out(x85) :|: TRUE 19.00/5.90 f2501_in(x86) -> f2269_in(x86) :|: TRUE 19.00/5.90 f2569_out(x87) -> f2568_out(x87) :|: TRUE 19.00/5.90 f2568_in(x88) -> f2569_in(x88) :|: TRUE 19.00/5.90 f2568_in(x89) -> f2570_in(x89) :|: TRUE 19.00/5.90 f2570_out(x90) -> f2568_out(x90) :|: TRUE 19.00/5.90 f2422_out(T820) -> f2591_out(T820) :|: TRUE 19.00/5.90 f2591_in(x91) -> f2422_in(x91) :|: TRUE 19.00/5.90 f2510_out(x92) -> f2506_out(x92) :|: TRUE 19.00/5.90 f2506_in(x93) -> f2510_in(x93) :|: TRUE 19.00/5.90 f2340_out(x94) -> f2339_out(x94) :|: TRUE 19.00/5.90 f2339_in(x95) -> f2341_in(x95) :|: TRUE 19.00/5.90 f2339_in(x96) -> f2340_in(x96) :|: TRUE 19.00/5.90 f2341_out(x97) -> f2339_out(x97) :|: TRUE 19.00/5.90 f2290_out(x98) -> f2269_out(x98) :|: TRUE 19.00/5.90 f2269_in(x99) -> f2290_in(x99) :|: TRUE 19.00/5.90 f2307_out(x100) -> f2295_out(one(x100)) :|: TRUE 19.00/5.90 f2308_out -> f2295_out(x101) :|: TRUE 19.00/5.90 f2295_in(x102) -> f2308_in :|: TRUE 19.00/5.90 f2295_in(one(x103)) -> f2307_in(x103) :|: TRUE 19.00/5.90 f2564_in(one(x104)) -> f2591_in(x104) :|: TRUE 19.00/5.90 f2564_in(x105) -> f2592_in :|: TRUE 19.00/5.90 f2591_out(x106) -> f2564_out(one(x106)) :|: TRUE 19.00/5.90 f2592_out -> f2564_out(x107) :|: TRUE 19.00/5.90 f2317_in(x108) -> f2334_in(x108) :|: TRUE 19.00/5.90 f2334_out(x109) -> f2317_out(x109) :|: TRUE 19.00/5.90 f2366_out(x110) -> f2341_out(x110) :|: TRUE 19.00/5.90 f2341_in(x111) -> f2366_in(x111) :|: TRUE 19.00/5.90 f2341_in(x112) -> f2365_in(x112) :|: TRUE 19.00/5.90 f2365_out(x113) -> f2341_out(x113) :|: TRUE 19.00/5.90 f2576_in(x114) -> f2586_in(x114) :|: TRUE 19.00/5.90 f2586_out(x115) -> f2576_out(x115) :|: TRUE 19.00/5.90 f2426_in(x116) -> f2427_in(x116) :|: TRUE 19.00/5.90 f2427_out(x117) -> f2426_out(x117) :|: TRUE 19.00/5.90 f2426_in(x118) -> f2428_in(x118) :|: TRUE 19.00/5.90 f2428_out(x119) -> f2426_out(x119) :|: TRUE 19.00/5.90 f2468_out(x120) -> f2434_out(x120) :|: TRUE 19.00/5.90 f2434_in(x121) -> f2469_in(x121) :|: TRUE 19.00/5.90 f2469_out(x122) -> f2434_out(x122) :|: TRUE 19.00/5.90 f2434_in(x123) -> f2468_in(x123) :|: TRUE 19.00/5.90 f2_in(T3) -> f32_in(T3) :|: TRUE 19.00/5.90 f32_out(x124) -> f2_out(x124) :|: TRUE 19.00/5.90 f32_in(x125) -> f34_in(x125) :|: TRUE 19.00/5.90 f33_out(x126) -> f32_out(x126) :|: TRUE 19.00/5.90 f34_out(x127) -> f32_out(x127) :|: TRUE 19.00/5.90 f32_in(x128) -> f33_in(x128) :|: TRUE 19.00/5.90 f38_out(x129) -> f34_out(x129) :|: TRUE 19.00/5.90 f34_in(x130) -> f38_in(x130) :|: TRUE 19.00/5.90 f34_in(x131) -> f39_in(x131) :|: TRUE 19.00/5.90 f39_out(x132) -> f34_out(x132) :|: TRUE 19.00/5.90 f91_out(T36) -> f39_out(T36) :|: TRUE 19.00/5.90 f39_in(x133) -> f98_in :|: TRUE 19.00/5.90 f39_in(x134) -> f91_in(x134) :|: TRUE 19.00/5.90 f98_out -> f39_out(x135) :|: TRUE 19.00/5.90 f91_in(x136) -> f130_in :|: TRUE 19.00/5.90 f130_out -> f131_in(x137) :|: TRUE 19.00/5.90 f131_out(x138) -> f91_out(x138) :|: TRUE 19.00/5.90 f131_in(x139) -> f2208_in(x139) :|: TRUE 19.00/5.90 f2208_out(x140) -> f131_out(x140) :|: TRUE 19.00/5.90 f2209_out(x141) -> f2208_out(x141) :|: TRUE 19.00/5.90 f2208_in(x142) -> f2209_in(x142) :|: TRUE 19.00/5.90 f2209_in(x143) -> f2210_in(x143) :|: TRUE 19.00/5.90 f2210_out(x144) -> f2209_out(x144) :|: TRUE 19.00/5.90 f2210_in(x145) -> f2212_in(x145) :|: TRUE 19.00/5.90 f2210_in(x146) -> f2211_in(x146) :|: TRUE 19.00/5.90 f2212_out(x147) -> f2210_out(x147) :|: TRUE 19.00/5.90 f2211_out(x148) -> f2210_out(x148) :|: TRUE 19.00/5.90 f2212_in(T462) -> f2258_in(T462) :|: TRUE 19.00/5.90 f2258_out(x149) -> f2212_out(x149) :|: TRUE 19.00/5.90 f2262_out(x150) -> f2258_out(x150) :|: TRUE 19.00/5.90 f2258_in(x151) -> f2262_in(x151) :|: TRUE 19.00/5.90 f2262_in(x152) -> f2264_in(x152) :|: TRUE 19.00/5.90 f2263_out(x153) -> f2262_out(x153) :|: TRUE 19.00/5.90 f2262_in(x154) -> f2263_in(x154) :|: TRUE 19.00/5.90 f2264_out(x155) -> f2262_out(x155) :|: TRUE 19.00/5.90 f2264_in(x156) -> f2593_in(x156) :|: TRUE 19.00/5.90 f2593_out(x157) -> f2264_out(x157) :|: TRUE 19.00/5.90 f2593_in(x158) -> f2595_in(x158) :|: TRUE 19.00/5.90 f2596_out(x159) -> f2593_out(x159) :|: TRUE 19.00/5.90 f2593_in(x160) -> f2596_in(x160) :|: TRUE 19.00/5.90 f2595_out(x161) -> f2593_out(x161) :|: TRUE 19.00/5.90 f2595_in(x162) -> f2598_in :|: TRUE 19.00/5.90 f2597_out(T838) -> f2595_out(one(T838)) :|: TRUE 19.00/5.90 f2595_in(one(x163)) -> f2597_in(x163) :|: TRUE 19.00/5.90 f2598_out -> f2595_out(x164) :|: TRUE 19.00/5.90 f2337_out(x165) -> f2597_out(x165) :|: TRUE 19.00/5.90 f2597_in(x166) -> f2337_in(x166) :|: TRUE 19.00/5.90 f2270_out -> f2263_out(x167) :|: TRUE 19.00/5.90 f2263_in(x168) -> f2270_in :|: TRUE 19.00/5.90 f2263_in(zero(x169)) -> f2269_in(x169) :|: TRUE 19.00/5.90 f2269_out(x170) -> f2263_out(zero(x170)) :|: TRUE 19.00/5.90 Start term: f2_in(T3) 19.00/5.90 19.00/5.90 ---------------------------------------- 19.00/5.90 19.00/5.90 (204) IRSwTSimpleDependencyGraphProof (EQUIVALENT) 19.00/5.90 Constructed simple dependency graph. 19.00/5.90 19.00/5.90 Simplified to the following IRSwTs: 19.00/5.90 19.00/5.90 19.00/5.90 ---------------------------------------- 19.00/5.90 19.00/5.90 (205) 19.00/5.90 TRUE 19.00/5.90 19.00/5.90 ---------------------------------------- 19.00/5.90 19.00/5.90 (206) 19.00/5.90 Obligation: 19.00/5.90 Rules: 19.00/5.90 f1041_out -> f1034_out :|: TRUE 19.00/5.90 f1034_in -> f1041_in :|: TRUE 19.00/5.90 f1041_in -> f1043_in :|: TRUE 19.00/5.90 f1041_in -> f1045_in :|: TRUE 19.00/5.90 f1045_out -> f1041_out :|: TRUE 19.00/5.90 f1043_out -> f1041_out :|: TRUE 19.00/5.90 f1034_out -> f1075_out :|: TRUE 19.00/5.90 f1075_in -> f1034_in :|: TRUE 19.00/5.90 f1016_out -> f1020_out :|: TRUE 19.00/5.90 f1020_in -> f1016_in :|: TRUE 19.00/5.90 f1056_in -> f1075_in :|: TRUE 19.00/5.90 f1077_out -> f1056_out :|: TRUE 19.00/5.90 f1075_out -> f1056_out :|: TRUE 19.00/5.90 f1056_in -> f1077_in :|: TRUE 19.00/5.90 f1060_in -> f1016_in :|: TRUE 19.00/5.90 f1016_out -> f1060_out :|: TRUE 19.00/5.90 f1016_in -> f1017_in :|: TRUE 19.00/5.90 f1017_out -> f1016_out :|: TRUE 19.00/5.90 f1017_in -> f1018_in :|: TRUE 19.00/5.90 f1018_out -> f1017_out :|: TRUE 19.00/5.90 f1019_out -> f1017_out :|: TRUE 19.00/5.90 f1017_in -> f1019_in :|: TRUE 19.00/5.90 f1019_in -> f1034_in :|: TRUE 19.00/5.90 f1019_in -> f1036_in :|: TRUE 19.00/5.90 f1034_out -> f1019_out :|: TRUE 19.00/5.90 f1036_out -> f1019_out :|: TRUE 19.00/5.90 f1045_in -> f1056_in :|: TRUE 19.00/5.90 f1045_in -> f1055_in :|: TRUE 19.00/5.90 f1056_out -> f1045_out :|: TRUE 19.00/5.90 f1055_out -> f1045_out :|: TRUE 19.00/5.90 f1020_out -> f1018_out :|: TRUE 19.00/5.90 f1021_out -> f1018_out :|: TRUE 19.00/5.90 f1018_in -> f1020_in :|: TRUE 19.00/5.90 f1018_in -> f1021_in :|: TRUE 19.00/5.90 f1060_out -> f1055_out :|: TRUE 19.00/5.90 f1055_in -> f1060_in :|: TRUE 19.00/5.90 f1062_out -> f1055_out :|: TRUE 19.00/5.91 f1055_in -> f1062_in :|: TRUE 19.00/5.91 f2_in(T3) -> f32_in(T3) :|: TRUE 19.00/5.91 f32_out(x) -> f2_out(x) :|: TRUE 19.00/5.91 f32_in(x1) -> f34_in(x1) :|: TRUE 19.00/5.91 f33_out(x2) -> f32_out(x2) :|: TRUE 19.00/5.91 f34_out(x3) -> f32_out(x3) :|: TRUE 19.00/5.91 f32_in(x4) -> f33_in(x4) :|: TRUE 19.00/5.91 f38_out(x5) -> f34_out(x5) :|: TRUE 19.00/5.91 f34_in(x6) -> f38_in(x6) :|: TRUE 19.00/5.91 f34_in(x7) -> f39_in(x7) :|: TRUE 19.00/5.91 f39_out(x8) -> f34_out(x8) :|: TRUE 19.00/5.91 f91_out(T36) -> f39_out(T36) :|: TRUE 19.00/5.91 f39_in(x9) -> f98_in :|: TRUE 19.00/5.91 f39_in(x10) -> f91_in(x10) :|: TRUE 19.00/5.91 f98_out -> f39_out(x11) :|: TRUE 19.00/5.91 f91_in(x12) -> f130_in :|: TRUE 19.00/5.91 f130_out -> f131_in(x13) :|: TRUE 19.00/5.91 f131_out(x14) -> f91_out(x14) :|: TRUE 19.00/5.91 f134_out -> f130_out :|: TRUE 19.00/5.91 f130_in -> f134_in :|: TRUE 19.00/5.91 f215_out -> f134_out :|: TRUE 19.00/5.91 f214_out -> f134_out :|: TRUE 19.00/5.91 f134_in -> f214_in :|: TRUE 19.00/5.91 f134_in -> f215_in :|: TRUE 19.00/5.91 f226_out -> f215_out :|: TRUE 19.00/5.91 f215_in -> f226_in :|: TRUE 19.00/5.91 f215_in -> f227_in :|: TRUE 19.00/5.91 f227_out -> f215_out :|: TRUE 19.00/5.91 f344_out -> f227_out :|: TRUE 19.00/5.91 f227_in -> f338_in :|: TRUE 19.00/5.91 f338_out -> f227_out :|: TRUE 19.00/5.91 f227_in -> f344_in :|: TRUE 19.00/5.91 f1002_out -> f1003_in :|: TRUE 19.00/5.91 f1003_out -> f338_out :|: TRUE 19.00/5.91 f338_in -> f1002_in :|: TRUE 19.00/5.91 f1003_in -> f1006_in :|: TRUE 19.00/5.91 f1006_out -> f1003_out :|: TRUE 19.00/5.91 f1006_in -> f1007_in :|: TRUE 19.00/5.91 f1007_out -> f1006_out :|: TRUE 19.00/5.91 f1007_in -> f1008_in :|: TRUE 19.00/5.91 f1008_out -> f1007_out :|: TRUE 19.00/5.91 f1008_in -> f1009_in :|: TRUE 19.00/5.91 f1009_out -> f1008_out :|: TRUE 19.00/5.91 f1010_out -> f1008_out :|: TRUE 19.00/5.91 f1008_in -> f1010_in :|: TRUE 19.00/5.91 f1012_out -> f1009_out :|: TRUE 19.00/5.91 f1009_in -> f1011_in :|: TRUE 19.00/5.91 f1011_out -> f1009_out :|: TRUE 19.00/5.91 f1009_in -> f1012_in :|: TRUE 19.00/5.91 f1013_out -> f1011_out :|: TRUE 19.00/5.91 f1011_in -> f1013_in :|: TRUE 19.00/5.91 f1015_out -> f1013_out :|: TRUE 19.00/5.91 f1013_in -> f1015_in :|: TRUE 19.00/5.91 f1014_out -> f1013_out :|: TRUE 19.00/5.91 f1013_in -> f1014_in :|: TRUE 19.00/5.91 f1016_out -> f1014_out :|: TRUE 19.00/5.91 f1014_in -> f1016_in :|: TRUE 19.00/5.91 f1010_in -> f1099_in :|: TRUE 19.00/5.91 f1099_out -> f1010_out :|: TRUE 19.00/5.91 f1109_out -> f1099_out :|: TRUE 19.00/5.91 f1099_in -> f1109_in :|: TRUE 19.00/5.91 f1109_in -> f1121_in :|: TRUE 19.00/5.91 f1121_out -> f1109_out :|: TRUE 19.00/5.91 f1109_in -> f1120_in :|: TRUE 19.00/5.91 f1120_out -> f1109_out :|: TRUE 19.00/5.91 f1121_in -> f2170_in :|: TRUE 19.00/5.91 f2170_out -> f1121_out :|: TRUE 19.00/5.91 f2172_out -> f2170_out :|: TRUE 19.00/5.91 f2171_out -> f2170_out :|: TRUE 19.00/5.91 f2170_in -> f2172_in :|: TRUE 19.00/5.91 f2170_in -> f2171_in :|: TRUE 19.00/5.91 f2171_in -> f2204_in :|: TRUE 19.00/5.91 f2203_out -> f2171_out :|: TRUE 19.00/5.91 f2171_in -> f2203_in :|: TRUE 19.00/5.91 f2204_out -> f2171_out :|: TRUE 19.00/5.91 f1347_out -> f2203_out :|: TRUE 19.00/5.91 f2203_in -> f1347_in :|: TRUE 19.00/5.91 f1347_in -> f1596_in :|: TRUE 19.00/5.91 f1596_out -> f1347_out :|: TRUE 19.00/5.91 f1596_in -> f1599_in :|: TRUE 19.00/5.91 f1599_out -> f1596_out :|: TRUE 19.00/5.91 f1598_out -> f1596_out :|: TRUE 19.00/5.91 f1596_in -> f1598_in :|: TRUE 19.00/5.91 f1607_out -> f1599_out :|: TRUE 19.00/5.91 f1599_in -> f1608_in :|: TRUE 19.00/5.91 f1608_out -> f1599_out :|: TRUE 19.00/5.91 f1599_in -> f1607_in :|: TRUE 19.00/5.91 f1615_out -> f1608_out :|: TRUE 19.00/5.91 f1608_in -> f1615_in :|: TRUE 19.00/5.91 f1615_in -> f1138_in :|: TRUE 19.00/5.91 f1138_out -> f1615_out :|: TRUE 19.00/5.91 f1143_out -> f1138_out :|: TRUE 19.00/5.91 f1138_in -> f1143_in :|: TRUE 19.00/5.91 f1143_in -> f1150_in :|: TRUE 19.00/5.91 f1149_out -> f1143_out :|: TRUE 19.00/5.91 f1150_out -> f1143_out :|: TRUE 19.00/5.91 f1143_in -> f1149_in :|: TRUE 19.00/5.91 f1150_in -> f1182_in :|: TRUE 19.00/5.91 f1182_out -> f1150_out :|: TRUE 19.00/5.91 f1150_in -> f1183_in :|: TRUE 19.00/5.91 f1183_out -> f1150_out :|: TRUE 19.00/5.91 f1316_out -> f1183_out :|: TRUE 19.00/5.91 f1183_in -> f1315_in :|: TRUE 19.00/5.91 f1315_out -> f1183_out :|: TRUE 19.00/5.91 f1183_in -> f1316_in :|: TRUE 19.00/5.91 f1316_in -> f1631_in :|: TRUE 19.00/5.91 f1316_in -> f1632_in :|: TRUE 19.00/5.91 f1632_out -> f1316_out :|: TRUE 19.00/5.91 f1631_out -> f1316_out :|: TRUE 19.00/5.91 f1631_in -> f1633_in :|: TRUE 19.00/5.91 f1633_out -> f1631_out :|: TRUE 19.00/5.91 f1635_out -> f1633_out :|: TRUE 19.00/5.91 f1634_out -> f1633_out :|: TRUE 19.00/5.91 f1633_in -> f1635_in :|: TRUE 19.00/5.91 f1633_in -> f1634_in :|: TRUE 19.00/5.91 f1640_out -> f1635_out :|: TRUE 19.00/5.91 f1635_in -> f1640_in :|: TRUE 19.00/5.91 f1635_in -> f1639_in :|: TRUE 19.00/5.91 f1639_out -> f1635_out :|: TRUE 19.00/5.91 f1709_out -> f1640_out :|: TRUE 19.00/5.91 f1640_in -> f1709_in :|: TRUE 19.00/5.91 f1640_in -> f1708_in :|: TRUE 19.00/5.91 f1708_out -> f1640_out :|: TRUE 19.00/5.91 f1709_in -> f1763_in :|: TRUE 19.00/5.91 f1763_out -> f1709_out :|: TRUE 19.00/5.91 f1764_out -> f1763_out :|: TRUE 19.00/5.91 f1763_in -> f1764_in :|: TRUE 19.00/5.91 f1764_in -> f1768_in :|: TRUE 19.00/5.91 f1768_out -> f1764_out :|: TRUE 19.00/5.91 f1764_in -> f1767_in :|: TRUE 19.00/5.91 f1767_out -> f1764_out :|: TRUE 19.00/5.91 f1768_in -> f1781_in :|: TRUE 19.00/5.91 f1781_out -> f1768_out :|: TRUE 19.00/5.91 f1768_in -> f1782_in :|: TRUE 19.00/5.91 f1782_out -> f1768_out :|: TRUE 19.00/5.91 f1782_in -> f2123_in :|: TRUE 19.00/5.91 f2124_out -> f1782_out :|: TRUE 19.00/5.91 f2123_out -> f1782_out :|: TRUE 19.00/5.91 f1782_in -> f2124_in :|: TRUE 19.00/5.91 f2123_in -> f2126_in :|: TRUE 19.00/5.91 f2125_out -> f2123_out :|: TRUE 19.00/5.91 f2126_out -> f2123_out :|: TRUE 19.00/5.91 f2123_in -> f2125_in :|: TRUE 19.00/5.91 f2125_in -> f2127_in :|: TRUE 19.00/5.91 f2127_out -> f2125_out :|: TRUE 19.00/5.91 f2127_in -> f2129_in :|: TRUE 19.00/5.91 f2127_in -> f2128_in :|: TRUE 19.00/5.91 f2128_out -> f2127_out :|: TRUE 19.00/5.91 f2129_out -> f2127_out :|: TRUE 19.00/5.91 f2132_out -> f2128_out :|: TRUE 19.00/5.91 f2131_out -> f2128_out :|: TRUE 19.00/5.91 f2128_in -> f2132_in :|: TRUE 19.00/5.91 f2128_in -> f2131_in :|: TRUE 19.00/5.91 f1016_out -> f2131_out :|: TRUE 19.00/5.91 f2131_in -> f1016_in :|: TRUE 19.00/5.91 f1140_out -> f1120_out :|: TRUE 19.00/5.91 f1138_out -> f1120_out :|: TRUE 19.00/5.91 f1120_in -> f1140_in :|: TRUE 19.00/5.91 f1120_in -> f1138_in :|: TRUE 19.00/5.91 f1712_out -> f1708_out :|: TRUE 19.00/5.91 f1713_out -> f1708_out :|: TRUE 19.00/5.91 f1708_in -> f1712_in :|: TRUE 19.00/5.91 f1708_in -> f1713_in :|: TRUE 19.00/5.91 f1712_in -> f1670_in :|: TRUE 19.00/5.91 f1670_out -> f1712_out :|: TRUE 19.00/5.91 f1670_in -> f1672_in :|: TRUE 19.00/5.91 f1672_out -> f1670_out :|: TRUE 19.00/5.91 f1673_out -> f1672_out :|: TRUE 19.00/5.91 f1672_in -> f1673_in :|: TRUE 19.00/5.91 f1672_in -> f1674_in :|: TRUE 19.00/5.91 f1674_out -> f1672_out :|: TRUE 19.00/5.91 f1683_out -> f1674_out :|: TRUE 19.00/5.91 f1674_in -> f1682_in :|: TRUE 19.00/5.91 f1682_out -> f1674_out :|: TRUE 19.00/5.91 f1674_in -> f1683_in :|: TRUE 19.00/5.91 f1684_out -> f1682_out :|: TRUE 19.00/5.91 f1682_in -> f1684_in :|: TRUE 19.00/5.91 f1686_out -> f1684_out :|: TRUE 19.00/5.91 f1684_in -> f1685_in :|: TRUE 19.00/5.91 f1684_in -> f1686_in :|: TRUE 19.00/5.91 f1685_out -> f1684_out :|: TRUE 19.00/5.91 f1693_out -> f1686_out :|: TRUE 19.00/5.91 f1692_out -> f1686_out :|: TRUE 19.00/5.91 f1686_in -> f1693_in :|: TRUE 19.00/5.91 f1686_in -> f1692_in :|: TRUE 19.00/5.91 f1692_in -> f1694_in :|: TRUE 19.00/5.91 f1694_out -> f1692_out :|: TRUE 19.00/5.91 f1692_in -> f1695_in :|: TRUE 19.00/5.91 f1695_out -> f1692_out :|: TRUE 19.00/5.91 f1694_in -> f1016_in :|: TRUE 19.00/5.91 f1016_out -> f1694_out :|: TRUE 19.00/5.91 f1781_in -> f2098_in :|: TRUE 19.00/5.91 f1781_in -> f2099_in :|: TRUE 19.00/5.91 f2099_out -> f1781_out :|: TRUE 19.00/5.91 f2098_out -> f1781_out :|: TRUE 19.00/5.91 f2098_in -> f2100_in :|: TRUE 19.00/5.91 f2100_out -> f2098_out :|: TRUE 19.00/5.91 f2100_in -> f2101_in :|: TRUE 19.00/5.91 f2101_out -> f2100_out :|: TRUE 19.00/5.91 f2102_out -> f2100_out :|: TRUE 19.00/5.91 f2100_in -> f2102_in :|: TRUE 19.00/5.91 f2104_out -> f2101_out :|: TRUE 19.00/5.91 f2101_in -> f2103_in :|: TRUE 19.00/5.91 f2101_in -> f2104_in :|: TRUE 19.00/5.91 f2103_out -> f2101_out :|: TRUE 19.00/5.91 f2103_in -> f1016_in :|: TRUE 19.00/5.91 f1016_out -> f2103_out :|: TRUE 19.00/5.91 f2102_in -> f2106_in :|: TRUE 19.00/5.91 f2105_out -> f2102_out :|: TRUE 19.00/5.91 f2106_out -> f2102_out :|: TRUE 19.00/5.91 f2102_in -> f2105_in :|: TRUE 19.00/5.91 f2108_out -> f2105_out :|: TRUE 19.00/5.91 f2107_out -> f2105_out :|: TRUE 19.00/5.91 f2105_in -> f2108_in :|: TRUE 19.00/5.91 f2105_in -> f2107_in :|: TRUE 19.00/5.91 f2107_in -> f1682_in :|: TRUE 19.00/5.91 f1682_out -> f2107_out :|: TRUE 19.00/5.91 f1670_out -> f1639_out :|: TRUE 19.00/5.91 f1639_in -> f1671_in :|: TRUE 19.00/5.91 f1671_out -> f1639_out :|: TRUE 19.00/5.91 f1639_in -> f1670_in :|: TRUE 19.00/5.91 f1676_out -> f1673_out :|: TRUE 19.00/5.91 f1673_in -> f1676_in :|: TRUE 19.00/5.91 f1673_in -> f1675_in :|: TRUE 19.00/5.91 f1675_out -> f1673_out :|: TRUE 19.00/5.91 f1016_out -> f1675_out :|: TRUE 19.00/5.91 f1675_in -> f1016_in :|: TRUE 19.00/5.91 f1206_out -> f1182_out :|: TRUE 19.00/5.91 f1208_out -> f1182_out :|: TRUE 19.00/5.91 f1182_in -> f1206_in :|: TRUE 19.00/5.91 f1182_in -> f1208_in :|: TRUE 19.00/5.91 f1206_in -> f1218_in :|: TRUE 19.00/5.91 f1218_out -> f1206_out :|: TRUE 19.00/5.91 f1218_in -> f1227_in :|: TRUE 19.00/5.91 f1226_out -> f1218_out :|: TRUE 19.00/5.91 f1227_out -> f1218_out :|: TRUE 19.00/5.91 f1218_in -> f1226_in :|: TRUE 19.00/5.91 f1238_out -> f1226_out :|: TRUE 19.00/5.91 f1226_in -> f1238_in :|: TRUE 19.00/5.91 f1241_out -> f1226_out :|: TRUE 19.00/5.91 f1226_in -> f1241_in :|: TRUE 19.00/5.91 f1238_in -> f1034_in :|: TRUE 19.00/5.91 f1034_out -> f1238_out :|: TRUE 19.00/5.91 f2136_out -> f2129_out :|: TRUE 19.00/5.91 f2135_out -> f2129_out :|: TRUE 19.00/5.91 f2129_in -> f2135_in :|: TRUE 19.00/5.91 f2129_in -> f2136_in :|: TRUE 19.00/5.91 f2164_out -> f2135_out :|: TRUE 19.00/5.91 f2135_in -> f2139_in :|: TRUE 19.00/5.91 f2135_in -> f2164_in :|: TRUE 19.00/5.91 f2139_out -> f2135_out :|: TRUE 19.00/5.91 f2139_in -> f1682_in :|: TRUE 19.00/5.91 f1682_out -> f2139_out :|: TRUE 19.00/5.91 f1252_out -> f1227_out :|: TRUE 19.00/5.91 f1253_out -> f1227_out :|: TRUE 19.00/5.91 f1227_in -> f1252_in :|: TRUE 19.00/5.91 f1227_in -> f1253_in :|: TRUE 19.00/5.91 f1258_out -> f1252_out :|: TRUE 19.00/5.91 f1252_in -> f1258_in :|: TRUE 19.00/5.91 f1252_in -> f1259_in :|: TRUE 19.00/5.91 f1259_out -> f1252_out :|: TRUE 19.00/5.91 f1016_out -> f1258_out :|: TRUE 19.00/5.91 f1258_in -> f1016_in :|: TRUE 19.00/5.91 f1350_out -> f1315_out :|: TRUE 19.00/5.91 f1347_out -> f1315_out :|: TRUE 19.00/5.91 f1315_in -> f1347_in :|: TRUE 19.00/5.91 f1315_in -> f1350_in :|: TRUE 19.00/5.91 f1604_out -> f1598_out :|: TRUE 19.00/5.91 f1598_in -> f1603_in :|: TRUE 19.00/5.91 f1598_in -> f1604_in :|: TRUE 19.00/5.91 f1603_out -> f1598_out :|: TRUE 19.00/5.91 f1603_in -> f1034_in :|: TRUE 19.00/5.91 f1034_out -> f1603_out :|: TRUE 19.00/5.91 f1611_out -> f1607_out :|: TRUE 19.00/5.91 f1612_out -> f1607_out :|: TRUE 19.00/5.91 f1607_in -> f1612_in :|: TRUE 19.00/5.91 f1607_in -> f1611_in :|: TRUE 19.00/5.91 f1611_in -> f1016_in :|: TRUE 19.00/5.91 f1016_out -> f1611_out :|: TRUE 19.00/5.91 Start term: f2_in(T3) 19.00/5.91 19.00/5.91 ---------------------------------------- 19.00/5.91 19.00/5.91 (207) IRSwTSimpleDependencyGraphProof (EQUIVALENT) 19.00/5.91 Constructed simple dependency graph. 19.00/5.91 19.00/5.91 Simplified to the following IRSwTs: 19.00/5.91 19.00/5.91 19.00/5.91 ---------------------------------------- 19.00/5.91 19.00/5.91 (208) 19.00/5.91 TRUE 19.00/5.91 19.00/5.91 ---------------------------------------- 19.00/5.91 19.00/5.91 (209) 19.00/5.91 Obligation: 19.00/5.91 Rules: 19.00/5.91 f1684_out -> f1682_out :|: TRUE 19.00/5.91 f1682_in -> f1684_in :|: TRUE 19.00/5.91 f1693_in -> f1700_in :|: TRUE 19.00/5.91 f1700_out -> f1693_out :|: TRUE 19.00/5.91 f1702_out -> f1693_out :|: TRUE 19.00/5.91 f1693_in -> f1702_in :|: TRUE 19.00/5.91 f1686_out -> f1684_out :|: TRUE 19.00/5.91 f1684_in -> f1685_in :|: TRUE 19.00/5.91 f1684_in -> f1686_in :|: TRUE 19.00/5.91 f1685_out -> f1684_out :|: TRUE 19.00/5.91 f1682_out -> f1700_out :|: TRUE 19.00/5.91 f1700_in -> f1682_in :|: TRUE 19.00/5.91 f1693_out -> f1686_out :|: TRUE 19.00/5.91 f1692_out -> f1686_out :|: TRUE 19.00/5.91 f1686_in -> f1693_in :|: TRUE 19.00/5.91 f1686_in -> f1692_in :|: TRUE 19.00/5.91 f2_in(T3) -> f32_in(T3) :|: TRUE 19.00/5.91 f32_out(x) -> f2_out(x) :|: TRUE 19.00/5.91 f32_in(x1) -> f34_in(x1) :|: TRUE 19.00/5.91 f33_out(x2) -> f32_out(x2) :|: TRUE 19.00/5.91 f34_out(x3) -> f32_out(x3) :|: TRUE 19.00/5.91 f32_in(x4) -> f33_in(x4) :|: TRUE 19.00/5.91 f38_out(x5) -> f34_out(x5) :|: TRUE 19.00/5.91 f34_in(x6) -> f38_in(x6) :|: TRUE 19.00/5.91 f34_in(x7) -> f39_in(x7) :|: TRUE 19.00/5.91 f39_out(x8) -> f34_out(x8) :|: TRUE 19.00/5.91 f91_out(T36) -> f39_out(T36) :|: TRUE 19.00/5.91 f39_in(x9) -> f98_in :|: TRUE 19.00/5.91 f39_in(x10) -> f91_in(x10) :|: TRUE 19.00/5.91 f98_out -> f39_out(x11) :|: TRUE 19.00/5.91 f91_in(x12) -> f130_in :|: TRUE 19.00/5.91 f130_out -> f131_in(x13) :|: TRUE 19.00/5.91 f131_out(x14) -> f91_out(x14) :|: TRUE 19.00/5.91 f134_out -> f130_out :|: TRUE 19.00/5.91 f130_in -> f134_in :|: TRUE 19.00/5.91 f215_out -> f134_out :|: TRUE 19.00/5.91 f214_out -> f134_out :|: TRUE 19.00/5.91 f134_in -> f214_in :|: TRUE 19.00/5.91 f134_in -> f215_in :|: TRUE 19.00/5.91 f226_out -> f215_out :|: TRUE 19.00/5.91 f215_in -> f226_in :|: TRUE 19.00/5.91 f215_in -> f227_in :|: TRUE 19.00/5.91 f227_out -> f215_out :|: TRUE 19.00/5.91 f344_out -> f227_out :|: TRUE 19.00/5.91 f227_in -> f338_in :|: TRUE 19.00/5.91 f338_out -> f227_out :|: TRUE 19.00/5.91 f227_in -> f344_in :|: TRUE 19.00/5.91 f1002_out -> f1003_in :|: TRUE 19.00/5.91 f1003_out -> f338_out :|: TRUE 19.00/5.91 f338_in -> f1002_in :|: TRUE 19.00/5.91 f1003_in -> f1006_in :|: TRUE 19.00/5.91 f1006_out -> f1003_out :|: TRUE 19.00/5.91 f1006_in -> f1007_in :|: TRUE 19.00/5.91 f1007_out -> f1006_out :|: TRUE 19.00/5.91 f1007_in -> f1008_in :|: TRUE 19.00/5.91 f1008_out -> f1007_out :|: TRUE 19.00/5.91 f1008_in -> f1009_in :|: TRUE 19.00/5.91 f1009_out -> f1008_out :|: TRUE 19.00/5.91 f1010_out -> f1008_out :|: TRUE 19.00/5.91 f1008_in -> f1010_in :|: TRUE 19.00/5.91 f1010_in -> f1099_in :|: TRUE 19.00/5.91 f1099_out -> f1010_out :|: TRUE 19.00/5.91 f1109_out -> f1099_out :|: TRUE 19.00/5.91 f1099_in -> f1109_in :|: TRUE 19.00/5.91 f1109_in -> f1121_in :|: TRUE 19.00/5.91 f1121_out -> f1109_out :|: TRUE 19.00/5.91 f1109_in -> f1120_in :|: TRUE 19.00/5.91 f1120_out -> f1109_out :|: TRUE 19.00/5.91 f1140_out -> f1120_out :|: TRUE 19.00/5.91 f1138_out -> f1120_out :|: TRUE 19.00/5.91 f1120_in -> f1140_in :|: TRUE 19.00/5.91 f1120_in -> f1138_in :|: TRUE 19.00/5.91 f1143_out -> f1138_out :|: TRUE 19.00/5.91 f1138_in -> f1143_in :|: TRUE 19.00/5.91 f1143_in -> f1150_in :|: TRUE 19.00/5.91 f1149_out -> f1143_out :|: TRUE 19.00/5.91 f1150_out -> f1143_out :|: TRUE 19.00/5.91 f1143_in -> f1149_in :|: TRUE 19.00/5.91 f1150_in -> f1182_in :|: TRUE 19.00/5.91 f1182_out -> f1150_out :|: TRUE 19.00/5.91 f1150_in -> f1183_in :|: TRUE 19.00/5.91 f1183_out -> f1150_out :|: TRUE 19.00/5.91 f1316_out -> f1183_out :|: TRUE 19.00/5.91 f1183_in -> f1315_in :|: TRUE 19.00/5.91 f1315_out -> f1183_out :|: TRUE 19.00/5.91 f1183_in -> f1316_in :|: TRUE 19.00/5.91 f1316_in -> f1631_in :|: TRUE 19.00/5.91 f1316_in -> f1632_in :|: TRUE 19.00/5.91 f1632_out -> f1316_out :|: TRUE 19.00/5.91 f1631_out -> f1316_out :|: TRUE 19.00/5.91 f1631_in -> f1633_in :|: TRUE 19.00/5.91 f1633_out -> f1631_out :|: TRUE 19.00/5.91 f1635_out -> f1633_out :|: TRUE 19.00/5.91 f1634_out -> f1633_out :|: TRUE 19.00/5.91 f1633_in -> f1635_in :|: TRUE 19.00/5.91 f1633_in -> f1634_in :|: TRUE 19.00/5.91 f1640_out -> f1635_out :|: TRUE 19.00/5.91 f1635_in -> f1640_in :|: TRUE 19.00/5.91 f1635_in -> f1639_in :|: TRUE 19.00/5.91 f1639_out -> f1635_out :|: TRUE 19.00/5.91 f1709_out -> f1640_out :|: TRUE 19.00/5.91 f1640_in -> f1709_in :|: TRUE 19.00/5.91 f1640_in -> f1708_in :|: TRUE 19.00/5.91 f1708_out -> f1640_out :|: TRUE 19.00/5.91 f1712_out -> f1708_out :|: TRUE 19.00/5.91 f1713_out -> f1708_out :|: TRUE 19.00/5.91 f1708_in -> f1712_in :|: TRUE 19.00/5.91 f1708_in -> f1713_in :|: TRUE 19.00/5.91 f1712_in -> f1670_in :|: TRUE 19.00/5.91 f1670_out -> f1712_out :|: TRUE 19.00/5.91 f1670_in -> f1672_in :|: TRUE 19.00/5.91 f1672_out -> f1670_out :|: TRUE 19.00/5.91 f1673_out -> f1672_out :|: TRUE 19.00/5.91 f1672_in -> f1673_in :|: TRUE 19.00/5.91 f1672_in -> f1674_in :|: TRUE 19.00/5.91 f1674_out -> f1672_out :|: TRUE 19.00/5.91 f1683_out -> f1674_out :|: TRUE 19.00/5.91 f1674_in -> f1682_in :|: TRUE 19.00/5.91 f1682_out -> f1674_out :|: TRUE 19.00/5.91 f1674_in -> f1683_in :|: TRUE 19.00/5.91 f1121_in -> f2170_in :|: TRUE 19.00/5.91 f2170_out -> f1121_out :|: TRUE 19.00/5.91 f2172_out -> f2170_out :|: TRUE 19.00/5.91 f2171_out -> f2170_out :|: TRUE 19.00/5.91 f2170_in -> f2172_in :|: TRUE 19.00/5.91 f2170_in -> f2171_in :|: TRUE 19.00/5.91 f2171_in -> f2204_in :|: TRUE 19.00/5.91 f2203_out -> f2171_out :|: TRUE 19.00/5.91 f2171_in -> f2203_in :|: TRUE 19.00/5.91 f2204_out -> f2171_out :|: TRUE 19.00/5.91 f1347_out -> f2203_out :|: TRUE 19.00/5.91 f2203_in -> f1347_in :|: TRUE 19.00/5.91 f1347_in -> f1596_in :|: TRUE 19.00/5.91 f1596_out -> f1347_out :|: TRUE 19.00/5.91 f1596_in -> f1599_in :|: TRUE 19.00/5.91 f1599_out -> f1596_out :|: TRUE 19.00/5.91 f1598_out -> f1596_out :|: TRUE 19.00/5.91 f1596_in -> f1598_in :|: TRUE 19.00/5.91 f1607_out -> f1599_out :|: TRUE 19.00/5.91 f1599_in -> f1608_in :|: TRUE 19.00/5.91 f1608_out -> f1599_out :|: TRUE 19.00/5.91 f1599_in -> f1607_in :|: TRUE 19.00/5.91 f1615_out -> f1608_out :|: TRUE 19.00/5.91 f1608_in -> f1615_in :|: TRUE 19.00/5.91 f1615_in -> f1138_in :|: TRUE 19.00/5.91 f1138_out -> f1615_out :|: TRUE 19.00/5.91 f1709_in -> f1763_in :|: TRUE 19.00/5.91 f1763_out -> f1709_out :|: TRUE 19.00/5.91 f1764_out -> f1763_out :|: TRUE 19.00/5.91 f1763_in -> f1764_in :|: TRUE 19.00/5.91 f1764_in -> f1768_in :|: TRUE 19.00/5.91 f1768_out -> f1764_out :|: TRUE 19.00/5.91 f1764_in -> f1767_in :|: TRUE 19.00/5.91 f1767_out -> f1764_out :|: TRUE 19.00/5.91 f1768_in -> f1781_in :|: TRUE 19.00/5.91 f1781_out -> f1768_out :|: TRUE 19.00/5.91 f1768_in -> f1782_in :|: TRUE 19.00/5.91 f1782_out -> f1768_out :|: TRUE 19.00/5.91 f1781_in -> f2098_in :|: TRUE 19.00/5.91 f1781_in -> f2099_in :|: TRUE 19.00/5.91 f2099_out -> f1781_out :|: TRUE 19.00/5.91 f2098_out -> f1781_out :|: TRUE 19.00/5.91 f2098_in -> f2100_in :|: TRUE 19.00/5.91 f2100_out -> f2098_out :|: TRUE 19.00/5.91 f2100_in -> f2101_in :|: TRUE 19.00/5.91 f2101_out -> f2100_out :|: TRUE 19.00/5.91 f2102_out -> f2100_out :|: TRUE 19.00/5.91 f2100_in -> f2102_in :|: TRUE 19.00/5.91 f2102_in -> f2106_in :|: TRUE 19.00/5.91 f2105_out -> f2102_out :|: TRUE 19.00/5.91 f2106_out -> f2102_out :|: TRUE 19.00/5.91 f2102_in -> f2105_in :|: TRUE 19.00/5.91 f2108_out -> f2105_out :|: TRUE 19.00/5.91 f2107_out -> f2105_out :|: TRUE 19.00/5.91 f2105_in -> f2108_in :|: TRUE 19.00/5.91 f2105_in -> f2107_in :|: TRUE 19.00/5.91 f2107_in -> f1682_in :|: TRUE 19.00/5.91 f1682_out -> f2107_out :|: TRUE 19.00/5.91 f1670_out -> f1639_out :|: TRUE 19.00/5.91 f1639_in -> f1671_in :|: TRUE 19.00/5.91 f1671_out -> f1639_out :|: TRUE 19.00/5.91 f1639_in -> f1670_in :|: TRUE 19.00/5.91 f1782_in -> f2123_in :|: TRUE 19.00/5.91 f2124_out -> f1782_out :|: TRUE 19.00/5.91 f2123_out -> f1782_out :|: TRUE 19.00/5.91 f1782_in -> f2124_in :|: TRUE 19.00/5.91 f2123_in -> f2126_in :|: TRUE 19.00/5.91 f2125_out -> f2123_out :|: TRUE 19.00/5.91 f2126_out -> f2123_out :|: TRUE 19.00/5.91 f2123_in -> f2125_in :|: TRUE 19.00/5.91 f2125_in -> f2127_in :|: TRUE 19.00/5.91 f2127_out -> f2125_out :|: TRUE 19.00/5.91 f2127_in -> f2129_in :|: TRUE 19.00/5.91 f2127_in -> f2128_in :|: TRUE 19.00/5.91 f2128_out -> f2127_out :|: TRUE 19.00/5.91 f2129_out -> f2127_out :|: TRUE 19.00/5.91 f2136_out -> f2129_out :|: TRUE 19.00/5.91 f2135_out -> f2129_out :|: TRUE 19.00/5.91 f2129_in -> f2135_in :|: TRUE 19.00/5.91 f2129_in -> f2136_in :|: TRUE 19.00/5.91 f2164_out -> f2135_out :|: TRUE 19.00/5.91 f2135_in -> f2139_in :|: TRUE 19.00/5.91 f2135_in -> f2164_in :|: TRUE 19.00/5.91 f2139_out -> f2135_out :|: TRUE 19.00/5.91 f2139_in -> f1682_in :|: TRUE 19.00/5.91 f1682_out -> f2139_out :|: TRUE 19.00/5.91 Start term: f2_in(T3) 19.00/5.91 19.00/5.91 ---------------------------------------- 19.00/5.91 19.00/5.91 (210) IRSwTSimpleDependencyGraphProof (EQUIVALENT) 19.00/5.91 Constructed simple dependency graph. 19.00/5.91 19.00/5.91 Simplified to the following IRSwTs: 19.00/5.91 19.00/5.91 19.00/5.91 ---------------------------------------- 19.00/5.91 19.00/5.91 (211) 19.00/5.91 TRUE 19.00/5.91 19.00/5.91 ---------------------------------------- 19.00/5.91 19.00/5.91 (212) 19.00/5.91 Obligation: 19.00/5.91 Rules: 19.00/5.91 f1768_in -> f1781_in :|: TRUE 19.00/5.91 f1781_out -> f1768_out :|: TRUE 19.00/5.91 f1768_in -> f1782_in :|: TRUE 19.00/5.91 f1782_out -> f1768_out :|: TRUE 19.00/5.91 f1615_in -> f1138_in :|: TRUE 19.00/5.91 f1138_out -> f1615_out :|: TRUE 19.00/5.91 f1206_in -> f1218_in :|: TRUE 19.00/5.91 f1218_out -> f1206_out :|: TRUE 19.00/5.91 f1615_out -> f1608_out :|: TRUE 19.00/5.91 f1608_in -> f1615_in :|: TRUE 19.00/5.91 f1138_out -> f1774_out :|: TRUE 19.00/5.91 f1774_in -> f1138_in :|: TRUE 19.00/5.91 f1282_out -> f1253_out :|: TRUE 19.00/5.91 f1253_in -> f1282_in :|: TRUE 19.00/5.91 f2122_in -> f1763_in :|: TRUE 19.00/5.91 f1763_out -> f2122_out :|: TRUE 19.00/5.91 f1218_in -> f1227_in :|: TRUE 19.00/5.91 f1226_out -> f1218_out :|: TRUE 19.00/5.91 f1227_out -> f1218_out :|: TRUE 19.00/5.91 f1218_in -> f1226_in :|: TRUE 19.00/5.91 f2136_out -> f2129_out :|: TRUE 19.00/5.91 f2135_out -> f2129_out :|: TRUE 19.00/5.91 f2129_in -> f2135_in :|: TRUE 19.00/5.91 f2129_in -> f2136_in :|: TRUE 19.00/5.91 f2168_in -> f1631_in :|: TRUE 19.00/5.91 f1631_out -> f2168_out :|: TRUE 19.00/5.91 f1143_out -> f1138_out :|: TRUE 19.00/5.91 f1138_in -> f1143_in :|: TRUE 19.00/5.91 f1596_in -> f1599_in :|: TRUE 19.00/5.91 f1599_out -> f1596_out :|: TRUE 19.00/5.91 f1598_out -> f1596_out :|: TRUE 19.00/5.91 f1596_in -> f1598_in :|: TRUE 19.00/5.91 f2123_in -> f2126_in :|: TRUE 19.00/5.91 f2125_out -> f2123_out :|: TRUE 19.00/5.91 f2126_out -> f2123_out :|: TRUE 19.00/5.91 f2123_in -> f2125_in :|: TRUE 19.00/5.91 f1763_out -> f2167_out :|: TRUE 19.00/5.91 f2167_in -> f1763_in :|: TRUE 19.00/5.91 f1347_in -> f1596_in :|: TRUE 19.00/5.91 f1596_out -> f1347_out :|: TRUE 19.00/5.91 f1350_out -> f1315_out :|: TRUE 19.00/5.91 f1347_out -> f1315_out :|: TRUE 19.00/5.91 f1315_in -> f1347_in :|: TRUE 19.00/5.91 f1315_in -> f1350_in :|: TRUE 19.00/5.91 f1782_in -> f2123_in :|: TRUE 19.00/5.91 f2124_out -> f1782_out :|: TRUE 19.00/5.91 f2123_out -> f1782_out :|: TRUE 19.00/5.91 f1782_in -> f2124_in :|: TRUE 19.00/5.91 f1764_out -> f1763_out :|: TRUE 19.00/5.91 f1763_in -> f1764_in :|: TRUE 19.00/5.91 f2136_in -> f2167_in :|: TRUE 19.00/5.91 f2167_out -> f2136_out :|: TRUE 19.00/5.91 f1316_in -> f1631_in :|: TRUE 19.00/5.91 f1316_in -> f1632_in :|: TRUE 19.00/5.91 f1632_out -> f1316_out :|: TRUE 19.00/5.91 f1631_out -> f1316_out :|: TRUE 19.00/5.91 f1635_out -> f1633_out :|: TRUE 19.00/5.91 f1634_out -> f1633_out :|: TRUE 19.00/5.91 f1633_in -> f1635_in :|: TRUE 19.00/5.91 f1633_in -> f1634_in :|: TRUE 19.00/5.91 f1316_out -> f1183_out :|: TRUE 19.00/5.91 f1183_in -> f1315_in :|: TRUE 19.00/5.91 f1315_out -> f1183_out :|: TRUE 19.00/5.91 f1183_in -> f1316_in :|: TRUE 19.00/5.91 f2100_in -> f2101_in :|: TRUE 19.00/5.91 f2101_out -> f2100_out :|: TRUE 19.00/5.91 f2102_out -> f2100_out :|: TRUE 19.00/5.91 f2100_in -> f2102_in :|: TRUE 19.00/5.91 f1252_out -> f1227_out :|: TRUE 19.00/5.91 f1253_out -> f1227_out :|: TRUE 19.00/5.91 f1227_in -> f1252_in :|: TRUE 19.00/5.91 f1227_in -> f1253_in :|: TRUE 19.00/5.91 f1157_in -> f1138_in :|: TRUE 19.00/5.91 f1138_out -> f1157_out :|: TRUE 19.00/5.91 f2106_in -> f2122_in :|: TRUE 19.00/5.91 f2122_out -> f2106_out :|: TRUE 19.00/5.91 f1781_in -> f2098_in :|: TRUE 19.00/5.91 f1781_in -> f2099_in :|: TRUE 19.00/5.91 f2099_out -> f1781_out :|: TRUE 19.00/5.91 f2098_out -> f1781_out :|: TRUE 19.00/5.91 f2098_in -> f2100_in :|: TRUE 19.00/5.91 f2100_out -> f2098_out :|: TRUE 19.00/5.91 f1709_in -> f1763_in :|: TRUE 19.00/5.91 f1763_out -> f1709_out :|: TRUE 19.00/5.91 f1709_out -> f1640_out :|: TRUE 19.00/5.91 f1640_in -> f1709_in :|: TRUE 19.00/5.91 f1640_in -> f1708_in :|: TRUE 19.00/5.91 f1708_out -> f1640_out :|: TRUE 19.00/5.91 f1138_out -> f1282_out :|: TRUE 19.00/5.91 f1282_in -> f1138_in :|: TRUE 19.00/5.91 f2127_in -> f2129_in :|: TRUE 19.00/5.91 f2127_in -> f2128_in :|: TRUE 19.00/5.91 f2128_out -> f2127_out :|: TRUE 19.00/5.91 f2129_out -> f2127_out :|: TRUE 19.00/5.91 f1206_out -> f1182_out :|: TRUE 19.00/5.91 f1208_out -> f1182_out :|: TRUE 19.00/5.91 f1182_in -> f1206_in :|: TRUE 19.00/5.91 f1182_in -> f1208_in :|: TRUE 19.00/5.91 f1607_out -> f1599_out :|: TRUE 19.00/5.91 f1599_in -> f1608_in :|: TRUE 19.00/5.91 f1608_out -> f1599_out :|: TRUE 19.00/5.91 f1599_in -> f1607_in :|: TRUE 19.00/5.91 f2102_in -> f2106_in :|: TRUE 19.00/5.91 f2105_out -> f2102_out :|: TRUE 19.00/5.91 f2106_out -> f2102_out :|: TRUE 19.00/5.91 f2102_in -> f2105_in :|: TRUE 19.00/5.91 f1143_in -> f1150_in :|: TRUE 19.00/5.91 f1149_out -> f1143_out :|: TRUE 19.00/5.91 f1150_out -> f1143_out :|: TRUE 19.00/5.91 f1143_in -> f1149_in :|: TRUE 19.00/5.91 f1774_out -> f1767_out :|: TRUE 19.00/5.91 f1767_in -> f1775_in :|: TRUE 19.00/5.91 f1775_out -> f1767_out :|: TRUE 19.00/5.91 f1767_in -> f1774_in :|: TRUE 19.00/5.91 f1150_in -> f1182_in :|: TRUE 19.00/5.91 f1182_out -> f1150_out :|: TRUE 19.00/5.91 f1150_in -> f1183_in :|: TRUE 19.00/5.91 f1183_out -> f1150_out :|: TRUE 19.00/5.91 f1640_out -> f1635_out :|: TRUE 19.00/5.91 f1635_in -> f1640_in :|: TRUE 19.00/5.91 f1635_in -> f1639_in :|: TRUE 19.00/5.91 f1639_out -> f1635_out :|: TRUE 19.00/5.91 f2125_in -> f2127_in :|: TRUE 19.00/5.91 f2127_out -> f2125_out :|: TRUE 19.00/5.91 f2124_in -> f2168_in :|: TRUE 19.00/5.91 f2169_out -> f2124_out :|: TRUE 19.00/5.91 f2168_out -> f2124_out :|: TRUE 19.00/5.91 f2124_in -> f2169_in :|: TRUE 19.00/5.91 f1631_in -> f1633_in :|: TRUE 19.00/5.91 f1633_out -> f1631_out :|: TRUE 19.00/5.91 f1157_out -> f1149_out :|: TRUE 19.00/5.91 f1149_in -> f1157_in :|: TRUE 19.00/5.91 f1149_in -> f1160_in :|: TRUE 19.00/5.91 f1160_out -> f1149_out :|: TRUE 19.00/5.91 f1764_in -> f1768_in :|: TRUE 19.00/5.91 f1768_out -> f1764_out :|: TRUE 19.00/5.91 f1764_in -> f1767_in :|: TRUE 19.00/5.91 f1767_out -> f1764_out :|: TRUE 19.00/5.91 f2_in(T3) -> f32_in(T3) :|: TRUE 19.00/5.91 f32_out(x) -> f2_out(x) :|: TRUE 19.00/5.91 f32_in(x1) -> f34_in(x1) :|: TRUE 19.00/5.91 f33_out(x2) -> f32_out(x2) :|: TRUE 19.00/5.91 f34_out(x3) -> f32_out(x3) :|: TRUE 19.00/5.91 f32_in(x4) -> f33_in(x4) :|: TRUE 19.00/5.91 f38_out(x5) -> f34_out(x5) :|: TRUE 19.00/5.91 f34_in(x6) -> f38_in(x6) :|: TRUE 19.00/5.91 f34_in(x7) -> f39_in(x7) :|: TRUE 19.00/5.91 f39_out(x8) -> f34_out(x8) :|: TRUE 19.00/5.91 f91_out(T36) -> f39_out(T36) :|: TRUE 19.00/5.91 f39_in(x9) -> f98_in :|: TRUE 19.00/5.91 f39_in(x10) -> f91_in(x10) :|: TRUE 19.00/5.91 f98_out -> f39_out(x11) :|: TRUE 19.00/5.91 f91_in(x12) -> f130_in :|: TRUE 19.00/5.91 f130_out -> f131_in(x13) :|: TRUE 19.00/5.91 f131_out(x14) -> f91_out(x14) :|: TRUE 19.00/5.91 f134_out -> f130_out :|: TRUE 19.00/5.91 f130_in -> f134_in :|: TRUE 19.00/5.91 f215_out -> f134_out :|: TRUE 19.00/5.91 f214_out -> f134_out :|: TRUE 19.00/5.91 f134_in -> f214_in :|: TRUE 19.00/5.91 f134_in -> f215_in :|: TRUE 19.00/5.91 f226_out -> f215_out :|: TRUE 19.00/5.91 f215_in -> f226_in :|: TRUE 19.00/5.91 f215_in -> f227_in :|: TRUE 19.00/5.91 f227_out -> f215_out :|: TRUE 19.00/5.91 f344_out -> f227_out :|: TRUE 19.00/5.91 f227_in -> f338_in :|: TRUE 19.00/5.91 f338_out -> f227_out :|: TRUE 19.00/5.91 f227_in -> f344_in :|: TRUE 19.00/5.91 f1002_out -> f1003_in :|: TRUE 19.00/5.91 f1003_out -> f338_out :|: TRUE 19.00/5.91 f338_in -> f1002_in :|: TRUE 19.00/5.91 f1003_in -> f1006_in :|: TRUE 19.00/5.91 f1006_out -> f1003_out :|: TRUE 19.00/5.91 f1006_in -> f1007_in :|: TRUE 19.00/5.91 f1007_out -> f1006_out :|: TRUE 19.00/5.91 f1007_in -> f1008_in :|: TRUE 19.00/5.91 f1008_out -> f1007_out :|: TRUE 19.00/5.91 f1008_in -> f1009_in :|: TRUE 19.00/5.91 f1009_out -> f1008_out :|: TRUE 19.00/5.91 f1010_out -> f1008_out :|: TRUE 19.00/5.91 f1008_in -> f1010_in :|: TRUE 19.00/5.91 f1010_in -> f1099_in :|: TRUE 19.00/5.91 f1099_out -> f1010_out :|: TRUE 19.00/5.91 f1109_out -> f1099_out :|: TRUE 19.00/5.91 f1099_in -> f1109_in :|: TRUE 19.00/5.91 f1109_in -> f1121_in :|: TRUE 19.00/5.91 f1121_out -> f1109_out :|: TRUE 19.00/5.91 f1109_in -> f1120_in :|: TRUE 19.00/5.91 f1120_out -> f1109_out :|: TRUE 19.00/5.91 f1121_in -> f2170_in :|: TRUE 19.00/5.91 f2170_out -> f1121_out :|: TRUE 19.00/5.91 f2172_out -> f2170_out :|: TRUE 19.00/5.91 f2171_out -> f2170_out :|: TRUE 19.00/5.91 f2170_in -> f2172_in :|: TRUE 19.00/5.91 f2170_in -> f2171_in :|: TRUE 19.00/5.91 f2171_in -> f2204_in :|: TRUE 19.00/5.91 f2203_out -> f2171_out :|: TRUE 19.00/5.91 f2171_in -> f2203_in :|: TRUE 19.00/5.91 f2204_out -> f2171_out :|: TRUE 19.00/5.91 f1347_out -> f2203_out :|: TRUE 19.00/5.91 f2203_in -> f1347_in :|: TRUE 19.00/5.91 f1140_out -> f1120_out :|: TRUE 19.00/5.91 f1138_out -> f1120_out :|: TRUE 19.00/5.91 f1120_in -> f1140_in :|: TRUE 19.00/5.91 f1120_in -> f1138_in :|: TRUE 19.00/5.91 Start term: f2_in(T3) 19.00/5.91 19.00/5.91 ---------------------------------------- 19.00/5.91 19.00/5.91 (213) IRSwTSimpleDependencyGraphProof (EQUIVALENT) 19.00/5.91 Constructed simple dependency graph. 19.00/5.91 19.00/5.91 Simplified to the following IRSwTs: 19.00/5.91 19.00/5.91 19.00/5.91 ---------------------------------------- 19.00/5.91 19.00/5.91 (214) 19.00/5.91 TRUE 19.00/5.91 19.00/5.91 ---------------------------------------- 19.00/5.91 19.00/5.91 (215) 19.00/5.91 Obligation: 19.00/5.91 Rules: 19.00/5.91 f1006_in -> f1007_in :|: TRUE 19.00/5.91 f1007_out -> f1006_out :|: TRUE 19.00/5.91 f1008_in -> f1009_in :|: TRUE 19.00/5.91 f1009_out -> f1008_out :|: TRUE 19.00/5.91 f1010_out -> f1008_out :|: TRUE 19.00/5.91 f1008_in -> f1010_in :|: TRUE 19.00/5.91 f1138_out -> f1774_out :|: TRUE 19.00/5.91 f1774_in -> f1138_in :|: TRUE 19.00/5.91 f226_in -> f267_in :|: TRUE 19.00/5.91 f267_out -> f226_out :|: TRUE 19.00/5.91 f226_in -> f276_in :|: TRUE 19.00/5.91 f276_out -> f226_out :|: TRUE 19.00/5.91 f1143_out -> f1138_out :|: TRUE 19.00/5.91 f1138_in -> f1143_in :|: TRUE 19.00/5.91 f1782_in -> f2123_in :|: TRUE 19.00/5.91 f2124_out -> f1782_out :|: TRUE 19.00/5.91 f2123_out -> f1782_out :|: TRUE 19.00/5.91 f1782_in -> f2124_in :|: TRUE 19.00/5.91 f1045_in -> f1056_in :|: TRUE 19.00/5.91 f1045_in -> f1055_in :|: TRUE 19.00/5.91 f1056_out -> f1045_out :|: TRUE 19.00/5.91 f1055_out -> f1045_out :|: TRUE 19.00/5.91 f2136_in -> f2167_in :|: TRUE 19.00/5.91 f2167_out -> f2136_out :|: TRUE 19.00/5.91 f267_in -> f130_in :|: TRUE 19.00/5.91 f130_out -> f267_out :|: TRUE 19.00/5.91 f2100_in -> f2101_in :|: TRUE 19.00/5.91 f2101_out -> f2100_out :|: TRUE 19.00/5.91 f2102_out -> f2100_out :|: TRUE 19.00/5.91 f2100_in -> f2102_in :|: TRUE 19.00/5.91 f1611_out -> f1607_out :|: TRUE 19.00/5.91 f1612_out -> f1607_out :|: TRUE 19.00/5.91 f1607_in -> f1612_in :|: TRUE 19.00/5.91 f1607_in -> f1611_in :|: TRUE 19.00/5.91 f1015_out -> f1013_out :|: TRUE 19.00/5.91 f1013_in -> f1015_in :|: TRUE 19.00/5.91 f1014_out -> f1013_out :|: TRUE 19.00/5.91 f1013_in -> f1014_in :|: TRUE 19.00/5.91 f1238_in -> f1034_in :|: TRUE 19.00/5.91 f1034_out -> f1238_out :|: TRUE 19.00/5.91 f1157_in -> f1138_in :|: TRUE 19.00/5.91 f1138_out -> f1157_out :|: TRUE 19.00/5.91 f1016_out -> f1020_out :|: TRUE 19.00/5.91 f1020_in -> f1016_in :|: TRUE 19.00/5.91 f1016_out -> f1258_out :|: TRUE 19.00/5.91 f1258_in -> f1016_in :|: TRUE 19.00/5.91 f2127_in -> f2129_in :|: TRUE 19.00/5.91 f2127_in -> f2128_in :|: TRUE 19.00/5.91 f2128_out -> f2127_out :|: TRUE 19.00/5.91 f2129_out -> f2127_out :|: TRUE 19.00/5.91 f1683_out -> f1674_out :|: TRUE 19.00/5.91 f1674_in -> f1682_in :|: TRUE 19.00/5.91 f1682_out -> f1674_out :|: TRUE 19.00/5.91 f1674_in -> f1683_in :|: TRUE 19.00/5.91 f1670_in -> f1672_in :|: TRUE 19.00/5.91 f1672_out -> f1670_out :|: TRUE 19.00/5.91 f2102_in -> f2106_in :|: TRUE 19.00/5.91 f2105_out -> f2102_out :|: TRUE 19.00/5.91 f2106_out -> f2102_out :|: TRUE 19.00/5.91 f2102_in -> f2105_in :|: TRUE 19.00/5.91 f1019_in -> f1034_in :|: TRUE 19.00/5.91 f1019_in -> f1036_in :|: TRUE 19.00/5.91 f1034_out -> f1019_out :|: TRUE 19.00/5.91 f1036_out -> f1019_out :|: TRUE 19.00/5.91 f1140_out -> f1120_out :|: TRUE 19.00/5.91 f1138_out -> f1120_out :|: TRUE 19.00/5.91 f1120_in -> f1140_in :|: TRUE 19.00/5.91 f1120_in -> f1138_in :|: TRUE 19.00/5.91 f1007_in -> f1008_in :|: TRUE 19.00/5.91 f1008_out -> f1007_out :|: TRUE 19.00/5.91 f1016_out -> f1014_out :|: TRUE 19.00/5.91 f1014_in -> f1016_in :|: TRUE 19.00/5.91 f1694_in -> f1016_in :|: TRUE 19.00/5.91 f1016_out -> f1694_out :|: TRUE 19.00/5.91 f1764_in -> f1768_in :|: TRUE 19.00/5.91 f1768_out -> f1764_out :|: TRUE 19.00/5.91 f1764_in -> f1767_in :|: TRUE 19.00/5.91 f1767_out -> f1764_out :|: TRUE 19.00/5.91 f1060_out -> f1055_out :|: TRUE 19.00/5.91 f1055_in -> f1060_in :|: TRUE 19.00/5.91 f1062_out -> f1055_out :|: TRUE 19.00/5.91 f1055_in -> f1062_in :|: TRUE 19.00/5.91 f2104_out -> f2101_out :|: TRUE 19.00/5.91 f2101_in -> f2103_in :|: TRUE 19.00/5.91 f2101_in -> f2104_in :|: TRUE 19.00/5.91 f2103_out -> f2101_out :|: TRUE 19.00/5.91 f1109_in -> f1121_in :|: TRUE 19.00/5.91 f1121_out -> f1109_out :|: TRUE 19.00/5.91 f1109_in -> f1120_in :|: TRUE 19.00/5.91 f1120_out -> f1109_out :|: TRUE 19.00/5.91 f1056_in -> f1075_in :|: TRUE 19.00/5.91 f1077_out -> f1056_out :|: TRUE 19.00/5.91 f1075_out -> f1056_out :|: TRUE 19.00/5.91 f1056_in -> f1077_in :|: TRUE 19.00/5.91 f1206_in -> f1218_in :|: TRUE 19.00/5.91 f1218_out -> f1206_out :|: TRUE 19.00/5.91 f226_out -> f215_out :|: TRUE 19.00/5.91 f215_in -> f226_in :|: TRUE 19.00/5.91 f215_in -> f227_in :|: TRUE 19.00/5.91 f227_out -> f215_out :|: TRUE 19.00/5.91 f1615_out -> f1608_out :|: TRUE 19.00/5.91 f1608_in -> f1615_in :|: TRUE 19.00/5.91 f1282_out -> f1253_out :|: TRUE 19.00/5.91 f1253_in -> f1282_in :|: TRUE 19.00/5.91 f1712_out -> f1708_out :|: TRUE 19.00/5.91 f1713_out -> f1708_out :|: TRUE 19.00/5.91 f1708_in -> f1712_in :|: TRUE 19.00/5.91 f1708_in -> f1713_in :|: TRUE 19.00/5.91 f1218_in -> f1227_in :|: TRUE 19.00/5.91 f1226_out -> f1218_out :|: TRUE 19.00/5.91 f1227_out -> f1218_out :|: TRUE 19.00/5.91 f1218_in -> f1226_in :|: TRUE 19.00/5.91 f2168_in -> f1631_in :|: TRUE 19.00/5.91 f1631_out -> f2168_out :|: TRUE 19.00/5.91 f1060_in -> f1016_in :|: TRUE 19.00/5.91 f1016_out -> f1060_out :|: TRUE 19.00/5.91 f1016_in -> f1017_in :|: TRUE 19.00/5.91 f1017_out -> f1016_out :|: TRUE 19.00/5.91 f1238_out -> f1226_out :|: TRUE 19.00/5.91 f1226_in -> f1238_in :|: TRUE 19.00/5.91 f1241_out -> f1226_out :|: TRUE 19.00/5.91 f1226_in -> f1241_in :|: TRUE 19.00/5.91 f1043_in -> f1048_in :|: TRUE 19.00/5.91 f1043_in -> f1050_in :|: TRUE 19.00/5.91 f1050_out -> f1043_out :|: TRUE 19.00/5.91 f1048_out -> f1043_out :|: TRUE 19.00/5.91 f1763_out -> f2167_out :|: TRUE 19.00/5.91 f2167_in -> f1763_in :|: TRUE 19.00/5.91 f1692_in -> f1694_in :|: TRUE 19.00/5.91 f1694_out -> f1692_out :|: TRUE 19.00/5.91 f1692_in -> f1695_in :|: TRUE 19.00/5.91 f1695_out -> f1692_out :|: TRUE 19.00/5.91 f1013_out -> f1011_out :|: TRUE 19.00/5.91 f1011_in -> f1013_in :|: TRUE 19.00/5.91 f1016_out -> f2131_out :|: TRUE 19.00/5.91 f2131_in -> f1016_in :|: TRUE 19.00/5.91 f1764_out -> f1763_out :|: TRUE 19.00/5.91 f1763_in -> f1764_in :|: TRUE 19.00/5.91 f1686_out -> f1684_out :|: TRUE 19.00/5.91 f1684_in -> f1685_in :|: TRUE 19.00/5.91 f1684_in -> f1686_in :|: TRUE 19.00/5.91 f1685_out -> f1684_out :|: TRUE 19.00/5.91 f2103_in -> f1016_in :|: TRUE 19.00/5.91 f1016_out -> f2103_out :|: TRUE 19.00/5.91 f134_out -> f130_out :|: TRUE 19.00/5.91 f130_in -> f134_in :|: TRUE 19.00/5.91 f2172_in -> f2205_in :|: TRUE 19.00/5.91 f2205_out -> f2172_out :|: TRUE 19.00/5.91 f215_out -> f134_out :|: TRUE 19.00/5.91 f214_out -> f134_out :|: TRUE 19.00/5.91 f134_in -> f214_in :|: TRUE 19.00/5.91 f134_in -> f215_in :|: TRUE 19.00/5.91 f1685_in -> f1688_in :|: TRUE 19.00/5.91 f1687_out -> f1685_out :|: TRUE 19.00/5.91 f1685_in -> f1687_in :|: TRUE 19.00/5.91 f1688_out -> f1685_out :|: TRUE 19.00/5.91 f1002_out -> f1003_in :|: TRUE 19.00/5.91 f1003_out -> f338_out :|: TRUE 19.00/5.91 f338_in -> f1002_in :|: TRUE 19.00/5.91 f1607_out -> f1599_out :|: TRUE 19.00/5.91 f1599_in -> f1608_in :|: TRUE 19.00/5.91 f1608_out -> f1599_out :|: TRUE 19.00/5.91 f1599_in -> f1607_in :|: TRUE 19.00/5.91 f1109_out -> f1099_out :|: TRUE 19.00/5.91 f1099_in -> f1109_in :|: TRUE 19.00/5.91 f1017_in -> f1018_in :|: TRUE 19.00/5.91 f1018_out -> f1017_out :|: TRUE 19.00/5.91 f1019_out -> f1017_out :|: TRUE 19.00/5.91 f1017_in -> f1019_in :|: TRUE 19.00/5.91 f1258_out -> f1252_out :|: TRUE 19.00/5.91 f1252_in -> f1258_in :|: TRUE 19.00/5.91 f1252_in -> f1259_in :|: TRUE 19.00/5.91 f1259_out -> f1252_out :|: TRUE 19.00/5.91 f1640_out -> f1635_out :|: TRUE 19.00/5.91 f1635_in -> f1640_in :|: TRUE 19.00/5.91 f1635_in -> f1639_in :|: TRUE 19.00/5.91 f1639_out -> f1635_out :|: TRUE 19.00/5.91 f2124_in -> f2168_in :|: TRUE 19.00/5.91 f2169_out -> f2124_out :|: TRUE 19.00/5.91 f2168_out -> f2124_out :|: TRUE 19.00/5.91 f2124_in -> f2169_in :|: TRUE 19.00/5.91 f1631_in -> f1633_in :|: TRUE 19.00/5.91 f1633_out -> f1631_out :|: TRUE 19.00/5.91 f1615_in -> f1138_in :|: TRUE 19.00/5.91 f1138_out -> f1615_out :|: TRUE 19.00/5.91 f1041_in -> f1043_in :|: TRUE 19.00/5.91 f1041_in -> f1045_in :|: TRUE 19.00/5.91 f1045_out -> f1041_out :|: TRUE 19.00/5.91 f1043_out -> f1041_out :|: TRUE 19.00/5.91 f1034_out -> f1075_out :|: TRUE 19.00/5.91 f1075_in -> f1034_in :|: TRUE 19.00/5.91 f1596_in -> f1599_in :|: TRUE 19.00/5.91 f1599_out -> f1596_out :|: TRUE 19.00/5.91 f1598_out -> f1596_out :|: TRUE 19.00/5.91 f1596_in -> f1598_in :|: TRUE 19.00/5.91 f2123_in -> f2126_in :|: TRUE 19.00/5.91 f2125_out -> f2123_out :|: TRUE 19.00/5.91 f2126_out -> f2123_out :|: TRUE 19.00/5.91 f2123_in -> f2125_in :|: TRUE 19.00/5.91 f1347_in -> f1596_in :|: TRUE 19.00/5.91 f1596_out -> f1347_out :|: TRUE 19.00/5.91 f1684_out -> f1682_out :|: TRUE 19.00/5.91 f1682_in -> f1684_in :|: TRUE 19.00/5.91 f1048_in -> f1048_out :|: TRUE 19.00/5.91 f1347_out -> f2203_out :|: TRUE 19.00/5.91 f2203_in -> f1347_in :|: TRUE 19.00/5.91 f1635_out -> f1633_out :|: TRUE 19.00/5.91 f1634_out -> f1633_out :|: TRUE 19.00/5.91 f1633_in -> f1635_in :|: TRUE 19.00/5.91 f1633_in -> f1634_in :|: TRUE 19.00/5.91 f1316_out -> f1183_out :|: TRUE 19.00/5.91 f1183_in -> f1315_in :|: TRUE 19.00/5.91 f1315_out -> f1183_out :|: TRUE 19.00/5.91 f1183_in -> f1316_in :|: TRUE 19.00/5.91 f1012_out -> f1009_out :|: TRUE 19.00/5.91 f1009_in -> f1011_in :|: TRUE 19.00/5.91 f1011_out -> f1009_out :|: TRUE 19.00/5.91 f1009_in -> f1012_in :|: TRUE 19.00/5.91 f1041_out -> f1034_out :|: TRUE 19.00/5.91 f1034_in -> f1041_in :|: TRUE 19.00/5.91 f2107_in -> f1682_in :|: TRUE 19.00/5.91 f1682_out -> f2107_out :|: TRUE 19.00/5.91 f2164_out -> f2135_out :|: TRUE 19.00/5.91 f2135_in -> f2139_in :|: TRUE 19.00/5.91 f2135_in -> f2164_in :|: TRUE 19.00/5.91 f2139_out -> f2135_out :|: TRUE 19.00/5.91 f1712_in -> f1670_in :|: TRUE 19.00/5.91 f1670_out -> f1712_out :|: TRUE 19.00/5.91 f2139_in -> f1682_in :|: TRUE 19.00/5.91 f1682_out -> f2139_out :|: TRUE 19.00/5.91 f2098_in -> f2100_in :|: TRUE 19.00/5.91 f2100_out -> f2098_out :|: TRUE 19.00/5.91 f1709_in -> f1763_in :|: TRUE 19.00/5.91 f1763_out -> f1709_out :|: TRUE 19.00/5.91 f1709_out -> f1640_out :|: TRUE 19.00/5.91 f1640_in -> f1709_in :|: TRUE 19.00/5.91 f1640_in -> f1708_in :|: TRUE 19.00/5.91 f1708_out -> f1640_out :|: TRUE 19.00/5.91 f1676_out -> f1673_out :|: TRUE 19.00/5.91 f1673_in -> f1676_in :|: TRUE 19.00/5.91 f1673_in -> f1675_in :|: TRUE 19.00/5.91 f1675_out -> f1673_out :|: TRUE 19.00/5.91 f1603_in -> f1034_in :|: TRUE 19.00/5.91 f1034_out -> f1603_out :|: TRUE 19.00/5.91 f1670_out -> f1639_out :|: TRUE 19.00/5.91 f1639_in -> f1671_in :|: TRUE 19.00/5.91 f1671_out -> f1639_out :|: TRUE 19.00/5.91 f1639_in -> f1670_in :|: TRUE 19.00/5.91 f1774_out -> f1767_out :|: TRUE 19.00/5.91 f1767_in -> f1775_in :|: TRUE 19.00/5.91 f1775_out -> f1767_out :|: TRUE 19.00/5.91 f1767_in -> f1774_in :|: TRUE 19.00/5.91 f1016_out -> f1675_out :|: TRUE 19.00/5.91 f1675_in -> f1016_in :|: TRUE 19.00/5.91 f1673_out -> f1672_out :|: TRUE 19.00/5.91 f1672_in -> f1673_in :|: TRUE 19.00/5.91 f1672_in -> f1674_in :|: TRUE 19.00/5.91 f1674_out -> f1672_out :|: TRUE 19.00/5.91 f1150_in -> f1182_in :|: TRUE 19.00/5.91 f1182_out -> f1150_out :|: TRUE 19.00/5.91 f1150_in -> f1183_in :|: TRUE 19.00/5.91 f1183_out -> f1150_out :|: TRUE 19.00/5.91 f1020_out -> f1018_out :|: TRUE 19.00/5.91 f1021_out -> f1018_out :|: TRUE 19.00/5.91 f1018_in -> f1020_in :|: TRUE 19.00/5.91 f1018_in -> f1021_in :|: TRUE 19.00/5.91 f1157_out -> f1149_out :|: TRUE 19.00/5.91 f1149_in -> f1157_in :|: TRUE 19.00/5.91 f1149_in -> f1160_in :|: TRUE 19.00/5.91 f1160_out -> f1149_out :|: TRUE 19.00/5.91 f1768_in -> f1781_in :|: TRUE 19.00/5.91 f1781_out -> f1768_out :|: TRUE 19.00/5.91 f1768_in -> f1782_in :|: TRUE 19.00/5.91 f1782_out -> f1768_out :|: TRUE 19.00/5.91 f2122_in -> f1763_in :|: TRUE 19.00/5.91 f1763_out -> f2122_out :|: TRUE 19.00/5.91 f2136_out -> f2129_out :|: TRUE 19.00/5.91 f2135_out -> f2129_out :|: TRUE 19.00/5.91 f2129_in -> f2135_in :|: TRUE 19.00/5.91 f2129_in -> f2136_in :|: TRUE 19.00/5.91 f1693_out -> f1686_out :|: TRUE 19.00/5.91 f1692_out -> f1686_out :|: TRUE 19.00/5.91 f1686_in -> f1693_in :|: TRUE 19.00/5.91 f1686_in -> f1692_in :|: TRUE 19.00/5.91 f1003_in -> f1006_in :|: TRUE 19.00/5.91 f1006_out -> f1003_out :|: TRUE 19.00/5.91 f2171_in -> f2204_in :|: TRUE 19.00/5.91 f2203_out -> f2171_out :|: TRUE 19.00/5.91 f2171_in -> f2203_in :|: TRUE 19.00/5.91 f2204_out -> f2171_out :|: TRUE 19.00/5.91 f2108_out -> f2105_out :|: TRUE 19.00/5.91 f2107_out -> f2105_out :|: TRUE 19.00/5.91 f2105_in -> f2108_in :|: TRUE 19.00/5.91 f2105_in -> f2107_in :|: TRUE 19.00/5.91 f1350_out -> f1315_out :|: TRUE 19.00/5.91 f1347_out -> f1315_out :|: TRUE 19.00/5.91 f1315_in -> f1347_in :|: TRUE 19.00/5.91 f1315_in -> f1350_in :|: TRUE 19.00/5.91 f1316_in -> f1631_in :|: TRUE 19.00/5.91 f1316_in -> f1632_in :|: TRUE 19.00/5.91 f1632_out -> f1316_out :|: TRUE 19.00/5.91 f1631_out -> f1316_out :|: TRUE 19.00/5.91 f1682_out -> f1700_out :|: TRUE 19.00/5.91 f1700_in -> f1682_in :|: TRUE 19.00/5.91 f1015_in -> f1083_in :|: TRUE 19.00/5.91 f1083_out -> f1015_out :|: TRUE 19.00/5.91 f1636_in -> f1636_out :|: TRUE 19.00/5.91 f2172_out -> f2170_out :|: TRUE 19.00/5.91 f2171_out -> f2170_out :|: TRUE 19.00/5.91 f2170_in -> f2172_in :|: TRUE 19.00/5.91 f2170_in -> f2171_in :|: TRUE 19.00/5.91 f2132_out -> f2128_out :|: TRUE 19.00/5.91 f2131_out -> f2128_out :|: TRUE 19.00/5.91 f2128_in -> f2132_in :|: TRUE 19.00/5.91 f2128_in -> f2131_in :|: TRUE 19.00/5.91 f1604_out -> f1598_out :|: TRUE 19.00/5.91 f1598_in -> f1603_in :|: TRUE 19.00/5.91 f1598_in -> f1604_in :|: TRUE 19.00/5.91 f1603_out -> f1598_out :|: TRUE 19.00/5.91 f1121_in -> f2170_in :|: TRUE 19.00/5.91 f2170_out -> f1121_out :|: TRUE 19.00/5.91 f1693_in -> f1700_in :|: TRUE 19.00/5.91 f1700_out -> f1693_out :|: TRUE 19.00/5.91 f1702_out -> f1693_out :|: TRUE 19.00/5.91 f1693_in -> f1702_in :|: TRUE 19.00/5.91 f1252_out -> f1227_out :|: TRUE 19.00/5.91 f1253_out -> f1227_out :|: TRUE 19.00/5.91 f1227_in -> f1252_in :|: TRUE 19.00/5.91 f1227_in -> f1253_in :|: TRUE 19.00/5.91 f2106_in -> f2122_in :|: TRUE 19.00/5.91 f2122_out -> f2106_out :|: TRUE 19.00/5.91 f1781_in -> f2098_in :|: TRUE 19.00/5.91 f1781_in -> f2099_in :|: TRUE 19.00/5.91 f2099_out -> f1781_out :|: TRUE 19.00/5.91 f2098_out -> f1781_out :|: TRUE 19.00/5.91 f1138_out -> f1282_out :|: TRUE 19.00/5.91 f1282_in -> f1138_in :|: TRUE 19.00/5.91 f1687_in -> f1687_out :|: TRUE 19.00/5.91 f344_out -> f227_out :|: TRUE 19.00/5.91 f227_in -> f338_in :|: TRUE 19.00/5.91 f338_out -> f227_out :|: TRUE 19.00/5.91 f227_in -> f344_in :|: TRUE 19.00/5.91 f1206_out -> f1182_out :|: TRUE 19.00/5.91 f1208_out -> f1182_out :|: TRUE 19.00/5.91 f1182_in -> f1206_in :|: TRUE 19.00/5.91 f1182_in -> f1208_in :|: TRUE 19.00/5.91 f1010_in -> f1099_in :|: TRUE 19.00/5.91 f1099_out -> f1010_out :|: TRUE 19.00/5.91 f1143_in -> f1150_in :|: TRUE 19.00/5.91 f1149_out -> f1143_out :|: TRUE 19.00/5.91 f1150_out -> f1143_out :|: TRUE 19.00/5.91 f1143_in -> f1149_in :|: TRUE 19.00/5.91 f1611_in -> f1016_in :|: TRUE 19.00/5.91 f1016_out -> f1611_out :|: TRUE 19.00/5.91 f1634_in -> f1637_in :|: TRUE 19.00/5.91 f1637_out -> f1634_out :|: TRUE 19.00/5.91 f1636_out -> f1634_out :|: TRUE 19.00/5.91 f1634_in -> f1636_in :|: TRUE 19.00/5.91 f2125_in -> f2127_in :|: TRUE 19.00/5.91 f2127_out -> f2125_out :|: TRUE 19.00/5.91 f130_out -> f1002_out :|: TRUE 19.00/5.91 f1002_in -> f130_in :|: TRUE 19.00/5.91 f2_in(T3) -> f32_in(T3) :|: TRUE 19.00/5.91 f32_out(x) -> f2_out(x) :|: TRUE 19.00/5.91 f32_in(x1) -> f34_in(x1) :|: TRUE 19.00/5.91 f33_out(x2) -> f32_out(x2) :|: TRUE 19.00/5.91 f34_out(x3) -> f32_out(x3) :|: TRUE 19.00/5.91 f32_in(x4) -> f33_in(x4) :|: TRUE 19.00/5.91 f38_out(x5) -> f34_out(x5) :|: TRUE 19.00/5.91 f34_in(x6) -> f38_in(x6) :|: TRUE 19.00/5.91 f34_in(x7) -> f39_in(x7) :|: TRUE 19.00/5.91 f39_out(x8) -> f34_out(x8) :|: TRUE 19.00/5.91 f91_out(T36) -> f39_out(T36) :|: TRUE 19.00/5.91 f39_in(x9) -> f98_in :|: TRUE 19.00/5.91 f39_in(x10) -> f91_in(x10) :|: TRUE 19.00/5.91 f98_out -> f39_out(x11) :|: TRUE 19.00/5.91 f91_in(x12) -> f130_in :|: TRUE 19.00/5.91 f130_out -> f131_in(x13) :|: TRUE 19.00/5.91 f131_out(x14) -> f91_out(x14) :|: TRUE 19.00/5.91 Start term: f2_in(T3) 19.00/5.91 19.00/5.91 ---------------------------------------- 19.00/5.91 19.00/5.91 (216) IRSwTSimpleDependencyGraphProof (EQUIVALENT) 19.00/5.91 Constructed simple dependency graph. 19.00/5.91 19.00/5.91 Simplified to the following IRSwTs: 19.00/5.91 19.00/5.91 intTRSProblem: 19.00/5.91 f226_in -> f267_in :|: TRUE 19.00/5.91 f267_in -> f130_in :|: TRUE 19.00/5.91 f215_in -> f226_in :|: TRUE 19.00/5.91 f215_in -> f227_in :|: TRUE 19.00/5.91 f130_in -> f134_in :|: TRUE 19.00/5.91 f134_in -> f215_in :|: TRUE 19.00/5.91 f338_in -> f1002_in :|: TRUE 19.00/5.91 f227_in -> f338_in :|: TRUE 19.00/5.91 f1002_in -> f130_in :|: TRUE 19.00/5.91 19.00/5.91 19.00/5.91 ---------------------------------------- 19.00/5.91 19.00/5.91 (217) 19.00/5.91 Obligation: 19.00/5.91 Rules: 19.00/5.91 f226_in -> f267_in :|: TRUE 19.00/5.91 f267_in -> f130_in :|: TRUE 19.00/5.91 f215_in -> f226_in :|: TRUE 19.00/5.91 f215_in -> f227_in :|: TRUE 19.00/5.91 f130_in -> f134_in :|: TRUE 19.00/5.91 f134_in -> f215_in :|: TRUE 19.00/5.91 f338_in -> f1002_in :|: TRUE 19.00/5.91 f227_in -> f338_in :|: TRUE 19.00/5.91 f1002_in -> f130_in :|: TRUE 19.00/5.91 19.00/5.91 ---------------------------------------- 19.00/5.91 19.00/5.91 (218) IntTRSCompressionProof (EQUIVALENT) 19.00/5.91 Compressed rules. 19.00/5.91 ---------------------------------------- 19.00/5.91 19.00/5.91 (219) 19.00/5.91 Obligation: 19.00/5.91 Rules: 19.00/5.91 f215_in -> f215_in :|: TRUE 19.00/5.91 19.00/5.91 ---------------------------------------- 19.00/5.91 19.00/5.91 (220) IRSFormatTransformerProof (EQUIVALENT) 19.00/5.91 Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). 19.00/5.91 ---------------------------------------- 19.00/5.91 19.00/5.91 (221) 19.00/5.91 Obligation: 19.00/5.91 Rules: 19.00/5.91 f215_in -> f215_in :|: TRUE 19.00/5.91 19.00/5.91 ---------------------------------------- 19.00/5.91 19.00/5.91 (222) IRSwTTerminationDigraphProof (EQUIVALENT) 19.00/5.91 Constructed termination digraph! 19.00/5.91 Nodes: 19.00/5.91 (1) f215_in -> f215_in :|: TRUE 19.00/5.91 19.00/5.91 Arcs: 19.00/5.91 (1) -> (1) 19.00/5.91 19.00/5.91 This digraph is fully evaluated! 19.00/5.91 ---------------------------------------- 19.00/5.91 19.00/5.91 (223) 19.00/5.91 Obligation: 19.00/5.91 19.00/5.91 Termination digraph: 19.00/5.91 Nodes: 19.00/5.91 (1) f215_in -> f215_in :|: TRUE 19.00/5.91 19.00/5.91 Arcs: 19.00/5.91 (1) -> (1) 19.00/5.91 19.00/5.91 This digraph is fully evaluated! 19.00/5.91 19.00/5.91 ---------------------------------------- 19.00/5.91 19.00/5.91 (224) FilterProof (EQUIVALENT) 19.00/5.91 Used the following sort dictionary for filtering: 19.00/5.91 f215_in() 19.00/5.91 Replaced non-predefined constructor symbols by 0. 19.00/5.91 ---------------------------------------- 19.00/5.91 19.00/5.91 (225) 19.00/5.91 Obligation: 19.00/5.91 Rules: 19.00/5.91 f215_in -> f215_in :|: TRUE 19.00/5.91 19.00/5.91 ---------------------------------------- 19.00/5.91 19.00/5.91 (226) IntTRSPeriodicNontermProof (COMPLETE) 19.00/5.91 Normalized system to the following form: 19.00/5.91 f(pc) -> f(1) :|: pc = 1 && TRUE 19.00/5.91 Witness term starting non-terminating reduction: f(1) 19.00/5.91 ---------------------------------------- 19.00/5.91 19.00/5.91 (227) 19.00/5.91 NO 19.00/5.91 19.00/5.91 ---------------------------------------- 19.00/5.91 19.00/5.91 (228) 19.00/5.91 Obligation: 19.00/5.91 Rules: 19.00/5.91 f38_out(T3) -> f34_out(T3) :|: TRUE 19.00/5.91 f34_in(x) -> f38_in(x) :|: TRUE 19.00/5.91 f34_in(x1) -> f39_in(x1) :|: TRUE 19.00/5.91 f39_out(x2) -> f34_out(x2) :|: TRUE 19.00/5.91 f2_in(x3) -> f32_in(x3) :|: TRUE 19.00/5.91 f32_out(x4) -> f2_out(x4) :|: TRUE 19.00/5.91 f40_in(T23) -> f2_in(T23) :|: TRUE 19.00/5.91 f2_out(x5) -> f40_out(x5) :|: TRUE 19.00/5.91 f41_out -> f38_out(x6) :|: TRUE 19.00/5.91 f38_in(x7) -> f41_in :|: TRUE 19.00/5.91 f38_in(zero(x8)) -> f40_in(x8) :|: TRUE 19.00/5.91 f40_out(x9) -> f38_out(zero(x9)) :|: TRUE 19.00/5.91 f32_in(x10) -> f34_in(x10) :|: TRUE 19.00/5.91 f33_out(x11) -> f32_out(x11) :|: TRUE 19.00/5.91 f34_out(x12) -> f32_out(x12) :|: TRUE 19.00/5.91 f32_in(x13) -> f33_in(x13) :|: TRUE 19.00/5.91 Start term: f2_in(T3) 19.00/5.91 19.00/5.91 ---------------------------------------- 19.00/5.91 19.00/5.91 (229) IRSwTSimpleDependencyGraphProof (EQUIVALENT) 19.00/5.91 Constructed simple dependency graph. 19.00/5.91 19.00/5.91 Simplified to the following IRSwTs: 19.00/5.91 19.00/5.91 intTRSProblem: 19.00/5.91 f34_in(x) -> f38_in(x) :|: TRUE 19.00/5.91 f2_in(x3) -> f32_in(x3) :|: TRUE 19.00/5.91 f40_in(T23) -> f2_in(T23) :|: TRUE 19.00/5.91 f38_in(zero(x8)) -> f40_in(x8) :|: TRUE 19.00/5.91 f32_in(x10) -> f34_in(x10) :|: TRUE 19.00/5.91 19.00/5.91 19.00/5.91 ---------------------------------------- 19.00/5.91 19.00/5.91 (230) 19.00/5.91 Obligation: 19.00/5.91 Rules: 19.00/5.91 f34_in(x) -> f38_in(x) :|: TRUE 19.00/5.91 f2_in(x3) -> f32_in(x3) :|: TRUE 19.00/5.91 f40_in(T23) -> f2_in(T23) :|: TRUE 19.00/5.91 f38_in(zero(x8)) -> f40_in(x8) :|: TRUE 19.00/5.91 f32_in(x10) -> f34_in(x10) :|: TRUE 19.00/5.91 19.00/5.91 ---------------------------------------- 19.00/5.91 19.00/5.91 (231) IntTRSCompressionProof (EQUIVALENT) 19.00/5.91 Compressed rules. 19.00/5.91 ---------------------------------------- 19.00/5.91 19.00/5.91 (232) 19.00/5.91 Obligation: 19.00/5.91 Rules: 19.00/5.91 f34_in(zero(x8:0)) -> f34_in(x8:0) :|: TRUE 19.00/5.91 19.00/5.91 ---------------------------------------- 19.00/5.91 19.00/5.91 (233) IRSFormatTransformerProof (EQUIVALENT) 19.00/5.91 Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). 19.00/5.91 ---------------------------------------- 19.00/5.91 19.00/5.91 (234) 19.00/5.91 Obligation: 19.00/5.91 Rules: 19.00/5.91 f34_in(zero(x8:0)) -> f34_in(x8:0) :|: TRUE 19.00/5.91 19.00/5.91 ---------------------------------------- 19.00/5.91 19.00/5.91 (235) IRSwTTerminationDigraphProof (EQUIVALENT) 19.00/5.91 Constructed termination digraph! 19.00/5.91 Nodes: 19.00/5.91 (1) f34_in(zero(x8:0)) -> f34_in(x8:0) :|: TRUE 19.00/5.91 19.00/5.91 Arcs: 19.00/5.91 (1) -> (1) 19.00/5.91 19.00/5.91 This digraph is fully evaluated! 19.00/5.91 ---------------------------------------- 19.00/5.91 19.00/5.91 (236) 19.00/5.91 Obligation: 19.00/5.91 19.00/5.91 Termination digraph: 19.00/5.91 Nodes: 19.00/5.91 (1) f34_in(zero(x8:0)) -> f34_in(x8:0) :|: TRUE 19.00/5.91 19.00/5.91 Arcs: 19.00/5.91 (1) -> (1) 19.00/5.91 19.00/5.91 This digraph is fully evaluated! 19.00/5.91 19.00/5.91 ---------------------------------------- 19.00/5.91 19.00/5.91 (237) TempFilterProof (SOUND) 19.00/5.91 Used the following sort dictionary for filtering: 19.00/5.91 f34_in(VARIABLE) 19.00/5.91 zero(VARIABLE) 19.00/5.91 Removed predefined arithmetic. 19.00/5.91 ---------------------------------------- 19.00/5.91 19.00/5.91 (238) 19.00/5.91 Obligation: 19.00/5.91 Rules: 19.00/5.91 f34_in(zero(x8:0)) -> f34_in(x8:0) 19.00/5.91 19.00/5.91 ---------------------------------------- 19.00/5.91 19.00/5.91 (239) IRSwTToQDPProof (SOUND) 19.00/5.91 Removed the integers and created a QDP-Problem. 19.00/5.91 ---------------------------------------- 19.00/5.91 19.00/5.91 (240) 19.00/5.91 Obligation: 19.00/5.91 Q DP problem: 19.00/5.91 The TRS P consists of the following rules: 19.00/5.91 19.00/5.91 f34_in(zero(x8:0)) -> f34_in(x8:0) 19.00/5.91 19.00/5.91 R is empty. 19.00/5.91 Q is empty. 19.00/5.91 We have to consider all (P,Q,R)-chains. 19.00/5.91 ---------------------------------------- 19.00/5.91 19.00/5.91 (241) QDPSizeChangeProof (EQUIVALENT) 19.00/5.91 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 19.00/5.91 19.00/5.91 From the DPs we obtained the following set of size-change graphs: 19.00/5.91 *f34_in(zero(x8:0)) -> f34_in(x8:0) 19.00/5.91 The graph contains the following edges 1 > 1 19.00/5.91 19.00/5.91 19.00/5.91 ---------------------------------------- 19.00/5.91 19.00/5.91 (242) 19.00/5.91 YES 19.08/5.96 EOF