63.38/17.09 MAYBE 63.56/17.18 proof of /export/starexec/sandbox/benchmark/theBenchmark.pl 63.56/17.18 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 63.56/17.18 63.56/17.18 63.56/17.18 Left Termination of the query pattern 63.56/17.18 63.56/17.18 p(a,g) 63.56/17.18 63.56/17.18 w.r.t. the given Prolog program could not be shown: 63.56/17.18 63.56/17.18 (0) Prolog 63.56/17.18 (1) PrologToPiTRSProof [SOUND, 0 ms] 63.56/17.18 (2) PiTRS 63.56/17.18 (3) DependencyPairsProof [EQUIVALENT, 41 ms] 63.56/17.18 (4) PiDP 63.56/17.18 (5) DependencyGraphProof [EQUIVALENT, 0 ms] 63.56/17.18 (6) AND 63.56/17.18 (7) PiDP 63.56/17.18 (8) UsableRulesProof [EQUIVALENT, 0 ms] 63.56/17.18 (9) PiDP 63.56/17.18 (10) PiDPToQDPProof [SOUND, 1 ms] 63.56/17.18 (11) QDP 63.56/17.18 (12) TransformationProof [SOUND, 0 ms] 63.56/17.18 (13) QDP 63.56/17.18 (14) TransformationProof [SOUND, 0 ms] 63.56/17.18 (15) QDP 63.56/17.18 (16) PiDP 63.56/17.18 (17) UsableRulesProof [EQUIVALENT, 0 ms] 63.56/17.18 (18) PiDP 63.56/17.18 (19) PiDP 63.56/17.18 (20) UsableRulesProof [EQUIVALENT, 1 ms] 63.56/17.18 (21) PiDP 63.56/17.18 (22) PiDP 63.56/17.18 (23) UsableRulesProof [EQUIVALENT, 0 ms] 63.56/17.18 (24) PiDP 63.56/17.18 (25) PiDP 63.56/17.18 (26) UsableRulesProof [EQUIVALENT, 0 ms] 63.56/17.18 (27) PiDP 63.56/17.18 (28) PiDP 63.56/17.18 (29) UsableRulesProof [EQUIVALENT, 0 ms] 63.56/17.18 (30) PiDP 63.56/17.18 (31) PrologToPiTRSProof [SOUND, 0 ms] 63.56/17.18 (32) PiTRS 63.56/17.18 (33) DependencyPairsProof [EQUIVALENT, 51 ms] 63.56/17.18 (34) PiDP 63.56/17.18 (35) DependencyGraphProof [EQUIVALENT, 0 ms] 63.56/17.18 (36) AND 63.56/17.18 (37) PiDP 63.56/17.18 (38) UsableRulesProof [EQUIVALENT, 0 ms] 63.56/17.18 (39) PiDP 63.56/17.18 (40) PiDPToQDPProof [SOUND, 3 ms] 63.56/17.18 (41) QDP 63.56/17.18 (42) TransformationProof [SOUND, 0 ms] 63.56/17.18 (43) QDP 63.56/17.18 (44) TransformationProof [SOUND, 0 ms] 63.56/17.18 (45) QDP 63.56/17.18 (46) PiDP 63.56/17.18 (47) UsableRulesProof [EQUIVALENT, 0 ms] 63.56/17.18 (48) PiDP 63.56/17.18 (49) PiDP 63.56/17.18 (50) UsableRulesProof [EQUIVALENT, 0 ms] 63.56/17.18 (51) PiDP 63.56/17.18 (52) PiDP 63.56/17.18 (53) UsableRulesProof [EQUIVALENT, 0 ms] 63.56/17.18 (54) PiDP 63.56/17.18 (55) PiDP 63.56/17.18 (56) UsableRulesProof [EQUIVALENT, 0 ms] 63.56/17.18 (57) PiDP 63.56/17.18 (58) PiDP 63.56/17.18 (59) UsableRulesProof [EQUIVALENT, 0 ms] 63.56/17.18 (60) PiDP 63.56/17.18 (61) PrologToTRSTransformerProof [SOUND, 51 ms] 63.56/17.18 (62) QTRS 63.56/17.18 (63) DependencyPairsProof [EQUIVALENT, 0 ms] 63.56/17.18 (64) QDP 63.56/17.18 (65) DependencyGraphProof [EQUIVALENT, 0 ms] 63.56/17.18 (66) AND 63.56/17.18 (67) QDP 63.56/17.18 (68) NonLoopProof [COMPLETE, 47 ms] 63.56/17.18 (69) NO 63.56/17.18 (70) QDP 63.56/17.18 (71) QDPSizeChangeProof [EQUIVALENT, 2 ms] 63.56/17.18 (72) YES 63.56/17.18 (73) QDP 63.56/17.18 (74) NonLoopProof [COMPLETE, 1072 ms] 63.56/17.18 (75) NO 63.56/17.18 (76) PrologToIRSwTTransformerProof [SOUND, 42 ms] 63.56/17.18 (77) AND 63.56/17.18 (78) IRSwT 63.56/17.18 (79) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms] 63.56/17.18 (80) IRSwT 63.56/17.18 (81) IntTRSCompressionProof [EQUIVALENT, 44 ms] 63.56/17.18 (82) IRSwT 63.56/17.18 (83) IRSFormatTransformerProof [EQUIVALENT, 0 ms] 63.56/17.18 (84) IRSwT 63.56/17.18 (85) IRSwTTerminationDigraphProof [EQUIVALENT, 7 ms] 63.56/17.18 (86) IRSwT 63.56/17.18 (87) FilterProof [EQUIVALENT, 0 ms] 63.56/17.18 (88) IntTRS 63.56/17.18 (89) IntTRSPeriodicNontermProof [COMPLETE, 1 ms] 63.56/17.18 (90) NO 63.56/17.18 (91) IRSwT 63.56/17.18 (92) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 2 ms] 63.56/17.18 (93) IRSwT 63.56/17.18 (94) IntTRSCompressionProof [EQUIVALENT, 10 ms] 63.56/17.18 (95) IRSwT 63.56/17.18 (96) IRSFormatTransformerProof [EQUIVALENT, 1 ms] 63.56/17.18 (97) IRSwT 63.56/17.18 (98) IRSwTTerminationDigraphProof [EQUIVALENT, 30 ms] 63.56/17.18 (99) IRSwT 63.56/17.18 (100) IntTRSCompressionProof [EQUIVALENT, 0 ms] 63.56/17.18 (101) IRSwT 63.56/17.18 (102) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] 63.56/17.18 (103) IRSwT 63.56/17.18 (104) IRSwTToIntTRSProof [SOUND, 0 ms] 63.56/17.18 (105) IRSwT 63.56/17.18 (106) IntTRSCompressionProof [EQUIVALENT, 0 ms] 63.56/17.18 (107) IRSwT 63.56/17.18 (108) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] 63.56/17.18 (109) IRSwT 63.56/17.18 (110) IntTRSPeriodicNontermProof [COMPLETE, 9 ms] 63.56/17.18 (111) NO 63.56/17.18 (112) IRSwT 63.56/17.18 (113) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms] 63.56/17.18 (114) IRSwT 63.56/17.18 (115) PrologToDTProblemTransformerProof [SOUND, 158 ms] 63.56/17.18 (116) TRIPLES 63.56/17.18 (117) TriplesToPiDPProof [SOUND, 1267 ms] 63.56/17.18 (118) PiDP 63.56/17.18 (119) DependencyGraphProof [EQUIVALENT, 18 ms] 63.56/17.18 (120) AND 63.56/17.18 (121) PiDP 63.56/17.18 (122) UsableRulesProof [EQUIVALENT, 0 ms] 63.56/17.18 (123) PiDP 63.56/17.18 (124) PiDPToQDPProof [SOUND, 0 ms] 63.56/17.18 (125) QDP 63.56/17.18 (126) TransformationProof [SOUND, 0 ms] 63.56/17.18 (127) QDP 63.56/17.18 (128) PiDP 63.56/17.18 (129) UsableRulesProof [EQUIVALENT, 0 ms] 63.56/17.18 (130) PiDP 63.56/17.18 (131) PiDP 63.56/17.18 (132) UsableRulesProof [EQUIVALENT, 0 ms] 63.56/17.18 (133) PiDP 63.56/17.18 (134) PiDP 63.56/17.18 (135) UsableRulesProof [EQUIVALENT, 0 ms] 63.56/17.18 (136) PiDP 63.56/17.18 (137) PiDP 63.56/17.18 (138) UsableRulesProof [EQUIVALENT, 0 ms] 63.56/17.18 (139) PiDP 63.56/17.18 (140) PiDP 63.56/17.18 (141) UsableRulesProof [EQUIVALENT, 0 ms] 63.56/17.18 (142) PiDP 63.56/17.18 63.56/17.18 63.56/17.18 ---------------------------------------- 63.56/17.18 63.56/17.18 (0) 63.56/17.18 Obligation: 63.56/17.18 Clauses: 63.56/17.18 63.56/17.18 p(d(e(t)), const(1)). 63.56/17.18 p(d(e(const(A))), const(0)). 63.56/17.18 p(d(e(+(X, Y))), +(DX, DY)) :- ','(p(d(e(X)), DX), p(d(e(Y)), DY)). 63.56/17.18 p(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) :- ','(p(d(e(X)), DX), p(d(e(Y)), DY)). 63.56/17.18 p(d(d(X)), DDX) :- ','(p(d(X), DX), p(d(e(DX)), DDX)). 63.56/17.18 63.56/17.18 63.56/17.18 Query: p(a,g) 63.56/17.18 ---------------------------------------- 63.56/17.18 63.56/17.18 (1) PrologToPiTRSProof (SOUND) 63.56/17.18 We use the technique of [TOCL09]. With regard to the inferred argument filtering the predicates were used in the following modes: 63.56/17.18 63.56/17.18 p_in_2: (f,b) (b,b) (b,f) (f,f) 63.56/17.18 63.56/17.18 Transforming Prolog into the following Term Rewriting System: 63.56/17.18 63.56/17.18 Pi-finite rewrite system: 63.56/17.18 The TRS R consists of the following rules: 63.56/17.18 63.56/17.18 p_in_ag(d(e(t)), const(1)) -> p_out_ag(d(e(t)), const(1)) 63.56/17.18 p_in_ag(d(e(const(A))), const(0)) -> p_out_ag(d(e(const(A))), const(0)) 63.56/17.18 p_in_ag(d(e(+(X, Y))), +(DX, DY)) -> U1_ag(X, Y, DX, DY, p_in_ag(d(e(X)), DX)) 63.56/17.18 p_in_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ag(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.18 p_in_gg(d(e(t)), const(1)) -> p_out_gg(d(e(t)), const(1)) 63.56/17.18 p_in_gg(d(e(const(A))), const(0)) -> p_out_gg(d(e(const(A))), const(0)) 63.56/17.18 p_in_gg(d(e(+(X, Y))), +(DX, DY)) -> U1_gg(X, Y, DX, DY, p_in_gg(d(e(X)), DX)) 63.56/17.18 p_in_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_gg(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.18 p_in_gg(d(d(X)), DDX) -> U5_gg(X, DDX, p_in_ga(d(X), DX)) 63.56/17.18 p_in_ga(d(e(t)), const(1)) -> p_out_ga(d(e(t)), const(1)) 63.56/17.18 p_in_ga(d(e(const(A))), const(0)) -> p_out_ga(d(e(const(A))), const(0)) 63.56/17.18 p_in_ga(d(e(+(X, Y))), +(DX, DY)) -> U1_ga(X, Y, DX, DY, p_in_ga(d(e(X)), DX)) 63.56/17.18 p_in_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ga(X, Y, DY, DX, p_in_ga(d(e(X)), DX)) 63.56/17.18 p_in_ga(d(d(X)), DDX) -> U5_ga(X, DDX, p_in_ga(d(X), DX)) 63.56/17.18 U5_ga(X, DDX, p_out_ga(d(X), DX)) -> U6_ga(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.18 U6_ga(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_ga(d(d(X)), DDX) 63.56/17.18 U3_ga(X, Y, DY, DX, p_out_ga(d(e(X)), DX)) -> U4_ga(X, Y, DY, DX, p_in_ga(d(e(Y)), DY)) 63.56/17.18 U4_ga(X, Y, DY, DX, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.18 U1_ga(X, Y, DX, DY, p_out_ga(d(e(X)), DX)) -> U2_ga(X, Y, DX, DY, p_in_ga(d(e(Y)), DY)) 63.56/17.18 U2_ga(X, Y, DX, DY, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(+(X, Y))), +(DX, DY)) 63.56/17.18 U5_gg(X, DDX, p_out_ga(d(X), DX)) -> U6_gg(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.18 U6_gg(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_gg(d(d(X)), DDX) 63.56/17.18 U3_gg(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_gg(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.18 U4_gg(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.18 U1_gg(X, Y, DX, DY, p_out_gg(d(e(X)), DX)) -> U2_gg(X, Y, DX, DY, p_in_gg(d(e(Y)), DY)) 63.56/17.18 U2_gg(X, Y, DX, DY, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(+(X, Y))), +(DX, DY)) 63.56/17.18 U3_ag(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_ag(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.18 U4_ag(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.18 p_in_ag(d(d(X)), DDX) -> U5_ag(X, DDX, p_in_aa(d(X), DX)) 63.56/17.18 p_in_aa(d(e(t)), const(1)) -> p_out_aa(d(e(t)), const(1)) 63.56/17.18 p_in_aa(d(e(const(A))), const(0)) -> p_out_aa(d(e(const(A))), const(0)) 63.56/17.18 p_in_aa(d(e(+(X, Y))), +(DX, DY)) -> U1_aa(X, Y, DX, DY, p_in_aa(d(e(X)), DX)) 63.56/17.18 p_in_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_aa(X, Y, DY, DX, p_in_aa(d(e(X)), DX)) 63.56/17.18 p_in_aa(d(d(X)), DDX) -> U5_aa(X, DDX, p_in_aa(d(X), DX)) 63.56/17.18 U5_aa(X, DDX, p_out_aa(d(X), DX)) -> U6_aa(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.18 U6_aa(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_aa(d(d(X)), DDX) 63.56/17.18 U3_aa(X, Y, DY, DX, p_out_aa(d(e(X)), DX)) -> U4_aa(X, Y, DY, DX, p_in_aa(d(e(Y)), DY)) 63.56/17.18 U4_aa(X, Y, DY, DX, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.18 U1_aa(X, Y, DX, DY, p_out_aa(d(e(X)), DX)) -> U2_aa(X, Y, DX, DY, p_in_aa(d(e(Y)), DY)) 63.56/17.18 U2_aa(X, Y, DX, DY, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(+(X, Y))), +(DX, DY)) 63.56/17.18 U5_ag(X, DDX, p_out_aa(d(X), DX)) -> U6_ag(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.18 U6_ag(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_ag(d(d(X)), DDX) 63.56/17.18 U1_ag(X, Y, DX, DY, p_out_ag(d(e(X)), DX)) -> U2_ag(X, Y, DX, DY, p_in_ag(d(e(Y)), DY)) 63.56/17.18 U2_ag(X, Y, DX, DY, p_out_ag(d(e(Y)), DY)) -> p_out_ag(d(e(+(X, Y))), +(DX, DY)) 63.56/17.18 63.56/17.18 The argument filtering Pi contains the following mapping: 63.56/17.18 p_in_ag(x1, x2) = p_in_ag(x2) 63.56/17.18 63.56/17.18 const(x1) = const 63.56/17.18 63.56/17.18 1 = 1 63.56/17.18 63.56/17.18 p_out_ag(x1, x2) = p_out_ag(x1) 63.56/17.18 63.56/17.18 0 = 0 63.56/17.18 63.56/17.18 +(x1, x2) = +(x1, x2) 63.56/17.18 63.56/17.18 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x4, x5) 63.56/17.18 63.56/17.18 *(x1, x2) = *(x1, x2) 63.56/17.18 63.56/17.18 U3_ag(x1, x2, x3, x4, x5) = U3_ag(x1, x2, x3, x5) 63.56/17.18 63.56/17.18 p_in_gg(x1, x2) = p_in_gg(x1, x2) 63.56/17.18 63.56/17.18 d(x1) = d(x1) 63.56/17.18 63.56/17.18 e(x1) = e(x1) 63.56/17.18 63.56/17.18 t = t 63.56/17.18 63.56/17.18 p_out_gg(x1, x2) = p_out_gg 63.56/17.18 63.56/17.18 U1_gg(x1, x2, x3, x4, x5) = U1_gg(x2, x4, x5) 63.56/17.18 63.56/17.18 U3_gg(x1, x2, x3, x4, x5) = U3_gg(x2, x3, x5) 63.56/17.18 63.56/17.18 U5_gg(x1, x2, x3) = U5_gg(x2, x3) 63.56/17.18 63.56/17.18 p_in_ga(x1, x2) = p_in_ga(x1) 63.56/17.18 63.56/17.18 p_out_ga(x1, x2) = p_out_ga(x2) 63.56/17.18 63.56/17.18 U1_ga(x1, x2, x3, x4, x5) = U1_ga(x2, x5) 63.56/17.18 63.56/17.18 U3_ga(x1, x2, x3, x4, x5) = U3_ga(x1, x2, x5) 63.56/17.18 63.56/17.18 U5_ga(x1, x2, x3) = U5_ga(x3) 63.56/17.18 63.56/17.18 U6_ga(x1, x2, x3, x4) = U6_ga(x4) 63.56/17.18 63.56/17.18 U4_ga(x1, x2, x3, x4, x5) = U4_ga(x1, x2, x4, x5) 63.56/17.18 63.56/17.18 U2_ga(x1, x2, x3, x4, x5) = U2_ga(x3, x5) 63.56/17.18 63.56/17.18 U6_gg(x1, x2, x3, x4) = U6_gg(x4) 63.56/17.18 63.56/17.18 U4_gg(x1, x2, x3, x4, x5) = U4_gg(x5) 63.56/17.18 63.56/17.18 U2_gg(x1, x2, x3, x4, x5) = U2_gg(x5) 63.56/17.18 63.56/17.18 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x1, x2, x5) 63.56/17.18 63.56/17.18 U5_ag(x1, x2, x3) = U5_ag(x2, x3) 63.56/17.18 63.56/17.18 p_in_aa(x1, x2) = p_in_aa 63.56/17.18 63.56/17.18 p_out_aa(x1, x2) = p_out_aa(x1, x2) 63.56/17.18 63.56/17.18 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 63.56/17.18 63.56/17.18 U3_aa(x1, x2, x3, x4, x5) = U3_aa(x5) 63.56/17.18 63.56/17.18 U5_aa(x1, x2, x3) = U5_aa(x3) 63.56/17.18 63.56/17.18 U6_aa(x1, x2, x3, x4) = U6_aa(x1, x4) 63.56/17.18 63.56/17.18 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x1, x4, x5) 63.56/17.18 63.56/17.18 U2_aa(x1, x2, x3, x4, x5) = U2_aa(x1, x3, x5) 63.56/17.18 63.56/17.18 U6_ag(x1, x2, x3, x4) = U6_ag(x1, x4) 63.56/17.18 63.56/17.18 U2_ag(x1, x2, x3, x4, x5) = U2_ag(x1, x5) 63.56/17.18 63.56/17.18 63.56/17.18 63.56/17.18 63.56/17.18 63.56/17.18 Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog 63.56/17.18 63.56/17.18 63.56/17.18 63.56/17.18 ---------------------------------------- 63.56/17.18 63.56/17.18 (2) 63.56/17.18 Obligation: 63.56/17.18 Pi-finite rewrite system: 63.56/17.18 The TRS R consists of the following rules: 63.56/17.18 63.56/17.18 p_in_ag(d(e(t)), const(1)) -> p_out_ag(d(e(t)), const(1)) 63.56/17.18 p_in_ag(d(e(const(A))), const(0)) -> p_out_ag(d(e(const(A))), const(0)) 63.56/17.18 p_in_ag(d(e(+(X, Y))), +(DX, DY)) -> U1_ag(X, Y, DX, DY, p_in_ag(d(e(X)), DX)) 63.56/17.18 p_in_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ag(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.18 p_in_gg(d(e(t)), const(1)) -> p_out_gg(d(e(t)), const(1)) 63.56/17.18 p_in_gg(d(e(const(A))), const(0)) -> p_out_gg(d(e(const(A))), const(0)) 63.56/17.18 p_in_gg(d(e(+(X, Y))), +(DX, DY)) -> U1_gg(X, Y, DX, DY, p_in_gg(d(e(X)), DX)) 63.56/17.18 p_in_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_gg(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.18 p_in_gg(d(d(X)), DDX) -> U5_gg(X, DDX, p_in_ga(d(X), DX)) 63.56/17.18 p_in_ga(d(e(t)), const(1)) -> p_out_ga(d(e(t)), const(1)) 63.56/17.18 p_in_ga(d(e(const(A))), const(0)) -> p_out_ga(d(e(const(A))), const(0)) 63.56/17.18 p_in_ga(d(e(+(X, Y))), +(DX, DY)) -> U1_ga(X, Y, DX, DY, p_in_ga(d(e(X)), DX)) 63.56/17.18 p_in_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ga(X, Y, DY, DX, p_in_ga(d(e(X)), DX)) 63.56/17.18 p_in_ga(d(d(X)), DDX) -> U5_ga(X, DDX, p_in_ga(d(X), DX)) 63.56/17.18 U5_ga(X, DDX, p_out_ga(d(X), DX)) -> U6_ga(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.18 U6_ga(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_ga(d(d(X)), DDX) 63.56/17.18 U3_ga(X, Y, DY, DX, p_out_ga(d(e(X)), DX)) -> U4_ga(X, Y, DY, DX, p_in_ga(d(e(Y)), DY)) 63.56/17.18 U4_ga(X, Y, DY, DX, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.18 U1_ga(X, Y, DX, DY, p_out_ga(d(e(X)), DX)) -> U2_ga(X, Y, DX, DY, p_in_ga(d(e(Y)), DY)) 63.56/17.18 U2_ga(X, Y, DX, DY, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(+(X, Y))), +(DX, DY)) 63.56/17.18 U5_gg(X, DDX, p_out_ga(d(X), DX)) -> U6_gg(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.18 U6_gg(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_gg(d(d(X)), DDX) 63.56/17.18 U3_gg(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_gg(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.18 U4_gg(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.18 U1_gg(X, Y, DX, DY, p_out_gg(d(e(X)), DX)) -> U2_gg(X, Y, DX, DY, p_in_gg(d(e(Y)), DY)) 63.56/17.18 U2_gg(X, Y, DX, DY, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(+(X, Y))), +(DX, DY)) 63.56/17.18 U3_ag(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_ag(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.18 U4_ag(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.18 p_in_ag(d(d(X)), DDX) -> U5_ag(X, DDX, p_in_aa(d(X), DX)) 63.56/17.18 p_in_aa(d(e(t)), const(1)) -> p_out_aa(d(e(t)), const(1)) 63.56/17.18 p_in_aa(d(e(const(A))), const(0)) -> p_out_aa(d(e(const(A))), const(0)) 63.56/17.18 p_in_aa(d(e(+(X, Y))), +(DX, DY)) -> U1_aa(X, Y, DX, DY, p_in_aa(d(e(X)), DX)) 63.56/17.18 p_in_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_aa(X, Y, DY, DX, p_in_aa(d(e(X)), DX)) 63.56/17.18 p_in_aa(d(d(X)), DDX) -> U5_aa(X, DDX, p_in_aa(d(X), DX)) 63.56/17.18 U5_aa(X, DDX, p_out_aa(d(X), DX)) -> U6_aa(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.18 U6_aa(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_aa(d(d(X)), DDX) 63.56/17.18 U3_aa(X, Y, DY, DX, p_out_aa(d(e(X)), DX)) -> U4_aa(X, Y, DY, DX, p_in_aa(d(e(Y)), DY)) 63.56/17.18 U4_aa(X, Y, DY, DX, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.18 U1_aa(X, Y, DX, DY, p_out_aa(d(e(X)), DX)) -> U2_aa(X, Y, DX, DY, p_in_aa(d(e(Y)), DY)) 63.56/17.18 U2_aa(X, Y, DX, DY, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(+(X, Y))), +(DX, DY)) 63.56/17.18 U5_ag(X, DDX, p_out_aa(d(X), DX)) -> U6_ag(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.18 U6_ag(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_ag(d(d(X)), DDX) 63.56/17.18 U1_ag(X, Y, DX, DY, p_out_ag(d(e(X)), DX)) -> U2_ag(X, Y, DX, DY, p_in_ag(d(e(Y)), DY)) 63.56/17.18 U2_ag(X, Y, DX, DY, p_out_ag(d(e(Y)), DY)) -> p_out_ag(d(e(+(X, Y))), +(DX, DY)) 63.56/17.18 63.56/17.18 The argument filtering Pi contains the following mapping: 63.56/17.18 p_in_ag(x1, x2) = p_in_ag(x2) 63.56/17.18 63.56/17.18 const(x1) = const 63.56/17.18 63.56/17.18 1 = 1 63.56/17.18 63.56/17.18 p_out_ag(x1, x2) = p_out_ag(x1) 63.56/17.18 63.56/17.18 0 = 0 63.56/17.18 63.56/17.18 +(x1, x2) = +(x1, x2) 63.56/17.18 63.56/17.18 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x4, x5) 63.56/17.18 63.56/17.18 *(x1, x2) = *(x1, x2) 63.56/17.18 63.56/17.18 U3_ag(x1, x2, x3, x4, x5) = U3_ag(x1, x2, x3, x5) 63.56/17.18 63.56/17.18 p_in_gg(x1, x2) = p_in_gg(x1, x2) 63.56/17.18 63.56/17.18 d(x1) = d(x1) 63.56/17.18 63.56/17.18 e(x1) = e(x1) 63.56/17.18 63.56/17.18 t = t 63.56/17.18 63.56/17.18 p_out_gg(x1, x2) = p_out_gg 63.56/17.18 63.56/17.18 U1_gg(x1, x2, x3, x4, x5) = U1_gg(x2, x4, x5) 63.56/17.18 63.56/17.18 U3_gg(x1, x2, x3, x4, x5) = U3_gg(x2, x3, x5) 63.56/17.18 63.56/17.18 U5_gg(x1, x2, x3) = U5_gg(x2, x3) 63.56/17.18 63.56/17.18 p_in_ga(x1, x2) = p_in_ga(x1) 63.56/17.18 63.56/17.18 p_out_ga(x1, x2) = p_out_ga(x2) 63.56/17.18 63.56/17.18 U1_ga(x1, x2, x3, x4, x5) = U1_ga(x2, x5) 63.56/17.18 63.56/17.18 U3_ga(x1, x2, x3, x4, x5) = U3_ga(x1, x2, x5) 63.56/17.18 63.56/17.18 U5_ga(x1, x2, x3) = U5_ga(x3) 63.56/17.18 63.56/17.18 U6_ga(x1, x2, x3, x4) = U6_ga(x4) 63.56/17.18 63.56/17.18 U4_ga(x1, x2, x3, x4, x5) = U4_ga(x1, x2, x4, x5) 63.56/17.18 63.56/17.18 U2_ga(x1, x2, x3, x4, x5) = U2_ga(x3, x5) 63.56/17.18 63.56/17.18 U6_gg(x1, x2, x3, x4) = U6_gg(x4) 63.56/17.18 63.56/17.18 U4_gg(x1, x2, x3, x4, x5) = U4_gg(x5) 63.56/17.18 63.56/17.18 U2_gg(x1, x2, x3, x4, x5) = U2_gg(x5) 63.56/17.18 63.56/17.18 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x1, x2, x5) 63.56/17.18 63.56/17.18 U5_ag(x1, x2, x3) = U5_ag(x2, x3) 63.56/17.18 63.56/17.18 p_in_aa(x1, x2) = p_in_aa 63.56/17.18 63.56/17.18 p_out_aa(x1, x2) = p_out_aa(x1, x2) 63.56/17.18 63.56/17.18 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 63.56/17.18 63.56/17.18 U3_aa(x1, x2, x3, x4, x5) = U3_aa(x5) 63.56/17.18 63.56/17.18 U5_aa(x1, x2, x3) = U5_aa(x3) 63.56/17.18 63.56/17.18 U6_aa(x1, x2, x3, x4) = U6_aa(x1, x4) 63.56/17.18 63.56/17.18 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x1, x4, x5) 63.56/17.18 63.56/17.18 U2_aa(x1, x2, x3, x4, x5) = U2_aa(x1, x3, x5) 63.56/17.18 63.56/17.18 U6_ag(x1, x2, x3, x4) = U6_ag(x1, x4) 63.56/17.18 63.56/17.18 U2_ag(x1, x2, x3, x4, x5) = U2_ag(x1, x5) 63.56/17.18 63.56/17.18 63.56/17.18 63.56/17.18 ---------------------------------------- 63.56/17.18 63.56/17.18 (3) DependencyPairsProof (EQUIVALENT) 63.56/17.18 Using Dependency Pairs [AG00,LOPSTR] we result in the following initial DP problem: 63.56/17.18 Pi DP problem: 63.56/17.18 The TRS P consists of the following rules: 63.56/17.18 63.56/17.18 P_IN_AG(d(e(+(X, Y))), +(DX, DY)) -> U1_AG(X, Y, DX, DY, p_in_ag(d(e(X)), DX)) 63.56/17.18 P_IN_AG(d(e(+(X, Y))), +(DX, DY)) -> P_IN_AG(d(e(X)), DX) 63.56/17.18 P_IN_AG(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_AG(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.18 P_IN_AG(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> P_IN_GG(d(e(X)), DX) 63.56/17.18 P_IN_GG(d(e(+(X, Y))), +(DX, DY)) -> U1_GG(X, Y, DX, DY, p_in_gg(d(e(X)), DX)) 63.56/17.18 P_IN_GG(d(e(+(X, Y))), +(DX, DY)) -> P_IN_GG(d(e(X)), DX) 63.56/17.18 P_IN_GG(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_GG(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.18 P_IN_GG(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> P_IN_GG(d(e(X)), DX) 63.56/17.18 P_IN_GG(d(d(X)), DDX) -> U5_GG(X, DDX, p_in_ga(d(X), DX)) 63.56/17.18 P_IN_GG(d(d(X)), DDX) -> P_IN_GA(d(X), DX) 63.56/17.18 P_IN_GA(d(e(+(X, Y))), +(DX, DY)) -> U1_GA(X, Y, DX, DY, p_in_ga(d(e(X)), DX)) 63.56/17.18 P_IN_GA(d(e(+(X, Y))), +(DX, DY)) -> P_IN_GA(d(e(X)), DX) 63.56/17.18 P_IN_GA(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_GA(X, Y, DY, DX, p_in_ga(d(e(X)), DX)) 63.56/17.18 P_IN_GA(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> P_IN_GA(d(e(X)), DX) 63.56/17.18 P_IN_GA(d(d(X)), DDX) -> U5_GA(X, DDX, p_in_ga(d(X), DX)) 63.56/17.18 P_IN_GA(d(d(X)), DDX) -> P_IN_GA(d(X), DX) 63.56/17.18 U5_GA(X, DDX, p_out_ga(d(X), DX)) -> U6_GA(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.18 U5_GA(X, DDX, p_out_ga(d(X), DX)) -> P_IN_GA(d(e(DX)), DDX) 63.56/17.18 U3_GA(X, Y, DY, DX, p_out_ga(d(e(X)), DX)) -> U4_GA(X, Y, DY, DX, p_in_ga(d(e(Y)), DY)) 63.56/17.18 U3_GA(X, Y, DY, DX, p_out_ga(d(e(X)), DX)) -> P_IN_GA(d(e(Y)), DY) 63.56/17.18 U1_GA(X, Y, DX, DY, p_out_ga(d(e(X)), DX)) -> U2_GA(X, Y, DX, DY, p_in_ga(d(e(Y)), DY)) 63.56/17.18 U1_GA(X, Y, DX, DY, p_out_ga(d(e(X)), DX)) -> P_IN_GA(d(e(Y)), DY) 63.56/17.18 U5_GG(X, DDX, p_out_ga(d(X), DX)) -> U6_GG(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.18 U5_GG(X, DDX, p_out_ga(d(X), DX)) -> P_IN_GG(d(e(DX)), DDX) 63.56/17.18 U3_GG(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_GG(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.18 U3_GG(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> P_IN_GG(d(e(Y)), DY) 63.56/17.18 U1_GG(X, Y, DX, DY, p_out_gg(d(e(X)), DX)) -> U2_GG(X, Y, DX, DY, p_in_gg(d(e(Y)), DY)) 63.56/17.18 U1_GG(X, Y, DX, DY, p_out_gg(d(e(X)), DX)) -> P_IN_GG(d(e(Y)), DY) 63.56/17.18 U3_AG(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_AG(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.18 U3_AG(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> P_IN_GG(d(e(Y)), DY) 63.56/17.18 P_IN_AG(d(d(X)), DDX) -> U5_AG(X, DDX, p_in_aa(d(X), DX)) 63.56/17.18 P_IN_AG(d(d(X)), DDX) -> P_IN_AA(d(X), DX) 63.56/17.18 P_IN_AA(d(e(+(X, Y))), +(DX, DY)) -> U1_AA(X, Y, DX, DY, p_in_aa(d(e(X)), DX)) 63.56/17.18 P_IN_AA(d(e(+(X, Y))), +(DX, DY)) -> P_IN_AA(d(e(X)), DX) 63.56/17.18 P_IN_AA(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_AA(X, Y, DY, DX, p_in_aa(d(e(X)), DX)) 63.56/17.18 P_IN_AA(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> P_IN_AA(d(e(X)), DX) 63.56/17.18 P_IN_AA(d(d(X)), DDX) -> U5_AA(X, DDX, p_in_aa(d(X), DX)) 63.56/17.18 P_IN_AA(d(d(X)), DDX) -> P_IN_AA(d(X), DX) 63.56/17.18 U5_AA(X, DDX, p_out_aa(d(X), DX)) -> U6_AA(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.18 U5_AA(X, DDX, p_out_aa(d(X), DX)) -> P_IN_GA(d(e(DX)), DDX) 63.56/17.18 U3_AA(X, Y, DY, DX, p_out_aa(d(e(X)), DX)) -> U4_AA(X, Y, DY, DX, p_in_aa(d(e(Y)), DY)) 63.56/17.18 U3_AA(X, Y, DY, DX, p_out_aa(d(e(X)), DX)) -> P_IN_AA(d(e(Y)), DY) 63.56/17.18 U1_AA(X, Y, DX, DY, p_out_aa(d(e(X)), DX)) -> U2_AA(X, Y, DX, DY, p_in_aa(d(e(Y)), DY)) 63.56/17.18 U1_AA(X, Y, DX, DY, p_out_aa(d(e(X)), DX)) -> P_IN_AA(d(e(Y)), DY) 63.56/17.18 U5_AG(X, DDX, p_out_aa(d(X), DX)) -> U6_AG(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.18 U5_AG(X, DDX, p_out_aa(d(X), DX)) -> P_IN_GG(d(e(DX)), DDX) 63.56/17.18 U1_AG(X, Y, DX, DY, p_out_ag(d(e(X)), DX)) -> U2_AG(X, Y, DX, DY, p_in_ag(d(e(Y)), DY)) 63.56/17.18 U1_AG(X, Y, DX, DY, p_out_ag(d(e(X)), DX)) -> P_IN_AG(d(e(Y)), DY) 63.56/17.18 63.56/17.18 The TRS R consists of the following rules: 63.56/17.18 63.56/17.18 p_in_ag(d(e(t)), const(1)) -> p_out_ag(d(e(t)), const(1)) 63.56/17.18 p_in_ag(d(e(const(A))), const(0)) -> p_out_ag(d(e(const(A))), const(0)) 63.56/17.18 p_in_ag(d(e(+(X, Y))), +(DX, DY)) -> U1_ag(X, Y, DX, DY, p_in_ag(d(e(X)), DX)) 63.56/17.18 p_in_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ag(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.18 p_in_gg(d(e(t)), const(1)) -> p_out_gg(d(e(t)), const(1)) 63.56/17.18 p_in_gg(d(e(const(A))), const(0)) -> p_out_gg(d(e(const(A))), const(0)) 63.56/17.18 p_in_gg(d(e(+(X, Y))), +(DX, DY)) -> U1_gg(X, Y, DX, DY, p_in_gg(d(e(X)), DX)) 63.56/17.18 p_in_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_gg(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.18 p_in_gg(d(d(X)), DDX) -> U5_gg(X, DDX, p_in_ga(d(X), DX)) 63.56/17.18 p_in_ga(d(e(t)), const(1)) -> p_out_ga(d(e(t)), const(1)) 63.56/17.18 p_in_ga(d(e(const(A))), const(0)) -> p_out_ga(d(e(const(A))), const(0)) 63.56/17.18 p_in_ga(d(e(+(X, Y))), +(DX, DY)) -> U1_ga(X, Y, DX, DY, p_in_ga(d(e(X)), DX)) 63.56/17.18 p_in_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ga(X, Y, DY, DX, p_in_ga(d(e(X)), DX)) 63.56/17.18 p_in_ga(d(d(X)), DDX) -> U5_ga(X, DDX, p_in_ga(d(X), DX)) 63.56/17.18 U5_ga(X, DDX, p_out_ga(d(X), DX)) -> U6_ga(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.18 U6_ga(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_ga(d(d(X)), DDX) 63.56/17.18 U3_ga(X, Y, DY, DX, p_out_ga(d(e(X)), DX)) -> U4_ga(X, Y, DY, DX, p_in_ga(d(e(Y)), DY)) 63.56/17.18 U4_ga(X, Y, DY, DX, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.18 U1_ga(X, Y, DX, DY, p_out_ga(d(e(X)), DX)) -> U2_ga(X, Y, DX, DY, p_in_ga(d(e(Y)), DY)) 63.56/17.18 U2_ga(X, Y, DX, DY, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(+(X, Y))), +(DX, DY)) 63.56/17.18 U5_gg(X, DDX, p_out_ga(d(X), DX)) -> U6_gg(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.18 U6_gg(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_gg(d(d(X)), DDX) 63.56/17.18 U3_gg(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_gg(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.18 U4_gg(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.18 U1_gg(X, Y, DX, DY, p_out_gg(d(e(X)), DX)) -> U2_gg(X, Y, DX, DY, p_in_gg(d(e(Y)), DY)) 63.56/17.18 U2_gg(X, Y, DX, DY, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(+(X, Y))), +(DX, DY)) 63.56/17.18 U3_ag(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_ag(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.18 U4_ag(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.18 p_in_ag(d(d(X)), DDX) -> U5_ag(X, DDX, p_in_aa(d(X), DX)) 63.56/17.18 p_in_aa(d(e(t)), const(1)) -> p_out_aa(d(e(t)), const(1)) 63.56/17.18 p_in_aa(d(e(const(A))), const(0)) -> p_out_aa(d(e(const(A))), const(0)) 63.56/17.18 p_in_aa(d(e(+(X, Y))), +(DX, DY)) -> U1_aa(X, Y, DX, DY, p_in_aa(d(e(X)), DX)) 63.56/17.18 p_in_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_aa(X, Y, DY, DX, p_in_aa(d(e(X)), DX)) 63.56/17.18 p_in_aa(d(d(X)), DDX) -> U5_aa(X, DDX, p_in_aa(d(X), DX)) 63.56/17.18 U5_aa(X, DDX, p_out_aa(d(X), DX)) -> U6_aa(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.18 U6_aa(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_aa(d(d(X)), DDX) 63.56/17.18 U3_aa(X, Y, DY, DX, p_out_aa(d(e(X)), DX)) -> U4_aa(X, Y, DY, DX, p_in_aa(d(e(Y)), DY)) 63.56/17.18 U4_aa(X, Y, DY, DX, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.18 U1_aa(X, Y, DX, DY, p_out_aa(d(e(X)), DX)) -> U2_aa(X, Y, DX, DY, p_in_aa(d(e(Y)), DY)) 63.56/17.18 U2_aa(X, Y, DX, DY, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(+(X, Y))), +(DX, DY)) 63.56/17.18 U5_ag(X, DDX, p_out_aa(d(X), DX)) -> U6_ag(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.18 U6_ag(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_ag(d(d(X)), DDX) 63.56/17.18 U1_ag(X, Y, DX, DY, p_out_ag(d(e(X)), DX)) -> U2_ag(X, Y, DX, DY, p_in_ag(d(e(Y)), DY)) 63.56/17.18 U2_ag(X, Y, DX, DY, p_out_ag(d(e(Y)), DY)) -> p_out_ag(d(e(+(X, Y))), +(DX, DY)) 63.56/17.18 63.56/17.18 The argument filtering Pi contains the following mapping: 63.56/17.18 p_in_ag(x1, x2) = p_in_ag(x2) 63.56/17.18 63.56/17.18 const(x1) = const 63.56/17.18 63.56/17.18 1 = 1 63.56/17.18 63.56/17.18 p_out_ag(x1, x2) = p_out_ag(x1) 63.56/17.18 63.56/17.18 0 = 0 63.56/17.18 63.56/17.18 +(x1, x2) = +(x1, x2) 63.56/17.18 63.56/17.18 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x4, x5) 63.56/17.18 63.56/17.18 *(x1, x2) = *(x1, x2) 63.56/17.18 63.56/17.18 U3_ag(x1, x2, x3, x4, x5) = U3_ag(x1, x2, x3, x5) 63.56/17.18 63.56/17.18 p_in_gg(x1, x2) = p_in_gg(x1, x2) 63.56/17.18 63.56/17.18 d(x1) = d(x1) 63.56/17.18 63.56/17.18 e(x1) = e(x1) 63.56/17.18 63.56/17.18 t = t 63.56/17.18 63.56/17.18 p_out_gg(x1, x2) = p_out_gg 63.56/17.18 63.56/17.18 U1_gg(x1, x2, x3, x4, x5) = U1_gg(x2, x4, x5) 63.56/17.18 63.56/17.18 U3_gg(x1, x2, x3, x4, x5) = U3_gg(x2, x3, x5) 63.56/17.18 63.56/17.18 U5_gg(x1, x2, x3) = U5_gg(x2, x3) 63.56/17.18 63.56/17.18 p_in_ga(x1, x2) = p_in_ga(x1) 63.56/17.18 63.56/17.18 p_out_ga(x1, x2) = p_out_ga(x2) 63.56/17.18 63.56/17.18 U1_ga(x1, x2, x3, x4, x5) = U1_ga(x2, x5) 63.56/17.18 63.56/17.18 U3_ga(x1, x2, x3, x4, x5) = U3_ga(x1, x2, x5) 63.56/17.18 63.56/17.18 U5_ga(x1, x2, x3) = U5_ga(x3) 63.56/17.18 63.56/17.18 U6_ga(x1, x2, x3, x4) = U6_ga(x4) 63.56/17.18 63.56/17.18 U4_ga(x1, x2, x3, x4, x5) = U4_ga(x1, x2, x4, x5) 63.56/17.18 63.56/17.18 U2_ga(x1, x2, x3, x4, x5) = U2_ga(x3, x5) 63.56/17.18 63.56/17.18 U6_gg(x1, x2, x3, x4) = U6_gg(x4) 63.56/17.18 63.56/17.18 U4_gg(x1, x2, x3, x4, x5) = U4_gg(x5) 63.56/17.18 63.56/17.18 U2_gg(x1, x2, x3, x4, x5) = U2_gg(x5) 63.56/17.18 63.56/17.18 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x1, x2, x5) 63.56/17.18 63.56/17.18 U5_ag(x1, x2, x3) = U5_ag(x2, x3) 63.56/17.18 63.56/17.18 p_in_aa(x1, x2) = p_in_aa 63.56/17.18 63.56/17.18 p_out_aa(x1, x2) = p_out_aa(x1, x2) 63.56/17.18 63.56/17.18 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 63.56/17.18 63.56/17.18 U3_aa(x1, x2, x3, x4, x5) = U3_aa(x5) 63.56/17.18 63.56/17.18 U5_aa(x1, x2, x3) = U5_aa(x3) 63.56/17.18 63.56/17.18 U6_aa(x1, x2, x3, x4) = U6_aa(x1, x4) 63.56/17.18 63.56/17.18 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x1, x4, x5) 63.56/17.18 63.56/17.18 U2_aa(x1, x2, x3, x4, x5) = U2_aa(x1, x3, x5) 63.56/17.18 63.56/17.18 U6_ag(x1, x2, x3, x4) = U6_ag(x1, x4) 63.56/17.18 63.56/17.18 U2_ag(x1, x2, x3, x4, x5) = U2_ag(x1, x5) 63.56/17.18 63.56/17.18 P_IN_AG(x1, x2) = P_IN_AG(x2) 63.56/17.18 63.56/17.18 U1_AG(x1, x2, x3, x4, x5) = U1_AG(x4, x5) 63.56/17.18 63.56/17.18 U3_AG(x1, x2, x3, x4, x5) = U3_AG(x1, x2, x3, x5) 63.56/17.18 63.56/17.18 P_IN_GG(x1, x2) = P_IN_GG(x1, x2) 63.56/17.18 63.56/17.18 U1_GG(x1, x2, x3, x4, x5) = U1_GG(x2, x4, x5) 63.56/17.18 63.56/17.18 U3_GG(x1, x2, x3, x4, x5) = U3_GG(x2, x3, x5) 63.56/17.18 63.56/17.18 U5_GG(x1, x2, x3) = U5_GG(x2, x3) 63.56/17.18 63.56/17.18 P_IN_GA(x1, x2) = P_IN_GA(x1) 63.56/17.18 63.56/17.18 U1_GA(x1, x2, x3, x4, x5) = U1_GA(x2, x5) 63.56/17.18 63.56/17.18 U3_GA(x1, x2, x3, x4, x5) = U3_GA(x1, x2, x5) 63.56/17.18 63.56/17.18 U5_GA(x1, x2, x3) = U5_GA(x3) 63.56/17.18 63.56/17.18 U6_GA(x1, x2, x3, x4) = U6_GA(x4) 63.56/17.18 63.56/17.18 U4_GA(x1, x2, x3, x4, x5) = U4_GA(x1, x2, x4, x5) 63.56/17.18 63.56/17.18 U2_GA(x1, x2, x3, x4, x5) = U2_GA(x3, x5) 63.56/17.18 63.56/17.18 U6_GG(x1, x2, x3, x4) = U6_GG(x4) 63.56/17.18 63.56/17.18 U4_GG(x1, x2, x3, x4, x5) = U4_GG(x5) 63.56/17.18 63.56/17.18 U2_GG(x1, x2, x3, x4, x5) = U2_GG(x5) 63.56/17.18 63.56/17.18 U4_AG(x1, x2, x3, x4, x5) = U4_AG(x1, x2, x5) 63.56/17.18 63.56/17.18 U5_AG(x1, x2, x3) = U5_AG(x2, x3) 63.56/17.18 63.56/17.18 P_IN_AA(x1, x2) = P_IN_AA 63.56/17.18 63.56/17.18 U1_AA(x1, x2, x3, x4, x5) = U1_AA(x5) 63.56/17.18 63.56/17.18 U3_AA(x1, x2, x3, x4, x5) = U3_AA(x5) 63.56/17.18 63.56/17.18 U5_AA(x1, x2, x3) = U5_AA(x3) 63.56/17.18 63.56/17.18 U6_AA(x1, x2, x3, x4) = U6_AA(x1, x4) 63.56/17.18 63.56/17.18 U4_AA(x1, x2, x3, x4, x5) = U4_AA(x1, x4, x5) 63.56/17.18 63.56/17.18 U2_AA(x1, x2, x3, x4, x5) = U2_AA(x1, x3, x5) 63.56/17.18 63.56/17.18 U6_AG(x1, x2, x3, x4) = U6_AG(x1, x4) 63.56/17.18 63.56/17.18 U2_AG(x1, x2, x3, x4, x5) = U2_AG(x1, x5) 63.56/17.18 63.56/17.18 63.56/17.18 We have to consider all (P,R,Pi)-chains 63.56/17.18 ---------------------------------------- 63.56/17.18 63.56/17.18 (4) 63.56/17.18 Obligation: 63.56/17.18 Pi DP problem: 63.56/17.18 The TRS P consists of the following rules: 63.56/17.18 63.56/17.18 P_IN_AG(d(e(+(X, Y))), +(DX, DY)) -> U1_AG(X, Y, DX, DY, p_in_ag(d(e(X)), DX)) 63.56/17.18 P_IN_AG(d(e(+(X, Y))), +(DX, DY)) -> P_IN_AG(d(e(X)), DX) 63.56/17.18 P_IN_AG(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_AG(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.18 P_IN_AG(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> P_IN_GG(d(e(X)), DX) 63.56/17.18 P_IN_GG(d(e(+(X, Y))), +(DX, DY)) -> U1_GG(X, Y, DX, DY, p_in_gg(d(e(X)), DX)) 63.56/17.18 P_IN_GG(d(e(+(X, Y))), +(DX, DY)) -> P_IN_GG(d(e(X)), DX) 63.56/17.18 P_IN_GG(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_GG(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.18 P_IN_GG(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> P_IN_GG(d(e(X)), DX) 63.56/17.18 P_IN_GG(d(d(X)), DDX) -> U5_GG(X, DDX, p_in_ga(d(X), DX)) 63.56/17.18 P_IN_GG(d(d(X)), DDX) -> P_IN_GA(d(X), DX) 63.56/17.18 P_IN_GA(d(e(+(X, Y))), +(DX, DY)) -> U1_GA(X, Y, DX, DY, p_in_ga(d(e(X)), DX)) 63.56/17.18 P_IN_GA(d(e(+(X, Y))), +(DX, DY)) -> P_IN_GA(d(e(X)), DX) 63.56/17.18 P_IN_GA(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_GA(X, Y, DY, DX, p_in_ga(d(e(X)), DX)) 63.56/17.18 P_IN_GA(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> P_IN_GA(d(e(X)), DX) 63.56/17.18 P_IN_GA(d(d(X)), DDX) -> U5_GA(X, DDX, p_in_ga(d(X), DX)) 63.56/17.18 P_IN_GA(d(d(X)), DDX) -> P_IN_GA(d(X), DX) 63.56/17.18 U5_GA(X, DDX, p_out_ga(d(X), DX)) -> U6_GA(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.18 U5_GA(X, DDX, p_out_ga(d(X), DX)) -> P_IN_GA(d(e(DX)), DDX) 63.56/17.18 U3_GA(X, Y, DY, DX, p_out_ga(d(e(X)), DX)) -> U4_GA(X, Y, DY, DX, p_in_ga(d(e(Y)), DY)) 63.56/17.18 U3_GA(X, Y, DY, DX, p_out_ga(d(e(X)), DX)) -> P_IN_GA(d(e(Y)), DY) 63.56/17.18 U1_GA(X, Y, DX, DY, p_out_ga(d(e(X)), DX)) -> U2_GA(X, Y, DX, DY, p_in_ga(d(e(Y)), DY)) 63.56/17.18 U1_GA(X, Y, DX, DY, p_out_ga(d(e(X)), DX)) -> P_IN_GA(d(e(Y)), DY) 63.56/17.18 U5_GG(X, DDX, p_out_ga(d(X), DX)) -> U6_GG(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.18 U5_GG(X, DDX, p_out_ga(d(X), DX)) -> P_IN_GG(d(e(DX)), DDX) 63.56/17.18 U3_GG(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_GG(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.18 U3_GG(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> P_IN_GG(d(e(Y)), DY) 63.56/17.18 U1_GG(X, Y, DX, DY, p_out_gg(d(e(X)), DX)) -> U2_GG(X, Y, DX, DY, p_in_gg(d(e(Y)), DY)) 63.56/17.18 U1_GG(X, Y, DX, DY, p_out_gg(d(e(X)), DX)) -> P_IN_GG(d(e(Y)), DY) 63.56/17.18 U3_AG(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_AG(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.18 U3_AG(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> P_IN_GG(d(e(Y)), DY) 63.56/17.18 P_IN_AG(d(d(X)), DDX) -> U5_AG(X, DDX, p_in_aa(d(X), DX)) 63.56/17.18 P_IN_AG(d(d(X)), DDX) -> P_IN_AA(d(X), DX) 63.56/17.18 P_IN_AA(d(e(+(X, Y))), +(DX, DY)) -> U1_AA(X, Y, DX, DY, p_in_aa(d(e(X)), DX)) 63.56/17.18 P_IN_AA(d(e(+(X, Y))), +(DX, DY)) -> P_IN_AA(d(e(X)), DX) 63.56/17.18 P_IN_AA(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_AA(X, Y, DY, DX, p_in_aa(d(e(X)), DX)) 63.56/17.18 P_IN_AA(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> P_IN_AA(d(e(X)), DX) 63.56/17.18 P_IN_AA(d(d(X)), DDX) -> U5_AA(X, DDX, p_in_aa(d(X), DX)) 63.56/17.18 P_IN_AA(d(d(X)), DDX) -> P_IN_AA(d(X), DX) 63.56/17.18 U5_AA(X, DDX, p_out_aa(d(X), DX)) -> U6_AA(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.18 U5_AA(X, DDX, p_out_aa(d(X), DX)) -> P_IN_GA(d(e(DX)), DDX) 63.56/17.18 U3_AA(X, Y, DY, DX, p_out_aa(d(e(X)), DX)) -> U4_AA(X, Y, DY, DX, p_in_aa(d(e(Y)), DY)) 63.56/17.18 U3_AA(X, Y, DY, DX, p_out_aa(d(e(X)), DX)) -> P_IN_AA(d(e(Y)), DY) 63.56/17.18 U1_AA(X, Y, DX, DY, p_out_aa(d(e(X)), DX)) -> U2_AA(X, Y, DX, DY, p_in_aa(d(e(Y)), DY)) 63.56/17.18 U1_AA(X, Y, DX, DY, p_out_aa(d(e(X)), DX)) -> P_IN_AA(d(e(Y)), DY) 63.56/17.18 U5_AG(X, DDX, p_out_aa(d(X), DX)) -> U6_AG(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.18 U5_AG(X, DDX, p_out_aa(d(X), DX)) -> P_IN_GG(d(e(DX)), DDX) 63.56/17.18 U1_AG(X, Y, DX, DY, p_out_ag(d(e(X)), DX)) -> U2_AG(X, Y, DX, DY, p_in_ag(d(e(Y)), DY)) 63.56/17.18 U1_AG(X, Y, DX, DY, p_out_ag(d(e(X)), DX)) -> P_IN_AG(d(e(Y)), DY) 63.56/17.18 63.56/17.18 The TRS R consists of the following rules: 63.56/17.18 63.56/17.18 p_in_ag(d(e(t)), const(1)) -> p_out_ag(d(e(t)), const(1)) 63.56/17.18 p_in_ag(d(e(const(A))), const(0)) -> p_out_ag(d(e(const(A))), const(0)) 63.56/17.18 p_in_ag(d(e(+(X, Y))), +(DX, DY)) -> U1_ag(X, Y, DX, DY, p_in_ag(d(e(X)), DX)) 63.56/17.18 p_in_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ag(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.18 p_in_gg(d(e(t)), const(1)) -> p_out_gg(d(e(t)), const(1)) 63.56/17.18 p_in_gg(d(e(const(A))), const(0)) -> p_out_gg(d(e(const(A))), const(0)) 63.56/17.18 p_in_gg(d(e(+(X, Y))), +(DX, DY)) -> U1_gg(X, Y, DX, DY, p_in_gg(d(e(X)), DX)) 63.56/17.18 p_in_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_gg(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.18 p_in_gg(d(d(X)), DDX) -> U5_gg(X, DDX, p_in_ga(d(X), DX)) 63.56/17.18 p_in_ga(d(e(t)), const(1)) -> p_out_ga(d(e(t)), const(1)) 63.56/17.18 p_in_ga(d(e(const(A))), const(0)) -> p_out_ga(d(e(const(A))), const(0)) 63.56/17.18 p_in_ga(d(e(+(X, Y))), +(DX, DY)) -> U1_ga(X, Y, DX, DY, p_in_ga(d(e(X)), DX)) 63.56/17.18 p_in_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ga(X, Y, DY, DX, p_in_ga(d(e(X)), DX)) 63.56/17.18 p_in_ga(d(d(X)), DDX) -> U5_ga(X, DDX, p_in_ga(d(X), DX)) 63.56/17.18 U5_ga(X, DDX, p_out_ga(d(X), DX)) -> U6_ga(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.18 U6_ga(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_ga(d(d(X)), DDX) 63.56/17.18 U3_ga(X, Y, DY, DX, p_out_ga(d(e(X)), DX)) -> U4_ga(X, Y, DY, DX, p_in_ga(d(e(Y)), DY)) 63.56/17.18 U4_ga(X, Y, DY, DX, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.18 U1_ga(X, Y, DX, DY, p_out_ga(d(e(X)), DX)) -> U2_ga(X, Y, DX, DY, p_in_ga(d(e(Y)), DY)) 63.56/17.18 U2_ga(X, Y, DX, DY, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(+(X, Y))), +(DX, DY)) 63.56/17.18 U5_gg(X, DDX, p_out_ga(d(X), DX)) -> U6_gg(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.18 U6_gg(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_gg(d(d(X)), DDX) 63.56/17.18 U3_gg(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_gg(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.18 U4_gg(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.18 U1_gg(X, Y, DX, DY, p_out_gg(d(e(X)), DX)) -> U2_gg(X, Y, DX, DY, p_in_gg(d(e(Y)), DY)) 63.56/17.18 U2_gg(X, Y, DX, DY, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(+(X, Y))), +(DX, DY)) 63.56/17.18 U3_ag(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_ag(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.18 U4_ag(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.18 p_in_ag(d(d(X)), DDX) -> U5_ag(X, DDX, p_in_aa(d(X), DX)) 63.56/17.18 p_in_aa(d(e(t)), const(1)) -> p_out_aa(d(e(t)), const(1)) 63.56/17.18 p_in_aa(d(e(const(A))), const(0)) -> p_out_aa(d(e(const(A))), const(0)) 63.56/17.18 p_in_aa(d(e(+(X, Y))), +(DX, DY)) -> U1_aa(X, Y, DX, DY, p_in_aa(d(e(X)), DX)) 63.56/17.18 p_in_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_aa(X, Y, DY, DX, p_in_aa(d(e(X)), DX)) 63.56/17.18 p_in_aa(d(d(X)), DDX) -> U5_aa(X, DDX, p_in_aa(d(X), DX)) 63.56/17.18 U5_aa(X, DDX, p_out_aa(d(X), DX)) -> U6_aa(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.18 U6_aa(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_aa(d(d(X)), DDX) 63.56/17.18 U3_aa(X, Y, DY, DX, p_out_aa(d(e(X)), DX)) -> U4_aa(X, Y, DY, DX, p_in_aa(d(e(Y)), DY)) 63.56/17.18 U4_aa(X, Y, DY, DX, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.18 U1_aa(X, Y, DX, DY, p_out_aa(d(e(X)), DX)) -> U2_aa(X, Y, DX, DY, p_in_aa(d(e(Y)), DY)) 63.56/17.18 U2_aa(X, Y, DX, DY, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(+(X, Y))), +(DX, DY)) 63.56/17.18 U5_ag(X, DDX, p_out_aa(d(X), DX)) -> U6_ag(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.18 U6_ag(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_ag(d(d(X)), DDX) 63.56/17.18 U1_ag(X, Y, DX, DY, p_out_ag(d(e(X)), DX)) -> U2_ag(X, Y, DX, DY, p_in_ag(d(e(Y)), DY)) 63.56/17.18 U2_ag(X, Y, DX, DY, p_out_ag(d(e(Y)), DY)) -> p_out_ag(d(e(+(X, Y))), +(DX, DY)) 63.56/17.18 63.56/17.18 The argument filtering Pi contains the following mapping: 63.56/17.18 p_in_ag(x1, x2) = p_in_ag(x2) 63.56/17.18 63.56/17.18 const(x1) = const 63.56/17.18 63.56/17.18 1 = 1 63.56/17.18 63.56/17.18 p_out_ag(x1, x2) = p_out_ag(x1) 63.56/17.18 63.56/17.18 0 = 0 63.56/17.18 63.56/17.18 +(x1, x2) = +(x1, x2) 63.56/17.18 63.56/17.18 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x4, x5) 63.56/17.18 63.56/17.18 *(x1, x2) = *(x1, x2) 63.56/17.18 63.56/17.18 U3_ag(x1, x2, x3, x4, x5) = U3_ag(x1, x2, x3, x5) 63.56/17.18 63.56/17.18 p_in_gg(x1, x2) = p_in_gg(x1, x2) 63.56/17.18 63.56/17.18 d(x1) = d(x1) 63.56/17.18 63.56/17.18 e(x1) = e(x1) 63.56/17.18 63.56/17.18 t = t 63.56/17.18 63.56/17.18 p_out_gg(x1, x2) = p_out_gg 63.56/17.18 63.56/17.18 U1_gg(x1, x2, x3, x4, x5) = U1_gg(x2, x4, x5) 63.56/17.18 63.56/17.18 U3_gg(x1, x2, x3, x4, x5) = U3_gg(x2, x3, x5) 63.56/17.18 63.56/17.18 U5_gg(x1, x2, x3) = U5_gg(x2, x3) 63.56/17.18 63.56/17.18 p_in_ga(x1, x2) = p_in_ga(x1) 63.56/17.18 63.56/17.18 p_out_ga(x1, x2) = p_out_ga(x2) 63.56/17.18 63.56/17.18 U1_ga(x1, x2, x3, x4, x5) = U1_ga(x2, x5) 63.56/17.18 63.56/17.18 U3_ga(x1, x2, x3, x4, x5) = U3_ga(x1, x2, x5) 63.56/17.18 63.56/17.18 U5_ga(x1, x2, x3) = U5_ga(x3) 63.56/17.18 63.56/17.18 U6_ga(x1, x2, x3, x4) = U6_ga(x4) 63.56/17.18 63.56/17.18 U4_ga(x1, x2, x3, x4, x5) = U4_ga(x1, x2, x4, x5) 63.56/17.18 63.56/17.18 U2_ga(x1, x2, x3, x4, x5) = U2_ga(x3, x5) 63.56/17.18 63.56/17.18 U6_gg(x1, x2, x3, x4) = U6_gg(x4) 63.56/17.18 63.56/17.18 U4_gg(x1, x2, x3, x4, x5) = U4_gg(x5) 63.56/17.18 63.56/17.18 U2_gg(x1, x2, x3, x4, x5) = U2_gg(x5) 63.56/17.18 63.56/17.18 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x1, x2, x5) 63.56/17.18 63.56/17.18 U5_ag(x1, x2, x3) = U5_ag(x2, x3) 63.56/17.18 63.56/17.18 p_in_aa(x1, x2) = p_in_aa 63.56/17.18 63.56/17.18 p_out_aa(x1, x2) = p_out_aa(x1, x2) 63.56/17.18 63.56/17.18 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 63.56/17.18 63.56/17.18 U3_aa(x1, x2, x3, x4, x5) = U3_aa(x5) 63.56/17.18 63.56/17.18 U5_aa(x1, x2, x3) = U5_aa(x3) 63.56/17.18 63.56/17.18 U6_aa(x1, x2, x3, x4) = U6_aa(x1, x4) 63.56/17.18 63.56/17.18 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x1, x4, x5) 63.56/17.18 63.56/17.18 U2_aa(x1, x2, x3, x4, x5) = U2_aa(x1, x3, x5) 63.56/17.18 63.56/17.18 U6_ag(x1, x2, x3, x4) = U6_ag(x1, x4) 63.56/17.18 63.56/17.18 U2_ag(x1, x2, x3, x4, x5) = U2_ag(x1, x5) 63.56/17.18 63.56/17.18 P_IN_AG(x1, x2) = P_IN_AG(x2) 63.56/17.18 63.56/17.18 U1_AG(x1, x2, x3, x4, x5) = U1_AG(x4, x5) 63.56/17.18 63.56/17.18 U3_AG(x1, x2, x3, x4, x5) = U3_AG(x1, x2, x3, x5) 63.56/17.18 63.56/17.18 P_IN_GG(x1, x2) = P_IN_GG(x1, x2) 63.56/17.18 63.56/17.18 U1_GG(x1, x2, x3, x4, x5) = U1_GG(x2, x4, x5) 63.56/17.18 63.56/17.18 U3_GG(x1, x2, x3, x4, x5) = U3_GG(x2, x3, x5) 63.56/17.18 63.56/17.18 U5_GG(x1, x2, x3) = U5_GG(x2, x3) 63.56/17.18 63.56/17.18 P_IN_GA(x1, x2) = P_IN_GA(x1) 63.56/17.18 63.56/17.18 U1_GA(x1, x2, x3, x4, x5) = U1_GA(x2, x5) 63.56/17.18 63.56/17.18 U3_GA(x1, x2, x3, x4, x5) = U3_GA(x1, x2, x5) 63.56/17.18 63.56/17.18 U5_GA(x1, x2, x3) = U5_GA(x3) 63.56/17.18 63.56/17.18 U6_GA(x1, x2, x3, x4) = U6_GA(x4) 63.56/17.18 63.56/17.18 U4_GA(x1, x2, x3, x4, x5) = U4_GA(x1, x2, x4, x5) 63.56/17.18 63.56/17.18 U2_GA(x1, x2, x3, x4, x5) = U2_GA(x3, x5) 63.56/17.18 63.56/17.18 U6_GG(x1, x2, x3, x4) = U6_GG(x4) 63.56/17.18 63.56/17.18 U4_GG(x1, x2, x3, x4, x5) = U4_GG(x5) 63.56/17.18 63.56/17.18 U2_GG(x1, x2, x3, x4, x5) = U2_GG(x5) 63.56/17.18 63.56/17.18 U4_AG(x1, x2, x3, x4, x5) = U4_AG(x1, x2, x5) 63.56/17.18 63.56/17.18 U5_AG(x1, x2, x3) = U5_AG(x2, x3) 63.56/17.18 63.56/17.18 P_IN_AA(x1, x2) = P_IN_AA 63.56/17.18 63.56/17.18 U1_AA(x1, x2, x3, x4, x5) = U1_AA(x5) 63.56/17.18 63.56/17.18 U3_AA(x1, x2, x3, x4, x5) = U3_AA(x5) 63.56/17.18 63.56/17.18 U5_AA(x1, x2, x3) = U5_AA(x3) 63.56/17.18 63.56/17.18 U6_AA(x1, x2, x3, x4) = U6_AA(x1, x4) 63.56/17.18 63.56/17.18 U4_AA(x1, x2, x3, x4, x5) = U4_AA(x1, x4, x5) 63.56/17.18 63.56/17.18 U2_AA(x1, x2, x3, x4, x5) = U2_AA(x1, x3, x5) 63.56/17.18 63.56/17.18 U6_AG(x1, x2, x3, x4) = U6_AG(x1, x4) 63.56/17.18 63.56/17.18 U2_AG(x1, x2, x3, x4, x5) = U2_AG(x1, x5) 63.56/17.18 63.56/17.18 63.56/17.18 We have to consider all (P,R,Pi)-chains 63.56/17.18 ---------------------------------------- 63.56/17.18 63.56/17.18 (5) DependencyGraphProof (EQUIVALENT) 63.56/17.18 The approximation of the Dependency Graph [LOPSTR] contains 6 SCCs with 25 less nodes. 63.56/17.18 ---------------------------------------- 63.56/17.18 63.56/17.18 (6) 63.56/17.18 Complex Obligation (AND) 63.56/17.18 63.56/17.18 ---------------------------------------- 63.56/17.18 63.56/17.18 (7) 63.56/17.18 Obligation: 63.56/17.18 Pi DP problem: 63.56/17.18 The TRS P consists of the following rules: 63.56/17.18 63.56/17.18 U1_AA(X, Y, DX, DY, p_out_aa(d(e(X)), DX)) -> P_IN_AA(d(e(Y)), DY) 63.56/17.18 P_IN_AA(d(e(+(X, Y))), +(DX, DY)) -> U1_AA(X, Y, DX, DY, p_in_aa(d(e(X)), DX)) 63.56/17.18 P_IN_AA(d(e(+(X, Y))), +(DX, DY)) -> P_IN_AA(d(e(X)), DX) 63.56/17.18 P_IN_AA(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_AA(X, Y, DY, DX, p_in_aa(d(e(X)), DX)) 63.56/17.18 U3_AA(X, Y, DY, DX, p_out_aa(d(e(X)), DX)) -> P_IN_AA(d(e(Y)), DY) 63.56/17.18 P_IN_AA(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> P_IN_AA(d(e(X)), DX) 63.56/17.18 63.56/17.18 The TRS R consists of the following rules: 63.56/17.18 63.56/17.18 p_in_ag(d(e(t)), const(1)) -> p_out_ag(d(e(t)), const(1)) 63.56/17.18 p_in_ag(d(e(const(A))), const(0)) -> p_out_ag(d(e(const(A))), const(0)) 63.56/17.18 p_in_ag(d(e(+(X, Y))), +(DX, DY)) -> U1_ag(X, Y, DX, DY, p_in_ag(d(e(X)), DX)) 63.56/17.18 p_in_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ag(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.18 p_in_gg(d(e(t)), const(1)) -> p_out_gg(d(e(t)), const(1)) 63.56/17.18 p_in_gg(d(e(const(A))), const(0)) -> p_out_gg(d(e(const(A))), const(0)) 63.56/17.18 p_in_gg(d(e(+(X, Y))), +(DX, DY)) -> U1_gg(X, Y, DX, DY, p_in_gg(d(e(X)), DX)) 63.56/17.18 p_in_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_gg(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.18 p_in_gg(d(d(X)), DDX) -> U5_gg(X, DDX, p_in_ga(d(X), DX)) 63.56/17.18 p_in_ga(d(e(t)), const(1)) -> p_out_ga(d(e(t)), const(1)) 63.56/17.18 p_in_ga(d(e(const(A))), const(0)) -> p_out_ga(d(e(const(A))), const(0)) 63.56/17.18 p_in_ga(d(e(+(X, Y))), +(DX, DY)) -> U1_ga(X, Y, DX, DY, p_in_ga(d(e(X)), DX)) 63.56/17.18 p_in_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ga(X, Y, DY, DX, p_in_ga(d(e(X)), DX)) 63.56/17.18 p_in_ga(d(d(X)), DDX) -> U5_ga(X, DDX, p_in_ga(d(X), DX)) 63.56/17.18 U5_ga(X, DDX, p_out_ga(d(X), DX)) -> U6_ga(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.18 U6_ga(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_ga(d(d(X)), DDX) 63.56/17.18 U3_ga(X, Y, DY, DX, p_out_ga(d(e(X)), DX)) -> U4_ga(X, Y, DY, DX, p_in_ga(d(e(Y)), DY)) 63.56/17.18 U4_ga(X, Y, DY, DX, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.18 U1_ga(X, Y, DX, DY, p_out_ga(d(e(X)), DX)) -> U2_ga(X, Y, DX, DY, p_in_ga(d(e(Y)), DY)) 63.56/17.18 U2_ga(X, Y, DX, DY, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(+(X, Y))), +(DX, DY)) 63.56/17.18 U5_gg(X, DDX, p_out_ga(d(X), DX)) -> U6_gg(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.18 U6_gg(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_gg(d(d(X)), DDX) 63.56/17.18 U3_gg(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_gg(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.18 U4_gg(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.18 U1_gg(X, Y, DX, DY, p_out_gg(d(e(X)), DX)) -> U2_gg(X, Y, DX, DY, p_in_gg(d(e(Y)), DY)) 63.56/17.18 U2_gg(X, Y, DX, DY, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(+(X, Y))), +(DX, DY)) 63.56/17.18 U3_ag(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_ag(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.18 U4_ag(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.18 p_in_ag(d(d(X)), DDX) -> U5_ag(X, DDX, p_in_aa(d(X), DX)) 63.56/17.18 p_in_aa(d(e(t)), const(1)) -> p_out_aa(d(e(t)), const(1)) 63.56/17.18 p_in_aa(d(e(const(A))), const(0)) -> p_out_aa(d(e(const(A))), const(0)) 63.56/17.18 p_in_aa(d(e(+(X, Y))), +(DX, DY)) -> U1_aa(X, Y, DX, DY, p_in_aa(d(e(X)), DX)) 63.56/17.18 p_in_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_aa(X, Y, DY, DX, p_in_aa(d(e(X)), DX)) 63.56/17.18 p_in_aa(d(d(X)), DDX) -> U5_aa(X, DDX, p_in_aa(d(X), DX)) 63.56/17.18 U5_aa(X, DDX, p_out_aa(d(X), DX)) -> U6_aa(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.18 U6_aa(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_aa(d(d(X)), DDX) 63.56/17.18 U3_aa(X, Y, DY, DX, p_out_aa(d(e(X)), DX)) -> U4_aa(X, Y, DY, DX, p_in_aa(d(e(Y)), DY)) 63.56/17.18 U4_aa(X, Y, DY, DX, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.18 U1_aa(X, Y, DX, DY, p_out_aa(d(e(X)), DX)) -> U2_aa(X, Y, DX, DY, p_in_aa(d(e(Y)), DY)) 63.56/17.18 U2_aa(X, Y, DX, DY, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(+(X, Y))), +(DX, DY)) 63.56/17.18 U5_ag(X, DDX, p_out_aa(d(X), DX)) -> U6_ag(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.18 U6_ag(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_ag(d(d(X)), DDX) 63.56/17.18 U1_ag(X, Y, DX, DY, p_out_ag(d(e(X)), DX)) -> U2_ag(X, Y, DX, DY, p_in_ag(d(e(Y)), DY)) 63.56/17.18 U2_ag(X, Y, DX, DY, p_out_ag(d(e(Y)), DY)) -> p_out_ag(d(e(+(X, Y))), +(DX, DY)) 63.56/17.18 63.56/17.18 The argument filtering Pi contains the following mapping: 63.56/17.18 p_in_ag(x1, x2) = p_in_ag(x2) 63.56/17.18 63.56/17.18 const(x1) = const 63.56/17.18 63.56/17.18 1 = 1 63.56/17.18 63.56/17.18 p_out_ag(x1, x2) = p_out_ag(x1) 63.56/17.18 63.56/17.18 0 = 0 63.56/17.18 63.56/17.18 +(x1, x2) = +(x1, x2) 63.56/17.18 63.56/17.18 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x4, x5) 63.56/17.18 63.56/17.18 *(x1, x2) = *(x1, x2) 63.56/17.18 63.56/17.18 U3_ag(x1, x2, x3, x4, x5) = U3_ag(x1, x2, x3, x5) 63.56/17.18 63.56/17.18 p_in_gg(x1, x2) = p_in_gg(x1, x2) 63.56/17.18 63.56/17.18 d(x1) = d(x1) 63.56/17.18 63.56/17.18 e(x1) = e(x1) 63.56/17.18 63.56/17.18 t = t 63.56/17.18 63.56/17.18 p_out_gg(x1, x2) = p_out_gg 63.56/17.18 63.56/17.18 U1_gg(x1, x2, x3, x4, x5) = U1_gg(x2, x4, x5) 63.56/17.18 63.56/17.18 U3_gg(x1, x2, x3, x4, x5) = U3_gg(x2, x3, x5) 63.56/17.18 63.56/17.19 U5_gg(x1, x2, x3) = U5_gg(x2, x3) 63.56/17.19 63.56/17.19 p_in_ga(x1, x2) = p_in_ga(x1) 63.56/17.19 63.56/17.19 p_out_ga(x1, x2) = p_out_ga(x2) 63.56/17.19 63.56/17.19 U1_ga(x1, x2, x3, x4, x5) = U1_ga(x2, x5) 63.56/17.19 63.56/17.19 U3_ga(x1, x2, x3, x4, x5) = U3_ga(x1, x2, x5) 63.56/17.19 63.56/17.19 U5_ga(x1, x2, x3) = U5_ga(x3) 63.56/17.19 63.56/17.19 U6_ga(x1, x2, x3, x4) = U6_ga(x4) 63.56/17.19 63.56/17.19 U4_ga(x1, x2, x3, x4, x5) = U4_ga(x1, x2, x4, x5) 63.56/17.19 63.56/17.19 U2_ga(x1, x2, x3, x4, x5) = U2_ga(x3, x5) 63.56/17.19 63.56/17.19 U6_gg(x1, x2, x3, x4) = U6_gg(x4) 63.56/17.19 63.56/17.19 U4_gg(x1, x2, x3, x4, x5) = U4_gg(x5) 63.56/17.19 63.56/17.19 U2_gg(x1, x2, x3, x4, x5) = U2_gg(x5) 63.56/17.19 63.56/17.19 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x1, x2, x5) 63.56/17.19 63.56/17.19 U5_ag(x1, x2, x3) = U5_ag(x2, x3) 63.56/17.19 63.56/17.19 p_in_aa(x1, x2) = p_in_aa 63.56/17.19 63.56/17.19 p_out_aa(x1, x2) = p_out_aa(x1, x2) 63.56/17.19 63.56/17.19 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 63.56/17.19 63.56/17.19 U3_aa(x1, x2, x3, x4, x5) = U3_aa(x5) 63.56/17.19 63.56/17.19 U5_aa(x1, x2, x3) = U5_aa(x3) 63.56/17.19 63.56/17.19 U6_aa(x1, x2, x3, x4) = U6_aa(x1, x4) 63.56/17.19 63.56/17.19 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x1, x4, x5) 63.56/17.19 63.56/17.19 U2_aa(x1, x2, x3, x4, x5) = U2_aa(x1, x3, x5) 63.56/17.19 63.56/17.19 U6_ag(x1, x2, x3, x4) = U6_ag(x1, x4) 63.56/17.19 63.56/17.19 U2_ag(x1, x2, x3, x4, x5) = U2_ag(x1, x5) 63.56/17.19 63.56/17.19 P_IN_AA(x1, x2) = P_IN_AA 63.56/17.19 63.56/17.19 U1_AA(x1, x2, x3, x4, x5) = U1_AA(x5) 63.56/17.19 63.56/17.19 U3_AA(x1, x2, x3, x4, x5) = U3_AA(x5) 63.56/17.19 63.56/17.19 63.56/17.19 We have to consider all (P,R,Pi)-chains 63.56/17.19 ---------------------------------------- 63.56/17.19 63.56/17.19 (8) UsableRulesProof (EQUIVALENT) 63.56/17.19 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 63.56/17.19 ---------------------------------------- 63.56/17.19 63.56/17.19 (9) 63.56/17.19 Obligation: 63.56/17.19 Pi DP problem: 63.56/17.19 The TRS P consists of the following rules: 63.56/17.19 63.56/17.19 U1_AA(X, Y, DX, DY, p_out_aa(d(e(X)), DX)) -> P_IN_AA(d(e(Y)), DY) 63.56/17.19 P_IN_AA(d(e(+(X, Y))), +(DX, DY)) -> U1_AA(X, Y, DX, DY, p_in_aa(d(e(X)), DX)) 63.56/17.19 P_IN_AA(d(e(+(X, Y))), +(DX, DY)) -> P_IN_AA(d(e(X)), DX) 63.56/17.19 P_IN_AA(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_AA(X, Y, DY, DX, p_in_aa(d(e(X)), DX)) 63.56/17.19 U3_AA(X, Y, DY, DX, p_out_aa(d(e(X)), DX)) -> P_IN_AA(d(e(Y)), DY) 63.56/17.19 P_IN_AA(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> P_IN_AA(d(e(X)), DX) 63.56/17.19 63.56/17.19 The TRS R consists of the following rules: 63.56/17.19 63.56/17.19 p_in_aa(d(e(t)), const(1)) -> p_out_aa(d(e(t)), const(1)) 63.56/17.19 p_in_aa(d(e(const(A))), const(0)) -> p_out_aa(d(e(const(A))), const(0)) 63.56/17.19 p_in_aa(d(e(+(X, Y))), +(DX, DY)) -> U1_aa(X, Y, DX, DY, p_in_aa(d(e(X)), DX)) 63.56/17.19 p_in_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_aa(X, Y, DY, DX, p_in_aa(d(e(X)), DX)) 63.56/17.19 U1_aa(X, Y, DX, DY, p_out_aa(d(e(X)), DX)) -> U2_aa(X, Y, DX, DY, p_in_aa(d(e(Y)), DY)) 63.56/17.19 U3_aa(X, Y, DY, DX, p_out_aa(d(e(X)), DX)) -> U4_aa(X, Y, DY, DX, p_in_aa(d(e(Y)), DY)) 63.56/17.19 U2_aa(X, Y, DX, DY, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(+(X, Y))), +(DX, DY)) 63.56/17.19 U4_aa(X, Y, DY, DX, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.19 63.56/17.19 The argument filtering Pi contains the following mapping: 63.56/17.19 const(x1) = const 63.56/17.19 63.56/17.19 1 = 1 63.56/17.19 63.56/17.19 0 = 0 63.56/17.19 63.56/17.19 +(x1, x2) = +(x1, x2) 63.56/17.19 63.56/17.19 *(x1, x2) = *(x1, x2) 63.56/17.19 63.56/17.19 d(x1) = d(x1) 63.56/17.19 63.56/17.19 e(x1) = e(x1) 63.56/17.19 63.56/17.19 t = t 63.56/17.19 63.56/17.19 p_in_aa(x1, x2) = p_in_aa 63.56/17.19 63.56/17.19 p_out_aa(x1, x2) = p_out_aa(x1, x2) 63.56/17.19 63.56/17.19 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 63.56/17.19 63.56/17.19 U3_aa(x1, x2, x3, x4, x5) = U3_aa(x5) 63.56/17.19 63.56/17.19 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x1, x4, x5) 63.56/17.19 63.56/17.19 U2_aa(x1, x2, x3, x4, x5) = U2_aa(x1, x3, x5) 63.56/17.19 63.56/17.19 P_IN_AA(x1, x2) = P_IN_AA 63.56/17.19 63.56/17.19 U1_AA(x1, x2, x3, x4, x5) = U1_AA(x5) 63.56/17.19 63.56/17.19 U3_AA(x1, x2, x3, x4, x5) = U3_AA(x5) 63.56/17.19 63.56/17.19 63.56/17.19 We have to consider all (P,R,Pi)-chains 63.56/17.19 ---------------------------------------- 63.56/17.19 63.56/17.19 (10) PiDPToQDPProof (SOUND) 63.56/17.19 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 63.56/17.19 ---------------------------------------- 63.56/17.19 63.56/17.19 (11) 63.56/17.19 Obligation: 63.56/17.19 Q DP problem: 63.56/17.19 The TRS P consists of the following rules: 63.56/17.19 63.56/17.19 U1_AA(p_out_aa(d(e(X)), DX)) -> P_IN_AA 63.56/17.19 P_IN_AA -> U1_AA(p_in_aa) 63.56/17.19 P_IN_AA -> P_IN_AA 63.56/17.19 P_IN_AA -> U3_AA(p_in_aa) 63.56/17.19 U3_AA(p_out_aa(d(e(X)), DX)) -> P_IN_AA 63.56/17.19 63.56/17.19 The TRS R consists of the following rules: 63.56/17.19 63.56/17.19 p_in_aa -> p_out_aa(d(e(t)), const) 63.56/17.19 p_in_aa -> p_out_aa(d(e(const)), const) 63.56/17.19 p_in_aa -> U1_aa(p_in_aa) 63.56/17.19 p_in_aa -> U3_aa(p_in_aa) 63.56/17.19 U1_aa(p_out_aa(d(e(X)), DX)) -> U2_aa(X, DX, p_in_aa) 63.56/17.19 U3_aa(p_out_aa(d(e(X)), DX)) -> U4_aa(X, DX, p_in_aa) 63.56/17.19 U2_aa(X, DX, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(+(X, Y))), +(DX, DY)) 63.56/17.19 U4_aa(X, DX, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.19 63.56/17.19 The set Q consists of the following terms: 63.56/17.19 63.56/17.19 p_in_aa 63.56/17.19 U1_aa(x0) 63.56/17.19 U3_aa(x0) 63.56/17.19 U2_aa(x0, x1, x2) 63.56/17.19 U4_aa(x0, x1, x2) 63.56/17.19 63.56/17.19 We have to consider all (P,Q,R)-chains. 63.56/17.19 ---------------------------------------- 63.56/17.19 63.56/17.19 (12) TransformationProof (SOUND) 63.56/17.19 By narrowing [LPAR04] the rule P_IN_AA -> U1_AA(p_in_aa) at position [0] we obtained the following new rules [LPAR04]: 63.56/17.19 63.56/17.19 (P_IN_AA -> U1_AA(p_out_aa(d(e(t)), const)),P_IN_AA -> U1_AA(p_out_aa(d(e(t)), const))) 63.56/17.19 (P_IN_AA -> U1_AA(p_out_aa(d(e(const)), const)),P_IN_AA -> U1_AA(p_out_aa(d(e(const)), const))) 63.56/17.19 (P_IN_AA -> U1_AA(U1_aa(p_in_aa)),P_IN_AA -> U1_AA(U1_aa(p_in_aa))) 63.56/17.19 (P_IN_AA -> U1_AA(U3_aa(p_in_aa)),P_IN_AA -> U1_AA(U3_aa(p_in_aa))) 63.56/17.19 63.56/17.19 63.56/17.19 ---------------------------------------- 63.56/17.19 63.56/17.19 (13) 63.56/17.19 Obligation: 63.56/17.19 Q DP problem: 63.56/17.19 The TRS P consists of the following rules: 63.56/17.19 63.56/17.19 U1_AA(p_out_aa(d(e(X)), DX)) -> P_IN_AA 63.56/17.19 P_IN_AA -> P_IN_AA 63.56/17.19 P_IN_AA -> U3_AA(p_in_aa) 63.56/17.19 U3_AA(p_out_aa(d(e(X)), DX)) -> P_IN_AA 63.56/17.19 P_IN_AA -> U1_AA(p_out_aa(d(e(t)), const)) 63.56/17.19 P_IN_AA -> U1_AA(p_out_aa(d(e(const)), const)) 63.56/17.19 P_IN_AA -> U1_AA(U1_aa(p_in_aa)) 63.56/17.19 P_IN_AA -> U1_AA(U3_aa(p_in_aa)) 63.56/17.19 63.56/17.19 The TRS R consists of the following rules: 63.56/17.19 63.56/17.19 p_in_aa -> p_out_aa(d(e(t)), const) 63.56/17.19 p_in_aa -> p_out_aa(d(e(const)), const) 63.56/17.19 p_in_aa -> U1_aa(p_in_aa) 63.56/17.19 p_in_aa -> U3_aa(p_in_aa) 63.56/17.19 U1_aa(p_out_aa(d(e(X)), DX)) -> U2_aa(X, DX, p_in_aa) 63.56/17.19 U3_aa(p_out_aa(d(e(X)), DX)) -> U4_aa(X, DX, p_in_aa) 63.56/17.19 U2_aa(X, DX, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(+(X, Y))), +(DX, DY)) 63.56/17.19 U4_aa(X, DX, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.19 63.56/17.19 The set Q consists of the following terms: 63.56/17.19 63.56/17.19 p_in_aa 63.56/17.19 U1_aa(x0) 63.56/17.19 U3_aa(x0) 63.56/17.19 U2_aa(x0, x1, x2) 63.56/17.19 U4_aa(x0, x1, x2) 63.56/17.19 63.56/17.19 We have to consider all (P,Q,R)-chains. 63.56/17.19 ---------------------------------------- 63.56/17.19 63.56/17.19 (14) TransformationProof (SOUND) 63.56/17.19 By narrowing [LPAR04] the rule P_IN_AA -> U3_AA(p_in_aa) at position [0] we obtained the following new rules [LPAR04]: 63.56/17.19 63.56/17.19 (P_IN_AA -> U3_AA(p_out_aa(d(e(t)), const)),P_IN_AA -> U3_AA(p_out_aa(d(e(t)), const))) 63.56/17.19 (P_IN_AA -> U3_AA(p_out_aa(d(e(const)), const)),P_IN_AA -> U3_AA(p_out_aa(d(e(const)), const))) 63.56/17.19 (P_IN_AA -> U3_AA(U1_aa(p_in_aa)),P_IN_AA -> U3_AA(U1_aa(p_in_aa))) 63.56/17.19 (P_IN_AA -> U3_AA(U3_aa(p_in_aa)),P_IN_AA -> U3_AA(U3_aa(p_in_aa))) 63.56/17.19 63.56/17.19 63.56/17.19 ---------------------------------------- 63.56/17.19 63.56/17.19 (15) 63.56/17.19 Obligation: 63.56/17.19 Q DP problem: 63.56/17.19 The TRS P consists of the following rules: 63.56/17.19 63.56/17.19 U1_AA(p_out_aa(d(e(X)), DX)) -> P_IN_AA 63.56/17.19 P_IN_AA -> P_IN_AA 63.56/17.19 U3_AA(p_out_aa(d(e(X)), DX)) -> P_IN_AA 63.56/17.19 P_IN_AA -> U1_AA(p_out_aa(d(e(t)), const)) 63.56/17.19 P_IN_AA -> U1_AA(p_out_aa(d(e(const)), const)) 63.56/17.19 P_IN_AA -> U1_AA(U1_aa(p_in_aa)) 63.56/17.19 P_IN_AA -> U1_AA(U3_aa(p_in_aa)) 63.56/17.19 P_IN_AA -> U3_AA(p_out_aa(d(e(t)), const)) 63.56/17.19 P_IN_AA -> U3_AA(p_out_aa(d(e(const)), const)) 63.56/17.19 P_IN_AA -> U3_AA(U1_aa(p_in_aa)) 63.56/17.19 P_IN_AA -> U3_AA(U3_aa(p_in_aa)) 63.56/17.19 63.56/17.19 The TRS R consists of the following rules: 63.56/17.19 63.56/17.19 p_in_aa -> p_out_aa(d(e(t)), const) 63.56/17.19 p_in_aa -> p_out_aa(d(e(const)), const) 63.56/17.19 p_in_aa -> U1_aa(p_in_aa) 63.56/17.19 p_in_aa -> U3_aa(p_in_aa) 63.56/17.19 U1_aa(p_out_aa(d(e(X)), DX)) -> U2_aa(X, DX, p_in_aa) 63.56/17.19 U3_aa(p_out_aa(d(e(X)), DX)) -> U4_aa(X, DX, p_in_aa) 63.56/17.19 U2_aa(X, DX, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(+(X, Y))), +(DX, DY)) 63.56/17.19 U4_aa(X, DX, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.19 63.56/17.19 The set Q consists of the following terms: 63.56/17.19 63.56/17.19 p_in_aa 63.56/17.19 U1_aa(x0) 63.56/17.19 U3_aa(x0) 63.56/17.19 U2_aa(x0, x1, x2) 63.56/17.19 U4_aa(x0, x1, x2) 63.56/17.19 63.56/17.19 We have to consider all (P,Q,R)-chains. 63.56/17.19 ---------------------------------------- 63.56/17.19 63.56/17.19 (16) 63.56/17.19 Obligation: 63.56/17.19 Pi DP problem: 63.56/17.19 The TRS P consists of the following rules: 63.56/17.19 63.56/17.19 U1_GA(X, Y, DX, DY, p_out_ga(d(e(X)), DX)) -> P_IN_GA(d(e(Y)), DY) 63.56/17.19 P_IN_GA(d(e(+(X, Y))), +(DX, DY)) -> U1_GA(X, Y, DX, DY, p_in_ga(d(e(X)), DX)) 63.56/17.19 P_IN_GA(d(e(+(X, Y))), +(DX, DY)) -> P_IN_GA(d(e(X)), DX) 63.56/17.19 P_IN_GA(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_GA(X, Y, DY, DX, p_in_ga(d(e(X)), DX)) 63.56/17.19 U3_GA(X, Y, DY, DX, p_out_ga(d(e(X)), DX)) -> P_IN_GA(d(e(Y)), DY) 63.56/17.19 P_IN_GA(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> P_IN_GA(d(e(X)), DX) 63.56/17.19 63.56/17.19 The TRS R consists of the following rules: 63.56/17.19 63.56/17.19 p_in_ag(d(e(t)), const(1)) -> p_out_ag(d(e(t)), const(1)) 63.56/17.19 p_in_ag(d(e(const(A))), const(0)) -> p_out_ag(d(e(const(A))), const(0)) 63.56/17.19 p_in_ag(d(e(+(X, Y))), +(DX, DY)) -> U1_ag(X, Y, DX, DY, p_in_ag(d(e(X)), DX)) 63.56/17.19 p_in_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ag(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.19 p_in_gg(d(e(t)), const(1)) -> p_out_gg(d(e(t)), const(1)) 63.56/17.19 p_in_gg(d(e(const(A))), const(0)) -> p_out_gg(d(e(const(A))), const(0)) 63.56/17.19 p_in_gg(d(e(+(X, Y))), +(DX, DY)) -> U1_gg(X, Y, DX, DY, p_in_gg(d(e(X)), DX)) 63.56/17.19 p_in_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_gg(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.19 p_in_gg(d(d(X)), DDX) -> U5_gg(X, DDX, p_in_ga(d(X), DX)) 63.56/17.19 p_in_ga(d(e(t)), const(1)) -> p_out_ga(d(e(t)), const(1)) 63.56/17.19 p_in_ga(d(e(const(A))), const(0)) -> p_out_ga(d(e(const(A))), const(0)) 63.56/17.19 p_in_ga(d(e(+(X, Y))), +(DX, DY)) -> U1_ga(X, Y, DX, DY, p_in_ga(d(e(X)), DX)) 63.56/17.19 p_in_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ga(X, Y, DY, DX, p_in_ga(d(e(X)), DX)) 63.56/17.19 p_in_ga(d(d(X)), DDX) -> U5_ga(X, DDX, p_in_ga(d(X), DX)) 63.56/17.19 U5_ga(X, DDX, p_out_ga(d(X), DX)) -> U6_ga(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.19 U6_ga(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_ga(d(d(X)), DDX) 63.56/17.19 U3_ga(X, Y, DY, DX, p_out_ga(d(e(X)), DX)) -> U4_ga(X, Y, DY, DX, p_in_ga(d(e(Y)), DY)) 63.56/17.19 U4_ga(X, Y, DY, DX, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.19 U1_ga(X, Y, DX, DY, p_out_ga(d(e(X)), DX)) -> U2_ga(X, Y, DX, DY, p_in_ga(d(e(Y)), DY)) 63.56/17.19 U2_ga(X, Y, DX, DY, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(+(X, Y))), +(DX, DY)) 63.56/17.19 U5_gg(X, DDX, p_out_ga(d(X), DX)) -> U6_gg(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.19 U6_gg(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_gg(d(d(X)), DDX) 63.56/17.19 U3_gg(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_gg(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.19 U4_gg(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.19 U1_gg(X, Y, DX, DY, p_out_gg(d(e(X)), DX)) -> U2_gg(X, Y, DX, DY, p_in_gg(d(e(Y)), DY)) 63.56/17.19 U2_gg(X, Y, DX, DY, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(+(X, Y))), +(DX, DY)) 63.56/17.19 U3_ag(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_ag(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.19 U4_ag(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.19 p_in_ag(d(d(X)), DDX) -> U5_ag(X, DDX, p_in_aa(d(X), DX)) 63.56/17.19 p_in_aa(d(e(t)), const(1)) -> p_out_aa(d(e(t)), const(1)) 63.56/17.19 p_in_aa(d(e(const(A))), const(0)) -> p_out_aa(d(e(const(A))), const(0)) 63.56/17.19 p_in_aa(d(e(+(X, Y))), +(DX, DY)) -> U1_aa(X, Y, DX, DY, p_in_aa(d(e(X)), DX)) 63.56/17.19 p_in_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_aa(X, Y, DY, DX, p_in_aa(d(e(X)), DX)) 63.56/17.19 p_in_aa(d(d(X)), DDX) -> U5_aa(X, DDX, p_in_aa(d(X), DX)) 63.56/17.19 U5_aa(X, DDX, p_out_aa(d(X), DX)) -> U6_aa(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.19 U6_aa(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_aa(d(d(X)), DDX) 63.56/17.19 U3_aa(X, Y, DY, DX, p_out_aa(d(e(X)), DX)) -> U4_aa(X, Y, DY, DX, p_in_aa(d(e(Y)), DY)) 63.56/17.19 U4_aa(X, Y, DY, DX, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.19 U1_aa(X, Y, DX, DY, p_out_aa(d(e(X)), DX)) -> U2_aa(X, Y, DX, DY, p_in_aa(d(e(Y)), DY)) 63.56/17.19 U2_aa(X, Y, DX, DY, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(+(X, Y))), +(DX, DY)) 63.56/17.19 U5_ag(X, DDX, p_out_aa(d(X), DX)) -> U6_ag(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.19 U6_ag(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_ag(d(d(X)), DDX) 63.56/17.19 U1_ag(X, Y, DX, DY, p_out_ag(d(e(X)), DX)) -> U2_ag(X, Y, DX, DY, p_in_ag(d(e(Y)), DY)) 63.56/17.19 U2_ag(X, Y, DX, DY, p_out_ag(d(e(Y)), DY)) -> p_out_ag(d(e(+(X, Y))), +(DX, DY)) 63.56/17.19 63.56/17.19 The argument filtering Pi contains the following mapping: 63.56/17.19 p_in_ag(x1, x2) = p_in_ag(x2) 63.56/17.19 63.56/17.19 const(x1) = const 63.56/17.19 63.56/17.19 1 = 1 63.56/17.19 63.56/17.19 p_out_ag(x1, x2) = p_out_ag(x1) 63.56/17.19 63.56/17.19 0 = 0 63.56/17.19 63.56/17.19 +(x1, x2) = +(x1, x2) 63.56/17.19 63.56/17.19 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x4, x5) 63.56/17.19 63.56/17.19 *(x1, x2) = *(x1, x2) 63.56/17.19 63.56/17.19 U3_ag(x1, x2, x3, x4, x5) = U3_ag(x1, x2, x3, x5) 63.56/17.19 63.56/17.19 p_in_gg(x1, x2) = p_in_gg(x1, x2) 63.56/17.19 63.56/17.19 d(x1) = d(x1) 63.56/17.19 63.56/17.19 e(x1) = e(x1) 63.56/17.19 63.56/17.19 t = t 63.56/17.19 63.56/17.19 p_out_gg(x1, x2) = p_out_gg 63.56/17.19 63.56/17.19 U1_gg(x1, x2, x3, x4, x5) = U1_gg(x2, x4, x5) 63.56/17.19 63.56/17.19 U3_gg(x1, x2, x3, x4, x5) = U3_gg(x2, x3, x5) 63.56/17.19 63.56/17.19 U5_gg(x1, x2, x3) = U5_gg(x2, x3) 63.56/17.19 63.56/17.19 p_in_ga(x1, x2) = p_in_ga(x1) 63.56/17.19 63.56/17.19 p_out_ga(x1, x2) = p_out_ga(x2) 63.56/17.19 63.56/17.19 U1_ga(x1, x2, x3, x4, x5) = U1_ga(x2, x5) 63.56/17.19 63.56/17.19 U3_ga(x1, x2, x3, x4, x5) = U3_ga(x1, x2, x5) 63.56/17.19 63.56/17.19 U5_ga(x1, x2, x3) = U5_ga(x3) 63.56/17.19 63.56/17.19 U6_ga(x1, x2, x3, x4) = U6_ga(x4) 63.56/17.19 63.56/17.19 U4_ga(x1, x2, x3, x4, x5) = U4_ga(x1, x2, x4, x5) 63.56/17.19 63.56/17.19 U2_ga(x1, x2, x3, x4, x5) = U2_ga(x3, x5) 63.56/17.19 63.56/17.19 U6_gg(x1, x2, x3, x4) = U6_gg(x4) 63.56/17.19 63.56/17.19 U4_gg(x1, x2, x3, x4, x5) = U4_gg(x5) 63.56/17.19 63.56/17.19 U2_gg(x1, x2, x3, x4, x5) = U2_gg(x5) 63.56/17.19 63.56/17.19 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x1, x2, x5) 63.56/17.19 63.56/17.19 U5_ag(x1, x2, x3) = U5_ag(x2, x3) 63.56/17.19 63.56/17.19 p_in_aa(x1, x2) = p_in_aa 63.56/17.19 63.56/17.19 p_out_aa(x1, x2) = p_out_aa(x1, x2) 63.56/17.19 63.56/17.19 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 63.56/17.19 63.56/17.19 U3_aa(x1, x2, x3, x4, x5) = U3_aa(x5) 63.56/17.19 63.56/17.19 U5_aa(x1, x2, x3) = U5_aa(x3) 63.56/17.19 63.56/17.19 U6_aa(x1, x2, x3, x4) = U6_aa(x1, x4) 63.56/17.19 63.56/17.19 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x1, x4, x5) 63.56/17.19 63.56/17.19 U2_aa(x1, x2, x3, x4, x5) = U2_aa(x1, x3, x5) 63.56/17.19 63.56/17.19 U6_ag(x1, x2, x3, x4) = U6_ag(x1, x4) 63.56/17.19 63.56/17.19 U2_ag(x1, x2, x3, x4, x5) = U2_ag(x1, x5) 63.56/17.19 63.56/17.19 P_IN_GA(x1, x2) = P_IN_GA(x1) 63.56/17.19 63.56/17.19 U1_GA(x1, x2, x3, x4, x5) = U1_GA(x2, x5) 63.56/17.19 63.56/17.19 U3_GA(x1, x2, x3, x4, x5) = U3_GA(x1, x2, x5) 63.56/17.19 63.56/17.19 63.56/17.19 We have to consider all (P,R,Pi)-chains 63.56/17.19 ---------------------------------------- 63.56/17.19 63.56/17.19 (17) UsableRulesProof (EQUIVALENT) 63.56/17.19 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 63.56/17.19 ---------------------------------------- 63.56/17.19 63.56/17.19 (18) 63.56/17.19 Obligation: 63.56/17.19 Pi DP problem: 63.56/17.19 The TRS P consists of the following rules: 63.56/17.19 63.56/17.19 U1_GA(X, Y, DX, DY, p_out_ga(d(e(X)), DX)) -> P_IN_GA(d(e(Y)), DY) 63.56/17.19 P_IN_GA(d(e(+(X, Y))), +(DX, DY)) -> U1_GA(X, Y, DX, DY, p_in_ga(d(e(X)), DX)) 63.56/17.19 P_IN_GA(d(e(+(X, Y))), +(DX, DY)) -> P_IN_GA(d(e(X)), DX) 63.56/17.19 P_IN_GA(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_GA(X, Y, DY, DX, p_in_ga(d(e(X)), DX)) 63.56/17.19 U3_GA(X, Y, DY, DX, p_out_ga(d(e(X)), DX)) -> P_IN_GA(d(e(Y)), DY) 63.56/17.19 P_IN_GA(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> P_IN_GA(d(e(X)), DX) 63.56/17.19 63.56/17.19 The TRS R consists of the following rules: 63.56/17.19 63.56/17.19 p_in_ga(d(e(t)), const(1)) -> p_out_ga(d(e(t)), const(1)) 63.56/17.19 p_in_ga(d(e(const(A))), const(0)) -> p_out_ga(d(e(const(A))), const(0)) 63.56/17.19 p_in_ga(d(e(+(X, Y))), +(DX, DY)) -> U1_ga(X, Y, DX, DY, p_in_ga(d(e(X)), DX)) 63.56/17.19 p_in_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ga(X, Y, DY, DX, p_in_ga(d(e(X)), DX)) 63.56/17.19 U1_ga(X, Y, DX, DY, p_out_ga(d(e(X)), DX)) -> U2_ga(X, Y, DX, DY, p_in_ga(d(e(Y)), DY)) 63.56/17.19 U3_ga(X, Y, DY, DX, p_out_ga(d(e(X)), DX)) -> U4_ga(X, Y, DY, DX, p_in_ga(d(e(Y)), DY)) 63.56/17.19 U2_ga(X, Y, DX, DY, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(+(X, Y))), +(DX, DY)) 63.56/17.19 U4_ga(X, Y, DY, DX, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.19 63.56/17.19 The argument filtering Pi contains the following mapping: 63.56/17.19 const(x1) = const 63.56/17.19 63.56/17.19 1 = 1 63.56/17.19 63.56/17.19 0 = 0 63.56/17.19 63.56/17.19 +(x1, x2) = +(x1, x2) 63.56/17.19 63.56/17.19 *(x1, x2) = *(x1, x2) 63.56/17.19 63.56/17.19 d(x1) = d(x1) 63.56/17.19 63.56/17.19 e(x1) = e(x1) 63.56/17.19 63.56/17.19 t = t 63.56/17.19 63.56/17.19 p_in_ga(x1, x2) = p_in_ga(x1) 63.56/17.19 63.56/17.19 p_out_ga(x1, x2) = p_out_ga(x2) 63.56/17.19 63.56/17.19 U1_ga(x1, x2, x3, x4, x5) = U1_ga(x2, x5) 63.56/17.19 63.56/17.19 U3_ga(x1, x2, x3, x4, x5) = U3_ga(x1, x2, x5) 63.56/17.19 63.56/17.19 U4_ga(x1, x2, x3, x4, x5) = U4_ga(x1, x2, x4, x5) 63.56/17.19 63.56/17.19 U2_ga(x1, x2, x3, x4, x5) = U2_ga(x3, x5) 63.56/17.19 63.56/17.19 P_IN_GA(x1, x2) = P_IN_GA(x1) 63.56/17.19 63.56/17.19 U1_GA(x1, x2, x3, x4, x5) = U1_GA(x2, x5) 63.56/17.19 63.56/17.19 U3_GA(x1, x2, x3, x4, x5) = U3_GA(x1, x2, x5) 63.56/17.19 63.56/17.19 63.56/17.19 We have to consider all (P,R,Pi)-chains 63.56/17.19 ---------------------------------------- 63.56/17.19 63.56/17.19 (19) 63.56/17.19 Obligation: 63.56/17.19 Pi DP problem: 63.56/17.19 The TRS P consists of the following rules: 63.56/17.19 63.56/17.19 P_IN_AA(d(d(X)), DDX) -> P_IN_AA(d(X), DX) 63.56/17.19 63.56/17.19 The TRS R consists of the following rules: 63.56/17.19 63.56/17.19 p_in_ag(d(e(t)), const(1)) -> p_out_ag(d(e(t)), const(1)) 63.56/17.19 p_in_ag(d(e(const(A))), const(0)) -> p_out_ag(d(e(const(A))), const(0)) 63.56/17.19 p_in_ag(d(e(+(X, Y))), +(DX, DY)) -> U1_ag(X, Y, DX, DY, p_in_ag(d(e(X)), DX)) 63.56/17.19 p_in_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ag(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.19 p_in_gg(d(e(t)), const(1)) -> p_out_gg(d(e(t)), const(1)) 63.56/17.19 p_in_gg(d(e(const(A))), const(0)) -> p_out_gg(d(e(const(A))), const(0)) 63.56/17.19 p_in_gg(d(e(+(X, Y))), +(DX, DY)) -> U1_gg(X, Y, DX, DY, p_in_gg(d(e(X)), DX)) 63.56/17.19 p_in_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_gg(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.19 p_in_gg(d(d(X)), DDX) -> U5_gg(X, DDX, p_in_ga(d(X), DX)) 63.56/17.19 p_in_ga(d(e(t)), const(1)) -> p_out_ga(d(e(t)), const(1)) 63.56/17.19 p_in_ga(d(e(const(A))), const(0)) -> p_out_ga(d(e(const(A))), const(0)) 63.56/17.19 p_in_ga(d(e(+(X, Y))), +(DX, DY)) -> U1_ga(X, Y, DX, DY, p_in_ga(d(e(X)), DX)) 63.56/17.19 p_in_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ga(X, Y, DY, DX, p_in_ga(d(e(X)), DX)) 63.56/17.19 p_in_ga(d(d(X)), DDX) -> U5_ga(X, DDX, p_in_ga(d(X), DX)) 63.56/17.19 U5_ga(X, DDX, p_out_ga(d(X), DX)) -> U6_ga(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.19 U6_ga(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_ga(d(d(X)), DDX) 63.56/17.19 U3_ga(X, Y, DY, DX, p_out_ga(d(e(X)), DX)) -> U4_ga(X, Y, DY, DX, p_in_ga(d(e(Y)), DY)) 63.56/17.19 U4_ga(X, Y, DY, DX, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.19 U1_ga(X, Y, DX, DY, p_out_ga(d(e(X)), DX)) -> U2_ga(X, Y, DX, DY, p_in_ga(d(e(Y)), DY)) 63.56/17.19 U2_ga(X, Y, DX, DY, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(+(X, Y))), +(DX, DY)) 63.56/17.19 U5_gg(X, DDX, p_out_ga(d(X), DX)) -> U6_gg(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.19 U6_gg(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_gg(d(d(X)), DDX) 63.56/17.19 U3_gg(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_gg(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.19 U4_gg(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.19 U1_gg(X, Y, DX, DY, p_out_gg(d(e(X)), DX)) -> U2_gg(X, Y, DX, DY, p_in_gg(d(e(Y)), DY)) 63.56/17.19 U2_gg(X, Y, DX, DY, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(+(X, Y))), +(DX, DY)) 63.56/17.19 U3_ag(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_ag(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.19 U4_ag(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.19 p_in_ag(d(d(X)), DDX) -> U5_ag(X, DDX, p_in_aa(d(X), DX)) 63.56/17.19 p_in_aa(d(e(t)), const(1)) -> p_out_aa(d(e(t)), const(1)) 63.56/17.19 p_in_aa(d(e(const(A))), const(0)) -> p_out_aa(d(e(const(A))), const(0)) 63.56/17.19 p_in_aa(d(e(+(X, Y))), +(DX, DY)) -> U1_aa(X, Y, DX, DY, p_in_aa(d(e(X)), DX)) 63.56/17.19 p_in_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_aa(X, Y, DY, DX, p_in_aa(d(e(X)), DX)) 63.56/17.19 p_in_aa(d(d(X)), DDX) -> U5_aa(X, DDX, p_in_aa(d(X), DX)) 63.56/17.19 U5_aa(X, DDX, p_out_aa(d(X), DX)) -> U6_aa(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.19 U6_aa(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_aa(d(d(X)), DDX) 63.56/17.19 U3_aa(X, Y, DY, DX, p_out_aa(d(e(X)), DX)) -> U4_aa(X, Y, DY, DX, p_in_aa(d(e(Y)), DY)) 63.56/17.19 U4_aa(X, Y, DY, DX, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.19 U1_aa(X, Y, DX, DY, p_out_aa(d(e(X)), DX)) -> U2_aa(X, Y, DX, DY, p_in_aa(d(e(Y)), DY)) 63.56/17.19 U2_aa(X, Y, DX, DY, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(+(X, Y))), +(DX, DY)) 63.56/17.19 U5_ag(X, DDX, p_out_aa(d(X), DX)) -> U6_ag(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.19 U6_ag(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_ag(d(d(X)), DDX) 63.56/17.19 U1_ag(X, Y, DX, DY, p_out_ag(d(e(X)), DX)) -> U2_ag(X, Y, DX, DY, p_in_ag(d(e(Y)), DY)) 63.56/17.19 U2_ag(X, Y, DX, DY, p_out_ag(d(e(Y)), DY)) -> p_out_ag(d(e(+(X, Y))), +(DX, DY)) 63.56/17.19 63.56/17.19 The argument filtering Pi contains the following mapping: 63.56/17.19 p_in_ag(x1, x2) = p_in_ag(x2) 63.56/17.19 63.56/17.19 const(x1) = const 63.56/17.19 63.56/17.19 1 = 1 63.56/17.19 63.56/17.19 p_out_ag(x1, x2) = p_out_ag(x1) 63.56/17.19 63.56/17.19 0 = 0 63.56/17.19 63.56/17.19 +(x1, x2) = +(x1, x2) 63.56/17.20 63.56/17.20 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x4, x5) 63.56/17.20 63.56/17.20 *(x1, x2) = *(x1, x2) 63.56/17.20 63.56/17.20 U3_ag(x1, x2, x3, x4, x5) = U3_ag(x1, x2, x3, x5) 63.56/17.20 63.56/17.20 p_in_gg(x1, x2) = p_in_gg(x1, x2) 63.56/17.20 63.56/17.20 d(x1) = d(x1) 63.56/17.20 63.56/17.20 e(x1) = e(x1) 63.56/17.20 63.56/17.20 t = t 63.56/17.20 63.56/17.20 p_out_gg(x1, x2) = p_out_gg 63.56/17.20 63.56/17.20 U1_gg(x1, x2, x3, x4, x5) = U1_gg(x2, x4, x5) 63.56/17.20 63.56/17.20 U3_gg(x1, x2, x3, x4, x5) = U3_gg(x2, x3, x5) 63.56/17.20 63.56/17.20 U5_gg(x1, x2, x3) = U5_gg(x2, x3) 63.56/17.20 63.56/17.20 p_in_ga(x1, x2) = p_in_ga(x1) 63.56/17.20 63.56/17.20 p_out_ga(x1, x2) = p_out_ga(x2) 63.56/17.20 63.56/17.20 U1_ga(x1, x2, x3, x4, x5) = U1_ga(x2, x5) 63.56/17.20 63.56/17.20 U3_ga(x1, x2, x3, x4, x5) = U3_ga(x1, x2, x5) 63.56/17.20 63.56/17.20 U5_ga(x1, x2, x3) = U5_ga(x3) 63.56/17.20 63.56/17.20 U6_ga(x1, x2, x3, x4) = U6_ga(x4) 63.56/17.20 63.56/17.20 U4_ga(x1, x2, x3, x4, x5) = U4_ga(x1, x2, x4, x5) 63.56/17.20 63.56/17.20 U2_ga(x1, x2, x3, x4, x5) = U2_ga(x3, x5) 63.56/17.20 63.56/17.20 U6_gg(x1, x2, x3, x4) = U6_gg(x4) 63.56/17.20 63.56/17.20 U4_gg(x1, x2, x3, x4, x5) = U4_gg(x5) 63.56/17.20 63.56/17.20 U2_gg(x1, x2, x3, x4, x5) = U2_gg(x5) 63.56/17.20 63.56/17.20 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x1, x2, x5) 63.56/17.20 63.56/17.20 U5_ag(x1, x2, x3) = U5_ag(x2, x3) 63.56/17.20 63.56/17.20 p_in_aa(x1, x2) = p_in_aa 63.56/17.20 63.56/17.20 p_out_aa(x1, x2) = p_out_aa(x1, x2) 63.56/17.20 63.56/17.20 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 63.56/17.20 63.56/17.20 U3_aa(x1, x2, x3, x4, x5) = U3_aa(x5) 63.56/17.20 63.56/17.20 U5_aa(x1, x2, x3) = U5_aa(x3) 63.56/17.20 63.56/17.20 U6_aa(x1, x2, x3, x4) = U6_aa(x1, x4) 63.56/17.20 63.56/17.20 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x1, x4, x5) 63.56/17.20 63.56/17.20 U2_aa(x1, x2, x3, x4, x5) = U2_aa(x1, x3, x5) 63.56/17.20 63.56/17.20 U6_ag(x1, x2, x3, x4) = U6_ag(x1, x4) 63.56/17.20 63.56/17.20 U2_ag(x1, x2, x3, x4, x5) = U2_ag(x1, x5) 63.56/17.20 63.56/17.20 P_IN_AA(x1, x2) = P_IN_AA 63.56/17.20 63.56/17.20 63.56/17.20 We have to consider all (P,R,Pi)-chains 63.56/17.20 ---------------------------------------- 63.56/17.20 63.56/17.20 (20) UsableRulesProof (EQUIVALENT) 63.56/17.20 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 63.56/17.20 ---------------------------------------- 63.56/17.20 63.56/17.20 (21) 63.56/17.20 Obligation: 63.56/17.20 Pi DP problem: 63.56/17.20 The TRS P consists of the following rules: 63.56/17.20 63.56/17.20 P_IN_AA(d(d(X)), DDX) -> P_IN_AA(d(X), DX) 63.56/17.20 63.56/17.20 R is empty. 63.56/17.20 The argument filtering Pi contains the following mapping: 63.56/17.20 d(x1) = d(x1) 63.56/17.20 63.56/17.20 P_IN_AA(x1, x2) = P_IN_AA 63.56/17.20 63.56/17.20 63.56/17.20 We have to consider all (P,R,Pi)-chains 63.56/17.20 ---------------------------------------- 63.56/17.20 63.56/17.20 (22) 63.56/17.20 Obligation: 63.56/17.20 Pi DP problem: 63.56/17.20 The TRS P consists of the following rules: 63.56/17.20 63.56/17.20 P_IN_GA(d(d(X)), DDX) -> P_IN_GA(d(X), DX) 63.56/17.20 63.56/17.20 The TRS R consists of the following rules: 63.56/17.20 63.56/17.20 p_in_ag(d(e(t)), const(1)) -> p_out_ag(d(e(t)), const(1)) 63.56/17.20 p_in_ag(d(e(const(A))), const(0)) -> p_out_ag(d(e(const(A))), const(0)) 63.56/17.20 p_in_ag(d(e(+(X, Y))), +(DX, DY)) -> U1_ag(X, Y, DX, DY, p_in_ag(d(e(X)), DX)) 63.56/17.20 p_in_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ag(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.20 p_in_gg(d(e(t)), const(1)) -> p_out_gg(d(e(t)), const(1)) 63.56/17.20 p_in_gg(d(e(const(A))), const(0)) -> p_out_gg(d(e(const(A))), const(0)) 63.56/17.20 p_in_gg(d(e(+(X, Y))), +(DX, DY)) -> U1_gg(X, Y, DX, DY, p_in_gg(d(e(X)), DX)) 63.56/17.20 p_in_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_gg(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.20 p_in_gg(d(d(X)), DDX) -> U5_gg(X, DDX, p_in_ga(d(X), DX)) 63.56/17.20 p_in_ga(d(e(t)), const(1)) -> p_out_ga(d(e(t)), const(1)) 63.56/17.20 p_in_ga(d(e(const(A))), const(0)) -> p_out_ga(d(e(const(A))), const(0)) 63.56/17.20 p_in_ga(d(e(+(X, Y))), +(DX, DY)) -> U1_ga(X, Y, DX, DY, p_in_ga(d(e(X)), DX)) 63.56/17.20 p_in_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ga(X, Y, DY, DX, p_in_ga(d(e(X)), DX)) 63.56/17.20 p_in_ga(d(d(X)), DDX) -> U5_ga(X, DDX, p_in_ga(d(X), DX)) 63.56/17.20 U5_ga(X, DDX, p_out_ga(d(X), DX)) -> U6_ga(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.20 U6_ga(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_ga(d(d(X)), DDX) 63.56/17.20 U3_ga(X, Y, DY, DX, p_out_ga(d(e(X)), DX)) -> U4_ga(X, Y, DY, DX, p_in_ga(d(e(Y)), DY)) 63.56/17.20 U4_ga(X, Y, DY, DX, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.20 U1_ga(X, Y, DX, DY, p_out_ga(d(e(X)), DX)) -> U2_ga(X, Y, DX, DY, p_in_ga(d(e(Y)), DY)) 63.56/17.20 U2_ga(X, Y, DX, DY, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(+(X, Y))), +(DX, DY)) 63.56/17.20 U5_gg(X, DDX, p_out_ga(d(X), DX)) -> U6_gg(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.20 U6_gg(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_gg(d(d(X)), DDX) 63.56/17.20 U3_gg(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_gg(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.20 U4_gg(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.20 U1_gg(X, Y, DX, DY, p_out_gg(d(e(X)), DX)) -> U2_gg(X, Y, DX, DY, p_in_gg(d(e(Y)), DY)) 63.56/17.20 U2_gg(X, Y, DX, DY, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(+(X, Y))), +(DX, DY)) 63.56/17.20 U3_ag(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_ag(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.20 U4_ag(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.20 p_in_ag(d(d(X)), DDX) -> U5_ag(X, DDX, p_in_aa(d(X), DX)) 63.56/17.20 p_in_aa(d(e(t)), const(1)) -> p_out_aa(d(e(t)), const(1)) 63.56/17.20 p_in_aa(d(e(const(A))), const(0)) -> p_out_aa(d(e(const(A))), const(0)) 63.56/17.20 p_in_aa(d(e(+(X, Y))), +(DX, DY)) -> U1_aa(X, Y, DX, DY, p_in_aa(d(e(X)), DX)) 63.56/17.20 p_in_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_aa(X, Y, DY, DX, p_in_aa(d(e(X)), DX)) 63.56/17.20 p_in_aa(d(d(X)), DDX) -> U5_aa(X, DDX, p_in_aa(d(X), DX)) 63.56/17.20 U5_aa(X, DDX, p_out_aa(d(X), DX)) -> U6_aa(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.20 U6_aa(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_aa(d(d(X)), DDX) 63.56/17.20 U3_aa(X, Y, DY, DX, p_out_aa(d(e(X)), DX)) -> U4_aa(X, Y, DY, DX, p_in_aa(d(e(Y)), DY)) 63.56/17.20 U4_aa(X, Y, DY, DX, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.20 U1_aa(X, Y, DX, DY, p_out_aa(d(e(X)), DX)) -> U2_aa(X, Y, DX, DY, p_in_aa(d(e(Y)), DY)) 63.56/17.20 U2_aa(X, Y, DX, DY, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(+(X, Y))), +(DX, DY)) 63.56/17.20 U5_ag(X, DDX, p_out_aa(d(X), DX)) -> U6_ag(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.20 U6_ag(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_ag(d(d(X)), DDX) 63.56/17.20 U1_ag(X, Y, DX, DY, p_out_ag(d(e(X)), DX)) -> U2_ag(X, Y, DX, DY, p_in_ag(d(e(Y)), DY)) 63.56/17.20 U2_ag(X, Y, DX, DY, p_out_ag(d(e(Y)), DY)) -> p_out_ag(d(e(+(X, Y))), +(DX, DY)) 63.56/17.20 63.56/17.20 The argument filtering Pi contains the following mapping: 63.56/17.20 p_in_ag(x1, x2) = p_in_ag(x2) 63.56/17.20 63.56/17.20 const(x1) = const 63.56/17.20 63.56/17.20 1 = 1 63.56/17.20 63.56/17.20 p_out_ag(x1, x2) = p_out_ag(x1) 63.56/17.20 63.56/17.20 0 = 0 63.56/17.20 63.56/17.20 +(x1, x2) = +(x1, x2) 63.56/17.20 63.56/17.20 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x4, x5) 63.56/17.20 63.56/17.20 *(x1, x2) = *(x1, x2) 63.56/17.20 63.56/17.20 U3_ag(x1, x2, x3, x4, x5) = U3_ag(x1, x2, x3, x5) 63.56/17.20 63.56/17.20 p_in_gg(x1, x2) = p_in_gg(x1, x2) 63.56/17.20 63.56/17.20 d(x1) = d(x1) 63.56/17.20 63.56/17.20 e(x1) = e(x1) 63.56/17.20 63.56/17.20 t = t 63.56/17.20 63.56/17.20 p_out_gg(x1, x2) = p_out_gg 63.56/17.20 63.56/17.20 U1_gg(x1, x2, x3, x4, x5) = U1_gg(x2, x4, x5) 63.56/17.20 63.56/17.20 U3_gg(x1, x2, x3, x4, x5) = U3_gg(x2, x3, x5) 63.56/17.20 63.56/17.20 U5_gg(x1, x2, x3) = U5_gg(x2, x3) 63.56/17.20 63.56/17.20 p_in_ga(x1, x2) = p_in_ga(x1) 63.56/17.20 63.56/17.20 p_out_ga(x1, x2) = p_out_ga(x2) 63.56/17.20 63.56/17.20 U1_ga(x1, x2, x3, x4, x5) = U1_ga(x2, x5) 63.56/17.20 63.56/17.20 U3_ga(x1, x2, x3, x4, x5) = U3_ga(x1, x2, x5) 63.56/17.20 63.56/17.20 U5_ga(x1, x2, x3) = U5_ga(x3) 63.56/17.20 63.56/17.20 U6_ga(x1, x2, x3, x4) = U6_ga(x4) 63.56/17.20 63.56/17.20 U4_ga(x1, x2, x3, x4, x5) = U4_ga(x1, x2, x4, x5) 63.56/17.20 63.56/17.20 U2_ga(x1, x2, x3, x4, x5) = U2_ga(x3, x5) 63.56/17.20 63.56/17.20 U6_gg(x1, x2, x3, x4) = U6_gg(x4) 63.56/17.20 63.56/17.20 U4_gg(x1, x2, x3, x4, x5) = U4_gg(x5) 63.56/17.20 63.56/17.20 U2_gg(x1, x2, x3, x4, x5) = U2_gg(x5) 63.56/17.20 63.56/17.20 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x1, x2, x5) 63.56/17.20 63.56/17.20 U5_ag(x1, x2, x3) = U5_ag(x2, x3) 63.56/17.20 63.56/17.20 p_in_aa(x1, x2) = p_in_aa 63.56/17.20 63.56/17.20 p_out_aa(x1, x2) = p_out_aa(x1, x2) 63.56/17.20 63.56/17.20 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 63.56/17.20 63.56/17.20 U3_aa(x1, x2, x3, x4, x5) = U3_aa(x5) 63.56/17.20 63.56/17.20 U5_aa(x1, x2, x3) = U5_aa(x3) 63.56/17.20 63.56/17.20 U6_aa(x1, x2, x3, x4) = U6_aa(x1, x4) 63.56/17.20 63.56/17.20 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x1, x4, x5) 63.56/17.20 63.56/17.20 U2_aa(x1, x2, x3, x4, x5) = U2_aa(x1, x3, x5) 63.56/17.20 63.56/17.20 U6_ag(x1, x2, x3, x4) = U6_ag(x1, x4) 63.56/17.20 63.56/17.20 U2_ag(x1, x2, x3, x4, x5) = U2_ag(x1, x5) 63.56/17.20 63.56/17.20 P_IN_GA(x1, x2) = P_IN_GA(x1) 63.56/17.20 63.56/17.20 63.56/17.20 We have to consider all (P,R,Pi)-chains 63.56/17.20 ---------------------------------------- 63.56/17.20 63.56/17.20 (23) UsableRulesProof (EQUIVALENT) 63.56/17.20 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 63.56/17.20 ---------------------------------------- 63.56/17.20 63.56/17.20 (24) 63.56/17.20 Obligation: 63.56/17.20 Pi DP problem: 63.56/17.20 The TRS P consists of the following rules: 63.56/17.20 63.56/17.20 P_IN_GA(d(d(X)), DDX) -> P_IN_GA(d(X), DX) 63.56/17.20 63.56/17.20 R is empty. 63.56/17.20 The argument filtering Pi contains the following mapping: 63.56/17.20 d(x1) = d(x1) 63.56/17.20 63.56/17.20 P_IN_GA(x1, x2) = P_IN_GA(x1) 63.56/17.20 63.56/17.20 63.56/17.20 We have to consider all (P,R,Pi)-chains 63.56/17.20 ---------------------------------------- 63.56/17.20 63.56/17.20 (25) 63.56/17.20 Obligation: 63.56/17.20 Pi DP problem: 63.56/17.20 The TRS P consists of the following rules: 63.56/17.20 63.56/17.20 U1_GG(X, Y, DX, DY, p_out_gg(d(e(X)), DX)) -> P_IN_GG(d(e(Y)), DY) 63.56/17.20 P_IN_GG(d(e(+(X, Y))), +(DX, DY)) -> U1_GG(X, Y, DX, DY, p_in_gg(d(e(X)), DX)) 63.56/17.20 P_IN_GG(d(e(+(X, Y))), +(DX, DY)) -> P_IN_GG(d(e(X)), DX) 63.56/17.20 P_IN_GG(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_GG(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.20 U3_GG(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> P_IN_GG(d(e(Y)), DY) 63.56/17.20 P_IN_GG(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> P_IN_GG(d(e(X)), DX) 63.56/17.20 63.56/17.20 The TRS R consists of the following rules: 63.56/17.20 63.56/17.20 p_in_ag(d(e(t)), const(1)) -> p_out_ag(d(e(t)), const(1)) 63.56/17.20 p_in_ag(d(e(const(A))), const(0)) -> p_out_ag(d(e(const(A))), const(0)) 63.56/17.20 p_in_ag(d(e(+(X, Y))), +(DX, DY)) -> U1_ag(X, Y, DX, DY, p_in_ag(d(e(X)), DX)) 63.56/17.20 p_in_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ag(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.20 p_in_gg(d(e(t)), const(1)) -> p_out_gg(d(e(t)), const(1)) 63.56/17.20 p_in_gg(d(e(const(A))), const(0)) -> p_out_gg(d(e(const(A))), const(0)) 63.56/17.20 p_in_gg(d(e(+(X, Y))), +(DX, DY)) -> U1_gg(X, Y, DX, DY, p_in_gg(d(e(X)), DX)) 63.56/17.20 p_in_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_gg(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.20 p_in_gg(d(d(X)), DDX) -> U5_gg(X, DDX, p_in_ga(d(X), DX)) 63.56/17.20 p_in_ga(d(e(t)), const(1)) -> p_out_ga(d(e(t)), const(1)) 63.56/17.20 p_in_ga(d(e(const(A))), const(0)) -> p_out_ga(d(e(const(A))), const(0)) 63.56/17.20 p_in_ga(d(e(+(X, Y))), +(DX, DY)) -> U1_ga(X, Y, DX, DY, p_in_ga(d(e(X)), DX)) 63.56/17.20 p_in_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ga(X, Y, DY, DX, p_in_ga(d(e(X)), DX)) 63.56/17.20 p_in_ga(d(d(X)), DDX) -> U5_ga(X, DDX, p_in_ga(d(X), DX)) 63.56/17.20 U5_ga(X, DDX, p_out_ga(d(X), DX)) -> U6_ga(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.20 U6_ga(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_ga(d(d(X)), DDX) 63.56/17.20 U3_ga(X, Y, DY, DX, p_out_ga(d(e(X)), DX)) -> U4_ga(X, Y, DY, DX, p_in_ga(d(e(Y)), DY)) 63.56/17.20 U4_ga(X, Y, DY, DX, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.20 U1_ga(X, Y, DX, DY, p_out_ga(d(e(X)), DX)) -> U2_ga(X, Y, DX, DY, p_in_ga(d(e(Y)), DY)) 63.56/17.20 U2_ga(X, Y, DX, DY, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(+(X, Y))), +(DX, DY)) 63.56/17.20 U5_gg(X, DDX, p_out_ga(d(X), DX)) -> U6_gg(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.20 U6_gg(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_gg(d(d(X)), DDX) 63.56/17.20 U3_gg(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_gg(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.20 U4_gg(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.20 U1_gg(X, Y, DX, DY, p_out_gg(d(e(X)), DX)) -> U2_gg(X, Y, DX, DY, p_in_gg(d(e(Y)), DY)) 63.56/17.20 U2_gg(X, Y, DX, DY, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(+(X, Y))), +(DX, DY)) 63.56/17.20 U3_ag(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_ag(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.20 U4_ag(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.20 p_in_ag(d(d(X)), DDX) -> U5_ag(X, DDX, p_in_aa(d(X), DX)) 63.56/17.20 p_in_aa(d(e(t)), const(1)) -> p_out_aa(d(e(t)), const(1)) 63.56/17.20 p_in_aa(d(e(const(A))), const(0)) -> p_out_aa(d(e(const(A))), const(0)) 63.56/17.20 p_in_aa(d(e(+(X, Y))), +(DX, DY)) -> U1_aa(X, Y, DX, DY, p_in_aa(d(e(X)), DX)) 63.56/17.20 p_in_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_aa(X, Y, DY, DX, p_in_aa(d(e(X)), DX)) 63.56/17.20 p_in_aa(d(d(X)), DDX) -> U5_aa(X, DDX, p_in_aa(d(X), DX)) 63.56/17.20 U5_aa(X, DDX, p_out_aa(d(X), DX)) -> U6_aa(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.20 U6_aa(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_aa(d(d(X)), DDX) 63.56/17.20 U3_aa(X, Y, DY, DX, p_out_aa(d(e(X)), DX)) -> U4_aa(X, Y, DY, DX, p_in_aa(d(e(Y)), DY)) 63.56/17.20 U4_aa(X, Y, DY, DX, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.20 U1_aa(X, Y, DX, DY, p_out_aa(d(e(X)), DX)) -> U2_aa(X, Y, DX, DY, p_in_aa(d(e(Y)), DY)) 63.56/17.20 U2_aa(X, Y, DX, DY, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(+(X, Y))), +(DX, DY)) 63.56/17.20 U5_ag(X, DDX, p_out_aa(d(X), DX)) -> U6_ag(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.20 U6_ag(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_ag(d(d(X)), DDX) 63.56/17.20 U1_ag(X, Y, DX, DY, p_out_ag(d(e(X)), DX)) -> U2_ag(X, Y, DX, DY, p_in_ag(d(e(Y)), DY)) 63.56/17.20 U2_ag(X, Y, DX, DY, p_out_ag(d(e(Y)), DY)) -> p_out_ag(d(e(+(X, Y))), +(DX, DY)) 63.56/17.20 63.56/17.20 The argument filtering Pi contains the following mapping: 63.56/17.20 p_in_ag(x1, x2) = p_in_ag(x2) 63.56/17.20 63.56/17.20 const(x1) = const 63.56/17.20 63.56/17.20 1 = 1 63.56/17.20 63.56/17.20 p_out_ag(x1, x2) = p_out_ag(x1) 63.56/17.20 63.56/17.20 0 = 0 63.56/17.20 63.56/17.20 +(x1, x2) = +(x1, x2) 63.56/17.20 63.56/17.20 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x4, x5) 63.56/17.20 63.56/17.20 *(x1, x2) = *(x1, x2) 63.56/17.20 63.56/17.20 U3_ag(x1, x2, x3, x4, x5) = U3_ag(x1, x2, x3, x5) 63.56/17.20 63.56/17.20 p_in_gg(x1, x2) = p_in_gg(x1, x2) 63.56/17.20 63.56/17.20 d(x1) = d(x1) 63.56/17.20 63.56/17.20 e(x1) = e(x1) 63.56/17.20 63.56/17.20 t = t 63.56/17.20 63.56/17.20 p_out_gg(x1, x2) = p_out_gg 63.56/17.20 63.56/17.20 U1_gg(x1, x2, x3, x4, x5) = U1_gg(x2, x4, x5) 63.56/17.20 63.56/17.20 U3_gg(x1, x2, x3, x4, x5) = U3_gg(x2, x3, x5) 63.56/17.20 63.56/17.20 U5_gg(x1, x2, x3) = U5_gg(x2, x3) 63.56/17.20 63.56/17.20 p_in_ga(x1, x2) = p_in_ga(x1) 63.56/17.20 63.56/17.20 p_out_ga(x1, x2) = p_out_ga(x2) 63.56/17.20 63.56/17.20 U1_ga(x1, x2, x3, x4, x5) = U1_ga(x2, x5) 63.56/17.20 63.56/17.20 U3_ga(x1, x2, x3, x4, x5) = U3_ga(x1, x2, x5) 63.56/17.20 63.56/17.20 U5_ga(x1, x2, x3) = U5_ga(x3) 63.56/17.20 63.56/17.20 U6_ga(x1, x2, x3, x4) = U6_ga(x4) 63.56/17.20 63.56/17.20 U4_ga(x1, x2, x3, x4, x5) = U4_ga(x1, x2, x4, x5) 63.56/17.20 63.56/17.20 U2_ga(x1, x2, x3, x4, x5) = U2_ga(x3, x5) 63.56/17.20 63.56/17.20 U6_gg(x1, x2, x3, x4) = U6_gg(x4) 63.56/17.20 63.56/17.20 U4_gg(x1, x2, x3, x4, x5) = U4_gg(x5) 63.56/17.20 63.56/17.20 U2_gg(x1, x2, x3, x4, x5) = U2_gg(x5) 63.56/17.20 63.56/17.20 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x1, x2, x5) 63.56/17.20 63.56/17.20 U5_ag(x1, x2, x3) = U5_ag(x2, x3) 63.56/17.20 63.56/17.20 p_in_aa(x1, x2) = p_in_aa 63.56/17.20 63.56/17.20 p_out_aa(x1, x2) = p_out_aa(x1, x2) 63.56/17.20 63.56/17.20 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 63.56/17.20 63.56/17.20 U3_aa(x1, x2, x3, x4, x5) = U3_aa(x5) 63.56/17.20 63.56/17.20 U5_aa(x1, x2, x3) = U5_aa(x3) 63.56/17.20 63.56/17.20 U6_aa(x1, x2, x3, x4) = U6_aa(x1, x4) 63.56/17.20 63.56/17.20 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x1, x4, x5) 63.56/17.20 63.56/17.20 U2_aa(x1, x2, x3, x4, x5) = U2_aa(x1, x3, x5) 63.56/17.20 63.56/17.20 U6_ag(x1, x2, x3, x4) = U6_ag(x1, x4) 63.56/17.21 63.56/17.21 U2_ag(x1, x2, x3, x4, x5) = U2_ag(x1, x5) 63.56/17.21 63.56/17.21 P_IN_GG(x1, x2) = P_IN_GG(x1, x2) 63.56/17.21 63.56/17.21 U1_GG(x1, x2, x3, x4, x5) = U1_GG(x2, x4, x5) 63.56/17.21 63.56/17.21 U3_GG(x1, x2, x3, x4, x5) = U3_GG(x2, x3, x5) 63.56/17.21 63.56/17.21 63.56/17.21 We have to consider all (P,R,Pi)-chains 63.56/17.21 ---------------------------------------- 63.56/17.21 63.56/17.21 (26) UsableRulesProof (EQUIVALENT) 63.56/17.21 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 63.56/17.21 ---------------------------------------- 63.56/17.21 63.56/17.21 (27) 63.56/17.21 Obligation: 63.56/17.21 Pi DP problem: 63.56/17.21 The TRS P consists of the following rules: 63.56/17.21 63.56/17.21 U1_GG(X, Y, DX, DY, p_out_gg(d(e(X)), DX)) -> P_IN_GG(d(e(Y)), DY) 63.56/17.21 P_IN_GG(d(e(+(X, Y))), +(DX, DY)) -> U1_GG(X, Y, DX, DY, p_in_gg(d(e(X)), DX)) 63.56/17.21 P_IN_GG(d(e(+(X, Y))), +(DX, DY)) -> P_IN_GG(d(e(X)), DX) 63.56/17.21 P_IN_GG(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_GG(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.21 U3_GG(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> P_IN_GG(d(e(Y)), DY) 63.56/17.21 P_IN_GG(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> P_IN_GG(d(e(X)), DX) 63.56/17.21 63.56/17.21 The TRS R consists of the following rules: 63.56/17.21 63.56/17.21 p_in_gg(d(e(t)), const(1)) -> p_out_gg(d(e(t)), const(1)) 63.56/17.21 p_in_gg(d(e(const(A))), const(0)) -> p_out_gg(d(e(const(A))), const(0)) 63.56/17.21 p_in_gg(d(e(+(X, Y))), +(DX, DY)) -> U1_gg(X, Y, DX, DY, p_in_gg(d(e(X)), DX)) 63.56/17.21 p_in_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_gg(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.21 U1_gg(X, Y, DX, DY, p_out_gg(d(e(X)), DX)) -> U2_gg(X, Y, DX, DY, p_in_gg(d(e(Y)), DY)) 63.56/17.21 U3_gg(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_gg(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.21 U2_gg(X, Y, DX, DY, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(+(X, Y))), +(DX, DY)) 63.56/17.21 U4_gg(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.21 63.56/17.21 The argument filtering Pi contains the following mapping: 63.56/17.21 const(x1) = const 63.56/17.21 63.56/17.21 1 = 1 63.56/17.21 63.56/17.21 0 = 0 63.56/17.21 63.56/17.21 +(x1, x2) = +(x1, x2) 63.56/17.21 63.56/17.21 *(x1, x2) = *(x1, x2) 63.56/17.21 63.56/17.21 p_in_gg(x1, x2) = p_in_gg(x1, x2) 63.56/17.21 63.56/17.21 d(x1) = d(x1) 63.56/17.21 63.56/17.21 e(x1) = e(x1) 63.56/17.21 63.56/17.21 t = t 63.56/17.21 63.56/17.21 p_out_gg(x1, x2) = p_out_gg 63.56/17.21 63.56/17.21 U1_gg(x1, x2, x3, x4, x5) = U1_gg(x2, x4, x5) 63.56/17.21 63.56/17.21 U3_gg(x1, x2, x3, x4, x5) = U3_gg(x2, x3, x5) 63.56/17.21 63.56/17.21 U4_gg(x1, x2, x3, x4, x5) = U4_gg(x5) 63.56/17.21 63.56/17.21 U2_gg(x1, x2, x3, x4, x5) = U2_gg(x5) 63.56/17.21 63.56/17.21 P_IN_GG(x1, x2) = P_IN_GG(x1, x2) 63.56/17.21 63.56/17.21 U1_GG(x1, x2, x3, x4, x5) = U1_GG(x2, x4, x5) 63.56/17.21 63.56/17.21 U3_GG(x1, x2, x3, x4, x5) = U3_GG(x2, x3, x5) 63.56/17.21 63.56/17.21 63.56/17.21 We have to consider all (P,R,Pi)-chains 63.56/17.21 ---------------------------------------- 63.56/17.21 63.56/17.21 (28) 63.56/17.21 Obligation: 63.56/17.21 Pi DP problem: 63.56/17.21 The TRS P consists of the following rules: 63.56/17.21 63.56/17.21 U1_AG(X, Y, DX, DY, p_out_ag(d(e(X)), DX)) -> P_IN_AG(d(e(Y)), DY) 63.56/17.21 P_IN_AG(d(e(+(X, Y))), +(DX, DY)) -> U1_AG(X, Y, DX, DY, p_in_ag(d(e(X)), DX)) 63.56/17.21 P_IN_AG(d(e(+(X, Y))), +(DX, DY)) -> P_IN_AG(d(e(X)), DX) 63.56/17.21 63.56/17.21 The TRS R consists of the following rules: 63.56/17.21 63.56/17.21 p_in_ag(d(e(t)), const(1)) -> p_out_ag(d(e(t)), const(1)) 63.56/17.21 p_in_ag(d(e(const(A))), const(0)) -> p_out_ag(d(e(const(A))), const(0)) 63.56/17.21 p_in_ag(d(e(+(X, Y))), +(DX, DY)) -> U1_ag(X, Y, DX, DY, p_in_ag(d(e(X)), DX)) 63.56/17.21 p_in_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ag(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.21 p_in_gg(d(e(t)), const(1)) -> p_out_gg(d(e(t)), const(1)) 63.56/17.21 p_in_gg(d(e(const(A))), const(0)) -> p_out_gg(d(e(const(A))), const(0)) 63.56/17.21 p_in_gg(d(e(+(X, Y))), +(DX, DY)) -> U1_gg(X, Y, DX, DY, p_in_gg(d(e(X)), DX)) 63.56/17.21 p_in_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_gg(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.21 p_in_gg(d(d(X)), DDX) -> U5_gg(X, DDX, p_in_ga(d(X), DX)) 63.56/17.21 p_in_ga(d(e(t)), const(1)) -> p_out_ga(d(e(t)), const(1)) 63.56/17.21 p_in_ga(d(e(const(A))), const(0)) -> p_out_ga(d(e(const(A))), const(0)) 63.56/17.21 p_in_ga(d(e(+(X, Y))), +(DX, DY)) -> U1_ga(X, Y, DX, DY, p_in_ga(d(e(X)), DX)) 63.56/17.21 p_in_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ga(X, Y, DY, DX, p_in_ga(d(e(X)), DX)) 63.56/17.21 p_in_ga(d(d(X)), DDX) -> U5_ga(X, DDX, p_in_ga(d(X), DX)) 63.56/17.21 U5_ga(X, DDX, p_out_ga(d(X), DX)) -> U6_ga(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.21 U6_ga(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_ga(d(d(X)), DDX) 63.56/17.21 U3_ga(X, Y, DY, DX, p_out_ga(d(e(X)), DX)) -> U4_ga(X, Y, DY, DX, p_in_ga(d(e(Y)), DY)) 63.56/17.21 U4_ga(X, Y, DY, DX, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.21 U1_ga(X, Y, DX, DY, p_out_ga(d(e(X)), DX)) -> U2_ga(X, Y, DX, DY, p_in_ga(d(e(Y)), DY)) 63.56/17.21 U2_ga(X, Y, DX, DY, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(+(X, Y))), +(DX, DY)) 63.56/17.21 U5_gg(X, DDX, p_out_ga(d(X), DX)) -> U6_gg(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.21 U6_gg(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_gg(d(d(X)), DDX) 63.56/17.21 U3_gg(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_gg(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.21 U4_gg(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.21 U1_gg(X, Y, DX, DY, p_out_gg(d(e(X)), DX)) -> U2_gg(X, Y, DX, DY, p_in_gg(d(e(Y)), DY)) 63.56/17.21 U2_gg(X, Y, DX, DY, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(+(X, Y))), +(DX, DY)) 63.56/17.21 U3_ag(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_ag(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.21 U4_ag(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.21 p_in_ag(d(d(X)), DDX) -> U5_ag(X, DDX, p_in_aa(d(X), DX)) 63.56/17.21 p_in_aa(d(e(t)), const(1)) -> p_out_aa(d(e(t)), const(1)) 63.56/17.21 p_in_aa(d(e(const(A))), const(0)) -> p_out_aa(d(e(const(A))), const(0)) 63.56/17.21 p_in_aa(d(e(+(X, Y))), +(DX, DY)) -> U1_aa(X, Y, DX, DY, p_in_aa(d(e(X)), DX)) 63.56/17.21 p_in_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_aa(X, Y, DY, DX, p_in_aa(d(e(X)), DX)) 63.56/17.21 p_in_aa(d(d(X)), DDX) -> U5_aa(X, DDX, p_in_aa(d(X), DX)) 63.56/17.21 U5_aa(X, DDX, p_out_aa(d(X), DX)) -> U6_aa(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.21 U6_aa(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_aa(d(d(X)), DDX) 63.56/17.21 U3_aa(X, Y, DY, DX, p_out_aa(d(e(X)), DX)) -> U4_aa(X, Y, DY, DX, p_in_aa(d(e(Y)), DY)) 63.56/17.21 U4_aa(X, Y, DY, DX, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.21 U1_aa(X, Y, DX, DY, p_out_aa(d(e(X)), DX)) -> U2_aa(X, Y, DX, DY, p_in_aa(d(e(Y)), DY)) 63.56/17.21 U2_aa(X, Y, DX, DY, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(+(X, Y))), +(DX, DY)) 63.56/17.21 U5_ag(X, DDX, p_out_aa(d(X), DX)) -> U6_ag(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.21 U6_ag(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_ag(d(d(X)), DDX) 63.56/17.21 U1_ag(X, Y, DX, DY, p_out_ag(d(e(X)), DX)) -> U2_ag(X, Y, DX, DY, p_in_ag(d(e(Y)), DY)) 63.56/17.21 U2_ag(X, Y, DX, DY, p_out_ag(d(e(Y)), DY)) -> p_out_ag(d(e(+(X, Y))), +(DX, DY)) 63.56/17.21 63.56/17.21 The argument filtering Pi contains the following mapping: 63.56/17.21 p_in_ag(x1, x2) = p_in_ag(x2) 63.56/17.21 63.56/17.21 const(x1) = const 63.56/17.21 63.56/17.21 1 = 1 63.56/17.21 63.56/17.21 p_out_ag(x1, x2) = p_out_ag(x1) 63.56/17.21 63.56/17.21 0 = 0 63.56/17.21 63.56/17.21 +(x1, x2) = +(x1, x2) 63.56/17.21 63.56/17.21 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x4, x5) 63.56/17.21 63.56/17.21 *(x1, x2) = *(x1, x2) 63.56/17.21 63.56/17.21 U3_ag(x1, x2, x3, x4, x5) = U3_ag(x1, x2, x3, x5) 63.56/17.21 63.56/17.21 p_in_gg(x1, x2) = p_in_gg(x1, x2) 63.56/17.21 63.56/17.21 d(x1) = d(x1) 63.56/17.21 63.56/17.21 e(x1) = e(x1) 63.56/17.21 63.56/17.21 t = t 63.56/17.21 63.56/17.21 p_out_gg(x1, x2) = p_out_gg 63.56/17.21 63.56/17.21 U1_gg(x1, x2, x3, x4, x5) = U1_gg(x2, x4, x5) 63.56/17.21 63.56/17.21 U3_gg(x1, x2, x3, x4, x5) = U3_gg(x2, x3, x5) 63.56/17.21 63.56/17.21 U5_gg(x1, x2, x3) = U5_gg(x2, x3) 63.56/17.21 63.56/17.21 p_in_ga(x1, x2) = p_in_ga(x1) 63.56/17.21 63.56/17.21 p_out_ga(x1, x2) = p_out_ga(x2) 63.56/17.21 63.56/17.21 U1_ga(x1, x2, x3, x4, x5) = U1_ga(x2, x5) 63.56/17.21 63.56/17.21 U3_ga(x1, x2, x3, x4, x5) = U3_ga(x1, x2, x5) 63.56/17.21 63.56/17.21 U5_ga(x1, x2, x3) = U5_ga(x3) 63.56/17.21 63.56/17.21 U6_ga(x1, x2, x3, x4) = U6_ga(x4) 63.56/17.21 63.56/17.21 U4_ga(x1, x2, x3, x4, x5) = U4_ga(x1, x2, x4, x5) 63.56/17.21 63.56/17.21 U2_ga(x1, x2, x3, x4, x5) = U2_ga(x3, x5) 63.56/17.21 63.56/17.21 U6_gg(x1, x2, x3, x4) = U6_gg(x4) 63.56/17.21 63.56/17.21 U4_gg(x1, x2, x3, x4, x5) = U4_gg(x5) 63.56/17.21 63.56/17.21 U2_gg(x1, x2, x3, x4, x5) = U2_gg(x5) 63.56/17.21 63.56/17.21 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x1, x2, x5) 63.56/17.21 63.56/17.21 U5_ag(x1, x2, x3) = U5_ag(x2, x3) 63.56/17.21 63.56/17.21 p_in_aa(x1, x2) = p_in_aa 63.56/17.21 63.56/17.21 p_out_aa(x1, x2) = p_out_aa(x1, x2) 63.56/17.21 63.56/17.21 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 63.56/17.21 63.56/17.21 U3_aa(x1, x2, x3, x4, x5) = U3_aa(x5) 63.56/17.21 63.56/17.21 U5_aa(x1, x2, x3) = U5_aa(x3) 63.56/17.21 63.56/17.21 U6_aa(x1, x2, x3, x4) = U6_aa(x1, x4) 63.56/17.21 63.56/17.21 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x1, x4, x5) 63.56/17.21 63.56/17.21 U2_aa(x1, x2, x3, x4, x5) = U2_aa(x1, x3, x5) 63.56/17.21 63.56/17.21 U6_ag(x1, x2, x3, x4) = U6_ag(x1, x4) 63.56/17.21 63.56/17.21 U2_ag(x1, x2, x3, x4, x5) = U2_ag(x1, x5) 63.56/17.21 63.56/17.21 P_IN_AG(x1, x2) = P_IN_AG(x2) 63.56/17.21 63.56/17.21 U1_AG(x1, x2, x3, x4, x5) = U1_AG(x4, x5) 63.56/17.21 63.56/17.21 63.56/17.21 We have to consider all (P,R,Pi)-chains 63.56/17.21 ---------------------------------------- 63.56/17.21 63.56/17.21 (29) UsableRulesProof (EQUIVALENT) 63.56/17.21 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 63.56/17.21 ---------------------------------------- 63.56/17.21 63.56/17.21 (30) 63.56/17.21 Obligation: 63.56/17.21 Pi DP problem: 63.56/17.21 The TRS P consists of the following rules: 63.56/17.21 63.56/17.21 U1_AG(X, Y, DX, DY, p_out_ag(d(e(X)), DX)) -> P_IN_AG(d(e(Y)), DY) 63.56/17.21 P_IN_AG(d(e(+(X, Y))), +(DX, DY)) -> U1_AG(X, Y, DX, DY, p_in_ag(d(e(X)), DX)) 63.56/17.21 P_IN_AG(d(e(+(X, Y))), +(DX, DY)) -> P_IN_AG(d(e(X)), DX) 63.56/17.21 63.56/17.21 The TRS R consists of the following rules: 63.56/17.21 63.56/17.21 p_in_ag(d(e(t)), const(1)) -> p_out_ag(d(e(t)), const(1)) 63.56/17.21 p_in_ag(d(e(const(A))), const(0)) -> p_out_ag(d(e(const(A))), const(0)) 63.56/17.21 p_in_ag(d(e(+(X, Y))), +(DX, DY)) -> U1_ag(X, Y, DX, DY, p_in_ag(d(e(X)), DX)) 63.56/17.21 p_in_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ag(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.21 U1_ag(X, Y, DX, DY, p_out_ag(d(e(X)), DX)) -> U2_ag(X, Y, DX, DY, p_in_ag(d(e(Y)), DY)) 63.56/17.21 U3_ag(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_ag(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.21 U2_ag(X, Y, DX, DY, p_out_ag(d(e(Y)), DY)) -> p_out_ag(d(e(+(X, Y))), +(DX, DY)) 63.56/17.21 p_in_gg(d(e(t)), const(1)) -> p_out_gg(d(e(t)), const(1)) 63.56/17.21 p_in_gg(d(e(const(A))), const(0)) -> p_out_gg(d(e(const(A))), const(0)) 63.56/17.21 p_in_gg(d(e(+(X, Y))), +(DX, DY)) -> U1_gg(X, Y, DX, DY, p_in_gg(d(e(X)), DX)) 63.56/17.21 p_in_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_gg(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.21 U4_ag(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.21 U1_gg(X, Y, DX, DY, p_out_gg(d(e(X)), DX)) -> U2_gg(X, Y, DX, DY, p_in_gg(d(e(Y)), DY)) 63.56/17.21 U3_gg(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_gg(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.21 U2_gg(X, Y, DX, DY, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(+(X, Y))), +(DX, DY)) 63.56/17.21 U4_gg(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.21 63.56/17.21 The argument filtering Pi contains the following mapping: 63.56/17.21 p_in_ag(x1, x2) = p_in_ag(x2) 63.56/17.21 63.56/17.21 const(x1) = const 63.56/17.21 63.56/17.21 1 = 1 63.56/17.21 63.56/17.21 p_out_ag(x1, x2) = p_out_ag(x1) 63.56/17.21 63.56/17.21 0 = 0 63.56/17.21 63.56/17.21 +(x1, x2) = +(x1, x2) 63.56/17.21 63.56/17.21 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x4, x5) 63.56/17.21 63.56/17.21 *(x1, x2) = *(x1, x2) 63.56/17.21 63.56/17.21 U3_ag(x1, x2, x3, x4, x5) = U3_ag(x1, x2, x3, x5) 63.56/17.21 63.56/17.21 p_in_gg(x1, x2) = p_in_gg(x1, x2) 63.56/17.21 63.56/17.21 d(x1) = d(x1) 63.56/17.21 63.56/17.21 e(x1) = e(x1) 63.56/17.21 63.56/17.21 t = t 63.56/17.21 63.56/17.21 p_out_gg(x1, x2) = p_out_gg 63.56/17.21 63.56/17.21 U1_gg(x1, x2, x3, x4, x5) = U1_gg(x2, x4, x5) 63.56/17.21 63.56/17.21 U3_gg(x1, x2, x3, x4, x5) = U3_gg(x2, x3, x5) 63.56/17.21 63.56/17.21 U4_gg(x1, x2, x3, x4, x5) = U4_gg(x5) 63.56/17.21 63.56/17.21 U2_gg(x1, x2, x3, x4, x5) = U2_gg(x5) 63.56/17.21 63.56/17.21 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x1, x2, x5) 63.56/17.21 63.56/17.21 U2_ag(x1, x2, x3, x4, x5) = U2_ag(x1, x5) 63.56/17.21 63.56/17.21 P_IN_AG(x1, x2) = P_IN_AG(x2) 63.56/17.21 63.56/17.21 U1_AG(x1, x2, x3, x4, x5) = U1_AG(x4, x5) 63.56/17.21 63.56/17.21 63.56/17.21 We have to consider all (P,R,Pi)-chains 63.56/17.21 ---------------------------------------- 63.56/17.21 63.56/17.21 (31) PrologToPiTRSProof (SOUND) 63.56/17.21 We use the technique of [TOCL09]. With regard to the inferred argument filtering the predicates were used in the following modes: 63.56/17.21 63.56/17.21 p_in_2: (f,b) (b,b) (b,f) (f,f) 63.56/17.21 63.56/17.21 Transforming Prolog into the following Term Rewriting System: 63.56/17.21 63.56/17.21 Pi-finite rewrite system: 63.56/17.21 The TRS R consists of the following rules: 63.56/17.21 63.56/17.21 p_in_ag(d(e(t)), const(1)) -> p_out_ag(d(e(t)), const(1)) 63.56/17.21 p_in_ag(d(e(const(A))), const(0)) -> p_out_ag(d(e(const(A))), const(0)) 63.56/17.21 p_in_ag(d(e(+(X, Y))), +(DX, DY)) -> U1_ag(X, Y, DX, DY, p_in_ag(d(e(X)), DX)) 63.56/17.21 p_in_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ag(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.21 p_in_gg(d(e(t)), const(1)) -> p_out_gg(d(e(t)), const(1)) 63.56/17.21 p_in_gg(d(e(const(A))), const(0)) -> p_out_gg(d(e(const(A))), const(0)) 63.56/17.21 p_in_gg(d(e(+(X, Y))), +(DX, DY)) -> U1_gg(X, Y, DX, DY, p_in_gg(d(e(X)), DX)) 63.56/17.21 p_in_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_gg(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.21 p_in_gg(d(d(X)), DDX) -> U5_gg(X, DDX, p_in_ga(d(X), DX)) 63.56/17.21 p_in_ga(d(e(t)), const(1)) -> p_out_ga(d(e(t)), const(1)) 63.56/17.21 p_in_ga(d(e(const(A))), const(0)) -> p_out_ga(d(e(const(A))), const(0)) 63.56/17.21 p_in_ga(d(e(+(X, Y))), +(DX, DY)) -> U1_ga(X, Y, DX, DY, p_in_ga(d(e(X)), DX)) 63.56/17.21 p_in_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ga(X, Y, DY, DX, p_in_ga(d(e(X)), DX)) 63.56/17.21 p_in_ga(d(d(X)), DDX) -> U5_ga(X, DDX, p_in_ga(d(X), DX)) 63.56/17.21 U5_ga(X, DDX, p_out_ga(d(X), DX)) -> U6_ga(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.21 U6_ga(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_ga(d(d(X)), DDX) 63.56/17.21 U3_ga(X, Y, DY, DX, p_out_ga(d(e(X)), DX)) -> U4_ga(X, Y, DY, DX, p_in_ga(d(e(Y)), DY)) 63.56/17.21 U4_ga(X, Y, DY, DX, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.21 U1_ga(X, Y, DX, DY, p_out_ga(d(e(X)), DX)) -> U2_ga(X, Y, DX, DY, p_in_ga(d(e(Y)), DY)) 63.56/17.21 U2_ga(X, Y, DX, DY, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(+(X, Y))), +(DX, DY)) 63.56/17.21 U5_gg(X, DDX, p_out_ga(d(X), DX)) -> U6_gg(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.21 U6_gg(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_gg(d(d(X)), DDX) 63.56/17.21 U3_gg(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_gg(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.21 U4_gg(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.21 U1_gg(X, Y, DX, DY, p_out_gg(d(e(X)), DX)) -> U2_gg(X, Y, DX, DY, p_in_gg(d(e(Y)), DY)) 63.56/17.21 U2_gg(X, Y, DX, DY, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(+(X, Y))), +(DX, DY)) 63.56/17.21 U3_ag(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_ag(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.21 U4_ag(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.21 p_in_ag(d(d(X)), DDX) -> U5_ag(X, DDX, p_in_aa(d(X), DX)) 63.56/17.21 p_in_aa(d(e(t)), const(1)) -> p_out_aa(d(e(t)), const(1)) 63.56/17.21 p_in_aa(d(e(const(A))), const(0)) -> p_out_aa(d(e(const(A))), const(0)) 63.56/17.21 p_in_aa(d(e(+(X, Y))), +(DX, DY)) -> U1_aa(X, Y, DX, DY, p_in_aa(d(e(X)), DX)) 63.56/17.21 p_in_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_aa(X, Y, DY, DX, p_in_aa(d(e(X)), DX)) 63.56/17.21 p_in_aa(d(d(X)), DDX) -> U5_aa(X, DDX, p_in_aa(d(X), DX)) 63.56/17.21 U5_aa(X, DDX, p_out_aa(d(X), DX)) -> U6_aa(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.21 U6_aa(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_aa(d(d(X)), DDX) 63.56/17.21 U3_aa(X, Y, DY, DX, p_out_aa(d(e(X)), DX)) -> U4_aa(X, Y, DY, DX, p_in_aa(d(e(Y)), DY)) 63.56/17.21 U4_aa(X, Y, DY, DX, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.21 U1_aa(X, Y, DX, DY, p_out_aa(d(e(X)), DX)) -> U2_aa(X, Y, DX, DY, p_in_aa(d(e(Y)), DY)) 63.56/17.21 U2_aa(X, Y, DX, DY, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(+(X, Y))), +(DX, DY)) 63.56/17.21 U5_ag(X, DDX, p_out_aa(d(X), DX)) -> U6_ag(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.21 U6_ag(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_ag(d(d(X)), DDX) 63.56/17.21 U1_ag(X, Y, DX, DY, p_out_ag(d(e(X)), DX)) -> U2_ag(X, Y, DX, DY, p_in_ag(d(e(Y)), DY)) 63.56/17.21 U2_ag(X, Y, DX, DY, p_out_ag(d(e(Y)), DY)) -> p_out_ag(d(e(+(X, Y))), +(DX, DY)) 63.56/17.21 63.56/17.21 The argument filtering Pi contains the following mapping: 63.56/17.21 p_in_ag(x1, x2) = p_in_ag(x2) 63.56/17.21 63.56/17.21 const(x1) = const 63.56/17.21 63.56/17.21 1 = 1 63.56/17.21 63.56/17.21 p_out_ag(x1, x2) = p_out_ag(x1, x2) 63.56/17.21 63.56/17.21 0 = 0 63.56/17.21 63.56/17.21 +(x1, x2) = +(x1, x2) 63.56/17.21 63.56/17.21 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x3, x4, x5) 63.56/17.21 63.56/17.21 *(x1, x2) = *(x1, x2) 63.56/17.21 63.56/17.21 U3_ag(x1, x2, x3, x4, x5) = U3_ag(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 p_in_gg(x1, x2) = p_in_gg(x1, x2) 63.56/17.21 63.56/17.21 d(x1) = d(x1) 63.56/17.21 63.56/17.21 e(x1) = e(x1) 63.56/17.21 63.56/17.21 t = t 63.56/17.21 63.56/17.21 p_out_gg(x1, x2) = p_out_gg(x1, x2) 63.56/17.21 63.56/17.21 U1_gg(x1, x2, x3, x4, x5) = U1_gg(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 U3_gg(x1, x2, x3, x4, x5) = U3_gg(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 U5_gg(x1, x2, x3) = U5_gg(x1, x2, x3) 63.56/17.21 63.56/17.21 p_in_ga(x1, x2) = p_in_ga(x1) 63.56/17.21 63.56/17.21 p_out_ga(x1, x2) = p_out_ga(x1, x2) 63.56/17.21 63.56/17.21 U1_ga(x1, x2, x3, x4, x5) = U1_ga(x1, x2, x5) 63.56/17.21 63.56/17.21 U3_ga(x1, x2, x3, x4, x5) = U3_ga(x1, x2, x5) 63.56/17.21 63.56/17.21 U5_ga(x1, x2, x3) = U5_ga(x1, x3) 63.56/17.21 63.56/17.21 U6_ga(x1, x2, x3, x4) = U6_ga(x1, x4) 63.56/17.21 63.56/17.21 U4_ga(x1, x2, x3, x4, x5) = U4_ga(x1, x2, x4, x5) 63.56/17.21 63.56/17.21 U2_ga(x1, x2, x3, x4, x5) = U2_ga(x1, x2, x3, x5) 63.56/17.21 63.56/17.21 U6_gg(x1, x2, x3, x4) = U6_gg(x1, x2, x4) 63.56/17.21 63.56/17.21 U4_gg(x1, x2, x3, x4, x5) = U4_gg(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 U2_gg(x1, x2, x3, x4, x5) = U2_gg(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 U5_ag(x1, x2, x3) = U5_ag(x2, x3) 63.56/17.21 63.56/17.21 p_in_aa(x1, x2) = p_in_aa 63.56/17.21 63.56/17.21 p_out_aa(x1, x2) = p_out_aa(x1, x2) 63.56/17.21 63.56/17.21 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 63.56/17.21 63.56/17.21 U3_aa(x1, x2, x3, x4, x5) = U3_aa(x5) 63.56/17.21 63.56/17.21 U5_aa(x1, x2, x3) = U5_aa(x3) 63.56/17.21 63.56/17.21 U6_aa(x1, x2, x3, x4) = U6_aa(x1, x4) 63.56/17.21 63.56/17.21 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x1, x4, x5) 63.56/17.21 63.56/17.21 U2_aa(x1, x2, x3, x4, x5) = U2_aa(x1, x3, x5) 63.56/17.21 63.56/17.21 U6_ag(x1, x2, x3, x4) = U6_ag(x1, x2, x4) 63.56/17.21 63.56/17.21 U2_ag(x1, x2, x3, x4, x5) = U2_ag(x1, x3, x4, x5) 63.56/17.21 63.56/17.21 63.56/17.21 63.56/17.21 63.56/17.21 63.56/17.21 Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog 63.56/17.21 63.56/17.21 63.56/17.21 63.56/17.21 ---------------------------------------- 63.56/17.21 63.56/17.21 (32) 63.56/17.21 Obligation: 63.56/17.21 Pi-finite rewrite system: 63.56/17.21 The TRS R consists of the following rules: 63.56/17.21 63.56/17.21 p_in_ag(d(e(t)), const(1)) -> p_out_ag(d(e(t)), const(1)) 63.56/17.21 p_in_ag(d(e(const(A))), const(0)) -> p_out_ag(d(e(const(A))), const(0)) 63.56/17.21 p_in_ag(d(e(+(X, Y))), +(DX, DY)) -> U1_ag(X, Y, DX, DY, p_in_ag(d(e(X)), DX)) 63.56/17.21 p_in_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ag(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.21 p_in_gg(d(e(t)), const(1)) -> p_out_gg(d(e(t)), const(1)) 63.56/17.21 p_in_gg(d(e(const(A))), const(0)) -> p_out_gg(d(e(const(A))), const(0)) 63.56/17.21 p_in_gg(d(e(+(X, Y))), +(DX, DY)) -> U1_gg(X, Y, DX, DY, p_in_gg(d(e(X)), DX)) 63.56/17.21 p_in_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_gg(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.21 p_in_gg(d(d(X)), DDX) -> U5_gg(X, DDX, p_in_ga(d(X), DX)) 63.56/17.21 p_in_ga(d(e(t)), const(1)) -> p_out_ga(d(e(t)), const(1)) 63.56/17.21 p_in_ga(d(e(const(A))), const(0)) -> p_out_ga(d(e(const(A))), const(0)) 63.56/17.21 p_in_ga(d(e(+(X, Y))), +(DX, DY)) -> U1_ga(X, Y, DX, DY, p_in_ga(d(e(X)), DX)) 63.56/17.21 p_in_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ga(X, Y, DY, DX, p_in_ga(d(e(X)), DX)) 63.56/17.21 p_in_ga(d(d(X)), DDX) -> U5_ga(X, DDX, p_in_ga(d(X), DX)) 63.56/17.21 U5_ga(X, DDX, p_out_ga(d(X), DX)) -> U6_ga(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.21 U6_ga(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_ga(d(d(X)), DDX) 63.56/17.21 U3_ga(X, Y, DY, DX, p_out_ga(d(e(X)), DX)) -> U4_ga(X, Y, DY, DX, p_in_ga(d(e(Y)), DY)) 63.56/17.21 U4_ga(X, Y, DY, DX, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.21 U1_ga(X, Y, DX, DY, p_out_ga(d(e(X)), DX)) -> U2_ga(X, Y, DX, DY, p_in_ga(d(e(Y)), DY)) 63.56/17.21 U2_ga(X, Y, DX, DY, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(+(X, Y))), +(DX, DY)) 63.56/17.21 U5_gg(X, DDX, p_out_ga(d(X), DX)) -> U6_gg(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.21 U6_gg(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_gg(d(d(X)), DDX) 63.56/17.21 U3_gg(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_gg(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.21 U4_gg(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.21 U1_gg(X, Y, DX, DY, p_out_gg(d(e(X)), DX)) -> U2_gg(X, Y, DX, DY, p_in_gg(d(e(Y)), DY)) 63.56/17.21 U2_gg(X, Y, DX, DY, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(+(X, Y))), +(DX, DY)) 63.56/17.21 U3_ag(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_ag(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.21 U4_ag(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.21 p_in_ag(d(d(X)), DDX) -> U5_ag(X, DDX, p_in_aa(d(X), DX)) 63.56/17.21 p_in_aa(d(e(t)), const(1)) -> p_out_aa(d(e(t)), const(1)) 63.56/17.21 p_in_aa(d(e(const(A))), const(0)) -> p_out_aa(d(e(const(A))), const(0)) 63.56/17.21 p_in_aa(d(e(+(X, Y))), +(DX, DY)) -> U1_aa(X, Y, DX, DY, p_in_aa(d(e(X)), DX)) 63.56/17.21 p_in_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_aa(X, Y, DY, DX, p_in_aa(d(e(X)), DX)) 63.56/17.21 p_in_aa(d(d(X)), DDX) -> U5_aa(X, DDX, p_in_aa(d(X), DX)) 63.56/17.21 U5_aa(X, DDX, p_out_aa(d(X), DX)) -> U6_aa(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.21 U6_aa(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_aa(d(d(X)), DDX) 63.56/17.21 U3_aa(X, Y, DY, DX, p_out_aa(d(e(X)), DX)) -> U4_aa(X, Y, DY, DX, p_in_aa(d(e(Y)), DY)) 63.56/17.21 U4_aa(X, Y, DY, DX, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.21 U1_aa(X, Y, DX, DY, p_out_aa(d(e(X)), DX)) -> U2_aa(X, Y, DX, DY, p_in_aa(d(e(Y)), DY)) 63.56/17.21 U2_aa(X, Y, DX, DY, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(+(X, Y))), +(DX, DY)) 63.56/17.21 U5_ag(X, DDX, p_out_aa(d(X), DX)) -> U6_ag(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.21 U6_ag(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_ag(d(d(X)), DDX) 63.56/17.21 U1_ag(X, Y, DX, DY, p_out_ag(d(e(X)), DX)) -> U2_ag(X, Y, DX, DY, p_in_ag(d(e(Y)), DY)) 63.56/17.21 U2_ag(X, Y, DX, DY, p_out_ag(d(e(Y)), DY)) -> p_out_ag(d(e(+(X, Y))), +(DX, DY)) 63.56/17.21 63.56/17.21 The argument filtering Pi contains the following mapping: 63.56/17.21 p_in_ag(x1, x2) = p_in_ag(x2) 63.56/17.21 63.56/17.21 const(x1) = const 63.56/17.21 63.56/17.21 1 = 1 63.56/17.21 63.56/17.21 p_out_ag(x1, x2) = p_out_ag(x1, x2) 63.56/17.21 63.56/17.21 0 = 0 63.56/17.21 63.56/17.21 +(x1, x2) = +(x1, x2) 63.56/17.21 63.56/17.21 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x3, x4, x5) 63.56/17.21 63.56/17.21 *(x1, x2) = *(x1, x2) 63.56/17.21 63.56/17.21 U3_ag(x1, x2, x3, x4, x5) = U3_ag(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 p_in_gg(x1, x2) = p_in_gg(x1, x2) 63.56/17.21 63.56/17.21 d(x1) = d(x1) 63.56/17.21 63.56/17.21 e(x1) = e(x1) 63.56/17.21 63.56/17.21 t = t 63.56/17.21 63.56/17.21 p_out_gg(x1, x2) = p_out_gg(x1, x2) 63.56/17.21 63.56/17.21 U1_gg(x1, x2, x3, x4, x5) = U1_gg(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 U3_gg(x1, x2, x3, x4, x5) = U3_gg(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 U5_gg(x1, x2, x3) = U5_gg(x1, x2, x3) 63.56/17.21 63.56/17.21 p_in_ga(x1, x2) = p_in_ga(x1) 63.56/17.21 63.56/17.21 p_out_ga(x1, x2) = p_out_ga(x1, x2) 63.56/17.21 63.56/17.21 U1_ga(x1, x2, x3, x4, x5) = U1_ga(x1, x2, x5) 63.56/17.21 63.56/17.21 U3_ga(x1, x2, x3, x4, x5) = U3_ga(x1, x2, x5) 63.56/17.21 63.56/17.21 U5_ga(x1, x2, x3) = U5_ga(x1, x3) 63.56/17.21 63.56/17.21 U6_ga(x1, x2, x3, x4) = U6_ga(x1, x4) 63.56/17.21 63.56/17.21 U4_ga(x1, x2, x3, x4, x5) = U4_ga(x1, x2, x4, x5) 63.56/17.21 63.56/17.21 U2_ga(x1, x2, x3, x4, x5) = U2_ga(x1, x2, x3, x5) 63.56/17.21 63.56/17.21 U6_gg(x1, x2, x3, x4) = U6_gg(x1, x2, x4) 63.56/17.21 63.56/17.21 U4_gg(x1, x2, x3, x4, x5) = U4_gg(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 U2_gg(x1, x2, x3, x4, x5) = U2_gg(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 U5_ag(x1, x2, x3) = U5_ag(x2, x3) 63.56/17.21 63.56/17.21 p_in_aa(x1, x2) = p_in_aa 63.56/17.21 63.56/17.21 p_out_aa(x1, x2) = p_out_aa(x1, x2) 63.56/17.21 63.56/17.21 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 63.56/17.21 63.56/17.21 U3_aa(x1, x2, x3, x4, x5) = U3_aa(x5) 63.56/17.21 63.56/17.21 U5_aa(x1, x2, x3) = U5_aa(x3) 63.56/17.21 63.56/17.21 U6_aa(x1, x2, x3, x4) = U6_aa(x1, x4) 63.56/17.21 63.56/17.21 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x1, x4, x5) 63.56/17.21 63.56/17.21 U2_aa(x1, x2, x3, x4, x5) = U2_aa(x1, x3, x5) 63.56/17.21 63.56/17.21 U6_ag(x1, x2, x3, x4) = U6_ag(x1, x2, x4) 63.56/17.21 63.56/17.21 U2_ag(x1, x2, x3, x4, x5) = U2_ag(x1, x3, x4, x5) 63.56/17.21 63.56/17.21 63.56/17.21 63.56/17.21 ---------------------------------------- 63.56/17.21 63.56/17.21 (33) DependencyPairsProof (EQUIVALENT) 63.56/17.21 Using Dependency Pairs [AG00,LOPSTR] we result in the following initial DP problem: 63.56/17.21 Pi DP problem: 63.56/17.21 The TRS P consists of the following rules: 63.56/17.21 63.56/17.21 P_IN_AG(d(e(+(X, Y))), +(DX, DY)) -> U1_AG(X, Y, DX, DY, p_in_ag(d(e(X)), DX)) 63.56/17.21 P_IN_AG(d(e(+(X, Y))), +(DX, DY)) -> P_IN_AG(d(e(X)), DX) 63.56/17.21 P_IN_AG(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_AG(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.21 P_IN_AG(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> P_IN_GG(d(e(X)), DX) 63.56/17.21 P_IN_GG(d(e(+(X, Y))), +(DX, DY)) -> U1_GG(X, Y, DX, DY, p_in_gg(d(e(X)), DX)) 63.56/17.21 P_IN_GG(d(e(+(X, Y))), +(DX, DY)) -> P_IN_GG(d(e(X)), DX) 63.56/17.21 P_IN_GG(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_GG(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.21 P_IN_GG(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> P_IN_GG(d(e(X)), DX) 63.56/17.21 P_IN_GG(d(d(X)), DDX) -> U5_GG(X, DDX, p_in_ga(d(X), DX)) 63.56/17.21 P_IN_GG(d(d(X)), DDX) -> P_IN_GA(d(X), DX) 63.56/17.21 P_IN_GA(d(e(+(X, Y))), +(DX, DY)) -> U1_GA(X, Y, DX, DY, p_in_ga(d(e(X)), DX)) 63.56/17.21 P_IN_GA(d(e(+(X, Y))), +(DX, DY)) -> P_IN_GA(d(e(X)), DX) 63.56/17.21 P_IN_GA(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_GA(X, Y, DY, DX, p_in_ga(d(e(X)), DX)) 63.56/17.21 P_IN_GA(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> P_IN_GA(d(e(X)), DX) 63.56/17.21 P_IN_GA(d(d(X)), DDX) -> U5_GA(X, DDX, p_in_ga(d(X), DX)) 63.56/17.21 P_IN_GA(d(d(X)), DDX) -> P_IN_GA(d(X), DX) 63.56/17.21 U5_GA(X, DDX, p_out_ga(d(X), DX)) -> U6_GA(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.21 U5_GA(X, DDX, p_out_ga(d(X), DX)) -> P_IN_GA(d(e(DX)), DDX) 63.56/17.21 U3_GA(X, Y, DY, DX, p_out_ga(d(e(X)), DX)) -> U4_GA(X, Y, DY, DX, p_in_ga(d(e(Y)), DY)) 63.56/17.21 U3_GA(X, Y, DY, DX, p_out_ga(d(e(X)), DX)) -> P_IN_GA(d(e(Y)), DY) 63.56/17.21 U1_GA(X, Y, DX, DY, p_out_ga(d(e(X)), DX)) -> U2_GA(X, Y, DX, DY, p_in_ga(d(e(Y)), DY)) 63.56/17.21 U1_GA(X, Y, DX, DY, p_out_ga(d(e(X)), DX)) -> P_IN_GA(d(e(Y)), DY) 63.56/17.21 U5_GG(X, DDX, p_out_ga(d(X), DX)) -> U6_GG(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.21 U5_GG(X, DDX, p_out_ga(d(X), DX)) -> P_IN_GG(d(e(DX)), DDX) 63.56/17.21 U3_GG(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_GG(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.21 U3_GG(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> P_IN_GG(d(e(Y)), DY) 63.56/17.21 U1_GG(X, Y, DX, DY, p_out_gg(d(e(X)), DX)) -> U2_GG(X, Y, DX, DY, p_in_gg(d(e(Y)), DY)) 63.56/17.21 U1_GG(X, Y, DX, DY, p_out_gg(d(e(X)), DX)) -> P_IN_GG(d(e(Y)), DY) 63.56/17.21 U3_AG(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_AG(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.21 U3_AG(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> P_IN_GG(d(e(Y)), DY) 63.56/17.21 P_IN_AG(d(d(X)), DDX) -> U5_AG(X, DDX, p_in_aa(d(X), DX)) 63.56/17.21 P_IN_AG(d(d(X)), DDX) -> P_IN_AA(d(X), DX) 63.56/17.21 P_IN_AA(d(e(+(X, Y))), +(DX, DY)) -> U1_AA(X, Y, DX, DY, p_in_aa(d(e(X)), DX)) 63.56/17.21 P_IN_AA(d(e(+(X, Y))), +(DX, DY)) -> P_IN_AA(d(e(X)), DX) 63.56/17.21 P_IN_AA(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_AA(X, Y, DY, DX, p_in_aa(d(e(X)), DX)) 63.56/17.21 P_IN_AA(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> P_IN_AA(d(e(X)), DX) 63.56/17.21 P_IN_AA(d(d(X)), DDX) -> U5_AA(X, DDX, p_in_aa(d(X), DX)) 63.56/17.21 P_IN_AA(d(d(X)), DDX) -> P_IN_AA(d(X), DX) 63.56/17.21 U5_AA(X, DDX, p_out_aa(d(X), DX)) -> U6_AA(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.21 U5_AA(X, DDX, p_out_aa(d(X), DX)) -> P_IN_GA(d(e(DX)), DDX) 63.56/17.21 U3_AA(X, Y, DY, DX, p_out_aa(d(e(X)), DX)) -> U4_AA(X, Y, DY, DX, p_in_aa(d(e(Y)), DY)) 63.56/17.21 U3_AA(X, Y, DY, DX, p_out_aa(d(e(X)), DX)) -> P_IN_AA(d(e(Y)), DY) 63.56/17.21 U1_AA(X, Y, DX, DY, p_out_aa(d(e(X)), DX)) -> U2_AA(X, Y, DX, DY, p_in_aa(d(e(Y)), DY)) 63.56/17.21 U1_AA(X, Y, DX, DY, p_out_aa(d(e(X)), DX)) -> P_IN_AA(d(e(Y)), DY) 63.56/17.21 U5_AG(X, DDX, p_out_aa(d(X), DX)) -> U6_AG(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.21 U5_AG(X, DDX, p_out_aa(d(X), DX)) -> P_IN_GG(d(e(DX)), DDX) 63.56/17.21 U1_AG(X, Y, DX, DY, p_out_ag(d(e(X)), DX)) -> U2_AG(X, Y, DX, DY, p_in_ag(d(e(Y)), DY)) 63.56/17.21 U1_AG(X, Y, DX, DY, p_out_ag(d(e(X)), DX)) -> P_IN_AG(d(e(Y)), DY) 63.56/17.21 63.56/17.21 The TRS R consists of the following rules: 63.56/17.21 63.56/17.21 p_in_ag(d(e(t)), const(1)) -> p_out_ag(d(e(t)), const(1)) 63.56/17.21 p_in_ag(d(e(const(A))), const(0)) -> p_out_ag(d(e(const(A))), const(0)) 63.56/17.21 p_in_ag(d(e(+(X, Y))), +(DX, DY)) -> U1_ag(X, Y, DX, DY, p_in_ag(d(e(X)), DX)) 63.56/17.21 p_in_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ag(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.21 p_in_gg(d(e(t)), const(1)) -> p_out_gg(d(e(t)), const(1)) 63.56/17.21 p_in_gg(d(e(const(A))), const(0)) -> p_out_gg(d(e(const(A))), const(0)) 63.56/17.21 p_in_gg(d(e(+(X, Y))), +(DX, DY)) -> U1_gg(X, Y, DX, DY, p_in_gg(d(e(X)), DX)) 63.56/17.21 p_in_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_gg(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.21 p_in_gg(d(d(X)), DDX) -> U5_gg(X, DDX, p_in_ga(d(X), DX)) 63.56/17.21 p_in_ga(d(e(t)), const(1)) -> p_out_ga(d(e(t)), const(1)) 63.56/17.21 p_in_ga(d(e(const(A))), const(0)) -> p_out_ga(d(e(const(A))), const(0)) 63.56/17.21 p_in_ga(d(e(+(X, Y))), +(DX, DY)) -> U1_ga(X, Y, DX, DY, p_in_ga(d(e(X)), DX)) 63.56/17.21 p_in_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ga(X, Y, DY, DX, p_in_ga(d(e(X)), DX)) 63.56/17.21 p_in_ga(d(d(X)), DDX) -> U5_ga(X, DDX, p_in_ga(d(X), DX)) 63.56/17.21 U5_ga(X, DDX, p_out_ga(d(X), DX)) -> U6_ga(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.21 U6_ga(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_ga(d(d(X)), DDX) 63.56/17.21 U3_ga(X, Y, DY, DX, p_out_ga(d(e(X)), DX)) -> U4_ga(X, Y, DY, DX, p_in_ga(d(e(Y)), DY)) 63.56/17.21 U4_ga(X, Y, DY, DX, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.21 U1_ga(X, Y, DX, DY, p_out_ga(d(e(X)), DX)) -> U2_ga(X, Y, DX, DY, p_in_ga(d(e(Y)), DY)) 63.56/17.21 U2_ga(X, Y, DX, DY, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(+(X, Y))), +(DX, DY)) 63.56/17.21 U5_gg(X, DDX, p_out_ga(d(X), DX)) -> U6_gg(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.21 U6_gg(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_gg(d(d(X)), DDX) 63.56/17.21 U3_gg(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_gg(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.21 U4_gg(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.21 U1_gg(X, Y, DX, DY, p_out_gg(d(e(X)), DX)) -> U2_gg(X, Y, DX, DY, p_in_gg(d(e(Y)), DY)) 63.56/17.21 U2_gg(X, Y, DX, DY, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(+(X, Y))), +(DX, DY)) 63.56/17.21 U3_ag(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_ag(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.21 U4_ag(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.21 p_in_ag(d(d(X)), DDX) -> U5_ag(X, DDX, p_in_aa(d(X), DX)) 63.56/17.21 p_in_aa(d(e(t)), const(1)) -> p_out_aa(d(e(t)), const(1)) 63.56/17.21 p_in_aa(d(e(const(A))), const(0)) -> p_out_aa(d(e(const(A))), const(0)) 63.56/17.21 p_in_aa(d(e(+(X, Y))), +(DX, DY)) -> U1_aa(X, Y, DX, DY, p_in_aa(d(e(X)), DX)) 63.56/17.21 p_in_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_aa(X, Y, DY, DX, p_in_aa(d(e(X)), DX)) 63.56/17.21 p_in_aa(d(d(X)), DDX) -> U5_aa(X, DDX, p_in_aa(d(X), DX)) 63.56/17.21 U5_aa(X, DDX, p_out_aa(d(X), DX)) -> U6_aa(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.21 U6_aa(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_aa(d(d(X)), DDX) 63.56/17.21 U3_aa(X, Y, DY, DX, p_out_aa(d(e(X)), DX)) -> U4_aa(X, Y, DY, DX, p_in_aa(d(e(Y)), DY)) 63.56/17.21 U4_aa(X, Y, DY, DX, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.21 U1_aa(X, Y, DX, DY, p_out_aa(d(e(X)), DX)) -> U2_aa(X, Y, DX, DY, p_in_aa(d(e(Y)), DY)) 63.56/17.21 U2_aa(X, Y, DX, DY, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(+(X, Y))), +(DX, DY)) 63.56/17.21 U5_ag(X, DDX, p_out_aa(d(X), DX)) -> U6_ag(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.21 U6_ag(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_ag(d(d(X)), DDX) 63.56/17.21 U1_ag(X, Y, DX, DY, p_out_ag(d(e(X)), DX)) -> U2_ag(X, Y, DX, DY, p_in_ag(d(e(Y)), DY)) 63.56/17.21 U2_ag(X, Y, DX, DY, p_out_ag(d(e(Y)), DY)) -> p_out_ag(d(e(+(X, Y))), +(DX, DY)) 63.56/17.21 63.56/17.21 The argument filtering Pi contains the following mapping: 63.56/17.21 p_in_ag(x1, x2) = p_in_ag(x2) 63.56/17.21 63.56/17.21 const(x1) = const 63.56/17.21 63.56/17.21 1 = 1 63.56/17.21 63.56/17.21 p_out_ag(x1, x2) = p_out_ag(x1, x2) 63.56/17.21 63.56/17.21 0 = 0 63.56/17.21 63.56/17.21 +(x1, x2) = +(x1, x2) 63.56/17.21 63.56/17.21 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x3, x4, x5) 63.56/17.21 63.56/17.21 *(x1, x2) = *(x1, x2) 63.56/17.21 63.56/17.21 U3_ag(x1, x2, x3, x4, x5) = U3_ag(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 p_in_gg(x1, x2) = p_in_gg(x1, x2) 63.56/17.21 63.56/17.21 d(x1) = d(x1) 63.56/17.21 63.56/17.21 e(x1) = e(x1) 63.56/17.21 63.56/17.21 t = t 63.56/17.21 63.56/17.21 p_out_gg(x1, x2) = p_out_gg(x1, x2) 63.56/17.21 63.56/17.21 U1_gg(x1, x2, x3, x4, x5) = U1_gg(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 U3_gg(x1, x2, x3, x4, x5) = U3_gg(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 U5_gg(x1, x2, x3) = U5_gg(x1, x2, x3) 63.56/17.21 63.56/17.21 p_in_ga(x1, x2) = p_in_ga(x1) 63.56/17.21 63.56/17.21 p_out_ga(x1, x2) = p_out_ga(x1, x2) 63.56/17.21 63.56/17.21 U1_ga(x1, x2, x3, x4, x5) = U1_ga(x1, x2, x5) 63.56/17.21 63.56/17.21 U3_ga(x1, x2, x3, x4, x5) = U3_ga(x1, x2, x5) 63.56/17.21 63.56/17.21 U5_ga(x1, x2, x3) = U5_ga(x1, x3) 63.56/17.21 63.56/17.21 U6_ga(x1, x2, x3, x4) = U6_ga(x1, x4) 63.56/17.21 63.56/17.21 U4_ga(x1, x2, x3, x4, x5) = U4_ga(x1, x2, x4, x5) 63.56/17.21 63.56/17.21 U2_ga(x1, x2, x3, x4, x5) = U2_ga(x1, x2, x3, x5) 63.56/17.21 63.56/17.21 U6_gg(x1, x2, x3, x4) = U6_gg(x1, x2, x4) 63.56/17.21 63.56/17.21 U4_gg(x1, x2, x3, x4, x5) = U4_gg(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 U2_gg(x1, x2, x3, x4, x5) = U2_gg(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 U5_ag(x1, x2, x3) = U5_ag(x2, x3) 63.56/17.21 63.56/17.21 p_in_aa(x1, x2) = p_in_aa 63.56/17.21 63.56/17.21 p_out_aa(x1, x2) = p_out_aa(x1, x2) 63.56/17.21 63.56/17.21 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 63.56/17.21 63.56/17.21 U3_aa(x1, x2, x3, x4, x5) = U3_aa(x5) 63.56/17.21 63.56/17.21 U5_aa(x1, x2, x3) = U5_aa(x3) 63.56/17.21 63.56/17.21 U6_aa(x1, x2, x3, x4) = U6_aa(x1, x4) 63.56/17.21 63.56/17.21 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x1, x4, x5) 63.56/17.21 63.56/17.21 U2_aa(x1, x2, x3, x4, x5) = U2_aa(x1, x3, x5) 63.56/17.21 63.56/17.21 U6_ag(x1, x2, x3, x4) = U6_ag(x1, x2, x4) 63.56/17.21 63.56/17.21 U2_ag(x1, x2, x3, x4, x5) = U2_ag(x1, x3, x4, x5) 63.56/17.21 63.56/17.21 P_IN_AG(x1, x2) = P_IN_AG(x2) 63.56/17.21 63.56/17.21 U1_AG(x1, x2, x3, x4, x5) = U1_AG(x3, x4, x5) 63.56/17.21 63.56/17.21 U3_AG(x1, x2, x3, x4, x5) = U3_AG(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 P_IN_GG(x1, x2) = P_IN_GG(x1, x2) 63.56/17.21 63.56/17.21 U1_GG(x1, x2, x3, x4, x5) = U1_GG(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 U3_GG(x1, x2, x3, x4, x5) = U3_GG(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 U5_GG(x1, x2, x3) = U5_GG(x1, x2, x3) 63.56/17.21 63.56/17.21 P_IN_GA(x1, x2) = P_IN_GA(x1) 63.56/17.21 63.56/17.21 U1_GA(x1, x2, x3, x4, x5) = U1_GA(x1, x2, x5) 63.56/17.21 63.56/17.21 U3_GA(x1, x2, x3, x4, x5) = U3_GA(x1, x2, x5) 63.56/17.21 63.56/17.21 U5_GA(x1, x2, x3) = U5_GA(x1, x3) 63.56/17.21 63.56/17.21 U6_GA(x1, x2, x3, x4) = U6_GA(x1, x4) 63.56/17.21 63.56/17.21 U4_GA(x1, x2, x3, x4, x5) = U4_GA(x1, x2, x4, x5) 63.56/17.21 63.56/17.21 U2_GA(x1, x2, x3, x4, x5) = U2_GA(x1, x2, x3, x5) 63.56/17.21 63.56/17.21 U6_GG(x1, x2, x3, x4) = U6_GG(x1, x2, x4) 63.56/17.21 63.56/17.21 U4_GG(x1, x2, x3, x4, x5) = U4_GG(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 U2_GG(x1, x2, x3, x4, x5) = U2_GG(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 U4_AG(x1, x2, x3, x4, x5) = U4_AG(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 U5_AG(x1, x2, x3) = U5_AG(x2, x3) 63.56/17.21 63.56/17.21 P_IN_AA(x1, x2) = P_IN_AA 63.56/17.21 63.56/17.21 U1_AA(x1, x2, x3, x4, x5) = U1_AA(x5) 63.56/17.21 63.56/17.21 U3_AA(x1, x2, x3, x4, x5) = U3_AA(x5) 63.56/17.21 63.56/17.21 U5_AA(x1, x2, x3) = U5_AA(x3) 63.56/17.21 63.56/17.21 U6_AA(x1, x2, x3, x4) = U6_AA(x1, x4) 63.56/17.21 63.56/17.21 U4_AA(x1, x2, x3, x4, x5) = U4_AA(x1, x4, x5) 63.56/17.21 63.56/17.21 U2_AA(x1, x2, x3, x4, x5) = U2_AA(x1, x3, x5) 63.56/17.21 63.56/17.21 U6_AG(x1, x2, x3, x4) = U6_AG(x1, x2, x4) 63.56/17.21 63.56/17.21 U2_AG(x1, x2, x3, x4, x5) = U2_AG(x1, x3, x4, x5) 63.56/17.21 63.56/17.21 63.56/17.21 We have to consider all (P,R,Pi)-chains 63.56/17.21 ---------------------------------------- 63.56/17.21 63.56/17.21 (34) 63.56/17.21 Obligation: 63.56/17.21 Pi DP problem: 63.56/17.21 The TRS P consists of the following rules: 63.56/17.21 63.56/17.21 P_IN_AG(d(e(+(X, Y))), +(DX, DY)) -> U1_AG(X, Y, DX, DY, p_in_ag(d(e(X)), DX)) 63.56/17.21 P_IN_AG(d(e(+(X, Y))), +(DX, DY)) -> P_IN_AG(d(e(X)), DX) 63.56/17.21 P_IN_AG(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_AG(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.21 P_IN_AG(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> P_IN_GG(d(e(X)), DX) 63.56/17.21 P_IN_GG(d(e(+(X, Y))), +(DX, DY)) -> U1_GG(X, Y, DX, DY, p_in_gg(d(e(X)), DX)) 63.56/17.21 P_IN_GG(d(e(+(X, Y))), +(DX, DY)) -> P_IN_GG(d(e(X)), DX) 63.56/17.21 P_IN_GG(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_GG(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.21 P_IN_GG(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> P_IN_GG(d(e(X)), DX) 63.56/17.21 P_IN_GG(d(d(X)), DDX) -> U5_GG(X, DDX, p_in_ga(d(X), DX)) 63.56/17.21 P_IN_GG(d(d(X)), DDX) -> P_IN_GA(d(X), DX) 63.56/17.21 P_IN_GA(d(e(+(X, Y))), +(DX, DY)) -> U1_GA(X, Y, DX, DY, p_in_ga(d(e(X)), DX)) 63.56/17.21 P_IN_GA(d(e(+(X, Y))), +(DX, DY)) -> P_IN_GA(d(e(X)), DX) 63.56/17.21 P_IN_GA(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_GA(X, Y, DY, DX, p_in_ga(d(e(X)), DX)) 63.56/17.21 P_IN_GA(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> P_IN_GA(d(e(X)), DX) 63.56/17.21 P_IN_GA(d(d(X)), DDX) -> U5_GA(X, DDX, p_in_ga(d(X), DX)) 63.56/17.21 P_IN_GA(d(d(X)), DDX) -> P_IN_GA(d(X), DX) 63.56/17.21 U5_GA(X, DDX, p_out_ga(d(X), DX)) -> U6_GA(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.21 U5_GA(X, DDX, p_out_ga(d(X), DX)) -> P_IN_GA(d(e(DX)), DDX) 63.56/17.21 U3_GA(X, Y, DY, DX, p_out_ga(d(e(X)), DX)) -> U4_GA(X, Y, DY, DX, p_in_ga(d(e(Y)), DY)) 63.56/17.21 U3_GA(X, Y, DY, DX, p_out_ga(d(e(X)), DX)) -> P_IN_GA(d(e(Y)), DY) 63.56/17.21 U1_GA(X, Y, DX, DY, p_out_ga(d(e(X)), DX)) -> U2_GA(X, Y, DX, DY, p_in_ga(d(e(Y)), DY)) 63.56/17.21 U1_GA(X, Y, DX, DY, p_out_ga(d(e(X)), DX)) -> P_IN_GA(d(e(Y)), DY) 63.56/17.21 U5_GG(X, DDX, p_out_ga(d(X), DX)) -> U6_GG(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.21 U5_GG(X, DDX, p_out_ga(d(X), DX)) -> P_IN_GG(d(e(DX)), DDX) 63.56/17.21 U3_GG(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_GG(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.21 U3_GG(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> P_IN_GG(d(e(Y)), DY) 63.56/17.21 U1_GG(X, Y, DX, DY, p_out_gg(d(e(X)), DX)) -> U2_GG(X, Y, DX, DY, p_in_gg(d(e(Y)), DY)) 63.56/17.21 U1_GG(X, Y, DX, DY, p_out_gg(d(e(X)), DX)) -> P_IN_GG(d(e(Y)), DY) 63.56/17.21 U3_AG(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_AG(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.21 U3_AG(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> P_IN_GG(d(e(Y)), DY) 63.56/17.21 P_IN_AG(d(d(X)), DDX) -> U5_AG(X, DDX, p_in_aa(d(X), DX)) 63.56/17.21 P_IN_AG(d(d(X)), DDX) -> P_IN_AA(d(X), DX) 63.56/17.21 P_IN_AA(d(e(+(X, Y))), +(DX, DY)) -> U1_AA(X, Y, DX, DY, p_in_aa(d(e(X)), DX)) 63.56/17.21 P_IN_AA(d(e(+(X, Y))), +(DX, DY)) -> P_IN_AA(d(e(X)), DX) 63.56/17.21 P_IN_AA(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_AA(X, Y, DY, DX, p_in_aa(d(e(X)), DX)) 63.56/17.21 P_IN_AA(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> P_IN_AA(d(e(X)), DX) 63.56/17.21 P_IN_AA(d(d(X)), DDX) -> U5_AA(X, DDX, p_in_aa(d(X), DX)) 63.56/17.21 P_IN_AA(d(d(X)), DDX) -> P_IN_AA(d(X), DX) 63.56/17.21 U5_AA(X, DDX, p_out_aa(d(X), DX)) -> U6_AA(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.21 U5_AA(X, DDX, p_out_aa(d(X), DX)) -> P_IN_GA(d(e(DX)), DDX) 63.56/17.21 U3_AA(X, Y, DY, DX, p_out_aa(d(e(X)), DX)) -> U4_AA(X, Y, DY, DX, p_in_aa(d(e(Y)), DY)) 63.56/17.21 U3_AA(X, Y, DY, DX, p_out_aa(d(e(X)), DX)) -> P_IN_AA(d(e(Y)), DY) 63.56/17.21 U1_AA(X, Y, DX, DY, p_out_aa(d(e(X)), DX)) -> U2_AA(X, Y, DX, DY, p_in_aa(d(e(Y)), DY)) 63.56/17.21 U1_AA(X, Y, DX, DY, p_out_aa(d(e(X)), DX)) -> P_IN_AA(d(e(Y)), DY) 63.56/17.21 U5_AG(X, DDX, p_out_aa(d(X), DX)) -> U6_AG(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.21 U5_AG(X, DDX, p_out_aa(d(X), DX)) -> P_IN_GG(d(e(DX)), DDX) 63.56/17.21 U1_AG(X, Y, DX, DY, p_out_ag(d(e(X)), DX)) -> U2_AG(X, Y, DX, DY, p_in_ag(d(e(Y)), DY)) 63.56/17.21 U1_AG(X, Y, DX, DY, p_out_ag(d(e(X)), DX)) -> P_IN_AG(d(e(Y)), DY) 63.56/17.21 63.56/17.21 The TRS R consists of the following rules: 63.56/17.21 63.56/17.21 p_in_ag(d(e(t)), const(1)) -> p_out_ag(d(e(t)), const(1)) 63.56/17.21 p_in_ag(d(e(const(A))), const(0)) -> p_out_ag(d(e(const(A))), const(0)) 63.56/17.21 p_in_ag(d(e(+(X, Y))), +(DX, DY)) -> U1_ag(X, Y, DX, DY, p_in_ag(d(e(X)), DX)) 63.56/17.21 p_in_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ag(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.21 p_in_gg(d(e(t)), const(1)) -> p_out_gg(d(e(t)), const(1)) 63.56/17.21 p_in_gg(d(e(const(A))), const(0)) -> p_out_gg(d(e(const(A))), const(0)) 63.56/17.21 p_in_gg(d(e(+(X, Y))), +(DX, DY)) -> U1_gg(X, Y, DX, DY, p_in_gg(d(e(X)), DX)) 63.56/17.21 p_in_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_gg(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.21 p_in_gg(d(d(X)), DDX) -> U5_gg(X, DDX, p_in_ga(d(X), DX)) 63.56/17.21 p_in_ga(d(e(t)), const(1)) -> p_out_ga(d(e(t)), const(1)) 63.56/17.21 p_in_ga(d(e(const(A))), const(0)) -> p_out_ga(d(e(const(A))), const(0)) 63.56/17.21 p_in_ga(d(e(+(X, Y))), +(DX, DY)) -> U1_ga(X, Y, DX, DY, p_in_ga(d(e(X)), DX)) 63.56/17.21 p_in_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ga(X, Y, DY, DX, p_in_ga(d(e(X)), DX)) 63.56/17.21 p_in_ga(d(d(X)), DDX) -> U5_ga(X, DDX, p_in_ga(d(X), DX)) 63.56/17.21 U5_ga(X, DDX, p_out_ga(d(X), DX)) -> U6_ga(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.21 U6_ga(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_ga(d(d(X)), DDX) 63.56/17.21 U3_ga(X, Y, DY, DX, p_out_ga(d(e(X)), DX)) -> U4_ga(X, Y, DY, DX, p_in_ga(d(e(Y)), DY)) 63.56/17.21 U4_ga(X, Y, DY, DX, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.21 U1_ga(X, Y, DX, DY, p_out_ga(d(e(X)), DX)) -> U2_ga(X, Y, DX, DY, p_in_ga(d(e(Y)), DY)) 63.56/17.21 U2_ga(X, Y, DX, DY, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(+(X, Y))), +(DX, DY)) 63.56/17.21 U5_gg(X, DDX, p_out_ga(d(X), DX)) -> U6_gg(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.21 U6_gg(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_gg(d(d(X)), DDX) 63.56/17.21 U3_gg(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_gg(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.21 U4_gg(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.21 U1_gg(X, Y, DX, DY, p_out_gg(d(e(X)), DX)) -> U2_gg(X, Y, DX, DY, p_in_gg(d(e(Y)), DY)) 63.56/17.21 U2_gg(X, Y, DX, DY, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(+(X, Y))), +(DX, DY)) 63.56/17.21 U3_ag(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_ag(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.21 U4_ag(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.21 p_in_ag(d(d(X)), DDX) -> U5_ag(X, DDX, p_in_aa(d(X), DX)) 63.56/17.21 p_in_aa(d(e(t)), const(1)) -> p_out_aa(d(e(t)), const(1)) 63.56/17.21 p_in_aa(d(e(const(A))), const(0)) -> p_out_aa(d(e(const(A))), const(0)) 63.56/17.21 p_in_aa(d(e(+(X, Y))), +(DX, DY)) -> U1_aa(X, Y, DX, DY, p_in_aa(d(e(X)), DX)) 63.56/17.21 p_in_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_aa(X, Y, DY, DX, p_in_aa(d(e(X)), DX)) 63.56/17.21 p_in_aa(d(d(X)), DDX) -> U5_aa(X, DDX, p_in_aa(d(X), DX)) 63.56/17.21 U5_aa(X, DDX, p_out_aa(d(X), DX)) -> U6_aa(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.21 U6_aa(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_aa(d(d(X)), DDX) 63.56/17.21 U3_aa(X, Y, DY, DX, p_out_aa(d(e(X)), DX)) -> U4_aa(X, Y, DY, DX, p_in_aa(d(e(Y)), DY)) 63.56/17.21 U4_aa(X, Y, DY, DX, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.21 U1_aa(X, Y, DX, DY, p_out_aa(d(e(X)), DX)) -> U2_aa(X, Y, DX, DY, p_in_aa(d(e(Y)), DY)) 63.56/17.21 U2_aa(X, Y, DX, DY, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(+(X, Y))), +(DX, DY)) 63.56/17.21 U5_ag(X, DDX, p_out_aa(d(X), DX)) -> U6_ag(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.21 U6_ag(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_ag(d(d(X)), DDX) 63.56/17.21 U1_ag(X, Y, DX, DY, p_out_ag(d(e(X)), DX)) -> U2_ag(X, Y, DX, DY, p_in_ag(d(e(Y)), DY)) 63.56/17.21 U2_ag(X, Y, DX, DY, p_out_ag(d(e(Y)), DY)) -> p_out_ag(d(e(+(X, Y))), +(DX, DY)) 63.56/17.21 63.56/17.21 The argument filtering Pi contains the following mapping: 63.56/17.21 p_in_ag(x1, x2) = p_in_ag(x2) 63.56/17.21 63.56/17.21 const(x1) = const 63.56/17.21 63.56/17.21 1 = 1 63.56/17.21 63.56/17.21 p_out_ag(x1, x2) = p_out_ag(x1, x2) 63.56/17.21 63.56/17.21 0 = 0 63.56/17.21 63.56/17.21 +(x1, x2) = +(x1, x2) 63.56/17.21 63.56/17.21 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x3, x4, x5) 63.56/17.21 63.56/17.21 *(x1, x2) = *(x1, x2) 63.56/17.21 63.56/17.21 U3_ag(x1, x2, x3, x4, x5) = U3_ag(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 p_in_gg(x1, x2) = p_in_gg(x1, x2) 63.56/17.21 63.56/17.21 d(x1) = d(x1) 63.56/17.21 63.56/17.21 e(x1) = e(x1) 63.56/17.21 63.56/17.21 t = t 63.56/17.21 63.56/17.21 p_out_gg(x1, x2) = p_out_gg(x1, x2) 63.56/17.21 63.56/17.21 U1_gg(x1, x2, x3, x4, x5) = U1_gg(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 U3_gg(x1, x2, x3, x4, x5) = U3_gg(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 U5_gg(x1, x2, x3) = U5_gg(x1, x2, x3) 63.56/17.21 63.56/17.21 p_in_ga(x1, x2) = p_in_ga(x1) 63.56/17.21 63.56/17.21 p_out_ga(x1, x2) = p_out_ga(x1, x2) 63.56/17.21 63.56/17.21 U1_ga(x1, x2, x3, x4, x5) = U1_ga(x1, x2, x5) 63.56/17.21 63.56/17.21 U3_ga(x1, x2, x3, x4, x5) = U3_ga(x1, x2, x5) 63.56/17.21 63.56/17.21 U5_ga(x1, x2, x3) = U5_ga(x1, x3) 63.56/17.21 63.56/17.21 U6_ga(x1, x2, x3, x4) = U6_ga(x1, x4) 63.56/17.21 63.56/17.21 U4_ga(x1, x2, x3, x4, x5) = U4_ga(x1, x2, x4, x5) 63.56/17.21 63.56/17.21 U2_ga(x1, x2, x3, x4, x5) = U2_ga(x1, x2, x3, x5) 63.56/17.21 63.56/17.21 U6_gg(x1, x2, x3, x4) = U6_gg(x1, x2, x4) 63.56/17.21 63.56/17.21 U4_gg(x1, x2, x3, x4, x5) = U4_gg(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 U2_gg(x1, x2, x3, x4, x5) = U2_gg(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 U5_ag(x1, x2, x3) = U5_ag(x2, x3) 63.56/17.21 63.56/17.21 p_in_aa(x1, x2) = p_in_aa 63.56/17.21 63.56/17.21 p_out_aa(x1, x2) = p_out_aa(x1, x2) 63.56/17.21 63.56/17.21 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 63.56/17.21 63.56/17.21 U3_aa(x1, x2, x3, x4, x5) = U3_aa(x5) 63.56/17.21 63.56/17.21 U5_aa(x1, x2, x3) = U5_aa(x3) 63.56/17.21 63.56/17.21 U6_aa(x1, x2, x3, x4) = U6_aa(x1, x4) 63.56/17.21 63.56/17.21 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x1, x4, x5) 63.56/17.21 63.56/17.21 U2_aa(x1, x2, x3, x4, x5) = U2_aa(x1, x3, x5) 63.56/17.21 63.56/17.21 U6_ag(x1, x2, x3, x4) = U6_ag(x1, x2, x4) 63.56/17.21 63.56/17.21 U2_ag(x1, x2, x3, x4, x5) = U2_ag(x1, x3, x4, x5) 63.56/17.21 63.56/17.21 P_IN_AG(x1, x2) = P_IN_AG(x2) 63.56/17.21 63.56/17.21 U1_AG(x1, x2, x3, x4, x5) = U1_AG(x3, x4, x5) 63.56/17.21 63.56/17.21 U3_AG(x1, x2, x3, x4, x5) = U3_AG(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 P_IN_GG(x1, x2) = P_IN_GG(x1, x2) 63.56/17.21 63.56/17.21 U1_GG(x1, x2, x3, x4, x5) = U1_GG(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 U3_GG(x1, x2, x3, x4, x5) = U3_GG(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 U5_GG(x1, x2, x3) = U5_GG(x1, x2, x3) 63.56/17.21 63.56/17.21 P_IN_GA(x1, x2) = P_IN_GA(x1) 63.56/17.21 63.56/17.21 U1_GA(x1, x2, x3, x4, x5) = U1_GA(x1, x2, x5) 63.56/17.21 63.56/17.21 U3_GA(x1, x2, x3, x4, x5) = U3_GA(x1, x2, x5) 63.56/17.21 63.56/17.21 U5_GA(x1, x2, x3) = U5_GA(x1, x3) 63.56/17.21 63.56/17.21 U6_GA(x1, x2, x3, x4) = U6_GA(x1, x4) 63.56/17.21 63.56/17.21 U4_GA(x1, x2, x3, x4, x5) = U4_GA(x1, x2, x4, x5) 63.56/17.21 63.56/17.21 U2_GA(x1, x2, x3, x4, x5) = U2_GA(x1, x2, x3, x5) 63.56/17.21 63.56/17.21 U6_GG(x1, x2, x3, x4) = U6_GG(x1, x2, x4) 63.56/17.21 63.56/17.21 U4_GG(x1, x2, x3, x4, x5) = U4_GG(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 U2_GG(x1, x2, x3, x4, x5) = U2_GG(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 U4_AG(x1, x2, x3, x4, x5) = U4_AG(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 U5_AG(x1, x2, x3) = U5_AG(x2, x3) 63.56/17.21 63.56/17.21 P_IN_AA(x1, x2) = P_IN_AA 63.56/17.21 63.56/17.21 U1_AA(x1, x2, x3, x4, x5) = U1_AA(x5) 63.56/17.21 63.56/17.21 U3_AA(x1, x2, x3, x4, x5) = U3_AA(x5) 63.56/17.21 63.56/17.21 U5_AA(x1, x2, x3) = U5_AA(x3) 63.56/17.21 63.56/17.21 U6_AA(x1, x2, x3, x4) = U6_AA(x1, x4) 63.56/17.21 63.56/17.21 U4_AA(x1, x2, x3, x4, x5) = U4_AA(x1, x4, x5) 63.56/17.21 63.56/17.21 U2_AA(x1, x2, x3, x4, x5) = U2_AA(x1, x3, x5) 63.56/17.21 63.56/17.21 U6_AG(x1, x2, x3, x4) = U6_AG(x1, x2, x4) 63.56/17.21 63.56/17.21 U2_AG(x1, x2, x3, x4, x5) = U2_AG(x1, x3, x4, x5) 63.56/17.21 63.56/17.21 63.56/17.21 We have to consider all (P,R,Pi)-chains 63.56/17.21 ---------------------------------------- 63.56/17.21 63.56/17.21 (35) DependencyGraphProof (EQUIVALENT) 63.56/17.21 The approximation of the Dependency Graph [LOPSTR] contains 6 SCCs with 25 less nodes. 63.56/17.21 ---------------------------------------- 63.56/17.21 63.56/17.21 (36) 63.56/17.21 Complex Obligation (AND) 63.56/17.21 63.56/17.21 ---------------------------------------- 63.56/17.21 63.56/17.21 (37) 63.56/17.21 Obligation: 63.56/17.21 Pi DP problem: 63.56/17.21 The TRS P consists of the following rules: 63.56/17.21 63.56/17.21 U1_AA(X, Y, DX, DY, p_out_aa(d(e(X)), DX)) -> P_IN_AA(d(e(Y)), DY) 63.56/17.21 P_IN_AA(d(e(+(X, Y))), +(DX, DY)) -> U1_AA(X, Y, DX, DY, p_in_aa(d(e(X)), DX)) 63.56/17.21 P_IN_AA(d(e(+(X, Y))), +(DX, DY)) -> P_IN_AA(d(e(X)), DX) 63.56/17.21 P_IN_AA(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_AA(X, Y, DY, DX, p_in_aa(d(e(X)), DX)) 63.56/17.21 U3_AA(X, Y, DY, DX, p_out_aa(d(e(X)), DX)) -> P_IN_AA(d(e(Y)), DY) 63.56/17.21 P_IN_AA(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> P_IN_AA(d(e(X)), DX) 63.56/17.21 63.56/17.21 The TRS R consists of the following rules: 63.56/17.21 63.56/17.21 p_in_ag(d(e(t)), const(1)) -> p_out_ag(d(e(t)), const(1)) 63.56/17.21 p_in_ag(d(e(const(A))), const(0)) -> p_out_ag(d(e(const(A))), const(0)) 63.56/17.21 p_in_ag(d(e(+(X, Y))), +(DX, DY)) -> U1_ag(X, Y, DX, DY, p_in_ag(d(e(X)), DX)) 63.56/17.21 p_in_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ag(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.21 p_in_gg(d(e(t)), const(1)) -> p_out_gg(d(e(t)), const(1)) 63.56/17.21 p_in_gg(d(e(const(A))), const(0)) -> p_out_gg(d(e(const(A))), const(0)) 63.56/17.21 p_in_gg(d(e(+(X, Y))), +(DX, DY)) -> U1_gg(X, Y, DX, DY, p_in_gg(d(e(X)), DX)) 63.56/17.21 p_in_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_gg(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.21 p_in_gg(d(d(X)), DDX) -> U5_gg(X, DDX, p_in_ga(d(X), DX)) 63.56/17.21 p_in_ga(d(e(t)), const(1)) -> p_out_ga(d(e(t)), const(1)) 63.56/17.21 p_in_ga(d(e(const(A))), const(0)) -> p_out_ga(d(e(const(A))), const(0)) 63.56/17.21 p_in_ga(d(e(+(X, Y))), +(DX, DY)) -> U1_ga(X, Y, DX, DY, p_in_ga(d(e(X)), DX)) 63.56/17.21 p_in_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ga(X, Y, DY, DX, p_in_ga(d(e(X)), DX)) 63.56/17.21 p_in_ga(d(d(X)), DDX) -> U5_ga(X, DDX, p_in_ga(d(X), DX)) 63.56/17.21 U5_ga(X, DDX, p_out_ga(d(X), DX)) -> U6_ga(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.21 U6_ga(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_ga(d(d(X)), DDX) 63.56/17.21 U3_ga(X, Y, DY, DX, p_out_ga(d(e(X)), DX)) -> U4_ga(X, Y, DY, DX, p_in_ga(d(e(Y)), DY)) 63.56/17.21 U4_ga(X, Y, DY, DX, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.21 U1_ga(X, Y, DX, DY, p_out_ga(d(e(X)), DX)) -> U2_ga(X, Y, DX, DY, p_in_ga(d(e(Y)), DY)) 63.56/17.21 U2_ga(X, Y, DX, DY, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(+(X, Y))), +(DX, DY)) 63.56/17.21 U5_gg(X, DDX, p_out_ga(d(X), DX)) -> U6_gg(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.21 U6_gg(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_gg(d(d(X)), DDX) 63.56/17.21 U3_gg(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_gg(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.21 U4_gg(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.21 U1_gg(X, Y, DX, DY, p_out_gg(d(e(X)), DX)) -> U2_gg(X, Y, DX, DY, p_in_gg(d(e(Y)), DY)) 63.56/17.21 U2_gg(X, Y, DX, DY, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(+(X, Y))), +(DX, DY)) 63.56/17.21 U3_ag(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_ag(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.21 U4_ag(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.21 p_in_ag(d(d(X)), DDX) -> U5_ag(X, DDX, p_in_aa(d(X), DX)) 63.56/17.21 p_in_aa(d(e(t)), const(1)) -> p_out_aa(d(e(t)), const(1)) 63.56/17.21 p_in_aa(d(e(const(A))), const(0)) -> p_out_aa(d(e(const(A))), const(0)) 63.56/17.21 p_in_aa(d(e(+(X, Y))), +(DX, DY)) -> U1_aa(X, Y, DX, DY, p_in_aa(d(e(X)), DX)) 63.56/17.21 p_in_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_aa(X, Y, DY, DX, p_in_aa(d(e(X)), DX)) 63.56/17.21 p_in_aa(d(d(X)), DDX) -> U5_aa(X, DDX, p_in_aa(d(X), DX)) 63.56/17.21 U5_aa(X, DDX, p_out_aa(d(X), DX)) -> U6_aa(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.21 U6_aa(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_aa(d(d(X)), DDX) 63.56/17.21 U3_aa(X, Y, DY, DX, p_out_aa(d(e(X)), DX)) -> U4_aa(X, Y, DY, DX, p_in_aa(d(e(Y)), DY)) 63.56/17.21 U4_aa(X, Y, DY, DX, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.21 U1_aa(X, Y, DX, DY, p_out_aa(d(e(X)), DX)) -> U2_aa(X, Y, DX, DY, p_in_aa(d(e(Y)), DY)) 63.56/17.21 U2_aa(X, Y, DX, DY, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(+(X, Y))), +(DX, DY)) 63.56/17.21 U5_ag(X, DDX, p_out_aa(d(X), DX)) -> U6_ag(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.21 U6_ag(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_ag(d(d(X)), DDX) 63.56/17.21 U1_ag(X, Y, DX, DY, p_out_ag(d(e(X)), DX)) -> U2_ag(X, Y, DX, DY, p_in_ag(d(e(Y)), DY)) 63.56/17.21 U2_ag(X, Y, DX, DY, p_out_ag(d(e(Y)), DY)) -> p_out_ag(d(e(+(X, Y))), +(DX, DY)) 63.56/17.21 63.56/17.21 The argument filtering Pi contains the following mapping: 63.56/17.21 p_in_ag(x1, x2) = p_in_ag(x2) 63.56/17.21 63.56/17.21 const(x1) = const 63.56/17.21 63.56/17.21 1 = 1 63.56/17.21 63.56/17.21 p_out_ag(x1, x2) = p_out_ag(x1, x2) 63.56/17.21 63.56/17.21 0 = 0 63.56/17.21 63.56/17.21 +(x1, x2) = +(x1, x2) 63.56/17.21 63.56/17.21 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x3, x4, x5) 63.56/17.21 63.56/17.21 *(x1, x2) = *(x1, x2) 63.56/17.21 63.56/17.21 U3_ag(x1, x2, x3, x4, x5) = U3_ag(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 p_in_gg(x1, x2) = p_in_gg(x1, x2) 63.56/17.21 63.56/17.21 d(x1) = d(x1) 63.56/17.21 63.56/17.21 e(x1) = e(x1) 63.56/17.21 63.56/17.21 t = t 63.56/17.21 63.56/17.21 p_out_gg(x1, x2) = p_out_gg(x1, x2) 63.56/17.21 63.56/17.21 U1_gg(x1, x2, x3, x4, x5) = U1_gg(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 U3_gg(x1, x2, x3, x4, x5) = U3_gg(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 U5_gg(x1, x2, x3) = U5_gg(x1, x2, x3) 63.56/17.21 63.56/17.21 p_in_ga(x1, x2) = p_in_ga(x1) 63.56/17.21 63.56/17.21 p_out_ga(x1, x2) = p_out_ga(x1, x2) 63.56/17.21 63.56/17.21 U1_ga(x1, x2, x3, x4, x5) = U1_ga(x1, x2, x5) 63.56/17.21 63.56/17.21 U3_ga(x1, x2, x3, x4, x5) = U3_ga(x1, x2, x5) 63.56/17.21 63.56/17.21 U5_ga(x1, x2, x3) = U5_ga(x1, x3) 63.56/17.21 63.56/17.21 U6_ga(x1, x2, x3, x4) = U6_ga(x1, x4) 63.56/17.21 63.56/17.21 U4_ga(x1, x2, x3, x4, x5) = U4_ga(x1, x2, x4, x5) 63.56/17.21 63.56/17.21 U2_ga(x1, x2, x3, x4, x5) = U2_ga(x1, x2, x3, x5) 63.56/17.21 63.56/17.21 U6_gg(x1, x2, x3, x4) = U6_gg(x1, x2, x4) 63.56/17.21 63.56/17.21 U4_gg(x1, x2, x3, x4, x5) = U4_gg(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 U2_gg(x1, x2, x3, x4, x5) = U2_gg(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x1, x2, x3, x4, x5) 63.56/17.21 63.56/17.21 U5_ag(x1, x2, x3) = U5_ag(x2, x3) 63.56/17.21 63.56/17.21 p_in_aa(x1, x2) = p_in_aa 63.56/17.21 63.56/17.21 p_out_aa(x1, x2) = p_out_aa(x1, x2) 63.56/17.21 63.56/17.21 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 63.56/17.21 63.56/17.21 U3_aa(x1, x2, x3, x4, x5) = U3_aa(x5) 63.56/17.21 63.56/17.21 U5_aa(x1, x2, x3) = U5_aa(x3) 63.56/17.21 63.56/17.21 U6_aa(x1, x2, x3, x4) = U6_aa(x1, x4) 63.56/17.21 63.56/17.21 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x1, x4, x5) 63.56/17.21 63.56/17.21 U2_aa(x1, x2, x3, x4, x5) = U2_aa(x1, x3, x5) 63.56/17.21 63.56/17.21 U6_ag(x1, x2, x3, x4) = U6_ag(x1, x2, x4) 63.56/17.21 63.56/17.21 U2_ag(x1, x2, x3, x4, x5) = U2_ag(x1, x3, x4, x5) 63.56/17.21 63.56/17.21 P_IN_AA(x1, x2) = P_IN_AA 63.56/17.21 63.56/17.21 U1_AA(x1, x2, x3, x4, x5) = U1_AA(x5) 63.56/17.21 63.56/17.21 U3_AA(x1, x2, x3, x4, x5) = U3_AA(x5) 63.56/17.21 63.56/17.21 63.56/17.21 We have to consider all (P,R,Pi)-chains 63.56/17.21 ---------------------------------------- 63.56/17.21 63.56/17.21 (38) UsableRulesProof (EQUIVALENT) 63.56/17.21 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 63.56/17.21 ---------------------------------------- 63.56/17.21 63.56/17.21 (39) 63.56/17.21 Obligation: 63.56/17.21 Pi DP problem: 63.56/17.21 The TRS P consists of the following rules: 63.56/17.21 63.56/17.21 U1_AA(X, Y, DX, DY, p_out_aa(d(e(X)), DX)) -> P_IN_AA(d(e(Y)), DY) 63.56/17.21 P_IN_AA(d(e(+(X, Y))), +(DX, DY)) -> U1_AA(X, Y, DX, DY, p_in_aa(d(e(X)), DX)) 63.56/17.21 P_IN_AA(d(e(+(X, Y))), +(DX, DY)) -> P_IN_AA(d(e(X)), DX) 63.56/17.21 P_IN_AA(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_AA(X, Y, DY, DX, p_in_aa(d(e(X)), DX)) 63.56/17.21 U3_AA(X, Y, DY, DX, p_out_aa(d(e(X)), DX)) -> P_IN_AA(d(e(Y)), DY) 63.56/17.21 P_IN_AA(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> P_IN_AA(d(e(X)), DX) 63.56/17.21 63.56/17.21 The TRS R consists of the following rules: 63.56/17.21 63.56/17.21 p_in_aa(d(e(t)), const(1)) -> p_out_aa(d(e(t)), const(1)) 63.56/17.21 p_in_aa(d(e(const(A))), const(0)) -> p_out_aa(d(e(const(A))), const(0)) 63.56/17.21 p_in_aa(d(e(+(X, Y))), +(DX, DY)) -> U1_aa(X, Y, DX, DY, p_in_aa(d(e(X)), DX)) 63.56/17.21 p_in_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_aa(X, Y, DY, DX, p_in_aa(d(e(X)), DX)) 63.56/17.21 U1_aa(X, Y, DX, DY, p_out_aa(d(e(X)), DX)) -> U2_aa(X, Y, DX, DY, p_in_aa(d(e(Y)), DY)) 63.56/17.21 U3_aa(X, Y, DY, DX, p_out_aa(d(e(X)), DX)) -> U4_aa(X, Y, DY, DX, p_in_aa(d(e(Y)), DY)) 63.56/17.21 U2_aa(X, Y, DX, DY, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(+(X, Y))), +(DX, DY)) 63.56/17.21 U4_aa(X, Y, DY, DX, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.21 63.56/17.21 The argument filtering Pi contains the following mapping: 63.56/17.21 const(x1) = const 63.56/17.21 63.56/17.21 1 = 1 63.56/17.21 63.56/17.21 0 = 0 63.56/17.21 63.56/17.21 +(x1, x2) = +(x1, x2) 63.56/17.21 63.56/17.21 *(x1, x2) = *(x1, x2) 63.56/17.21 63.56/17.21 d(x1) = d(x1) 63.56/17.21 63.56/17.21 e(x1) = e(x1) 63.56/17.21 63.56/17.21 t = t 63.56/17.21 63.56/17.21 p_in_aa(x1, x2) = p_in_aa 63.56/17.21 63.56/17.21 p_out_aa(x1, x2) = p_out_aa(x1, x2) 63.56/17.21 63.56/17.21 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 63.56/17.21 63.56/17.21 U3_aa(x1, x2, x3, x4, x5) = U3_aa(x5) 63.56/17.21 63.56/17.21 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x1, x4, x5) 63.56/17.21 63.56/17.21 U2_aa(x1, x2, x3, x4, x5) = U2_aa(x1, x3, x5) 63.56/17.21 63.56/17.21 P_IN_AA(x1, x2) = P_IN_AA 63.56/17.21 63.56/17.21 U1_AA(x1, x2, x3, x4, x5) = U1_AA(x5) 63.56/17.21 63.56/17.21 U3_AA(x1, x2, x3, x4, x5) = U3_AA(x5) 63.56/17.21 63.56/17.21 63.56/17.21 We have to consider all (P,R,Pi)-chains 63.56/17.21 ---------------------------------------- 63.56/17.21 63.56/17.21 (40) PiDPToQDPProof (SOUND) 63.56/17.21 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 63.56/17.21 ---------------------------------------- 63.56/17.21 63.56/17.21 (41) 63.56/17.21 Obligation: 63.56/17.21 Q DP problem: 63.56/17.21 The TRS P consists of the following rules: 63.56/17.21 63.56/17.21 U1_AA(p_out_aa(d(e(X)), DX)) -> P_IN_AA 63.56/17.21 P_IN_AA -> U1_AA(p_in_aa) 63.56/17.21 P_IN_AA -> P_IN_AA 63.56/17.21 P_IN_AA -> U3_AA(p_in_aa) 63.56/17.21 U3_AA(p_out_aa(d(e(X)), DX)) -> P_IN_AA 63.56/17.21 63.56/17.21 The TRS R consists of the following rules: 63.56/17.21 63.56/17.21 p_in_aa -> p_out_aa(d(e(t)), const) 63.56/17.21 p_in_aa -> p_out_aa(d(e(const)), const) 63.56/17.21 p_in_aa -> U1_aa(p_in_aa) 63.56/17.21 p_in_aa -> U3_aa(p_in_aa) 63.56/17.21 U1_aa(p_out_aa(d(e(X)), DX)) -> U2_aa(X, DX, p_in_aa) 63.56/17.21 U3_aa(p_out_aa(d(e(X)), DX)) -> U4_aa(X, DX, p_in_aa) 63.56/17.21 U2_aa(X, DX, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(+(X, Y))), +(DX, DY)) 63.56/17.21 U4_aa(X, DX, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.21 63.56/17.21 The set Q consists of the following terms: 63.56/17.21 63.56/17.21 p_in_aa 63.56/17.21 U1_aa(x0) 63.56/17.21 U3_aa(x0) 63.56/17.21 U2_aa(x0, x1, x2) 63.56/17.21 U4_aa(x0, x1, x2) 63.56/17.21 63.56/17.21 We have to consider all (P,Q,R)-chains. 63.56/17.21 ---------------------------------------- 63.56/17.21 63.56/17.21 (42) TransformationProof (SOUND) 63.56/17.21 By narrowing [LPAR04] the rule P_IN_AA -> U1_AA(p_in_aa) at position [0] we obtained the following new rules [LPAR04]: 63.56/17.21 63.56/17.21 (P_IN_AA -> U1_AA(p_out_aa(d(e(t)), const)),P_IN_AA -> U1_AA(p_out_aa(d(e(t)), const))) 63.56/17.21 (P_IN_AA -> U1_AA(p_out_aa(d(e(const)), const)),P_IN_AA -> U1_AA(p_out_aa(d(e(const)), const))) 63.56/17.21 (P_IN_AA -> U1_AA(U1_aa(p_in_aa)),P_IN_AA -> U1_AA(U1_aa(p_in_aa))) 63.56/17.21 (P_IN_AA -> U1_AA(U3_aa(p_in_aa)),P_IN_AA -> U1_AA(U3_aa(p_in_aa))) 63.56/17.21 63.56/17.21 63.56/17.21 ---------------------------------------- 63.56/17.21 63.56/17.21 (43) 63.56/17.21 Obligation: 63.56/17.21 Q DP problem: 63.56/17.21 The TRS P consists of the following rules: 63.56/17.21 63.56/17.21 U1_AA(p_out_aa(d(e(X)), DX)) -> P_IN_AA 63.56/17.21 P_IN_AA -> P_IN_AA 63.56/17.21 P_IN_AA -> U3_AA(p_in_aa) 63.56/17.21 U3_AA(p_out_aa(d(e(X)), DX)) -> P_IN_AA 63.56/17.21 P_IN_AA -> U1_AA(p_out_aa(d(e(t)), const)) 63.56/17.21 P_IN_AA -> U1_AA(p_out_aa(d(e(const)), const)) 63.56/17.21 P_IN_AA -> U1_AA(U1_aa(p_in_aa)) 63.56/17.21 P_IN_AA -> U1_AA(U3_aa(p_in_aa)) 63.56/17.21 63.56/17.21 The TRS R consists of the following rules: 63.56/17.21 63.56/17.21 p_in_aa -> p_out_aa(d(e(t)), const) 63.56/17.21 p_in_aa -> p_out_aa(d(e(const)), const) 63.56/17.21 p_in_aa -> U1_aa(p_in_aa) 63.56/17.21 p_in_aa -> U3_aa(p_in_aa) 63.56/17.21 U1_aa(p_out_aa(d(e(X)), DX)) -> U2_aa(X, DX, p_in_aa) 63.56/17.21 U3_aa(p_out_aa(d(e(X)), DX)) -> U4_aa(X, DX, p_in_aa) 63.56/17.21 U2_aa(X, DX, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(+(X, Y))), +(DX, DY)) 63.56/17.21 U4_aa(X, DX, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.21 63.56/17.21 The set Q consists of the following terms: 63.56/17.21 63.56/17.21 p_in_aa 63.56/17.21 U1_aa(x0) 63.56/17.21 U3_aa(x0) 63.56/17.21 U2_aa(x0, x1, x2) 63.56/17.21 U4_aa(x0, x1, x2) 63.56/17.21 63.56/17.21 We have to consider all (P,Q,R)-chains. 63.56/17.21 ---------------------------------------- 63.56/17.21 63.56/17.21 (44) TransformationProof (SOUND) 63.56/17.21 By narrowing [LPAR04] the rule P_IN_AA -> U3_AA(p_in_aa) at position [0] we obtained the following new rules [LPAR04]: 63.56/17.21 63.56/17.21 (P_IN_AA -> U3_AA(p_out_aa(d(e(t)), const)),P_IN_AA -> U3_AA(p_out_aa(d(e(t)), const))) 63.56/17.21 (P_IN_AA -> U3_AA(p_out_aa(d(e(const)), const)),P_IN_AA -> U3_AA(p_out_aa(d(e(const)), const))) 63.56/17.21 (P_IN_AA -> U3_AA(U1_aa(p_in_aa)),P_IN_AA -> U3_AA(U1_aa(p_in_aa))) 63.56/17.21 (P_IN_AA -> U3_AA(U3_aa(p_in_aa)),P_IN_AA -> U3_AA(U3_aa(p_in_aa))) 63.56/17.21 63.56/17.21 63.56/17.21 ---------------------------------------- 63.56/17.21 63.56/17.21 (45) 63.56/17.21 Obligation: 63.56/17.21 Q DP problem: 63.56/17.21 The TRS P consists of the following rules: 63.56/17.21 63.56/17.21 U1_AA(p_out_aa(d(e(X)), DX)) -> P_IN_AA 63.56/17.21 P_IN_AA -> P_IN_AA 63.56/17.21 U3_AA(p_out_aa(d(e(X)), DX)) -> P_IN_AA 63.56/17.21 P_IN_AA -> U1_AA(p_out_aa(d(e(t)), const)) 63.56/17.21 P_IN_AA -> U1_AA(p_out_aa(d(e(const)), const)) 63.56/17.21 P_IN_AA -> U1_AA(U1_aa(p_in_aa)) 63.56/17.21 P_IN_AA -> U1_AA(U3_aa(p_in_aa)) 63.56/17.21 P_IN_AA -> U3_AA(p_out_aa(d(e(t)), const)) 63.56/17.21 P_IN_AA -> U3_AA(p_out_aa(d(e(const)), const)) 63.56/17.21 P_IN_AA -> U3_AA(U1_aa(p_in_aa)) 63.56/17.21 P_IN_AA -> U3_AA(U3_aa(p_in_aa)) 63.56/17.21 63.56/17.21 The TRS R consists of the following rules: 63.56/17.21 63.56/17.21 p_in_aa -> p_out_aa(d(e(t)), const) 63.56/17.21 p_in_aa -> p_out_aa(d(e(const)), const) 63.56/17.21 p_in_aa -> U1_aa(p_in_aa) 63.56/17.21 p_in_aa -> U3_aa(p_in_aa) 63.56/17.21 U1_aa(p_out_aa(d(e(X)), DX)) -> U2_aa(X, DX, p_in_aa) 63.56/17.21 U3_aa(p_out_aa(d(e(X)), DX)) -> U4_aa(X, DX, p_in_aa) 63.56/17.21 U2_aa(X, DX, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(+(X, Y))), +(DX, DY)) 63.56/17.21 U4_aa(X, DX, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.21 63.56/17.21 The set Q consists of the following terms: 63.56/17.21 63.56/17.21 p_in_aa 63.56/17.21 U1_aa(x0) 63.56/17.21 U3_aa(x0) 63.56/17.21 U2_aa(x0, x1, x2) 63.56/17.21 U4_aa(x0, x1, x2) 63.56/17.21 63.56/17.21 We have to consider all (P,Q,R)-chains. 63.56/17.21 ---------------------------------------- 63.56/17.21 63.56/17.21 (46) 63.56/17.21 Obligation: 63.56/17.21 Pi DP problem: 63.56/17.21 The TRS P consists of the following rules: 63.56/17.21 63.56/17.21 U1_GA(X, Y, DX, DY, p_out_ga(d(e(X)), DX)) -> P_IN_GA(d(e(Y)), DY) 63.56/17.21 P_IN_GA(d(e(+(X, Y))), +(DX, DY)) -> U1_GA(X, Y, DX, DY, p_in_ga(d(e(X)), DX)) 63.56/17.21 P_IN_GA(d(e(+(X, Y))), +(DX, DY)) -> P_IN_GA(d(e(X)), DX) 63.56/17.21 P_IN_GA(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_GA(X, Y, DY, DX, p_in_ga(d(e(X)), DX)) 63.56/17.21 U3_GA(X, Y, DY, DX, p_out_ga(d(e(X)), DX)) -> P_IN_GA(d(e(Y)), DY) 63.56/17.21 P_IN_GA(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> P_IN_GA(d(e(X)), DX) 63.56/17.21 63.56/17.21 The TRS R consists of the following rules: 63.56/17.21 63.56/17.21 p_in_ag(d(e(t)), const(1)) -> p_out_ag(d(e(t)), const(1)) 63.56/17.21 p_in_ag(d(e(const(A))), const(0)) -> p_out_ag(d(e(const(A))), const(0)) 63.56/17.21 p_in_ag(d(e(+(X, Y))), +(DX, DY)) -> U1_ag(X, Y, DX, DY, p_in_ag(d(e(X)), DX)) 63.56/17.21 p_in_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ag(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.21 p_in_gg(d(e(t)), const(1)) -> p_out_gg(d(e(t)), const(1)) 63.56/17.21 p_in_gg(d(e(const(A))), const(0)) -> p_out_gg(d(e(const(A))), const(0)) 63.56/17.21 p_in_gg(d(e(+(X, Y))), +(DX, DY)) -> U1_gg(X, Y, DX, DY, p_in_gg(d(e(X)), DX)) 63.56/17.21 p_in_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_gg(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.56/17.21 p_in_gg(d(d(X)), DDX) -> U5_gg(X, DDX, p_in_ga(d(X), DX)) 63.56/17.21 p_in_ga(d(e(t)), const(1)) -> p_out_ga(d(e(t)), const(1)) 63.56/17.21 p_in_ga(d(e(const(A))), const(0)) -> p_out_ga(d(e(const(A))), const(0)) 63.56/17.21 p_in_ga(d(e(+(X, Y))), +(DX, DY)) -> U1_ga(X, Y, DX, DY, p_in_ga(d(e(X)), DX)) 63.56/17.21 p_in_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ga(X, Y, DY, DX, p_in_ga(d(e(X)), DX)) 63.56/17.21 p_in_ga(d(d(X)), DDX) -> U5_ga(X, DDX, p_in_ga(d(X), DX)) 63.56/17.21 U5_ga(X, DDX, p_out_ga(d(X), DX)) -> U6_ga(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.56/17.21 U6_ga(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_ga(d(d(X)), DDX) 63.56/17.21 U3_ga(X, Y, DY, DX, p_out_ga(d(e(X)), DX)) -> U4_ga(X, Y, DY, DX, p_in_ga(d(e(Y)), DY)) 63.56/17.21 U4_ga(X, Y, DY, DX, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.21 U1_ga(X, Y, DX, DY, p_out_ga(d(e(X)), DX)) -> U2_ga(X, Y, DX, DY, p_in_ga(d(e(Y)), DY)) 63.56/17.21 U2_ga(X, Y, DX, DY, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(+(X, Y))), +(DX, DY)) 63.56/17.21 U5_gg(X, DDX, p_out_ga(d(X), DX)) -> U6_gg(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.56/17.21 U6_gg(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_gg(d(d(X)), DDX) 63.56/17.21 U3_gg(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_gg(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.56/17.21 U4_gg(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.56/17.21 U1_gg(X, Y, DX, DY, p_out_gg(d(e(X)), DX)) -> U2_gg(X, Y, DX, DY, p_in_gg(d(e(Y)), DY)) 63.56/17.21 U2_gg(X, Y, DX, DY, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(+(X, Y))), +(DX, DY)) 63.93/17.23 U3_ag(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_ag(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.93/17.23 U4_ag(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.93/17.23 p_in_ag(d(d(X)), DDX) -> U5_ag(X, DDX, p_in_aa(d(X), DX)) 63.93/17.23 p_in_aa(d(e(t)), const(1)) -> p_out_aa(d(e(t)), const(1)) 63.93/17.23 p_in_aa(d(e(const(A))), const(0)) -> p_out_aa(d(e(const(A))), const(0)) 63.93/17.23 p_in_aa(d(e(+(X, Y))), +(DX, DY)) -> U1_aa(X, Y, DX, DY, p_in_aa(d(e(X)), DX)) 63.93/17.23 p_in_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_aa(X, Y, DY, DX, p_in_aa(d(e(X)), DX)) 63.93/17.23 p_in_aa(d(d(X)), DDX) -> U5_aa(X, DDX, p_in_aa(d(X), DX)) 63.93/17.23 U5_aa(X, DDX, p_out_aa(d(X), DX)) -> U6_aa(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.93/17.23 U6_aa(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_aa(d(d(X)), DDX) 63.93/17.23 U3_aa(X, Y, DY, DX, p_out_aa(d(e(X)), DX)) -> U4_aa(X, Y, DY, DX, p_in_aa(d(e(Y)), DY)) 63.93/17.23 U4_aa(X, Y, DY, DX, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.93/17.23 U1_aa(X, Y, DX, DY, p_out_aa(d(e(X)), DX)) -> U2_aa(X, Y, DX, DY, p_in_aa(d(e(Y)), DY)) 63.93/17.23 U2_aa(X, Y, DX, DY, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(+(X, Y))), +(DX, DY)) 63.93/17.23 U5_ag(X, DDX, p_out_aa(d(X), DX)) -> U6_ag(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.93/17.23 U6_ag(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_ag(d(d(X)), DDX) 63.93/17.23 U1_ag(X, Y, DX, DY, p_out_ag(d(e(X)), DX)) -> U2_ag(X, Y, DX, DY, p_in_ag(d(e(Y)), DY)) 63.93/17.23 U2_ag(X, Y, DX, DY, p_out_ag(d(e(Y)), DY)) -> p_out_ag(d(e(+(X, Y))), +(DX, DY)) 63.93/17.23 63.93/17.23 The argument filtering Pi contains the following mapping: 63.93/17.23 p_in_ag(x1, x2) = p_in_ag(x2) 63.93/17.23 63.93/17.23 const(x1) = const 63.93/17.23 63.93/17.23 1 = 1 63.93/17.23 63.93/17.23 p_out_ag(x1, x2) = p_out_ag(x1, x2) 63.93/17.23 63.93/17.23 0 = 0 63.93/17.23 63.93/17.23 +(x1, x2) = +(x1, x2) 63.93/17.23 63.93/17.23 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x3, x4, x5) 63.93/17.23 63.93/17.23 *(x1, x2) = *(x1, x2) 63.93/17.23 63.93/17.23 U3_ag(x1, x2, x3, x4, x5) = U3_ag(x1, x2, x3, x4, x5) 63.93/17.23 63.93/17.23 p_in_gg(x1, x2) = p_in_gg(x1, x2) 63.93/17.23 63.93/17.23 d(x1) = d(x1) 63.93/17.23 63.93/17.23 e(x1) = e(x1) 63.93/17.23 63.93/17.23 t = t 63.93/17.23 63.93/17.23 p_out_gg(x1, x2) = p_out_gg(x1, x2) 63.93/17.23 63.93/17.23 U1_gg(x1, x2, x3, x4, x5) = U1_gg(x1, x2, x3, x4, x5) 63.93/17.23 63.93/17.23 U3_gg(x1, x2, x3, x4, x5) = U3_gg(x1, x2, x3, x4, x5) 63.93/17.23 63.93/17.23 U5_gg(x1, x2, x3) = U5_gg(x1, x2, x3) 63.93/17.23 63.93/17.23 p_in_ga(x1, x2) = p_in_ga(x1) 63.93/17.23 63.93/17.23 p_out_ga(x1, x2) = p_out_ga(x1, x2) 63.93/17.23 63.93/17.23 U1_ga(x1, x2, x3, x4, x5) = U1_ga(x1, x2, x5) 63.93/17.23 63.93/17.23 U3_ga(x1, x2, x3, x4, x5) = U3_ga(x1, x2, x5) 63.93/17.23 63.93/17.23 U5_ga(x1, x2, x3) = U5_ga(x1, x3) 63.93/17.23 63.93/17.23 U6_ga(x1, x2, x3, x4) = U6_ga(x1, x4) 63.93/17.23 63.93/17.23 U4_ga(x1, x2, x3, x4, x5) = U4_ga(x1, x2, x4, x5) 63.93/17.23 63.93/17.23 U2_ga(x1, x2, x3, x4, x5) = U2_ga(x1, x2, x3, x5) 63.93/17.23 63.93/17.23 U6_gg(x1, x2, x3, x4) = U6_gg(x1, x2, x4) 63.93/17.23 63.93/17.23 U4_gg(x1, x2, x3, x4, x5) = U4_gg(x1, x2, x3, x4, x5) 63.93/17.23 63.93/17.23 U2_gg(x1, x2, x3, x4, x5) = U2_gg(x1, x2, x3, x4, x5) 63.93/17.23 63.93/17.23 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x1, x2, x3, x4, x5) 63.93/17.23 63.93/17.23 U5_ag(x1, x2, x3) = U5_ag(x2, x3) 63.93/17.23 63.93/17.23 p_in_aa(x1, x2) = p_in_aa 63.93/17.23 63.93/17.23 p_out_aa(x1, x2) = p_out_aa(x1, x2) 63.93/17.23 63.93/17.23 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 63.93/17.23 63.93/17.23 U3_aa(x1, x2, x3, x4, x5) = U3_aa(x5) 63.93/17.23 63.93/17.23 U5_aa(x1, x2, x3) = U5_aa(x3) 63.93/17.23 63.93/17.23 U6_aa(x1, x2, x3, x4) = U6_aa(x1, x4) 63.93/17.23 63.93/17.23 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x1, x4, x5) 63.93/17.23 63.93/17.23 U2_aa(x1, x2, x3, x4, x5) = U2_aa(x1, x3, x5) 63.93/17.23 63.93/17.23 U6_ag(x1, x2, x3, x4) = U6_ag(x1, x2, x4) 63.93/17.23 63.93/17.23 U2_ag(x1, x2, x3, x4, x5) = U2_ag(x1, x3, x4, x5) 63.93/17.23 63.93/17.23 P_IN_GA(x1, x2) = P_IN_GA(x1) 63.93/17.23 63.93/17.23 U1_GA(x1, x2, x3, x4, x5) = U1_GA(x1, x2, x5) 63.93/17.23 63.93/17.23 U3_GA(x1, x2, x3, x4, x5) = U3_GA(x1, x2, x5) 63.93/17.23 63.93/17.23 63.93/17.23 We have to consider all (P,R,Pi)-chains 63.93/17.23 ---------------------------------------- 63.93/17.23 63.93/17.23 (47) UsableRulesProof (EQUIVALENT) 63.93/17.23 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 63.93/17.23 ---------------------------------------- 63.93/17.23 63.93/17.23 (48) 63.93/17.23 Obligation: 63.93/17.23 Pi DP problem: 63.93/17.23 The TRS P consists of the following rules: 63.93/17.23 63.93/17.23 U1_GA(X, Y, DX, DY, p_out_ga(d(e(X)), DX)) -> P_IN_GA(d(e(Y)), DY) 63.93/17.23 P_IN_GA(d(e(+(X, Y))), +(DX, DY)) -> U1_GA(X, Y, DX, DY, p_in_ga(d(e(X)), DX)) 63.93/17.23 P_IN_GA(d(e(+(X, Y))), +(DX, DY)) -> P_IN_GA(d(e(X)), DX) 63.93/17.23 P_IN_GA(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_GA(X, Y, DY, DX, p_in_ga(d(e(X)), DX)) 63.93/17.23 U3_GA(X, Y, DY, DX, p_out_ga(d(e(X)), DX)) -> P_IN_GA(d(e(Y)), DY) 63.93/17.23 P_IN_GA(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> P_IN_GA(d(e(X)), DX) 63.93/17.23 63.93/17.23 The TRS R consists of the following rules: 63.93/17.23 63.93/17.23 p_in_ga(d(e(t)), const(1)) -> p_out_ga(d(e(t)), const(1)) 63.93/17.23 p_in_ga(d(e(const(A))), const(0)) -> p_out_ga(d(e(const(A))), const(0)) 63.93/17.23 p_in_ga(d(e(+(X, Y))), +(DX, DY)) -> U1_ga(X, Y, DX, DY, p_in_ga(d(e(X)), DX)) 63.93/17.23 p_in_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ga(X, Y, DY, DX, p_in_ga(d(e(X)), DX)) 63.93/17.23 U1_ga(X, Y, DX, DY, p_out_ga(d(e(X)), DX)) -> U2_ga(X, Y, DX, DY, p_in_ga(d(e(Y)), DY)) 63.93/17.23 U3_ga(X, Y, DY, DX, p_out_ga(d(e(X)), DX)) -> U4_ga(X, Y, DY, DX, p_in_ga(d(e(Y)), DY)) 63.93/17.23 U2_ga(X, Y, DX, DY, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(+(X, Y))), +(DX, DY)) 63.93/17.23 U4_ga(X, Y, DY, DX, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.93/17.23 63.93/17.23 The argument filtering Pi contains the following mapping: 63.93/17.23 const(x1) = const 63.93/17.23 63.93/17.23 1 = 1 63.93/17.23 63.93/17.23 0 = 0 63.93/17.23 63.93/17.23 +(x1, x2) = +(x1, x2) 63.93/17.23 63.93/17.23 *(x1, x2) = *(x1, x2) 63.93/17.23 63.93/17.23 d(x1) = d(x1) 63.93/17.23 63.93/17.23 e(x1) = e(x1) 63.93/17.23 63.93/17.23 t = t 63.93/17.23 63.93/17.23 p_in_ga(x1, x2) = p_in_ga(x1) 63.93/17.23 63.93/17.23 p_out_ga(x1, x2) = p_out_ga(x1, x2) 63.93/17.23 63.93/17.23 U1_ga(x1, x2, x3, x4, x5) = U1_ga(x1, x2, x5) 63.93/17.23 63.93/17.23 U3_ga(x1, x2, x3, x4, x5) = U3_ga(x1, x2, x5) 63.93/17.23 63.93/17.23 U4_ga(x1, x2, x3, x4, x5) = U4_ga(x1, x2, x4, x5) 63.93/17.23 63.93/17.23 U2_ga(x1, x2, x3, x4, x5) = U2_ga(x1, x2, x3, x5) 63.93/17.23 63.93/17.23 P_IN_GA(x1, x2) = P_IN_GA(x1) 63.93/17.23 63.93/17.23 U1_GA(x1, x2, x3, x4, x5) = U1_GA(x1, x2, x5) 63.93/17.23 63.93/17.23 U3_GA(x1, x2, x3, x4, x5) = U3_GA(x1, x2, x5) 63.93/17.23 63.93/17.23 63.93/17.23 We have to consider all (P,R,Pi)-chains 63.93/17.23 ---------------------------------------- 63.93/17.23 63.93/17.23 (49) 63.93/17.23 Obligation: 63.93/17.23 Pi DP problem: 63.93/17.23 The TRS P consists of the following rules: 63.93/17.23 63.93/17.23 P_IN_AA(d(d(X)), DDX) -> P_IN_AA(d(X), DX) 63.93/17.23 63.93/17.23 The TRS R consists of the following rules: 63.93/17.23 63.93/17.23 p_in_ag(d(e(t)), const(1)) -> p_out_ag(d(e(t)), const(1)) 63.93/17.23 p_in_ag(d(e(const(A))), const(0)) -> p_out_ag(d(e(const(A))), const(0)) 63.93/17.23 p_in_ag(d(e(+(X, Y))), +(DX, DY)) -> U1_ag(X, Y, DX, DY, p_in_ag(d(e(X)), DX)) 63.93/17.23 p_in_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ag(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.93/17.23 p_in_gg(d(e(t)), const(1)) -> p_out_gg(d(e(t)), const(1)) 63.93/17.23 p_in_gg(d(e(const(A))), const(0)) -> p_out_gg(d(e(const(A))), const(0)) 63.93/17.23 p_in_gg(d(e(+(X, Y))), +(DX, DY)) -> U1_gg(X, Y, DX, DY, p_in_gg(d(e(X)), DX)) 63.93/17.23 p_in_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_gg(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.93/17.23 p_in_gg(d(d(X)), DDX) -> U5_gg(X, DDX, p_in_ga(d(X), DX)) 63.93/17.23 p_in_ga(d(e(t)), const(1)) -> p_out_ga(d(e(t)), const(1)) 63.93/17.23 p_in_ga(d(e(const(A))), const(0)) -> p_out_ga(d(e(const(A))), const(0)) 63.93/17.23 p_in_ga(d(e(+(X, Y))), +(DX, DY)) -> U1_ga(X, Y, DX, DY, p_in_ga(d(e(X)), DX)) 63.93/17.23 p_in_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ga(X, Y, DY, DX, p_in_ga(d(e(X)), DX)) 63.93/17.23 p_in_ga(d(d(X)), DDX) -> U5_ga(X, DDX, p_in_ga(d(X), DX)) 63.93/17.23 U5_ga(X, DDX, p_out_ga(d(X), DX)) -> U6_ga(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.93/17.23 U6_ga(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_ga(d(d(X)), DDX) 63.93/17.23 U3_ga(X, Y, DY, DX, p_out_ga(d(e(X)), DX)) -> U4_ga(X, Y, DY, DX, p_in_ga(d(e(Y)), DY)) 63.93/17.23 U4_ga(X, Y, DY, DX, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.93/17.23 U1_ga(X, Y, DX, DY, p_out_ga(d(e(X)), DX)) -> U2_ga(X, Y, DX, DY, p_in_ga(d(e(Y)), DY)) 63.93/17.23 U2_ga(X, Y, DX, DY, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(+(X, Y))), +(DX, DY)) 63.93/17.23 U5_gg(X, DDX, p_out_ga(d(X), DX)) -> U6_gg(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.93/17.23 U6_gg(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_gg(d(d(X)), DDX) 63.93/17.23 U3_gg(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_gg(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.93/17.23 U4_gg(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.93/17.23 U1_gg(X, Y, DX, DY, p_out_gg(d(e(X)), DX)) -> U2_gg(X, Y, DX, DY, p_in_gg(d(e(Y)), DY)) 63.93/17.23 U2_gg(X, Y, DX, DY, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(+(X, Y))), +(DX, DY)) 63.93/17.23 U3_ag(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_ag(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.93/17.23 U4_ag(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.93/17.23 p_in_ag(d(d(X)), DDX) -> U5_ag(X, DDX, p_in_aa(d(X), DX)) 63.93/17.23 p_in_aa(d(e(t)), const(1)) -> p_out_aa(d(e(t)), const(1)) 63.93/17.23 p_in_aa(d(e(const(A))), const(0)) -> p_out_aa(d(e(const(A))), const(0)) 63.93/17.23 p_in_aa(d(e(+(X, Y))), +(DX, DY)) -> U1_aa(X, Y, DX, DY, p_in_aa(d(e(X)), DX)) 63.93/17.23 p_in_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_aa(X, Y, DY, DX, p_in_aa(d(e(X)), DX)) 63.93/17.23 p_in_aa(d(d(X)), DDX) -> U5_aa(X, DDX, p_in_aa(d(X), DX)) 63.93/17.23 U5_aa(X, DDX, p_out_aa(d(X), DX)) -> U6_aa(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.93/17.23 U6_aa(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_aa(d(d(X)), DDX) 63.93/17.23 U3_aa(X, Y, DY, DX, p_out_aa(d(e(X)), DX)) -> U4_aa(X, Y, DY, DX, p_in_aa(d(e(Y)), DY)) 63.93/17.23 U4_aa(X, Y, DY, DX, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.93/17.23 U1_aa(X, Y, DX, DY, p_out_aa(d(e(X)), DX)) -> U2_aa(X, Y, DX, DY, p_in_aa(d(e(Y)), DY)) 63.93/17.23 U2_aa(X, Y, DX, DY, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(+(X, Y))), +(DX, DY)) 63.93/17.23 U5_ag(X, DDX, p_out_aa(d(X), DX)) -> U6_ag(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.93/17.23 U6_ag(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_ag(d(d(X)), DDX) 63.93/17.23 U1_ag(X, Y, DX, DY, p_out_ag(d(e(X)), DX)) -> U2_ag(X, Y, DX, DY, p_in_ag(d(e(Y)), DY)) 63.93/17.23 U2_ag(X, Y, DX, DY, p_out_ag(d(e(Y)), DY)) -> p_out_ag(d(e(+(X, Y))), +(DX, DY)) 63.93/17.23 63.93/17.23 The argument filtering Pi contains the following mapping: 63.93/17.23 p_in_ag(x1, x2) = p_in_ag(x2) 63.93/17.23 63.93/17.23 const(x1) = const 63.93/17.23 63.93/17.23 1 = 1 63.93/17.23 63.93/17.23 p_out_ag(x1, x2) = p_out_ag(x1, x2) 63.93/17.23 63.93/17.23 0 = 0 63.93/17.23 63.93/17.23 +(x1, x2) = +(x1, x2) 63.93/17.23 63.93/17.23 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x3, x4, x5) 63.93/17.23 63.93/17.23 *(x1, x2) = *(x1, x2) 63.93/17.23 63.93/17.23 U3_ag(x1, x2, x3, x4, x5) = U3_ag(x1, x2, x3, x4, x5) 63.93/17.23 63.93/17.23 p_in_gg(x1, x2) = p_in_gg(x1, x2) 63.93/17.23 63.93/17.23 d(x1) = d(x1) 63.93/17.23 63.93/17.23 e(x1) = e(x1) 63.93/17.23 63.93/17.23 t = t 63.93/17.23 63.93/17.23 p_out_gg(x1, x2) = p_out_gg(x1, x2) 63.93/17.23 63.93/17.23 U1_gg(x1, x2, x3, x4, x5) = U1_gg(x1, x2, x3, x4, x5) 63.93/17.23 63.93/17.23 U3_gg(x1, x2, x3, x4, x5) = U3_gg(x1, x2, x3, x4, x5) 63.93/17.23 63.93/17.23 U5_gg(x1, x2, x3) = U5_gg(x1, x2, x3) 63.93/17.23 63.93/17.23 p_in_ga(x1, x2) = p_in_ga(x1) 63.93/17.23 63.93/17.23 p_out_ga(x1, x2) = p_out_ga(x1, x2) 63.93/17.23 63.93/17.23 U1_ga(x1, x2, x3, x4, x5) = U1_ga(x1, x2, x5) 63.93/17.23 63.93/17.23 U3_ga(x1, x2, x3, x4, x5) = U3_ga(x1, x2, x5) 63.93/17.23 63.93/17.23 U5_ga(x1, x2, x3) = U5_ga(x1, x3) 63.93/17.23 63.93/17.23 U6_ga(x1, x2, x3, x4) = U6_ga(x1, x4) 63.93/17.23 63.93/17.23 U4_ga(x1, x2, x3, x4, x5) = U4_ga(x1, x2, x4, x5) 63.93/17.23 63.93/17.23 U2_ga(x1, x2, x3, x4, x5) = U2_ga(x1, x2, x3, x5) 63.93/17.23 63.93/17.23 U6_gg(x1, x2, x3, x4) = U6_gg(x1, x2, x4) 63.93/17.23 63.93/17.23 U4_gg(x1, x2, x3, x4, x5) = U4_gg(x1, x2, x3, x4, x5) 63.93/17.23 63.93/17.23 U2_gg(x1, x2, x3, x4, x5) = U2_gg(x1, x2, x3, x4, x5) 63.93/17.23 63.93/17.23 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x1, x2, x3, x4, x5) 63.93/17.23 63.93/17.23 U5_ag(x1, x2, x3) = U5_ag(x2, x3) 63.93/17.23 63.93/17.23 p_in_aa(x1, x2) = p_in_aa 63.93/17.23 63.93/17.23 p_out_aa(x1, x2) = p_out_aa(x1, x2) 63.93/17.23 63.93/17.23 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 63.93/17.23 63.93/17.23 U3_aa(x1, x2, x3, x4, x5) = U3_aa(x5) 63.93/17.23 63.93/17.23 U5_aa(x1, x2, x3) = U5_aa(x3) 63.93/17.23 63.93/17.23 U6_aa(x1, x2, x3, x4) = U6_aa(x1, x4) 63.93/17.23 63.93/17.23 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x1, x4, x5) 63.93/17.23 63.93/17.23 U2_aa(x1, x2, x3, x4, x5) = U2_aa(x1, x3, x5) 63.93/17.23 63.93/17.23 U6_ag(x1, x2, x3, x4) = U6_ag(x1, x2, x4) 63.93/17.23 63.93/17.23 U2_ag(x1, x2, x3, x4, x5) = U2_ag(x1, x3, x4, x5) 63.93/17.23 63.93/17.23 P_IN_AA(x1, x2) = P_IN_AA 63.93/17.23 63.93/17.23 63.93/17.23 We have to consider all (P,R,Pi)-chains 63.93/17.23 ---------------------------------------- 63.93/17.23 63.93/17.23 (50) UsableRulesProof (EQUIVALENT) 63.93/17.23 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 63.93/17.23 ---------------------------------------- 63.93/17.23 63.93/17.23 (51) 63.93/17.23 Obligation: 63.93/17.23 Pi DP problem: 63.93/17.23 The TRS P consists of the following rules: 63.93/17.23 63.93/17.23 P_IN_AA(d(d(X)), DDX) -> P_IN_AA(d(X), DX) 63.93/17.23 63.93/17.23 R is empty. 63.93/17.23 The argument filtering Pi contains the following mapping: 63.93/17.23 d(x1) = d(x1) 63.93/17.23 63.93/17.23 P_IN_AA(x1, x2) = P_IN_AA 63.93/17.23 63.93/17.23 63.93/17.23 We have to consider all (P,R,Pi)-chains 63.93/17.23 ---------------------------------------- 63.93/17.23 63.93/17.23 (52) 63.93/17.23 Obligation: 63.93/17.23 Pi DP problem: 63.93/17.23 The TRS P consists of the following rules: 63.93/17.23 63.93/17.23 P_IN_GA(d(d(X)), DDX) -> P_IN_GA(d(X), DX) 63.93/17.23 63.93/17.23 The TRS R consists of the following rules: 63.93/17.23 63.93/17.23 p_in_ag(d(e(t)), const(1)) -> p_out_ag(d(e(t)), const(1)) 63.93/17.23 p_in_ag(d(e(const(A))), const(0)) -> p_out_ag(d(e(const(A))), const(0)) 63.93/17.23 p_in_ag(d(e(+(X, Y))), +(DX, DY)) -> U1_ag(X, Y, DX, DY, p_in_ag(d(e(X)), DX)) 63.93/17.23 p_in_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ag(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.93/17.23 p_in_gg(d(e(t)), const(1)) -> p_out_gg(d(e(t)), const(1)) 63.93/17.23 p_in_gg(d(e(const(A))), const(0)) -> p_out_gg(d(e(const(A))), const(0)) 63.93/17.23 p_in_gg(d(e(+(X, Y))), +(DX, DY)) -> U1_gg(X, Y, DX, DY, p_in_gg(d(e(X)), DX)) 63.93/17.23 p_in_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_gg(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.93/17.23 p_in_gg(d(d(X)), DDX) -> U5_gg(X, DDX, p_in_ga(d(X), DX)) 63.93/17.23 p_in_ga(d(e(t)), const(1)) -> p_out_ga(d(e(t)), const(1)) 63.93/17.23 p_in_ga(d(e(const(A))), const(0)) -> p_out_ga(d(e(const(A))), const(0)) 63.93/17.23 p_in_ga(d(e(+(X, Y))), +(DX, DY)) -> U1_ga(X, Y, DX, DY, p_in_ga(d(e(X)), DX)) 63.93/17.23 p_in_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ga(X, Y, DY, DX, p_in_ga(d(e(X)), DX)) 63.93/17.23 p_in_ga(d(d(X)), DDX) -> U5_ga(X, DDX, p_in_ga(d(X), DX)) 63.93/17.23 U5_ga(X, DDX, p_out_ga(d(X), DX)) -> U6_ga(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.93/17.23 U6_ga(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_ga(d(d(X)), DDX) 63.93/17.23 U3_ga(X, Y, DY, DX, p_out_ga(d(e(X)), DX)) -> U4_ga(X, Y, DY, DX, p_in_ga(d(e(Y)), DY)) 63.93/17.23 U4_ga(X, Y, DY, DX, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.93/17.23 U1_ga(X, Y, DX, DY, p_out_ga(d(e(X)), DX)) -> U2_ga(X, Y, DX, DY, p_in_ga(d(e(Y)), DY)) 63.93/17.23 U2_ga(X, Y, DX, DY, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(+(X, Y))), +(DX, DY)) 63.93/17.23 U5_gg(X, DDX, p_out_ga(d(X), DX)) -> U6_gg(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.93/17.23 U6_gg(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_gg(d(d(X)), DDX) 63.93/17.23 U3_gg(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_gg(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.93/17.23 U4_gg(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.93/17.23 U1_gg(X, Y, DX, DY, p_out_gg(d(e(X)), DX)) -> U2_gg(X, Y, DX, DY, p_in_gg(d(e(Y)), DY)) 63.93/17.23 U2_gg(X, Y, DX, DY, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(+(X, Y))), +(DX, DY)) 63.93/17.23 U3_ag(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_ag(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.93/17.23 U4_ag(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.93/17.23 p_in_ag(d(d(X)), DDX) -> U5_ag(X, DDX, p_in_aa(d(X), DX)) 63.93/17.23 p_in_aa(d(e(t)), const(1)) -> p_out_aa(d(e(t)), const(1)) 63.93/17.23 p_in_aa(d(e(const(A))), const(0)) -> p_out_aa(d(e(const(A))), const(0)) 63.93/17.23 p_in_aa(d(e(+(X, Y))), +(DX, DY)) -> U1_aa(X, Y, DX, DY, p_in_aa(d(e(X)), DX)) 63.93/17.23 p_in_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_aa(X, Y, DY, DX, p_in_aa(d(e(X)), DX)) 63.93/17.23 p_in_aa(d(d(X)), DDX) -> U5_aa(X, DDX, p_in_aa(d(X), DX)) 63.93/17.23 U5_aa(X, DDX, p_out_aa(d(X), DX)) -> U6_aa(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.93/17.23 U6_aa(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_aa(d(d(X)), DDX) 63.93/17.23 U3_aa(X, Y, DY, DX, p_out_aa(d(e(X)), DX)) -> U4_aa(X, Y, DY, DX, p_in_aa(d(e(Y)), DY)) 63.93/17.23 U4_aa(X, Y, DY, DX, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.93/17.23 U1_aa(X, Y, DX, DY, p_out_aa(d(e(X)), DX)) -> U2_aa(X, Y, DX, DY, p_in_aa(d(e(Y)), DY)) 63.93/17.23 U2_aa(X, Y, DX, DY, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(+(X, Y))), +(DX, DY)) 63.93/17.23 U5_ag(X, DDX, p_out_aa(d(X), DX)) -> U6_ag(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.93/17.23 U6_ag(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_ag(d(d(X)), DDX) 63.93/17.23 U1_ag(X, Y, DX, DY, p_out_ag(d(e(X)), DX)) -> U2_ag(X, Y, DX, DY, p_in_ag(d(e(Y)), DY)) 63.93/17.23 U2_ag(X, Y, DX, DY, p_out_ag(d(e(Y)), DY)) -> p_out_ag(d(e(+(X, Y))), +(DX, DY)) 63.93/17.23 63.93/17.23 The argument filtering Pi contains the following mapping: 63.93/17.23 p_in_ag(x1, x2) = p_in_ag(x2) 63.93/17.23 63.93/17.23 const(x1) = const 63.93/17.23 63.93/17.23 1 = 1 63.93/17.23 63.93/17.23 p_out_ag(x1, x2) = p_out_ag(x1, x2) 63.93/17.23 63.93/17.23 0 = 0 63.93/17.23 63.93/17.23 +(x1, x2) = +(x1, x2) 63.93/17.23 63.93/17.23 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x3, x4, x5) 63.93/17.23 63.93/17.23 *(x1, x2) = *(x1, x2) 63.93/17.23 63.93/17.23 U3_ag(x1, x2, x3, x4, x5) = U3_ag(x1, x2, x3, x4, x5) 63.93/17.23 63.93/17.23 p_in_gg(x1, x2) = p_in_gg(x1, x2) 63.93/17.23 63.93/17.23 d(x1) = d(x1) 63.93/17.23 63.93/17.23 e(x1) = e(x1) 63.93/17.23 63.93/17.23 t = t 63.93/17.23 63.93/17.23 p_out_gg(x1, x2) = p_out_gg(x1, x2) 63.93/17.23 63.93/17.23 U1_gg(x1, x2, x3, x4, x5) = U1_gg(x1, x2, x3, x4, x5) 63.93/17.23 63.93/17.23 U3_gg(x1, x2, x3, x4, x5) = U3_gg(x1, x2, x3, x4, x5) 63.93/17.23 63.93/17.23 U5_gg(x1, x2, x3) = U5_gg(x1, x2, x3) 63.93/17.23 63.93/17.23 p_in_ga(x1, x2) = p_in_ga(x1) 63.93/17.23 63.93/17.23 p_out_ga(x1, x2) = p_out_ga(x1, x2) 63.93/17.23 63.93/17.23 U1_ga(x1, x2, x3, x4, x5) = U1_ga(x1, x2, x5) 63.93/17.23 63.93/17.23 U3_ga(x1, x2, x3, x4, x5) = U3_ga(x1, x2, x5) 63.93/17.23 63.93/17.23 U5_ga(x1, x2, x3) = U5_ga(x1, x3) 63.93/17.23 63.93/17.23 U6_ga(x1, x2, x3, x4) = U6_ga(x1, x4) 63.93/17.23 63.93/17.23 U4_ga(x1, x2, x3, x4, x5) = U4_ga(x1, x2, x4, x5) 63.93/17.23 63.93/17.23 U2_ga(x1, x2, x3, x4, x5) = U2_ga(x1, x2, x3, x5) 63.93/17.23 63.93/17.23 U6_gg(x1, x2, x3, x4) = U6_gg(x1, x2, x4) 63.93/17.23 63.93/17.23 U4_gg(x1, x2, x3, x4, x5) = U4_gg(x1, x2, x3, x4, x5) 63.93/17.23 63.93/17.23 U2_gg(x1, x2, x3, x4, x5) = U2_gg(x1, x2, x3, x4, x5) 63.93/17.23 63.93/17.23 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x1, x2, x3, x4, x5) 63.93/17.23 63.93/17.23 U5_ag(x1, x2, x3) = U5_ag(x2, x3) 63.93/17.23 63.93/17.23 p_in_aa(x1, x2) = p_in_aa 63.93/17.23 63.93/17.23 p_out_aa(x1, x2) = p_out_aa(x1, x2) 63.93/17.23 63.93/17.23 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 63.93/17.23 63.93/17.23 U3_aa(x1, x2, x3, x4, x5) = U3_aa(x5) 63.93/17.23 63.93/17.23 U5_aa(x1, x2, x3) = U5_aa(x3) 63.93/17.23 63.93/17.23 U6_aa(x1, x2, x3, x4) = U6_aa(x1, x4) 63.93/17.23 63.93/17.23 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x1, x4, x5) 63.93/17.23 63.93/17.23 U2_aa(x1, x2, x3, x4, x5) = U2_aa(x1, x3, x5) 63.93/17.23 63.93/17.23 U6_ag(x1, x2, x3, x4) = U6_ag(x1, x2, x4) 63.93/17.23 63.93/17.23 U2_ag(x1, x2, x3, x4, x5) = U2_ag(x1, x3, x4, x5) 63.93/17.23 63.93/17.23 P_IN_GA(x1, x2) = P_IN_GA(x1) 63.93/17.23 63.93/17.23 63.93/17.23 We have to consider all (P,R,Pi)-chains 63.93/17.23 ---------------------------------------- 63.93/17.23 63.93/17.23 (53) UsableRulesProof (EQUIVALENT) 63.93/17.23 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 63.93/17.23 ---------------------------------------- 63.93/17.23 63.93/17.23 (54) 63.93/17.23 Obligation: 63.93/17.23 Pi DP problem: 63.93/17.23 The TRS P consists of the following rules: 63.93/17.23 63.93/17.23 P_IN_GA(d(d(X)), DDX) -> P_IN_GA(d(X), DX) 63.93/17.23 63.93/17.23 R is empty. 63.93/17.23 The argument filtering Pi contains the following mapping: 63.93/17.23 d(x1) = d(x1) 63.93/17.23 63.93/17.23 P_IN_GA(x1, x2) = P_IN_GA(x1) 63.93/17.23 63.93/17.23 63.93/17.23 We have to consider all (P,R,Pi)-chains 63.93/17.23 ---------------------------------------- 63.93/17.23 63.93/17.23 (55) 63.93/17.23 Obligation: 63.93/17.23 Pi DP problem: 63.93/17.23 The TRS P consists of the following rules: 63.93/17.23 63.93/17.23 U1_GG(X, Y, DX, DY, p_out_gg(d(e(X)), DX)) -> P_IN_GG(d(e(Y)), DY) 63.93/17.23 P_IN_GG(d(e(+(X, Y))), +(DX, DY)) -> U1_GG(X, Y, DX, DY, p_in_gg(d(e(X)), DX)) 63.93/17.23 P_IN_GG(d(e(+(X, Y))), +(DX, DY)) -> P_IN_GG(d(e(X)), DX) 63.93/17.23 P_IN_GG(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_GG(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.93/17.23 U3_GG(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> P_IN_GG(d(e(Y)), DY) 63.93/17.23 P_IN_GG(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> P_IN_GG(d(e(X)), DX) 63.93/17.23 63.93/17.23 The TRS R consists of the following rules: 63.93/17.23 63.93/17.23 p_in_ag(d(e(t)), const(1)) -> p_out_ag(d(e(t)), const(1)) 63.93/17.23 p_in_ag(d(e(const(A))), const(0)) -> p_out_ag(d(e(const(A))), const(0)) 63.93/17.23 p_in_ag(d(e(+(X, Y))), +(DX, DY)) -> U1_ag(X, Y, DX, DY, p_in_ag(d(e(X)), DX)) 63.93/17.23 p_in_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ag(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.93/17.23 p_in_gg(d(e(t)), const(1)) -> p_out_gg(d(e(t)), const(1)) 63.93/17.23 p_in_gg(d(e(const(A))), const(0)) -> p_out_gg(d(e(const(A))), const(0)) 63.93/17.23 p_in_gg(d(e(+(X, Y))), +(DX, DY)) -> U1_gg(X, Y, DX, DY, p_in_gg(d(e(X)), DX)) 63.93/17.23 p_in_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_gg(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.93/17.23 p_in_gg(d(d(X)), DDX) -> U5_gg(X, DDX, p_in_ga(d(X), DX)) 63.93/17.23 p_in_ga(d(e(t)), const(1)) -> p_out_ga(d(e(t)), const(1)) 63.93/17.23 p_in_ga(d(e(const(A))), const(0)) -> p_out_ga(d(e(const(A))), const(0)) 63.93/17.23 p_in_ga(d(e(+(X, Y))), +(DX, DY)) -> U1_ga(X, Y, DX, DY, p_in_ga(d(e(X)), DX)) 63.93/17.23 p_in_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ga(X, Y, DY, DX, p_in_ga(d(e(X)), DX)) 63.93/17.23 p_in_ga(d(d(X)), DDX) -> U5_ga(X, DDX, p_in_ga(d(X), DX)) 63.93/17.23 U5_ga(X, DDX, p_out_ga(d(X), DX)) -> U6_ga(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.93/17.23 U6_ga(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_ga(d(d(X)), DDX) 63.93/17.23 U3_ga(X, Y, DY, DX, p_out_ga(d(e(X)), DX)) -> U4_ga(X, Y, DY, DX, p_in_ga(d(e(Y)), DY)) 63.93/17.23 U4_ga(X, Y, DY, DX, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.93/17.23 U1_ga(X, Y, DX, DY, p_out_ga(d(e(X)), DX)) -> U2_ga(X, Y, DX, DY, p_in_ga(d(e(Y)), DY)) 63.93/17.23 U2_ga(X, Y, DX, DY, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(+(X, Y))), +(DX, DY)) 63.93/17.23 U5_gg(X, DDX, p_out_ga(d(X), DX)) -> U6_gg(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.93/17.23 U6_gg(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_gg(d(d(X)), DDX) 63.93/17.23 U3_gg(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_gg(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.93/17.23 U4_gg(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.93/17.23 U1_gg(X, Y, DX, DY, p_out_gg(d(e(X)), DX)) -> U2_gg(X, Y, DX, DY, p_in_gg(d(e(Y)), DY)) 63.93/17.23 U2_gg(X, Y, DX, DY, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(+(X, Y))), +(DX, DY)) 63.93/17.23 U3_ag(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_ag(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.93/17.23 U4_ag(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.93/17.23 p_in_ag(d(d(X)), DDX) -> U5_ag(X, DDX, p_in_aa(d(X), DX)) 63.93/17.23 p_in_aa(d(e(t)), const(1)) -> p_out_aa(d(e(t)), const(1)) 63.93/17.23 p_in_aa(d(e(const(A))), const(0)) -> p_out_aa(d(e(const(A))), const(0)) 63.93/17.23 p_in_aa(d(e(+(X, Y))), +(DX, DY)) -> U1_aa(X, Y, DX, DY, p_in_aa(d(e(X)), DX)) 63.93/17.23 p_in_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_aa(X, Y, DY, DX, p_in_aa(d(e(X)), DX)) 63.93/17.23 p_in_aa(d(d(X)), DDX) -> U5_aa(X, DDX, p_in_aa(d(X), DX)) 63.93/17.23 U5_aa(X, DDX, p_out_aa(d(X), DX)) -> U6_aa(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.93/17.23 U6_aa(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_aa(d(d(X)), DDX) 63.93/17.23 U3_aa(X, Y, DY, DX, p_out_aa(d(e(X)), DX)) -> U4_aa(X, Y, DY, DX, p_in_aa(d(e(Y)), DY)) 63.93/17.23 U4_aa(X, Y, DY, DX, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.93/17.23 U1_aa(X, Y, DX, DY, p_out_aa(d(e(X)), DX)) -> U2_aa(X, Y, DX, DY, p_in_aa(d(e(Y)), DY)) 63.93/17.23 U2_aa(X, Y, DX, DY, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(+(X, Y))), +(DX, DY)) 63.93/17.23 U5_ag(X, DDX, p_out_aa(d(X), DX)) -> U6_ag(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.93/17.23 U6_ag(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_ag(d(d(X)), DDX) 63.93/17.23 U1_ag(X, Y, DX, DY, p_out_ag(d(e(X)), DX)) -> U2_ag(X, Y, DX, DY, p_in_ag(d(e(Y)), DY)) 63.93/17.23 U2_ag(X, Y, DX, DY, p_out_ag(d(e(Y)), DY)) -> p_out_ag(d(e(+(X, Y))), +(DX, DY)) 63.93/17.23 63.93/17.23 The argument filtering Pi contains the following mapping: 63.93/17.23 p_in_ag(x1, x2) = p_in_ag(x2) 63.93/17.23 63.93/17.23 const(x1) = const 63.93/17.23 63.93/17.23 1 = 1 63.93/17.23 63.93/17.23 p_out_ag(x1, x2) = p_out_ag(x1, x2) 63.93/17.23 63.93/17.23 0 = 0 63.93/17.23 63.93/17.23 +(x1, x2) = +(x1, x2) 63.93/17.23 63.93/17.23 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x3, x4, x5) 63.93/17.23 63.93/17.23 *(x1, x2) = *(x1, x2) 63.93/17.23 63.93/17.23 U3_ag(x1, x2, x3, x4, x5) = U3_ag(x1, x2, x3, x4, x5) 63.93/17.23 63.93/17.23 p_in_gg(x1, x2) = p_in_gg(x1, x2) 63.93/17.23 63.93/17.23 d(x1) = d(x1) 63.93/17.23 63.93/17.23 e(x1) = e(x1) 63.93/17.23 63.93/17.23 t = t 63.93/17.23 63.93/17.23 p_out_gg(x1, x2) = p_out_gg(x1, x2) 63.93/17.23 63.93/17.23 U1_gg(x1, x2, x3, x4, x5) = U1_gg(x1, x2, x3, x4, x5) 63.93/17.23 63.93/17.23 U3_gg(x1, x2, x3, x4, x5) = U3_gg(x1, x2, x3, x4, x5) 63.93/17.23 63.93/17.23 U5_gg(x1, x2, x3) = U5_gg(x1, x2, x3) 63.93/17.23 63.93/17.23 p_in_ga(x1, x2) = p_in_ga(x1) 63.93/17.23 63.93/17.23 p_out_ga(x1, x2) = p_out_ga(x1, x2) 63.93/17.23 63.93/17.23 U1_ga(x1, x2, x3, x4, x5) = U1_ga(x1, x2, x5) 63.93/17.23 63.93/17.23 U3_ga(x1, x2, x3, x4, x5) = U3_ga(x1, x2, x5) 63.93/17.23 63.93/17.23 U5_ga(x1, x2, x3) = U5_ga(x1, x3) 63.93/17.23 63.93/17.23 U6_ga(x1, x2, x3, x4) = U6_ga(x1, x4) 63.93/17.23 63.93/17.23 U4_ga(x1, x2, x3, x4, x5) = U4_ga(x1, x2, x4, x5) 63.93/17.23 63.93/17.23 U2_ga(x1, x2, x3, x4, x5) = U2_ga(x1, x2, x3, x5) 63.93/17.23 63.93/17.23 U6_gg(x1, x2, x3, x4) = U6_gg(x1, x2, x4) 63.93/17.23 63.93/17.23 U4_gg(x1, x2, x3, x4, x5) = U4_gg(x1, x2, x3, x4, x5) 63.93/17.23 63.93/17.23 U2_gg(x1, x2, x3, x4, x5) = U2_gg(x1, x2, x3, x4, x5) 63.93/17.23 63.93/17.23 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x1, x2, x3, x4, x5) 63.93/17.23 63.93/17.23 U5_ag(x1, x2, x3) = U5_ag(x2, x3) 63.93/17.23 63.93/17.23 p_in_aa(x1, x2) = p_in_aa 63.93/17.23 63.93/17.23 p_out_aa(x1, x2) = p_out_aa(x1, x2) 63.93/17.23 63.93/17.23 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 63.93/17.23 63.93/17.23 U3_aa(x1, x2, x3, x4, x5) = U3_aa(x5) 63.93/17.23 63.93/17.23 U5_aa(x1, x2, x3) = U5_aa(x3) 63.93/17.23 63.93/17.23 U6_aa(x1, x2, x3, x4) = U6_aa(x1, x4) 63.93/17.23 63.93/17.23 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x1, x4, x5) 63.93/17.23 63.93/17.23 U2_aa(x1, x2, x3, x4, x5) = U2_aa(x1, x3, x5) 63.93/17.23 63.93/17.23 U6_ag(x1, x2, x3, x4) = U6_ag(x1, x2, x4) 63.93/17.23 63.93/17.23 U2_ag(x1, x2, x3, x4, x5) = U2_ag(x1, x3, x4, x5) 63.93/17.23 63.93/17.23 P_IN_GG(x1, x2) = P_IN_GG(x1, x2) 63.93/17.23 63.93/17.23 U1_GG(x1, x2, x3, x4, x5) = U1_GG(x1, x2, x3, x4, x5) 63.93/17.23 63.93/17.23 U3_GG(x1, x2, x3, x4, x5) = U3_GG(x1, x2, x3, x4, x5) 63.93/17.23 63.93/17.23 63.93/17.23 We have to consider all (P,R,Pi)-chains 63.93/17.23 ---------------------------------------- 63.93/17.23 63.93/17.23 (56) UsableRulesProof (EQUIVALENT) 63.93/17.23 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 63.93/17.23 ---------------------------------------- 63.93/17.23 63.93/17.23 (57) 63.93/17.23 Obligation: 63.93/17.23 Pi DP problem: 63.93/17.23 The TRS P consists of the following rules: 63.93/17.23 63.93/17.23 U1_GG(X, Y, DX, DY, p_out_gg(d(e(X)), DX)) -> P_IN_GG(d(e(Y)), DY) 63.93/17.23 P_IN_GG(d(e(+(X, Y))), +(DX, DY)) -> U1_GG(X, Y, DX, DY, p_in_gg(d(e(X)), DX)) 63.93/17.23 P_IN_GG(d(e(+(X, Y))), +(DX, DY)) -> P_IN_GG(d(e(X)), DX) 63.93/17.23 P_IN_GG(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_GG(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.93/17.23 U3_GG(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> P_IN_GG(d(e(Y)), DY) 63.93/17.23 P_IN_GG(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> P_IN_GG(d(e(X)), DX) 63.93/17.23 63.93/17.23 The TRS R consists of the following rules: 63.93/17.23 63.93/17.23 p_in_gg(d(e(t)), const(1)) -> p_out_gg(d(e(t)), const(1)) 63.93/17.23 p_in_gg(d(e(const(A))), const(0)) -> p_out_gg(d(e(const(A))), const(0)) 63.93/17.23 p_in_gg(d(e(+(X, Y))), +(DX, DY)) -> U1_gg(X, Y, DX, DY, p_in_gg(d(e(X)), DX)) 63.93/17.23 p_in_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_gg(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.93/17.23 U1_gg(X, Y, DX, DY, p_out_gg(d(e(X)), DX)) -> U2_gg(X, Y, DX, DY, p_in_gg(d(e(Y)), DY)) 63.93/17.23 U3_gg(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_gg(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.93/17.27 U2_gg(X, Y, DX, DY, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(+(X, Y))), +(DX, DY)) 63.93/17.27 U4_gg(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.93/17.27 63.93/17.27 The argument filtering Pi contains the following mapping: 63.93/17.27 const(x1) = const 63.93/17.27 63.93/17.27 1 = 1 63.93/17.27 63.93/17.27 0 = 0 63.93/17.27 63.93/17.27 +(x1, x2) = +(x1, x2) 63.93/17.27 63.93/17.27 *(x1, x2) = *(x1, x2) 63.93/17.27 63.93/17.27 p_in_gg(x1, x2) = p_in_gg(x1, x2) 63.93/17.27 63.93/17.27 d(x1) = d(x1) 63.93/17.27 63.93/17.27 e(x1) = e(x1) 63.93/17.27 63.93/17.27 t = t 63.93/17.27 63.93/17.27 p_out_gg(x1, x2) = p_out_gg(x1, x2) 63.93/17.27 63.93/17.27 U1_gg(x1, x2, x3, x4, x5) = U1_gg(x1, x2, x3, x4, x5) 63.93/17.27 63.93/17.27 U3_gg(x1, x2, x3, x4, x5) = U3_gg(x1, x2, x3, x4, x5) 63.93/17.27 63.93/17.27 U4_gg(x1, x2, x3, x4, x5) = U4_gg(x1, x2, x3, x4, x5) 63.93/17.27 63.93/17.27 U2_gg(x1, x2, x3, x4, x5) = U2_gg(x1, x2, x3, x4, x5) 63.93/17.27 63.93/17.27 P_IN_GG(x1, x2) = P_IN_GG(x1, x2) 63.93/17.27 63.93/17.27 U1_GG(x1, x2, x3, x4, x5) = U1_GG(x1, x2, x3, x4, x5) 63.93/17.27 63.93/17.27 U3_GG(x1, x2, x3, x4, x5) = U3_GG(x1, x2, x3, x4, x5) 63.93/17.27 63.93/17.27 63.93/17.27 We have to consider all (P,R,Pi)-chains 63.93/17.27 ---------------------------------------- 63.93/17.27 63.93/17.27 (58) 63.93/17.27 Obligation: 63.93/17.27 Pi DP problem: 63.93/17.27 The TRS P consists of the following rules: 63.93/17.27 63.93/17.27 U1_AG(X, Y, DX, DY, p_out_ag(d(e(X)), DX)) -> P_IN_AG(d(e(Y)), DY) 63.93/17.27 P_IN_AG(d(e(+(X, Y))), +(DX, DY)) -> U1_AG(X, Y, DX, DY, p_in_ag(d(e(X)), DX)) 63.93/17.27 P_IN_AG(d(e(+(X, Y))), +(DX, DY)) -> P_IN_AG(d(e(X)), DX) 63.93/17.27 63.93/17.27 The TRS R consists of the following rules: 63.93/17.27 63.93/17.27 p_in_ag(d(e(t)), const(1)) -> p_out_ag(d(e(t)), const(1)) 63.93/17.27 p_in_ag(d(e(const(A))), const(0)) -> p_out_ag(d(e(const(A))), const(0)) 63.93/17.27 p_in_ag(d(e(+(X, Y))), +(DX, DY)) -> U1_ag(X, Y, DX, DY, p_in_ag(d(e(X)), DX)) 63.93/17.27 p_in_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ag(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.93/17.27 p_in_gg(d(e(t)), const(1)) -> p_out_gg(d(e(t)), const(1)) 63.93/17.27 p_in_gg(d(e(const(A))), const(0)) -> p_out_gg(d(e(const(A))), const(0)) 63.93/17.27 p_in_gg(d(e(+(X, Y))), +(DX, DY)) -> U1_gg(X, Y, DX, DY, p_in_gg(d(e(X)), DX)) 63.93/17.27 p_in_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_gg(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.93/17.27 p_in_gg(d(d(X)), DDX) -> U5_gg(X, DDX, p_in_ga(d(X), DX)) 63.93/17.27 p_in_ga(d(e(t)), const(1)) -> p_out_ga(d(e(t)), const(1)) 63.93/17.27 p_in_ga(d(e(const(A))), const(0)) -> p_out_ga(d(e(const(A))), const(0)) 63.93/17.27 p_in_ga(d(e(+(X, Y))), +(DX, DY)) -> U1_ga(X, Y, DX, DY, p_in_ga(d(e(X)), DX)) 63.93/17.27 p_in_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ga(X, Y, DY, DX, p_in_ga(d(e(X)), DX)) 63.93/17.27 p_in_ga(d(d(X)), DDX) -> U5_ga(X, DDX, p_in_ga(d(X), DX)) 63.93/17.27 U5_ga(X, DDX, p_out_ga(d(X), DX)) -> U6_ga(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.93/17.27 U6_ga(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_ga(d(d(X)), DDX) 63.93/17.27 U3_ga(X, Y, DY, DX, p_out_ga(d(e(X)), DX)) -> U4_ga(X, Y, DY, DX, p_in_ga(d(e(Y)), DY)) 63.93/17.27 U4_ga(X, Y, DY, DX, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.93/17.27 U1_ga(X, Y, DX, DY, p_out_ga(d(e(X)), DX)) -> U2_ga(X, Y, DX, DY, p_in_ga(d(e(Y)), DY)) 63.93/17.27 U2_ga(X, Y, DX, DY, p_out_ga(d(e(Y)), DY)) -> p_out_ga(d(e(+(X, Y))), +(DX, DY)) 63.93/17.27 U5_gg(X, DDX, p_out_ga(d(X), DX)) -> U6_gg(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.93/17.27 U6_gg(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_gg(d(d(X)), DDX) 63.93/17.27 U3_gg(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_gg(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.93/17.27 U4_gg(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.93/17.27 U1_gg(X, Y, DX, DY, p_out_gg(d(e(X)), DX)) -> U2_gg(X, Y, DX, DY, p_in_gg(d(e(Y)), DY)) 63.93/17.27 U2_gg(X, Y, DX, DY, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(+(X, Y))), +(DX, DY)) 63.93/17.27 U3_ag(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_ag(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.93/17.27 U4_ag(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.93/17.27 p_in_ag(d(d(X)), DDX) -> U5_ag(X, DDX, p_in_aa(d(X), DX)) 63.93/17.27 p_in_aa(d(e(t)), const(1)) -> p_out_aa(d(e(t)), const(1)) 63.93/17.27 p_in_aa(d(e(const(A))), const(0)) -> p_out_aa(d(e(const(A))), const(0)) 63.93/17.27 p_in_aa(d(e(+(X, Y))), +(DX, DY)) -> U1_aa(X, Y, DX, DY, p_in_aa(d(e(X)), DX)) 63.93/17.27 p_in_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_aa(X, Y, DY, DX, p_in_aa(d(e(X)), DX)) 63.93/17.27 p_in_aa(d(d(X)), DDX) -> U5_aa(X, DDX, p_in_aa(d(X), DX)) 63.93/17.27 U5_aa(X, DDX, p_out_aa(d(X), DX)) -> U6_aa(X, DDX, DX, p_in_ga(d(e(DX)), DDX)) 63.93/17.27 U6_aa(X, DDX, DX, p_out_ga(d(e(DX)), DDX)) -> p_out_aa(d(d(X)), DDX) 63.93/17.27 U3_aa(X, Y, DY, DX, p_out_aa(d(e(X)), DX)) -> U4_aa(X, Y, DY, DX, p_in_aa(d(e(Y)), DY)) 63.93/17.27 U4_aa(X, Y, DY, DX, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.93/17.27 U1_aa(X, Y, DX, DY, p_out_aa(d(e(X)), DX)) -> U2_aa(X, Y, DX, DY, p_in_aa(d(e(Y)), DY)) 63.93/17.27 U2_aa(X, Y, DX, DY, p_out_aa(d(e(Y)), DY)) -> p_out_aa(d(e(+(X, Y))), +(DX, DY)) 63.93/17.27 U5_ag(X, DDX, p_out_aa(d(X), DX)) -> U6_ag(X, DDX, DX, p_in_gg(d(e(DX)), DDX)) 63.93/17.27 U6_ag(X, DDX, DX, p_out_gg(d(e(DX)), DDX)) -> p_out_ag(d(d(X)), DDX) 63.93/17.27 U1_ag(X, Y, DX, DY, p_out_ag(d(e(X)), DX)) -> U2_ag(X, Y, DX, DY, p_in_ag(d(e(Y)), DY)) 63.93/17.27 U2_ag(X, Y, DX, DY, p_out_ag(d(e(Y)), DY)) -> p_out_ag(d(e(+(X, Y))), +(DX, DY)) 63.93/17.27 63.93/17.27 The argument filtering Pi contains the following mapping: 63.93/17.27 p_in_ag(x1, x2) = p_in_ag(x2) 63.93/17.27 63.93/17.27 const(x1) = const 63.93/17.27 63.93/17.27 1 = 1 63.93/17.27 63.93/17.27 p_out_ag(x1, x2) = p_out_ag(x1, x2) 63.93/17.27 63.93/17.27 0 = 0 63.93/17.27 63.93/17.27 +(x1, x2) = +(x1, x2) 63.93/17.27 63.93/17.27 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x3, x4, x5) 63.93/17.27 63.93/17.27 *(x1, x2) = *(x1, x2) 63.93/17.27 63.93/17.27 U3_ag(x1, x2, x3, x4, x5) = U3_ag(x1, x2, x3, x4, x5) 63.93/17.27 63.93/17.27 p_in_gg(x1, x2) = p_in_gg(x1, x2) 63.93/17.27 63.93/17.27 d(x1) = d(x1) 63.93/17.27 63.93/17.27 e(x1) = e(x1) 63.93/17.27 63.93/17.27 t = t 63.93/17.27 63.93/17.27 p_out_gg(x1, x2) = p_out_gg(x1, x2) 63.93/17.27 63.93/17.27 U1_gg(x1, x2, x3, x4, x5) = U1_gg(x1, x2, x3, x4, x5) 63.93/17.27 63.93/17.27 U3_gg(x1, x2, x3, x4, x5) = U3_gg(x1, x2, x3, x4, x5) 63.93/17.27 63.93/17.27 U5_gg(x1, x2, x3) = U5_gg(x1, x2, x3) 63.93/17.27 63.93/17.27 p_in_ga(x1, x2) = p_in_ga(x1) 63.93/17.27 63.93/17.27 p_out_ga(x1, x2) = p_out_ga(x1, x2) 63.93/17.27 63.93/17.27 U1_ga(x1, x2, x3, x4, x5) = U1_ga(x1, x2, x5) 63.93/17.27 63.93/17.27 U3_ga(x1, x2, x3, x4, x5) = U3_ga(x1, x2, x5) 63.93/17.27 63.93/17.27 U5_ga(x1, x2, x3) = U5_ga(x1, x3) 63.93/17.27 63.93/17.27 U6_ga(x1, x2, x3, x4) = U6_ga(x1, x4) 63.93/17.27 63.93/17.27 U4_ga(x1, x2, x3, x4, x5) = U4_ga(x1, x2, x4, x5) 63.93/17.27 63.93/17.27 U2_ga(x1, x2, x3, x4, x5) = U2_ga(x1, x2, x3, x5) 63.93/17.27 63.93/17.27 U6_gg(x1, x2, x3, x4) = U6_gg(x1, x2, x4) 63.93/17.27 63.93/17.27 U4_gg(x1, x2, x3, x4, x5) = U4_gg(x1, x2, x3, x4, x5) 63.93/17.27 63.93/17.27 U2_gg(x1, x2, x3, x4, x5) = U2_gg(x1, x2, x3, x4, x5) 63.93/17.27 63.93/17.27 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x1, x2, x3, x4, x5) 63.93/17.27 63.93/17.27 U5_ag(x1, x2, x3) = U5_ag(x2, x3) 63.93/17.27 63.93/17.27 p_in_aa(x1, x2) = p_in_aa 63.93/17.27 63.93/17.27 p_out_aa(x1, x2) = p_out_aa(x1, x2) 63.93/17.27 63.93/17.27 U1_aa(x1, x2, x3, x4, x5) = U1_aa(x5) 63.93/17.27 63.93/17.27 U3_aa(x1, x2, x3, x4, x5) = U3_aa(x5) 63.93/17.27 63.93/17.27 U5_aa(x1, x2, x3) = U5_aa(x3) 63.93/17.27 63.93/17.27 U6_aa(x1, x2, x3, x4) = U6_aa(x1, x4) 63.93/17.27 63.93/17.27 U4_aa(x1, x2, x3, x4, x5) = U4_aa(x1, x4, x5) 63.93/17.27 63.93/17.27 U2_aa(x1, x2, x3, x4, x5) = U2_aa(x1, x3, x5) 63.93/17.27 63.93/17.27 U6_ag(x1, x2, x3, x4) = U6_ag(x1, x2, x4) 63.93/17.27 63.93/17.27 U2_ag(x1, x2, x3, x4, x5) = U2_ag(x1, x3, x4, x5) 63.93/17.27 63.93/17.27 P_IN_AG(x1, x2) = P_IN_AG(x2) 63.93/17.27 63.93/17.27 U1_AG(x1, x2, x3, x4, x5) = U1_AG(x3, x4, x5) 63.93/17.27 63.93/17.27 63.93/17.27 We have to consider all (P,R,Pi)-chains 63.93/17.27 ---------------------------------------- 63.93/17.27 63.93/17.27 (59) UsableRulesProof (EQUIVALENT) 63.93/17.27 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 63.93/17.27 ---------------------------------------- 63.93/17.27 63.93/17.27 (60) 63.93/17.27 Obligation: 63.93/17.27 Pi DP problem: 63.93/17.27 The TRS P consists of the following rules: 63.93/17.27 63.93/17.27 U1_AG(X, Y, DX, DY, p_out_ag(d(e(X)), DX)) -> P_IN_AG(d(e(Y)), DY) 63.93/17.27 P_IN_AG(d(e(+(X, Y))), +(DX, DY)) -> U1_AG(X, Y, DX, DY, p_in_ag(d(e(X)), DX)) 63.93/17.27 P_IN_AG(d(e(+(X, Y))), +(DX, DY)) -> P_IN_AG(d(e(X)), DX) 63.93/17.27 63.93/17.27 The TRS R consists of the following rules: 63.93/17.27 63.93/17.27 p_in_ag(d(e(t)), const(1)) -> p_out_ag(d(e(t)), const(1)) 63.93/17.27 p_in_ag(d(e(const(A))), const(0)) -> p_out_ag(d(e(const(A))), const(0)) 63.93/17.27 p_in_ag(d(e(+(X, Y))), +(DX, DY)) -> U1_ag(X, Y, DX, DY, p_in_ag(d(e(X)), DX)) 63.93/17.27 p_in_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_ag(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.93/17.27 U1_ag(X, Y, DX, DY, p_out_ag(d(e(X)), DX)) -> U2_ag(X, Y, DX, DY, p_in_ag(d(e(Y)), DY)) 63.93/17.27 U3_ag(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_ag(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.93/17.27 U2_ag(X, Y, DX, DY, p_out_ag(d(e(Y)), DY)) -> p_out_ag(d(e(+(X, Y))), +(DX, DY)) 63.93/17.27 p_in_gg(d(e(t)), const(1)) -> p_out_gg(d(e(t)), const(1)) 63.93/17.27 p_in_gg(d(e(const(A))), const(0)) -> p_out_gg(d(e(const(A))), const(0)) 63.93/17.27 p_in_gg(d(e(+(X, Y))), +(DX, DY)) -> U1_gg(X, Y, DX, DY, p_in_gg(d(e(X)), DX)) 63.93/17.27 p_in_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) -> U3_gg(X, Y, DY, DX, p_in_gg(d(e(X)), DX)) 63.93/17.27 U4_ag(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_ag(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.93/17.27 U1_gg(X, Y, DX, DY, p_out_gg(d(e(X)), DX)) -> U2_gg(X, Y, DX, DY, p_in_gg(d(e(Y)), DY)) 63.93/17.27 U3_gg(X, Y, DY, DX, p_out_gg(d(e(X)), DX)) -> U4_gg(X, Y, DY, DX, p_in_gg(d(e(Y)), DY)) 63.93/17.27 U2_gg(X, Y, DX, DY, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(+(X, Y))), +(DX, DY)) 63.93/17.27 U4_gg(X, Y, DY, DX, p_out_gg(d(e(Y)), DY)) -> p_out_gg(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) 63.93/17.27 63.93/17.27 The argument filtering Pi contains the following mapping: 63.93/17.27 p_in_ag(x1, x2) = p_in_ag(x2) 63.93/17.27 63.93/17.27 const(x1) = const 63.93/17.27 63.93/17.27 1 = 1 63.93/17.27 63.93/17.27 p_out_ag(x1, x2) = p_out_ag(x1, x2) 63.93/17.27 63.93/17.27 0 = 0 63.93/17.27 63.93/17.27 +(x1, x2) = +(x1, x2) 63.93/17.27 63.93/17.27 U1_ag(x1, x2, x3, x4, x5) = U1_ag(x3, x4, x5) 63.93/17.27 63.93/17.27 *(x1, x2) = *(x1, x2) 63.93/17.27 63.93/17.27 U3_ag(x1, x2, x3, x4, x5) = U3_ag(x1, x2, x3, x4, x5) 63.93/17.27 63.93/17.27 p_in_gg(x1, x2) = p_in_gg(x1, x2) 63.93/17.27 63.93/17.27 d(x1) = d(x1) 63.93/17.27 63.93/17.27 e(x1) = e(x1) 63.93/17.27 63.93/17.27 t = t 63.93/17.27 63.93/17.27 p_out_gg(x1, x2) = p_out_gg(x1, x2) 63.93/17.27 63.93/17.27 U1_gg(x1, x2, x3, x4, x5) = U1_gg(x1, x2, x3, x4, x5) 63.93/17.27 63.93/17.27 U3_gg(x1, x2, x3, x4, x5) = U3_gg(x1, x2, x3, x4, x5) 63.93/17.27 63.93/17.27 U4_gg(x1, x2, x3, x4, x5) = U4_gg(x1, x2, x3, x4, x5) 63.93/17.27 63.93/17.27 U2_gg(x1, x2, x3, x4, x5) = U2_gg(x1, x2, x3, x4, x5) 63.93/17.27 63.93/17.27 U4_ag(x1, x2, x3, x4, x5) = U4_ag(x1, x2, x3, x4, x5) 63.93/17.27 63.93/17.27 U2_ag(x1, x2, x3, x4, x5) = U2_ag(x1, x3, x4, x5) 63.93/17.27 63.93/17.27 P_IN_AG(x1, x2) = P_IN_AG(x2) 63.93/17.27 63.93/17.27 U1_AG(x1, x2, x3, x4, x5) = U1_AG(x3, x4, x5) 63.93/17.27 63.93/17.27 63.93/17.27 We have to consider all (P,R,Pi)-chains 63.93/17.27 ---------------------------------------- 63.93/17.27 63.93/17.27 (61) PrologToTRSTransformerProof (SOUND) 63.93/17.27 Transformed Prolog program to TRS. 63.93/17.27 63.93/17.27 { 63.93/17.27 "root": 4, 63.93/17.27 "program": { 63.93/17.27 "directives": [], 63.93/17.27 "clauses": [ 63.93/17.27 [ 63.93/17.27 "(p (d (e (t))) (const (1)))", 63.93/17.27 null 63.93/17.27 ], 63.93/17.27 [ 63.93/17.27 "(p (d (e (const A))) (const (0)))", 63.93/17.27 null 63.93/17.27 ], 63.93/17.27 [ 63.93/17.27 "(p (d (e (+ X Y))) (+ DX DY))", 63.93/17.27 "(',' (p (d (e X)) DX) (p (d (e Y)) DY))" 63.93/17.27 ], 63.93/17.27 [ 63.93/17.27 "(p (d (e (* X Y))) (+ (* X DY) (* Y DX)))", 63.93/17.27 "(',' (p (d (e X)) DX) (p (d (e Y)) DY))" 63.93/17.27 ], 63.93/17.27 [ 63.93/17.27 "(p (d (d X)) DDX)", 63.93/17.27 "(',' (p (d X) DX) (p (d (e DX)) DDX))" 63.93/17.27 ] 63.93/17.27 ] 63.93/17.27 }, 63.93/17.27 "graph": { 63.93/17.27 "nodes": { 63.93/17.27 "type": "Nodes", 63.93/17.27 "470": { 63.93/17.27 "goal": [], 63.93/17.27 "kb": { 63.93/17.27 "nonunifying": [], 63.93/17.27 "intvars": {}, 63.93/17.27 "arithmetic": { 63.93/17.27 "type": "PlainIntegerRelationState", 63.93/17.27 "relations": [] 63.93/17.27 }, 63.93/17.27 "ground": [], 63.93/17.27 "free": [], 63.93/17.27 "exprvars": [] 63.93/17.27 } 63.93/17.27 }, 63.93/17.27 "471": { 63.93/17.27 "goal": [{ 63.93/17.27 "clause": 1, 63.93/17.27 "scope": 3, 63.93/17.27 "term": "(p (d T102) X100)" 63.93/17.27 }], 63.93/17.27 "kb": { 63.93/17.27 "nonunifying": [], 63.93/17.27 "intvars": {}, 63.93/17.27 "arithmetic": { 63.93/17.27 "type": "PlainIntegerRelationState", 63.93/17.27 "relations": [] 63.93/17.27 }, 63.93/17.27 "ground": [], 63.93/17.27 "free": ["X100"], 63.93/17.27 "exprvars": [] 63.93/17.27 } 63.93/17.27 }, 63.93/17.27 "230": { 63.93/17.27 "goal": [], 63.93/17.27 "kb": { 63.93/17.27 "nonunifying": [], 63.93/17.27 "intvars": {}, 63.93/17.27 "arithmetic": { 63.93/17.27 "type": "PlainIntegerRelationState", 63.93/17.27 "relations": [] 63.93/17.27 }, 63.93/17.27 "ground": [], 63.93/17.27 "free": [], 63.93/17.27 "exprvars": [] 63.93/17.27 } 63.93/17.27 }, 63.93/17.27 "472": { 63.93/17.27 "goal": [ 63.93/17.27 { 63.93/17.27 "clause": 2, 63.93/17.27 "scope": 3, 63.93/17.27 "term": "(p (d T102) X100)" 63.93/17.27 }, 63.93/17.27 { 63.93/17.27 "clause": 3, 63.93/17.27 "scope": 3, 63.93/17.27 "term": "(p (d T102) X100)" 63.93/17.27 }, 63.93/17.27 { 63.93/17.27 "clause": 4, 63.93/17.27 "scope": 3, 63.93/17.27 "term": "(p (d T102) X100)" 63.93/17.27 } 63.93/17.27 ], 63.93/17.27 "kb": { 63.93/17.27 "nonunifying": [], 63.93/17.27 "intvars": {}, 63.93/17.27 "arithmetic": { 63.93/17.27 "type": "PlainIntegerRelationState", 63.93/17.27 "relations": [] 63.93/17.27 }, 63.93/17.27 "ground": [], 63.93/17.27 "free": ["X100"], 63.93/17.27 "exprvars": [] 63.93/17.27 } 63.93/17.27 }, 63.93/17.27 "231": { 63.93/17.27 "goal": [], 63.93/17.27 "kb": { 63.93/17.27 "nonunifying": [], 63.93/17.27 "intvars": {}, 63.93/17.27 "arithmetic": { 63.93/17.27 "type": "PlainIntegerRelationState", 63.93/17.27 "relations": [] 63.93/17.27 }, 63.93/17.27 "ground": [], 63.93/17.27 "free": [], 63.93/17.27 "exprvars": [] 63.93/17.27 } 63.93/17.27 }, 63.93/17.27 "232": { 63.93/17.27 "goal": [{ 63.93/17.27 "clause": 1, 63.93/17.27 "scope": 1, 63.93/17.27 "term": "(p T1 T2)" 63.93/17.27 }], 63.93/17.27 "kb": { 63.93/17.27 "nonunifying": [], 63.93/17.27 "intvars": {}, 63.93/17.27 "arithmetic": { 63.93/17.27 "type": "PlainIntegerRelationState", 63.93/17.27 "relations": [] 63.93/17.27 }, 63.93/17.27 "ground": ["T2"], 63.93/17.27 "free": [], 63.93/17.27 "exprvars": [] 63.93/17.27 } 63.93/17.27 }, 63.93/17.27 "430": { 63.93/17.27 "goal": [{ 63.93/17.27 "clause": -1, 63.93/17.27 "scope": -1, 63.93/17.27 "term": "(true)" 63.93/17.27 }], 63.93/17.27 "kb": { 63.93/17.27 "nonunifying": [], 63.93/17.27 "intvars": {}, 63.93/17.27 "arithmetic": { 63.93/17.27 "type": "PlainIntegerRelationState", 63.93/17.27 "relations": [] 63.93/17.27 }, 63.93/17.27 "ground": [], 63.93/17.27 "free": [], 63.93/17.27 "exprvars": [] 63.93/17.27 } 63.93/17.27 }, 63.93/17.27 "233": { 63.93/17.27 "goal": [ 63.93/17.27 { 63.93/17.27 "clause": 2, 63.93/17.27 "scope": 1, 63.93/17.27 "term": "(p T1 T2)" 63.93/17.27 }, 63.93/17.27 { 63.93/17.27 "clause": 3, 63.93/17.27 "scope": 1, 63.93/17.27 "term": "(p T1 T2)" 63.93/17.27 }, 63.93/17.27 { 63.93/17.27 "clause": 4, 63.93/17.27 "scope": 1, 63.93/17.27 "term": "(p T1 T2)" 63.93/17.27 } 63.93/17.27 ], 63.93/17.27 "kb": { 63.93/17.27 "nonunifying": [], 63.93/17.27 "intvars": {}, 63.93/17.27 "arithmetic": { 63.93/17.27 "type": "PlainIntegerRelationState", 63.93/17.27 "relations": [] 63.93/17.27 }, 63.93/17.27 "ground": ["T2"], 63.93/17.27 "free": [], 63.93/17.27 "exprvars": [] 63.93/17.27 } 63.93/17.27 }, 63.93/17.27 "475": { 63.93/17.27 "goal": [{ 63.93/17.27 "clause": -1, 63.93/17.27 "scope": -1, 63.93/17.27 "term": "(true)" 63.93/17.27 }], 63.93/17.27 "kb": { 63.93/17.27 "nonunifying": [], 63.93/17.27 "intvars": {}, 63.93/17.27 "arithmetic": { 63.93/17.27 "type": "PlainIntegerRelationState", 63.93/17.27 "relations": [] 63.93/17.27 }, 63.93/17.27 "ground": [], 63.93/17.27 "free": [], 63.93/17.27 "exprvars": [] 63.93/17.27 } 63.93/17.27 }, 63.93/17.27 "234": { 63.93/17.27 "goal": [{ 63.93/17.27 "clause": -1, 63.93/17.27 "scope": -1, 63.93/17.27 "term": "(true)" 63.93/17.27 }], 63.93/17.27 "kb": { 63.93/17.27 "nonunifying": [], 63.93/17.27 "intvars": {}, 63.93/17.27 "arithmetic": { 63.93/17.27 "type": "PlainIntegerRelationState", 63.93/17.27 "relations": [] 63.93/17.27 }, 63.93/17.27 "ground": [], 63.93/17.27 "free": [], 63.93/17.27 "exprvars": [] 63.93/17.27 } 63.93/17.27 }, 63.93/17.27 "476": { 63.93/17.27 "goal": [], 63.93/17.27 "kb": { 63.93/17.27 "nonunifying": [], 63.93/17.27 "intvars": {}, 63.93/17.27 "arithmetic": { 63.93/17.27 "type": "PlainIntegerRelationState", 63.93/17.27 "relations": [] 63.93/17.27 }, 63.93/17.27 "ground": [], 63.93/17.27 "free": [], 63.93/17.27 "exprvars": [] 63.93/17.27 } 63.93/17.27 }, 63.93/17.27 "235": { 63.93/17.27 "goal": [], 63.93/17.27 "kb": { 63.93/17.27 "nonunifying": [], 63.93/17.27 "intvars": {}, 63.93/17.27 "arithmetic": { 63.93/17.27 "type": "PlainIntegerRelationState", 63.93/17.27 "relations": [] 63.93/17.27 }, 63.93/17.27 "ground": [], 63.93/17.27 "free": [], 63.93/17.27 "exprvars": [] 63.93/17.27 } 63.93/17.27 }, 63.93/17.27 "433": { 63.93/17.27 "goal": [], 63.93/17.27 "kb": { 63.93/17.27 "nonunifying": [], 63.93/17.27 "intvars": {}, 63.93/17.27 "arithmetic": { 63.93/17.27 "type": "PlainIntegerRelationState", 63.93/17.27 "relations": [] 63.93/17.27 }, 63.93/17.27 "ground": [], 63.93/17.27 "free": [], 63.93/17.27 "exprvars": [] 63.93/17.27 } 63.93/17.27 }, 63.93/17.27 "477": { 63.93/17.27 "goal": [], 63.93/17.27 "kb": { 63.93/17.27 "nonunifying": [], 63.93/17.27 "intvars": {}, 63.93/17.27 "arithmetic": { 63.93/17.27 "type": "PlainIntegerRelationState", 63.93/17.27 "relations": [] 63.93/17.27 }, 63.93/17.27 "ground": [], 63.93/17.27 "free": [], 63.93/17.27 "exprvars": [] 63.93/17.27 } 63.93/17.27 }, 63.93/17.27 "434": { 63.93/17.27 "goal": [], 63.93/17.27 "kb": { 63.93/17.27 "nonunifying": [], 63.93/17.27 "intvars": {}, 63.93/17.27 "arithmetic": { 63.93/17.27 "type": "PlainIntegerRelationState", 63.93/17.27 "relations": [] 63.93/17.27 }, 63.93/17.27 "ground": [], 63.93/17.27 "free": [], 63.93/17.27 "exprvars": [] 63.93/17.27 } 63.93/17.27 }, 63.93/17.27 "237": { 63.93/17.27 "goal": [], 63.93/17.27 "kb": { 63.93/17.27 "nonunifying": [], 63.93/17.27 "intvars": {}, 63.93/17.27 "arithmetic": { 63.93/17.27 "type": "PlainIntegerRelationState", 63.93/17.27 "relations": [] 63.93/17.27 }, 63.93/17.27 "ground": [], 63.93/17.27 "free": [], 63.93/17.27 "exprvars": [] 63.93/17.27 } 63.93/17.27 }, 63.93/17.27 "435": { 63.93/17.27 "goal": [{ 63.93/17.27 "clause": 2, 63.93/17.27 "scope": 2, 63.93/17.27 "term": "(p (d (e T48)) T49)" 63.93/17.27 }], 63.93/17.27 "kb": { 63.93/17.27 "nonunifying": [], 63.93/17.27 "intvars": {}, 63.93/17.27 "arithmetic": { 63.93/17.27 "type": "PlainIntegerRelationState", 63.93/17.27 "relations": [] 63.93/17.27 }, 63.93/17.27 "ground": [ 63.93/17.27 "T49", 63.93/17.27 "T48" 63.93/17.27 ], 63.93/17.27 "free": [], 63.93/17.27 "exprvars": [] 63.93/17.27 } 63.93/17.27 }, 63.93/17.27 "436": { 63.93/17.27 "goal": [ 63.93/17.27 { 63.93/17.27 "clause": 3, 63.93/17.27 "scope": 2, 63.93/17.27 "term": "(p (d (e T48)) T49)" 63.93/17.27 }, 63.93/17.27 { 63.93/17.27 "clause": 4, 63.93/17.27 "scope": 2, 63.93/17.27 "term": "(p (d (e T48)) T49)" 63.93/17.27 } 63.93/17.27 ], 63.93/17.27 "kb": { 63.93/17.27 "nonunifying": [], 63.93/17.27 "intvars": {}, 63.93/17.27 "arithmetic": { 63.93/17.27 "type": "PlainIntegerRelationState", 63.93/17.27 "relations": [] 63.93/17.27 }, 63.93/17.27 "ground": [ 63.93/17.27 "T49", 63.93/17.27 "T48" 63.93/17.27 ], 63.93/17.27 "free": [], 63.93/17.27 "exprvars": [] 63.93/17.27 } 63.93/17.27 }, 63.93/17.27 "239": { 63.93/17.27 "goal": [{ 63.93/17.27 "clause": 2, 63.93/17.27 "scope": 1, 63.93/17.27 "term": "(p T1 T2)" 63.93/17.27 }], 63.93/17.27 "kb": { 63.93/17.27 "nonunifying": [], 63.93/17.27 "intvars": {}, 63.93/17.27 "arithmetic": { 63.93/17.27 "type": "PlainIntegerRelationState", 63.93/17.27 "relations": [] 63.93/17.27 }, 63.93/17.27 "ground": ["T2"], 63.93/17.27 "free": [], 63.93/17.27 "exprvars": [] 63.93/17.27 } 63.93/17.27 }, 63.93/17.27 "437": { 63.93/17.27 "goal": [{ 63.93/17.27 "clause": -1, 63.93/17.27 "scope": -1, 63.93/17.27 "term": "(',' (p (d (e T72)) T74) (p (d (e T73)) T75))" 63.93/17.27 }], 63.93/17.27 "kb": { 63.93/17.27 "nonunifying": [], 63.93/17.27 "intvars": {}, 63.93/17.27 "arithmetic": { 63.93/17.27 "type": "PlainIntegerRelationState", 63.93/17.27 "relations": [] 63.93/17.27 }, 63.93/17.27 "ground": [ 63.93/17.27 "T72", 63.93/17.27 "T73", 63.93/17.27 "T74", 63.93/17.27 "T75" 63.93/17.27 ], 63.93/17.27 "free": [], 63.93/17.27 "exprvars": [] 63.93/17.27 } 63.93/17.27 }, 63.93/17.27 "438": { 63.93/17.27 "goal": [], 63.93/17.27 "kb": { 63.93/17.27 "nonunifying": [], 63.93/17.27 "intvars": {}, 63.93/17.27 "arithmetic": { 63.93/17.27 "type": "PlainIntegerRelationState", 63.93/17.27 "relations": [] 63.93/17.27 }, 63.93/17.27 "ground": [], 63.93/17.27 "free": [], 63.93/17.27 "exprvars": [] 63.93/17.27 } 63.93/17.27 }, 63.93/17.27 "14": { 63.93/17.27 "goal": [ 63.93/17.27 { 63.93/17.27 "clause": 0, 63.93/17.27 "scope": 1, 63.93/17.27 "term": "(p T1 T2)" 63.93/17.27 }, 63.93/17.27 { 63.93/17.27 "clause": 1, 63.93/17.27 "scope": 1, 63.93/17.27 "term": "(p T1 T2)" 63.93/17.27 }, 63.93/17.27 { 63.93/17.27 "clause": 2, 63.93/17.27 "scope": 1, 63.93/17.27 "term": "(p T1 T2)" 63.93/17.27 }, 63.93/17.27 { 63.93/17.27 "clause": 3, 63.93/17.27 "scope": 1, 63.93/17.27 "term": "(p T1 T2)" 63.93/17.27 }, 63.93/17.27 { 63.93/17.27 "clause": 4, 63.93/17.27 "scope": 1, 63.93/17.27 "term": "(p T1 T2)" 63.93/17.27 } 63.93/17.27 ], 63.93/17.27 "kb": { 63.93/17.27 "nonunifying": [], 63.93/17.27 "intvars": {}, 63.93/17.27 "arithmetic": { 63.93/17.27 "type": "PlainIntegerRelationState", 63.93/17.27 "relations": [] 63.93/17.27 }, 63.93/17.27 "ground": ["T2"], 63.93/17.27 "free": [], 63.93/17.27 "exprvars": [] 63.93/17.27 } 63.93/17.27 }, 63.93/17.27 "240": { 63.93/17.27 "goal": [ 63.93/17.27 { 63.93/17.27 "clause": 3, 63.93/17.27 "scope": 1, 63.93/17.27 "term": "(p T1 T2)" 63.93/17.27 }, 63.93/17.27 { 63.93/17.27 "clause": 4, 63.93/17.27 "scope": 1, 63.93/17.27 "term": "(p T1 T2)" 63.93/17.27 } 63.93/17.27 ], 63.93/17.27 "kb": { 63.93/17.27 "nonunifying": [], 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63.93/17.28 "term": "(true)" 63.93/17.28 }], 63.93/17.28 "kb": { 63.93/17.28 "nonunifying": [], 63.93/17.28 "intvars": {}, 63.93/17.28 "arithmetic": { 63.93/17.28 "type": "PlainIntegerRelationState", 63.93/17.28 "relations": [] 63.93/17.28 }, 63.93/17.28 "ground": [], 63.93/17.28 "free": [], 63.93/17.28 "exprvars": [] 63.93/17.28 } 63.93/17.28 }, 63.93/17.28 "467": { 63.93/17.28 "goal": [ 63.93/17.28 { 63.93/17.28 "clause": 1, 63.93/17.28 "scope": 3, 63.93/17.28 "term": "(p (d T102) X100)" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "clause": 2, 63.93/17.28 "scope": 3, 63.93/17.28 "term": "(p (d T102) X100)" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "clause": 3, 63.93/17.28 "scope": 3, 63.93/17.28 "term": "(p (d T102) X100)" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "clause": 4, 63.93/17.28 "scope": 3, 63.93/17.28 "term": "(p (d T102) X100)" 63.93/17.28 } 63.93/17.28 ], 63.93/17.28 "kb": { 63.93/17.28 "nonunifying": [], 63.93/17.28 "intvars": {}, 63.93/17.28 "arithmetic": { 63.93/17.28 "type": "PlainIntegerRelationState", 63.93/17.28 "relations": [] 63.93/17.28 }, 63.93/17.28 "ground": [], 63.93/17.28 "free": ["X100"], 63.93/17.28 "exprvars": [] 63.93/17.28 } 63.93/17.28 }, 63.93/17.28 "347": { 63.93/17.28 "goal": [{ 63.93/17.28 "clause": -1, 63.93/17.28 "scope": -1, 63.93/17.28 "term": "(p (d (e T30)) T27)" 63.93/17.28 }], 63.93/17.28 "kb": { 63.93/17.28 "nonunifying": [], 63.93/17.28 "intvars": {}, 63.93/17.28 "arithmetic": { 63.93/17.28 "type": "PlainIntegerRelationState", 63.93/17.28 "relations": [] 63.93/17.28 }, 63.93/17.28 "ground": ["T27"], 63.93/17.28 "free": [], 63.93/17.28 "exprvars": [] 63.93/17.28 } 63.93/17.28 }, 63.93/17.28 "424": { 63.93/17.28 "goal": [], 63.93/17.28 "kb": { 63.93/17.28 "nonunifying": [], 63.93/17.28 "intvars": {}, 63.93/17.28 "arithmetic": { 63.93/17.28 "type": "PlainIntegerRelationState", 63.93/17.28 "relations": [] 63.93/17.28 }, 63.93/17.28 "ground": [], 63.93/17.28 "free": [], 63.93/17.28 "exprvars": [] 63.93/17.28 } 63.93/17.28 }, 63.93/17.28 "468": { 63.93/17.28 "goal": [{ 63.93/17.28 "clause": -1, 63.93/17.28 "scope": -1, 63.93/17.28 "term": "(true)" 63.93/17.28 }], 63.93/17.28 "kb": { 63.93/17.28 "nonunifying": [], 63.93/17.28 "intvars": {}, 63.93/17.28 "arithmetic": { 63.93/17.28 "type": "PlainIntegerRelationState", 63.93/17.28 "relations": [] 63.93/17.28 }, 63.93/17.28 "ground": [], 63.93/17.28 "free": [], 63.93/17.28 "exprvars": [] 63.93/17.28 } 63.93/17.28 }, 63.93/17.28 "545": { 63.93/17.28 "goal": [{ 63.93/17.28 "clause": -1, 63.93/17.28 "scope": -1, 63.93/17.28 "term": "(',' (p (d T138) X175) (p (d (e X175)) X176))" 63.93/17.28 }], 63.93/17.28 "kb": { 63.93/17.28 "nonunifying": [], 63.93/17.28 "intvars": {}, 63.93/17.28 "arithmetic": { 63.93/17.28 "type": "PlainIntegerRelationState", 63.93/17.28 "relations": [] 63.93/17.28 }, 63.93/17.28 "ground": [], 63.93/17.28 "free": [ 63.93/17.28 "X176", 63.93/17.28 "X175" 63.93/17.28 ], 63.93/17.28 "exprvars": [] 63.93/17.28 } 63.93/17.28 }, 63.93/17.28 "425": { 63.93/17.28 "goal": [], 63.93/17.28 "kb": { 63.93/17.28 "nonunifying": [], 63.93/17.28 "intvars": {}, 63.93/17.28 "arithmetic": { 63.93/17.28 "type": "PlainIntegerRelationState", 63.93/17.28 "relations": [] 63.93/17.28 }, 63.93/17.28 "ground": [], 63.93/17.28 "free": [], 63.93/17.28 "exprvars": [] 63.93/17.28 } 63.93/17.28 }, 63.93/17.28 "469": { 63.93/17.28 "goal": [], 63.93/17.28 "kb": { 63.93/17.28 "nonunifying": [], 63.93/17.28 "intvars": {}, 63.93/17.28 "arithmetic": { 63.93/17.28 "type": "PlainIntegerRelationState", 63.93/17.28 "relations": [] 63.93/17.28 }, 63.93/17.28 "ground": [], 63.93/17.28 "free": [], 63.93/17.28 "exprvars": [] 63.93/17.28 } 63.93/17.28 }, 63.93/17.28 "502": { 63.93/17.28 "goal": [{ 63.93/17.28 "clause": -1, 63.93/17.28 "scope": -1, 63.93/17.28 "term": "(p (d (e T119)) X134)" 63.93/17.28 }], 63.93/17.28 "kb": { 63.93/17.28 "nonunifying": [], 63.93/17.28 "intvars": {}, 63.93/17.28 "arithmetic": { 63.93/17.28 "type": "PlainIntegerRelationState", 63.93/17.28 "relations": [] 63.93/17.28 }, 63.93/17.28 "ground": [], 63.93/17.28 "free": ["X134"], 63.93/17.28 "exprvars": [] 63.93/17.28 } 63.93/17.28 }, 63.93/17.28 "546": { 63.93/17.28 "goal": [], 63.93/17.28 "kb": { 63.93/17.28 "nonunifying": [], 63.93/17.28 "intvars": {}, 63.93/17.28 "arithmetic": { 63.93/17.28 "type": "PlainIntegerRelationState", 63.93/17.28 "relations": [] 63.93/17.28 }, 63.93/17.28 "ground": [], 63.93/17.28 "free": [], 63.93/17.28 "exprvars": [] 63.93/17.28 } 63.93/17.28 }, 63.93/17.28 "547": { 63.93/17.28 "goal": [{ 63.93/17.28 "clause": -1, 63.93/17.28 "scope": -1, 63.93/17.28 "term": "(p (d T138) X175)" 63.93/17.28 }], 63.93/17.28 "kb": { 63.93/17.28 "nonunifying": [], 63.93/17.28 "intvars": {}, 63.93/17.28 "arithmetic": { 63.93/17.28 "type": "PlainIntegerRelationState", 63.93/17.28 "relations": [] 63.93/17.28 }, 63.93/17.28 "ground": [], 63.93/17.28 "free": ["X175"], 63.93/17.28 "exprvars": [] 63.93/17.28 } 63.93/17.28 }, 63.93/17.28 "229": { 63.93/17.28 "goal": [{ 63.93/17.28 "clause": -1, 63.93/17.28 "scope": -1, 63.93/17.28 "term": "(true)" 63.93/17.28 }], 63.93/17.28 "kb": { 63.93/17.28 "nonunifying": [], 63.93/17.28 "intvars": {}, 63.93/17.28 "arithmetic": { 63.93/17.28 "type": "PlainIntegerRelationState", 63.93/17.28 "relations": [] 63.93/17.28 }, 63.93/17.28 "ground": [], 63.93/17.28 "free": [], 63.93/17.28 "exprvars": [] 63.93/17.28 } 63.93/17.28 }, 63.93/17.28 "504": { 63.93/17.28 "goal": [{ 63.93/17.28 "clause": -1, 63.93/17.28 "scope": -1, 63.93/17.28 "term": "(p (d (e T122)) X135)" 63.93/17.28 }], 63.93/17.28 "kb": { 63.93/17.28 "nonunifying": [], 63.93/17.28 "intvars": {}, 63.93/17.28 "arithmetic": { 63.93/17.28 "type": "PlainIntegerRelationState", 63.93/17.28 "relations": [] 63.93/17.28 }, 63.93/17.28 "ground": [], 63.93/17.28 "free": ["X135"], 63.93/17.28 "exprvars": [] 63.93/17.28 } 63.93/17.28 }, 63.93/17.28 "548": { 63.93/17.28 "goal": [{ 63.93/17.28 "clause": -1, 63.93/17.28 "scope": -1, 63.93/17.28 "term": "(p (d (e T139)) X176)" 63.93/17.28 }], 63.93/17.28 "kb": { 63.93/17.28 "nonunifying": [], 63.93/17.28 "intvars": {}, 63.93/17.28 "arithmetic": { 63.93/17.28 "type": "PlainIntegerRelationState", 63.93/17.28 "relations": [] 63.93/17.28 }, 63.93/17.28 "ground": [], 63.93/17.28 "free": ["X176"], 63.93/17.28 "exprvars": [] 63.93/17.28 } 63.93/17.28 }, 63.93/17.28 "428": { 63.93/17.28 "goal": [{ 63.93/17.28 "clause": 1, 63.93/17.28 "scope": 2, 63.93/17.28 "term": "(p (d (e T48)) T49)" 63.93/17.28 }], 63.93/17.28 "kb": { 63.93/17.28 "nonunifying": [], 63.93/17.28 "intvars": {}, 63.93/17.28 "arithmetic": { 63.93/17.28 "type": "PlainIntegerRelationState", 63.93/17.28 "relations": [] 63.93/17.28 }, 63.93/17.28 "ground": [ 63.93/17.28 "T49", 63.93/17.28 "T48" 63.93/17.28 ], 63.93/17.28 "free": [], 63.93/17.28 "exprvars": [] 63.93/17.28 } 63.93/17.28 }, 63.93/17.28 "429": { 63.93/17.28 "goal": [ 63.93/17.28 { 63.93/17.28 "clause": 2, 63.93/17.28 "scope": 2, 63.93/17.28 "term": "(p (d (e T48)) T49)" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "clause": 3, 63.93/17.28 "scope": 2, 63.93/17.28 "term": "(p (d (e T48)) T49)" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "clause": 4, 63.93/17.28 "scope": 2, 63.93/17.28 "term": "(p (d (e T48)) T49)" 63.93/17.28 } 63.93/17.28 ], 63.93/17.28 "kb": { 63.93/17.28 "nonunifying": [], 63.93/17.28 "intvars": {}, 63.93/17.28 "arithmetic": { 63.93/17.28 "type": "PlainIntegerRelationState", 63.93/17.28 "relations": [] 63.93/17.28 }, 63.93/17.28 "ground": [ 63.93/17.28 "T49", 63.93/17.28 "T48" 63.93/17.28 ], 63.93/17.28 "free": [], 63.93/17.28 "exprvars": [] 63.93/17.28 } 63.93/17.28 }, 63.93/17.28 "508": { 63.93/17.28 "goal": [{ 63.93/17.28 "clause": 3, 63.93/17.28 "scope": 3, 63.93/17.28 "term": "(p (d T102) X100)" 63.93/17.28 }], 63.93/17.28 "kb": { 63.93/17.28 "nonunifying": [], 63.93/17.28 "intvars": {}, 63.93/17.28 "arithmetic": { 63.93/17.28 "type": "PlainIntegerRelationState", 63.93/17.28 "relations": [] 63.93/17.28 }, 63.93/17.28 "ground": [], 63.93/17.28 "free": ["X100"], 63.93/17.28 "exprvars": [] 63.93/17.28 } 63.93/17.28 }, 63.93/17.28 "509": { 63.93/17.28 "goal": [{ 63.93/17.28 "clause": 4, 63.93/17.28 "scope": 3, 63.93/17.28 "term": "(p (d T102) X100)" 63.93/17.28 }], 63.93/17.28 "kb": { 63.93/17.28 "nonunifying": [], 63.93/17.28 "intvars": {}, 63.93/17.28 "arithmetic": { 63.93/17.28 "type": "PlainIntegerRelationState", 63.93/17.28 "relations": [] 63.93/17.28 }, 63.93/17.28 "ground": [], 63.93/17.28 "free": ["X100"], 63.93/17.28 "exprvars": [] 63.93/17.28 } 63.93/17.28 } 63.93/17.28 }, 63.93/17.28 "edges": [ 63.93/17.28 { 63.93/17.28 "from": 4, 63.93/17.28 "to": 14, 63.93/17.28 "label": "CASE" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 14, 63.93/17.28 "to": 29, 63.93/17.28 "label": "PARALLEL" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 14, 63.93/17.28 "to": 30, 63.93/17.28 "label": "PARALLEL" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 29, 63.93/17.28 "to": 229, 63.93/17.28 "label": "EVAL with clause\np(d(e(t)), const(1)).\nand substitutionT1 -> d(e(t)),\nT2 -> const(1)" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 29, 63.93/17.28 "to": 230, 63.93/17.28 "label": "EVAL-BACKTRACK" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 30, 63.93/17.28 "to": 232, 63.93/17.28 "label": "PARALLEL" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 30, 63.93/17.28 "to": 233, 63.93/17.28 "label": "PARALLEL" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 229, 63.93/17.28 "to": 231, 63.93/17.28 "label": "SUCCESS" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 232, 63.93/17.28 "to": 234, 63.93/17.28 "label": "EVAL with clause\np(d(e(const(X5))), const(0)).\nand substitutionX5 -> T7,\nT1 -> d(e(const(T7))),\nT2 -> const(0)" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 232, 63.93/17.28 "to": 235, 63.93/17.28 "label": "EVAL-BACKTRACK" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 233, 63.93/17.28 "to": 239, 63.93/17.28 "label": "PARALLEL" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 233, 63.93/17.28 "to": 240, 63.93/17.28 "label": "PARALLEL" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 234, 63.93/17.28 "to": 237, 63.93/17.28 "label": "SUCCESS" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 239, 63.93/17.28 "to": 340, 63.93/17.28 "label": "EVAL with clause\np(d(e(+(X22, X23))), +(X24, X25)) :- ','(p(d(e(X22)), X24), p(d(e(X23)), X25)).\nand substitutionX22 -> T28,\nX23 -> T29,\nT1 -> d(e(+(T28, T29))),\nX24 -> T26,\nX25 -> T27,\nT2 -> +(T26, T27),\nT24 -> T28,\nT25 -> T29" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 239, 63.93/17.28 "to": 342, 63.93/17.28 "label": "EVAL-BACKTRACK" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 240, 63.93/17.28 "to": 401, 63.93/17.28 "label": "PARALLEL" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 240, 63.93/17.28 "to": 402, 63.93/17.28 "label": "PARALLEL" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 340, 63.93/17.28 "to": 344, 63.93/17.28 "label": "SPLIT 1" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 340, 63.93/17.28 "to": 347, 63.93/17.28 "label": "SPLIT 2\nnew knowledge:\nT26 is ground\nreplacements:T29 -> T30" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 344, 63.93/17.28 "to": 4, 63.93/17.28 "label": "INSTANCE with matching:\nT1 -> d(e(T28))\nT2 -> T26" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 347, 63.93/17.28 "to": 4, 63.93/17.28 "label": "INSTANCE with matching:\nT1 -> d(e(T30))\nT2 -> T27" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 401, 63.93/17.28 "to": 411, 63.93/17.28 "label": "EVAL with clause\np(d(e(*(X42, X43))), +(*(X42, X44), *(X43, X45))) :- ','(p(d(e(X42)), X45), p(d(e(X43)), X44)).\nand substitutionX42 -> T47,\nX43 -> T48,\nT1 -> d(e(*(T47, T48))),\nX44 -> T49,\nX45 -> T50,\nT2 -> +(*(T47, T49), *(T48, T50))" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 401, 63.93/17.28 "to": 412, 63.93/17.28 "label": "EVAL-BACKTRACK" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 402, 63.93/17.28 "to": 457, 63.93/17.28 "label": "EVAL with clause\np(d(d(X98)), X99) :- ','(p(d(X98), X100), p(d(e(X100)), X99)).\nand substitutionX98 -> T102,\nT1 -> d(d(T102)),\nT2 -> T101,\nX99 -> T101,\nT100 -> T102" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 402, 63.93/17.28 "to": 458, 63.93/17.28 "label": "EVAL-BACKTRACK" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 411, 63.93/17.28 "to": 416, 63.93/17.28 "label": "SPLIT 1" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 411, 63.93/17.28 "to": 417, 63.93/17.28 "label": "SPLIT 2\nnew knowledge:\nT47 is ground\nT50 is ground" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 416, 63.93/17.28 "to": 417, 63.93/17.28 "label": "INSTANCE with matching:\nT48 -> T47\nT49 -> T50" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 417, 63.93/17.28 "to": 420, 63.93/17.28 "label": "CASE" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 420, 63.93/17.28 "to": 421, 63.93/17.28 "label": "PARALLEL" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 420, 63.93/17.28 "to": 422, 63.93/17.28 "label": "PARALLEL" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 421, 63.93/17.28 "to": 423, 63.93/17.28 "label": "EVAL with clause\np(d(e(t)), const(1)).\nand substitutionT48 -> t,\nT49 -> const(1)" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 421, 63.93/17.28 "to": 424, 63.93/17.28 "label": "EVAL-BACKTRACK" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 422, 63.93/17.28 "to": 428, 63.93/17.28 "label": "PARALLEL" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 422, 63.93/17.28 "to": 429, 63.93/17.28 "label": "PARALLEL" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 423, 63.93/17.28 "to": 425, 63.93/17.28 "label": "SUCCESS" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 428, 63.93/17.28 "to": 430, 63.93/17.28 "label": "EVAL with clause\np(d(e(const(X50))), const(0)).\nand substitutionX50 -> T55,\nT48 -> const(T55),\nT49 -> const(0)" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 428, 63.93/17.28 "to": 433, 63.93/17.28 "label": "EVAL-BACKTRACK" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 429, 63.93/17.28 "to": 435, 63.93/17.28 "label": "PARALLEL" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 429, 63.93/17.28 "to": 436, 63.93/17.28 "label": "PARALLEL" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 430, 63.93/17.28 "to": 434, 63.93/17.28 "label": "SUCCESS" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 435, 63.93/17.28 "to": 437, 63.93/17.28 "label": "EVAL with clause\np(d(e(+(X67, X68))), +(X69, X70)) :- ','(p(d(e(X67)), X69), p(d(e(X68)), X70)).\nand substitutionX67 -> T72,\nX68 -> T73,\nT48 -> +(T72, T73),\nX69 -> T74,\nX70 -> T75,\nT49 -> +(T74, T75)" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 435, 63.93/17.28 "to": 438, 63.93/17.28 "label": "EVAL-BACKTRACK" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 436, 63.93/17.28 "to": 441, 63.93/17.28 "label": "PARALLEL" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 436, 63.93/17.28 "to": 442, 63.93/17.28 "label": "PARALLEL" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 437, 63.93/17.28 "to": 411, 63.93/17.28 "label": "INSTANCE with matching:\nT47 -> T72\nT50 -> T74\nT48 -> T73\nT49 -> T75" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 441, 63.93/17.28 "to": 448, 63.93/17.28 "label": "EVAL with clause\np(d(e(*(X87, X88))), +(*(X87, X89), *(X88, X90))) :- ','(p(d(e(X87)), X90), p(d(e(X88)), X89)).\nand substitutionX87 -> T92,\nX88 -> T93,\nT48 -> *(T92, T93),\nX89 -> T94,\nX90 -> T95,\nT49 -> +(*(T92, T94), *(T93, T95))" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 441, 63.93/17.28 "to": 449, 63.93/17.28 "label": "EVAL-BACKTRACK" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 442, 63.93/17.28 "to": 454, 63.93/17.28 "label": "BACKTRACK\nfor clause: p(d(d(X)), DDX) :- ','(p(d(X), DX), p(d(e(DX)), DDX))because of non-unification" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 448, 63.93/17.28 "to": 411, 63.93/17.28 "label": "INSTANCE with matching:\nT47 -> T92\nT50 -> T95\nT48 -> T93\nT49 -> T94" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 457, 63.93/17.28 "to": 461, 63.93/17.28 "label": "SPLIT 1" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 457, 63.93/17.28 "to": 462, 63.93/17.28 "label": "SPLIT 2\nreplacements:X100 -> T103" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 461, 63.93/17.28 "to": 465, 63.93/17.28 "label": "CASE" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 462, 63.93/17.28 "to": 4, 63.93/17.28 "label": "INSTANCE with matching:\nT1 -> d(e(T103))\nT2 -> T101" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 465, 63.93/17.28 "to": 466, 63.93/17.28 "label": "PARALLEL" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 465, 63.93/17.28 "to": 467, 63.93/17.28 "label": "PARALLEL" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 466, 63.93/17.28 "to": 468, 63.93/17.28 "label": "EVAL with clause\np(d(e(t)), const(1)).\nand substitutionT102 -> e(t),\nX100 -> const(1)" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 466, 63.93/17.28 "to": 469, 63.93/17.28 "label": "EVAL-BACKTRACK" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 467, 63.93/17.28 "to": 471, 63.93/17.28 "label": "PARALLEL" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 467, 63.93/17.28 "to": 472, 63.93/17.28 "label": "PARALLEL" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 468, 63.93/17.28 "to": 470, 63.93/17.28 "label": "SUCCESS" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 471, 63.93/17.28 "to": 475, 63.93/17.28 "label": "EVAL with clause\np(d(e(const(X105))), const(0)).\nand substitutionX105 -> T108,\nT102 -> e(const(T108)),\nX100 -> const(0)" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 471, 63.93/17.28 "to": 476, 63.93/17.28 "label": "EVAL-BACKTRACK" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 472, 63.93/17.28 "to": 483, 63.93/17.28 "label": "PARALLEL" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 472, 63.93/17.28 "to": 484, 63.93/17.28 "label": "PARALLEL" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 475, 63.93/17.28 "to": 477, 63.93/17.28 "label": "SUCCESS" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 483, 63.93/17.28 "to": 495, 63.93/17.28 "label": "EVAL with clause\np(d(e(+(X130, X131))), +(X132, X133)) :- ','(p(d(e(X130)), X132), p(d(e(X131)), X133)).\nand substitutionX130 -> T119,\nX131 -> T120,\nT102 -> e(+(T119, T120)),\nX132 -> X134,\nX133 -> X135,\nX100 -> +(X134, X135),\nT117 -> T119,\nT118 -> T120" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 483, 63.93/17.28 "to": 496, 63.93/17.28 "label": "EVAL-BACKTRACK" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 484, 63.93/17.28 "to": 508, 63.93/17.28 "label": "PARALLEL" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 484, 63.93/17.28 "to": 509, 63.93/17.28 "label": "PARALLEL" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 495, 63.93/17.28 "to": 502, 63.93/17.28 "label": "SPLIT 1" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 495, 63.93/17.28 "to": 504, 63.93/17.28 "label": "SPLIT 2\nreplacements:X134 -> T121,\nT120 -> T122" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 502, 63.93/17.28 "to": 461, 63.93/17.28 "label": "INSTANCE with matching:\nT102 -> e(T119)\nX100 -> X134" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 504, 63.93/17.28 "to": 461, 63.93/17.28 "label": "INSTANCE with matching:\nT102 -> e(T122)\nX100 -> X135" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 508, 63.93/17.28 "to": 522, 63.93/17.28 "label": "EVAL with clause\np(d(e(*(X160, X161))), +(*(X160, X162), *(X161, X163))) :- ','(p(d(e(X160)), X163), p(d(e(X161)), X162)).\nand substitutionX160 -> T133,\nX161 -> T134,\nT102 -> e(*(T133, T134)),\nX162 -> X164,\nX163 -> X165,\nX100 -> +(*(T133, X164), *(T134, X165)),\nT131 -> T133,\nT132 -> T134" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 508, 63.93/17.28 "to": 523, 63.93/17.28 "label": "EVAL-BACKTRACK" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 509, 63.93/17.28 "to": 545, 63.93/17.28 "label": "EVAL with clause\np(d(d(X173)), X174) :- ','(p(d(X173), X175), p(d(e(X175)), X174)).\nand substitutionX173 -> T138,\nT102 -> d(T138),\nX100 -> X176,\nX174 -> X176,\nT137 -> T138" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 509, 63.93/17.28 "to": 546, 63.93/17.28 "label": "EVAL-BACKTRACK" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 522, 63.93/17.28 "to": 495, 63.93/17.28 "label": "INSTANCE with matching:\nT119 -> T133\nX134 -> X165\nT120 -> T134\nX135 -> X164" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 545, 63.93/17.28 "to": 547, 63.93/17.28 "label": "SPLIT 1" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 545, 63.93/17.28 "to": 548, 63.93/17.28 "label": "SPLIT 2\nreplacements:X175 -> T139" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 547, 63.93/17.28 "to": 461, 63.93/17.28 "label": "INSTANCE with matching:\nT102 -> T138\nX100 -> X175" 63.93/17.28 }, 63.93/17.28 { 63.93/17.28 "from": 548, 63.93/17.28 "to": 461, 63.93/17.28 "label": "INSTANCE with matching:\nT102 -> e(T139)\nX100 -> X176" 63.93/17.28 } 63.93/17.28 ], 63.93/17.28 "type": "Graph" 63.93/17.28 } 63.93/17.28 } 63.93/17.28 63.93/17.28 ---------------------------------------- 63.93/17.28 63.93/17.28 (62) 63.93/17.28 Obligation: 63.93/17.28 Q restricted rewrite system: 63.93/17.28 The TRS R consists of the following rules: 63.93/17.28 63.93/17.28 f4_in(const(1)) -> f4_out1 63.93/17.28 f4_in(const(0)) -> f4_out1 63.93/17.28 f4_in(+(T26, T27)) -> U1(f340_in(T26, T27), +(T26, T27)) 63.93/17.28 U1(f340_out1, +(T26, T27)) -> f4_out1 63.93/17.28 f4_in(+(*(T47, T49), *(T48, T50))) -> U2(f411_in(T47, T50, T48, T49), +(*(T47, T49), *(T48, T50))) 63.93/17.28 U2(f411_out1, +(*(T47, T49), *(T48, T50))) -> f4_out1 63.93/17.28 f4_in(T101) -> U3(f457_in(T101), T101) 63.93/17.28 U3(f457_out1, T101) -> f4_out1 63.93/17.28 f417_in(t, const(1)) -> f417_out1 63.93/17.28 f417_in(const(T55), const(0)) -> f417_out1 63.93/17.28 f417_in(+(T72, T73), +(T74, T75)) -> U4(f411_in(T72, T74, T73, T75), +(T72, T73), +(T74, T75)) 63.93/17.28 U4(f411_out1, +(T72, T73), +(T74, T75)) -> f417_out1 63.93/17.28 f417_in(*(T92, T93), +(*(T92, T94), *(T93, T95))) -> U5(f411_in(T92, T95, T93, T94), *(T92, T93), +(*(T92, T94), *(T93, T95))) 63.93/17.28 U5(f411_out1, *(T92, T93), +(*(T92, T94), *(T93, T95))) -> f417_out1 63.93/17.28 f461_in -> f461_out1 63.93/17.28 f461_in -> U6(f495_in) 63.93/17.28 U6(f495_out1) -> f461_out1 63.93/17.28 f461_in -> U7(f495_in) 63.93/17.28 U7(f495_out1) -> f461_out1 63.93/17.28 f461_in -> U8(f545_in) 63.93/17.28 U8(f545_out1) -> f461_out1 63.93/17.28 f340_in(T26, T27) -> U9(f4_in(T26), T26, T27) 63.93/17.28 U9(f4_out1, T26, T27) -> U10(f4_in(T27), T26, T27) 63.93/17.28 U10(f4_out1, T26, T27) -> f340_out1 63.93/17.28 f411_in(T47, T50, T48, T49) -> U11(f417_in(T47, T50), T47, T50, T48, T49) 63.93/17.28 U11(f417_out1, T47, T50, T48, T49) -> U12(f417_in(T48, T49), T47, T50, T48, T49) 63.93/17.28 U12(f417_out1, T47, T50, T48, T49) -> f411_out1 63.93/17.28 f457_in(T101) -> U13(f461_in, T101) 63.93/17.28 U13(f461_out1, T101) -> U14(f4_in(T101), T101) 63.93/17.28 U14(f4_out1, T101) -> f457_out1 63.93/17.28 f495_in -> U15(f461_in) 63.93/17.28 U15(f461_out1) -> U16(f461_in) 63.93/17.28 U16(f461_out1) -> f495_out1 63.93/17.28 f545_in -> U17(f461_in) 63.93/17.28 U17(f461_out1) -> U18(f461_in) 63.93/17.28 U18(f461_out1) -> f545_out1 63.93/17.28 63.93/17.28 Q is empty. 63.93/17.28 63.93/17.28 ---------------------------------------- 63.93/17.28 63.93/17.28 (63) DependencyPairsProof (EQUIVALENT) 63.93/17.28 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 63.93/17.28 ---------------------------------------- 63.93/17.28 63.93/17.28 (64) 63.93/17.28 Obligation: 63.93/17.28 Q DP problem: 63.93/17.28 The TRS P consists of the following rules: 63.93/17.28 63.93/17.28 F4_IN(+(T26, T27)) -> U1^1(f340_in(T26, T27), +(T26, T27)) 63.93/17.28 F4_IN(+(T26, T27)) -> F340_IN(T26, T27) 63.93/17.28 F4_IN(+(*(T47, T49), *(T48, T50))) -> U2^1(f411_in(T47, T50, T48, T49), +(*(T47, T49), *(T48, T50))) 63.93/17.28 F4_IN(+(*(T47, T49), *(T48, T50))) -> F411_IN(T47, T50, T48, T49) 63.93/17.28 F4_IN(T101) -> U3^1(f457_in(T101), T101) 63.93/17.28 F4_IN(T101) -> F457_IN(T101) 63.93/17.28 F417_IN(+(T72, T73), +(T74, T75)) -> U4^1(f411_in(T72, T74, T73, T75), +(T72, T73), +(T74, T75)) 63.93/17.28 F417_IN(+(T72, T73), +(T74, T75)) -> F411_IN(T72, T74, T73, T75) 63.93/17.28 F417_IN(*(T92, T93), +(*(T92, T94), *(T93, T95))) -> U5^1(f411_in(T92, T95, T93, T94), *(T92, T93), +(*(T92, T94), *(T93, T95))) 63.93/17.28 F417_IN(*(T92, T93), +(*(T92, T94), *(T93, T95))) -> F411_IN(T92, T95, T93, T94) 63.93/17.28 F461_IN -> U6^1(f495_in) 63.93/17.28 F461_IN -> F495_IN 63.93/17.28 F461_IN -> U7^1(f495_in) 63.93/17.28 F461_IN -> U8^1(f545_in) 63.93/17.28 F461_IN -> F545_IN 63.93/17.28 F340_IN(T26, T27) -> U9^1(f4_in(T26), T26, T27) 63.93/17.28 F340_IN(T26, T27) -> F4_IN(T26) 63.93/17.28 U9^1(f4_out1, T26, T27) -> U10^1(f4_in(T27), T26, T27) 63.93/17.28 U9^1(f4_out1, T26, T27) -> F4_IN(T27) 63.93/17.28 F411_IN(T47, T50, T48, T49) -> U11^1(f417_in(T47, T50), T47, T50, T48, T49) 63.93/17.28 F411_IN(T47, T50, T48, T49) -> F417_IN(T47, T50) 63.93/17.28 U11^1(f417_out1, T47, T50, T48, T49) -> U12^1(f417_in(T48, T49), T47, T50, T48, T49) 63.93/17.28 U11^1(f417_out1, T47, T50, T48, T49) -> F417_IN(T48, T49) 63.93/17.29 F457_IN(T101) -> U13^1(f461_in, T101) 63.93/17.29 F457_IN(T101) -> F461_IN 63.93/17.29 U13^1(f461_out1, T101) -> U14^1(f4_in(T101), T101) 63.93/17.29 U13^1(f461_out1, T101) -> F4_IN(T101) 63.93/17.29 F495_IN -> U15^1(f461_in) 63.93/17.29 F495_IN -> F461_IN 63.93/17.29 U15^1(f461_out1) -> U16^1(f461_in) 63.93/17.29 U15^1(f461_out1) -> F461_IN 63.93/17.29 F545_IN -> U17^1(f461_in) 63.93/17.29 F545_IN -> F461_IN 63.93/17.29 U17^1(f461_out1) -> U18^1(f461_in) 63.93/17.29 U17^1(f461_out1) -> F461_IN 63.93/17.29 63.93/17.29 The TRS R consists of the following rules: 63.93/17.29 63.93/17.29 f4_in(const(1)) -> f4_out1 63.93/17.29 f4_in(const(0)) -> f4_out1 63.93/17.29 f4_in(+(T26, T27)) -> U1(f340_in(T26, T27), +(T26, T27)) 63.93/17.29 U1(f340_out1, +(T26, T27)) -> f4_out1 63.93/17.29 f4_in(+(*(T47, T49), *(T48, T50))) -> U2(f411_in(T47, T50, T48, T49), +(*(T47, T49), *(T48, T50))) 63.93/17.29 U2(f411_out1, +(*(T47, T49), *(T48, T50))) -> f4_out1 63.93/17.29 f4_in(T101) -> U3(f457_in(T101), T101) 63.93/17.29 U3(f457_out1, T101) -> f4_out1 63.93/17.29 f417_in(t, const(1)) -> f417_out1 63.93/17.29 f417_in(const(T55), const(0)) -> f417_out1 63.93/17.29 f417_in(+(T72, T73), +(T74, T75)) -> U4(f411_in(T72, T74, T73, T75), +(T72, T73), +(T74, T75)) 63.93/17.29 U4(f411_out1, +(T72, T73), +(T74, T75)) -> f417_out1 63.93/17.29 f417_in(*(T92, T93), +(*(T92, T94), *(T93, T95))) -> U5(f411_in(T92, T95, T93, T94), *(T92, T93), +(*(T92, T94), *(T93, T95))) 63.93/17.29 U5(f411_out1, *(T92, T93), +(*(T92, T94), *(T93, T95))) -> f417_out1 63.93/17.29 f461_in -> f461_out1 63.93/17.29 f461_in -> U6(f495_in) 63.93/17.29 U6(f495_out1) -> f461_out1 63.93/17.29 f461_in -> U7(f495_in) 63.93/17.29 U7(f495_out1) -> f461_out1 63.93/17.29 f461_in -> U8(f545_in) 63.93/17.29 U8(f545_out1) -> f461_out1 63.93/17.29 f340_in(T26, T27) -> U9(f4_in(T26), T26, T27) 63.93/17.29 U9(f4_out1, T26, T27) -> U10(f4_in(T27), T26, T27) 63.93/17.29 U10(f4_out1, T26, T27) -> f340_out1 63.93/17.29 f411_in(T47, T50, T48, T49) -> U11(f417_in(T47, T50), T47, T50, T48, T49) 63.93/17.29 U11(f417_out1, T47, T50, T48, T49) -> U12(f417_in(T48, T49), T47, T50, T48, T49) 63.93/17.29 U12(f417_out1, T47, T50, T48, T49) -> f411_out1 63.93/17.29 f457_in(T101) -> U13(f461_in, T101) 63.93/17.29 U13(f461_out1, T101) -> U14(f4_in(T101), T101) 63.93/17.29 U14(f4_out1, T101) -> f457_out1 63.93/17.29 f495_in -> U15(f461_in) 63.93/17.29 U15(f461_out1) -> U16(f461_in) 63.93/17.29 U16(f461_out1) -> f495_out1 63.93/17.29 f545_in -> U17(f461_in) 63.93/17.29 U17(f461_out1) -> U18(f461_in) 63.93/17.29 U18(f461_out1) -> f545_out1 63.93/17.29 63.93/17.29 Q is empty. 63.93/17.29 We have to consider all minimal (P,Q,R)-chains. 63.93/17.29 ---------------------------------------- 63.93/17.29 63.93/17.29 (65) DependencyGraphProof (EQUIVALENT) 63.93/17.29 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 3 SCCs with 15 less nodes. 63.93/17.29 ---------------------------------------- 63.93/17.29 63.93/17.29 (66) 63.93/17.29 Complex Obligation (AND) 63.93/17.29 63.93/17.29 ---------------------------------------- 63.93/17.29 63.93/17.29 (67) 63.93/17.29 Obligation: 63.93/17.29 Q DP problem: 63.93/17.29 The TRS P consists of the following rules: 63.93/17.29 63.93/17.29 F461_IN -> F495_IN 63.93/17.29 F495_IN -> U15^1(f461_in) 63.93/17.29 U15^1(f461_out1) -> F461_IN 63.93/17.29 F461_IN -> F545_IN 63.93/17.29 F545_IN -> U17^1(f461_in) 63.93/17.29 U17^1(f461_out1) -> F461_IN 63.93/17.29 F545_IN -> F461_IN 63.93/17.29 F495_IN -> F461_IN 63.93/17.29 63.93/17.29 The TRS R consists of the following rules: 63.93/17.29 63.93/17.29 f4_in(const(1)) -> f4_out1 63.93/17.29 f4_in(const(0)) -> f4_out1 63.93/17.29 f4_in(+(T26, T27)) -> U1(f340_in(T26, T27), +(T26, T27)) 63.93/17.29 U1(f340_out1, +(T26, T27)) -> f4_out1 63.93/17.29 f4_in(+(*(T47, T49), *(T48, T50))) -> U2(f411_in(T47, T50, T48, T49), +(*(T47, T49), *(T48, T50))) 63.93/17.29 U2(f411_out1, +(*(T47, T49), *(T48, T50))) -> f4_out1 63.93/17.29 f4_in(T101) -> U3(f457_in(T101), T101) 63.93/17.29 U3(f457_out1, T101) -> f4_out1 63.93/17.29 f417_in(t, const(1)) -> f417_out1 63.93/17.29 f417_in(const(T55), const(0)) -> f417_out1 63.93/17.29 f417_in(+(T72, T73), +(T74, T75)) -> U4(f411_in(T72, T74, T73, T75), +(T72, T73), +(T74, T75)) 63.93/17.29 U4(f411_out1, +(T72, T73), +(T74, T75)) -> f417_out1 63.93/17.29 f417_in(*(T92, T93), +(*(T92, T94), *(T93, T95))) -> U5(f411_in(T92, T95, T93, T94), *(T92, T93), +(*(T92, T94), *(T93, T95))) 63.93/17.29 U5(f411_out1, *(T92, T93), +(*(T92, T94), *(T93, T95))) -> f417_out1 63.93/17.29 f461_in -> f461_out1 63.93/17.29 f461_in -> U6(f495_in) 63.93/17.29 U6(f495_out1) -> f461_out1 63.93/17.29 f461_in -> U7(f495_in) 63.93/17.29 U7(f495_out1) -> f461_out1 63.93/17.29 f461_in -> U8(f545_in) 63.93/17.29 U8(f545_out1) -> f461_out1 63.93/17.29 f340_in(T26, T27) -> U9(f4_in(T26), T26, T27) 63.93/17.29 U9(f4_out1, T26, T27) -> U10(f4_in(T27), T26, T27) 63.93/17.29 U10(f4_out1, T26, T27) -> f340_out1 63.93/17.29 f411_in(T47, T50, T48, T49) -> U11(f417_in(T47, T50), T47, T50, T48, T49) 63.93/17.29 U11(f417_out1, T47, T50, T48, T49) -> U12(f417_in(T48, T49), T47, T50, T48, T49) 63.93/17.29 U12(f417_out1, T47, T50, T48, T49) -> f411_out1 63.93/17.29 f457_in(T101) -> U13(f461_in, T101) 63.93/17.29 U13(f461_out1, T101) -> U14(f4_in(T101), T101) 63.93/17.29 U14(f4_out1, T101) -> f457_out1 63.93/17.29 f495_in -> U15(f461_in) 63.93/17.29 U15(f461_out1) -> U16(f461_in) 63.93/17.29 U16(f461_out1) -> f495_out1 63.93/17.29 f545_in -> U17(f461_in) 63.93/17.29 U17(f461_out1) -> U18(f461_in) 63.93/17.29 U18(f461_out1) -> f545_out1 63.93/17.29 63.93/17.29 Q is empty. 63.93/17.29 We have to consider all minimal (P,Q,R)-chains. 63.93/17.29 ---------------------------------------- 63.93/17.29 63.93/17.29 (68) NonLoopProof (COMPLETE) 63.93/17.29 By Theorem 8 [NONLOOP] we deduce infiniteness of the QDP. 63.93/17.29 We apply the theorem with m = 1, b = 0, 63.93/17.29 σ' = [ ], and μ' = [ ] on the rule 63.93/17.29 F495_IN[ ]^n[ ] -> F495_IN[ ]^n[ ] 63.93/17.29 This rule is correct for the QDP as the following derivation shows: 63.93/17.29 63.93/17.29 F495_IN[ ]^n[ ] -> F495_IN[ ]^n[ ] 63.93/17.29 by Narrowing at position: [] 63.93/17.29 F495_IN[ ]^n[ ] -> F461_IN[ ]^n[ ] 63.93/17.29 by Rule from TRS P 63.93/17.29 63.93/17.29 F461_IN[ ]^n[ ] -> F495_IN[ ]^n[ ] 63.93/17.29 by Rule from TRS P 63.93/17.29 ---------------------------------------- 63.93/17.29 63.93/17.29 (69) 63.93/17.29 NO 63.93/17.29 63.93/17.29 ---------------------------------------- 63.93/17.29 63.93/17.29 (70) 63.93/17.29 Obligation: 63.93/17.29 Q DP problem: 63.93/17.29 The TRS P consists of the following rules: 63.93/17.29 63.93/17.29 F417_IN(+(T72, T73), +(T74, T75)) -> F411_IN(T72, T74, T73, T75) 63.93/17.29 F411_IN(T47, T50, T48, T49) -> U11^1(f417_in(T47, T50), T47, T50, T48, T49) 63.93/17.29 U11^1(f417_out1, T47, T50, T48, T49) -> F417_IN(T48, T49) 63.93/17.29 F417_IN(*(T92, T93), +(*(T92, T94), *(T93, T95))) -> F411_IN(T92, T95, T93, T94) 63.93/17.29 F411_IN(T47, T50, T48, T49) -> F417_IN(T47, T50) 63.93/17.29 63.93/17.29 The TRS R consists of the following rules: 63.93/17.29 63.93/17.29 f4_in(const(1)) -> f4_out1 63.93/17.29 f4_in(const(0)) -> f4_out1 63.93/17.29 f4_in(+(T26, T27)) -> U1(f340_in(T26, T27), +(T26, T27)) 63.93/17.29 U1(f340_out1, +(T26, T27)) -> f4_out1 63.93/17.29 f4_in(+(*(T47, T49), *(T48, T50))) -> U2(f411_in(T47, T50, T48, T49), +(*(T47, T49), *(T48, T50))) 63.93/17.29 U2(f411_out1, +(*(T47, T49), *(T48, T50))) -> f4_out1 63.93/17.29 f4_in(T101) -> U3(f457_in(T101), T101) 63.93/17.29 U3(f457_out1, T101) -> f4_out1 63.93/17.29 f417_in(t, const(1)) -> f417_out1 63.93/17.29 f417_in(const(T55), const(0)) -> f417_out1 63.93/17.29 f417_in(+(T72, T73), +(T74, T75)) -> U4(f411_in(T72, T74, T73, T75), +(T72, T73), +(T74, T75)) 63.93/17.29 U4(f411_out1, +(T72, T73), +(T74, T75)) -> f417_out1 63.93/17.29 f417_in(*(T92, T93), +(*(T92, T94), *(T93, T95))) -> U5(f411_in(T92, T95, T93, T94), *(T92, T93), +(*(T92, T94), *(T93, T95))) 63.93/17.29 U5(f411_out1, *(T92, T93), +(*(T92, T94), *(T93, T95))) -> f417_out1 63.93/17.29 f461_in -> f461_out1 63.93/17.29 f461_in -> U6(f495_in) 63.93/17.29 U6(f495_out1) -> f461_out1 63.93/17.29 f461_in -> U7(f495_in) 63.93/17.29 U7(f495_out1) -> f461_out1 63.93/17.29 f461_in -> U8(f545_in) 63.93/17.29 U8(f545_out1) -> f461_out1 63.93/17.29 f340_in(T26, T27) -> U9(f4_in(T26), T26, T27) 63.93/17.29 U9(f4_out1, T26, T27) -> U10(f4_in(T27), T26, T27) 63.93/17.29 U10(f4_out1, T26, T27) -> f340_out1 63.93/17.29 f411_in(T47, T50, T48, T49) -> U11(f417_in(T47, T50), T47, T50, T48, T49) 63.93/17.29 U11(f417_out1, T47, T50, T48, T49) -> U12(f417_in(T48, T49), T47, T50, T48, T49) 63.93/17.29 U12(f417_out1, T47, T50, T48, T49) -> f411_out1 63.93/17.29 f457_in(T101) -> U13(f461_in, T101) 63.93/17.29 U13(f461_out1, T101) -> U14(f4_in(T101), T101) 63.93/17.29 U14(f4_out1, T101) -> f457_out1 63.93/17.29 f495_in -> U15(f461_in) 63.93/17.29 U15(f461_out1) -> U16(f461_in) 63.93/17.29 U16(f461_out1) -> f495_out1 63.93/17.29 f545_in -> U17(f461_in) 63.93/17.29 U17(f461_out1) -> U18(f461_in) 63.93/17.29 U18(f461_out1) -> f545_out1 63.93/17.29 63.93/17.29 Q is empty. 63.93/17.29 We have to consider all minimal (P,Q,R)-chains. 63.93/17.29 ---------------------------------------- 63.93/17.29 63.93/17.29 (71) QDPSizeChangeProof (EQUIVALENT) 63.93/17.29 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. 63.93/17.29 63.93/17.29 From the DPs we obtained the following set of size-change graphs: 63.93/17.29 *F411_IN(T47, T50, T48, T49) -> F417_IN(T47, T50) 63.93/17.29 The graph contains the following edges 1 >= 1, 2 >= 2 63.93/17.29 63.93/17.29 63.93/17.29 *F411_IN(T47, T50, T48, T49) -> U11^1(f417_in(T47, T50), T47, T50, T48, T49) 63.93/17.29 The graph contains the following edges 1 >= 2, 2 >= 3, 3 >= 4, 4 >= 5 63.93/17.29 63.93/17.29 63.93/17.29 *U11^1(f417_out1, T47, T50, T48, T49) -> F417_IN(T48, T49) 63.93/17.29 The graph contains the following edges 4 >= 1, 5 >= 2 63.93/17.29 63.93/17.29 63.93/17.29 *F417_IN(+(T72, T73), +(T74, T75)) -> F411_IN(T72, T74, T73, T75) 63.93/17.29 The graph contains the following edges 1 > 1, 2 > 2, 1 > 3, 2 > 4 64.24/17.31 64.24/17.31 64.24/17.31 *F417_IN(*(T92, T93), +(*(T92, T94), *(T93, T95))) -> F411_IN(T92, T95, T93, T94) 64.24/17.31 The graph contains the following edges 1 > 1, 2 > 1, 2 > 2, 1 > 3, 2 > 3, 2 > 4 64.24/17.31 64.24/17.31 64.24/17.31 ---------------------------------------- 64.24/17.31 64.24/17.31 (72) 64.24/17.31 YES 64.24/17.31 64.24/17.31 ---------------------------------------- 64.24/17.31 64.24/17.31 (73) 64.24/17.31 Obligation: 64.24/17.31 Q DP problem: 64.24/17.31 The TRS P consists of the following rules: 64.24/17.31 64.24/17.31 F4_IN(+(T26, T27)) -> F340_IN(T26, T27) 64.24/17.31 F340_IN(T26, T27) -> U9^1(f4_in(T26), T26, T27) 64.24/17.31 U9^1(f4_out1, T26, T27) -> F4_IN(T27) 64.24/17.31 F4_IN(T101) -> F457_IN(T101) 64.24/17.31 F457_IN(T101) -> U13^1(f461_in, T101) 64.24/17.31 U13^1(f461_out1, T101) -> F4_IN(T101) 64.24/17.31 F340_IN(T26, T27) -> F4_IN(T26) 64.24/17.31 64.24/17.31 The TRS R consists of the following rules: 64.24/17.31 64.24/17.31 f4_in(const(1)) -> f4_out1 64.24/17.31 f4_in(const(0)) -> f4_out1 64.24/17.31 f4_in(+(T26, T27)) -> U1(f340_in(T26, T27), +(T26, T27)) 64.24/17.31 U1(f340_out1, +(T26, T27)) -> f4_out1 64.24/17.31 f4_in(+(*(T47, T49), *(T48, T50))) -> U2(f411_in(T47, T50, T48, T49), +(*(T47, T49), *(T48, T50))) 64.24/17.31 U2(f411_out1, +(*(T47, T49), *(T48, T50))) -> f4_out1 64.24/17.31 f4_in(T101) -> U3(f457_in(T101), T101) 64.24/17.31 U3(f457_out1, T101) -> f4_out1 64.24/17.31 f417_in(t, const(1)) -> f417_out1 64.24/17.31 f417_in(const(T55), const(0)) -> f417_out1 64.24/17.31 f417_in(+(T72, T73), +(T74, T75)) -> U4(f411_in(T72, T74, T73, T75), +(T72, T73), +(T74, T75)) 64.24/17.31 U4(f411_out1, +(T72, T73), +(T74, T75)) -> f417_out1 64.24/17.31 f417_in(*(T92, T93), +(*(T92, T94), *(T93, T95))) -> U5(f411_in(T92, T95, T93, T94), *(T92, T93), +(*(T92, T94), *(T93, T95))) 64.24/17.31 U5(f411_out1, *(T92, T93), +(*(T92, T94), *(T93, T95))) -> f417_out1 64.24/17.31 f461_in -> f461_out1 64.24/17.31 f461_in -> U6(f495_in) 64.24/17.31 U6(f495_out1) -> f461_out1 64.24/17.31 f461_in -> U7(f495_in) 64.24/17.31 U7(f495_out1) -> f461_out1 64.24/17.31 f461_in -> U8(f545_in) 64.24/17.31 U8(f545_out1) -> f461_out1 64.24/17.31 f340_in(T26, T27) -> U9(f4_in(T26), T26, T27) 64.24/17.31 U9(f4_out1, T26, T27) -> U10(f4_in(T27), T26, T27) 64.24/17.31 U10(f4_out1, T26, T27) -> f340_out1 64.24/17.31 f411_in(T47, T50, T48, T49) -> U11(f417_in(T47, T50), T47, T50, T48, T49) 64.24/17.31 U11(f417_out1, T47, T50, T48, T49) -> U12(f417_in(T48, T49), T47, T50, T48, T49) 64.24/17.31 U12(f417_out1, T47, T50, T48, T49) -> f411_out1 64.24/17.31 f457_in(T101) -> U13(f461_in, T101) 64.24/17.31 U13(f461_out1, T101) -> U14(f4_in(T101), T101) 64.24/17.31 U14(f4_out1, T101) -> f457_out1 64.24/17.31 f495_in -> U15(f461_in) 64.24/17.31 U15(f461_out1) -> U16(f461_in) 64.24/17.31 U16(f461_out1) -> f495_out1 64.24/17.31 f545_in -> U17(f461_in) 64.24/17.31 U17(f461_out1) -> U18(f461_in) 64.24/17.31 U18(f461_out1) -> f545_out1 64.24/17.31 64.24/17.31 Q is empty. 64.24/17.31 We have to consider all minimal (P,Q,R)-chains. 64.24/17.31 ---------------------------------------- 64.24/17.31 64.24/17.31 (74) NonLoopProof (COMPLETE) 64.24/17.31 By Theorem 8 [NONLOOP] we deduce infiniteness of the QDP. 64.24/17.31 We apply the theorem with m = 1, b = 0, 64.24/17.31 σ' = [ ], and μ' = [ ] on the rule 64.24/17.31 U13^1(f461_out1, x0)[ ]^n[ ] -> U13^1(f461_out1, x0)[ ]^n[ ] 64.24/17.31 This rule is correct for the QDP as the following derivation shows: 64.24/17.31 64.24/17.31 U13^1(f461_out1, x0)[ ]^n[ ] -> U13^1(f461_out1, x0)[ ]^n[ ] 64.24/17.31 by Narrowing at position: [] 64.24/17.31 intermediate steps: Instantiation 64.24/17.31 U13^1(f461_out1, T101)[ ]^n[ ] -> F4_IN(T101)[ ]^n[ ] 64.24/17.31 by Rule from TRS P 64.24/17.31 64.24/17.31 intermediate steps: Instantiation - Instantiation 64.24/17.31 F4_IN(x0)[ ]^n[ ] -> U13^1(f461_out1, x0)[ ]^n[ ] 64.24/17.31 by Narrowing at position: [0] 64.24/17.31 F4_IN(x0)[ ]^n[ ] -> U13^1(f461_in, x0)[ ]^n[ ] 64.24/17.31 by Narrowing at position: [] 64.24/17.31 intermediate steps: Instantiation 64.24/17.31 F4_IN(T101)[ ]^n[ ] -> F457_IN(T101)[ ]^n[ ] 64.24/17.31 by Rule from TRS P 64.24/17.31 64.24/17.31 intermediate steps: Instantiation - Instantiation 64.24/17.31 F457_IN(T101)[ ]^n[ ] -> U13^1(f461_in, T101)[ ]^n[ ] 64.24/17.31 by Rule from TRS P 64.24/17.31 64.24/17.31 f461_in[ ]^n[ ] -> f461_out1[ ]^n[ ] 64.24/17.31 by Rule from TRS R 64.24/17.31 ---------------------------------------- 64.24/17.31 64.24/17.31 (75) 64.24/17.31 NO 64.24/17.31 64.24/17.31 ---------------------------------------- 64.24/17.31 64.24/17.31 (76) PrologToIRSwTTransformerProof (SOUND) 64.24/17.31 Transformed Prolog program to IRSwT according to method in Master Thesis of A. Weinert 64.24/17.31 64.24/17.31 { 64.24/17.31 "root": 27, 64.24/17.31 "program": { 64.24/17.31 "directives": [], 64.24/17.31 "clauses": [ 64.24/17.31 [ 64.24/17.31 "(p (d (e (t))) (const (1)))", 64.24/17.31 null 64.24/17.31 ], 64.24/17.31 [ 64.24/17.31 "(p (d (e (const A))) (const (0)))", 64.24/17.31 null 64.24/17.31 ], 64.24/17.31 [ 64.24/17.31 "(p (d (e (+ X Y))) (+ DX DY))", 64.24/17.31 "(',' (p (d (e X)) DX) (p (d (e Y)) DY))" 64.24/17.31 ], 64.24/17.31 [ 64.24/17.31 "(p (d (e (* X Y))) (+ (* X DY) (* Y DX)))", 64.24/17.31 "(',' (p (d (e X)) DX) (p (d (e Y)) DY))" 64.24/17.31 ], 64.24/17.31 [ 64.24/17.31 "(p (d (d X)) DDX)", 64.24/17.31 "(',' (p (d X) DX) (p (d (e DX)) DDX))" 64.24/17.31 ] 64.24/17.31 ] 64.24/17.31 }, 64.24/17.31 "graph": { 64.24/17.31 "nodes": { 64.24/17.31 "88": { 64.24/17.31 "goal": [{ 64.24/17.31 "clause": -1, 64.24/17.31 "scope": -1, 64.24/17.31 "term": "(true)" 64.24/17.31 }], 64.24/17.31 "kb": { 64.24/17.31 "nonunifying": [], 64.24/17.31 "intvars": {}, 64.24/17.31 "arithmetic": { 64.24/17.31 "type": "PlainIntegerRelationState", 64.24/17.31 "relations": [] 64.24/17.31 }, 64.24/17.31 "ground": [], 64.24/17.31 "free": [], 64.24/17.31 "exprvars": [] 64.24/17.31 } 64.24/17.31 }, 64.24/17.31 "390": { 64.24/17.31 "goal": [ 64.24/17.31 { 64.24/17.31 "clause": 0, 64.24/17.31 "scope": 2, 64.24/17.31 "term": "(p (d (e T48)) T49)" 64.24/17.31 }, 64.24/17.31 { 64.24/17.31 "clause": 1, 64.24/17.31 "scope": 2, 64.24/17.31 "term": "(p (d (e T48)) T49)" 64.24/17.31 }, 64.24/17.31 { 64.24/17.31 "clause": 2, 64.24/17.31 "scope": 2, 64.24/17.31 "term": "(p (d (e T48)) T49)" 64.24/17.31 }, 64.24/17.31 { 64.24/17.31 "clause": 3, 64.24/17.31 "scope": 2, 64.24/17.31 "term": "(p (d (e T48)) T49)" 64.24/17.31 }, 64.24/17.31 { 64.24/17.31 "clause": 4, 64.24/17.31 "scope": 2, 64.24/17.31 "term": "(p (d (e T48)) T49)" 64.24/17.31 } 64.24/17.31 ], 64.24/17.31 "kb": { 64.24/17.31 "nonunifying": [], 64.24/17.31 "intvars": {}, 64.24/17.31 "arithmetic": { 64.24/17.31 "type": "PlainIntegerRelationState", 64.24/17.31 "relations": [] 64.24/17.31 }, 64.24/17.31 "ground": [ 64.24/17.31 "T49", 64.24/17.31 "T48" 64.24/17.31 ], 64.24/17.31 "free": [], 64.24/17.31 "exprvars": [] 64.24/17.31 } 64.24/17.31 }, 64.24/17.31 "391": { 64.24/17.31 "goal": [{ 64.24/17.31 "clause": 0, 64.24/17.31 "scope": 2, 64.24/17.31 "term": "(p (d (e T48)) T49)" 64.24/17.31 }], 64.24/17.31 "kb": { 64.24/17.31 "nonunifying": [], 64.24/17.31 "intvars": {}, 64.24/17.31 "arithmetic": { 64.24/17.31 "type": "PlainIntegerRelationState", 64.24/17.31 "relations": [] 64.24/17.31 }, 64.24/17.31 "ground": [ 64.24/17.31 "T49", 64.24/17.31 "T48" 64.24/17.31 ], 64.24/17.31 "free": [], 64.24/17.31 "exprvars": [] 64.24/17.31 } 64.24/17.31 }, 64.24/17.31 "type": "Nodes", 64.24/17.31 "392": { 64.24/17.31 "goal": [ 64.24/17.31 { 64.24/17.31 "clause": 1, 64.24/17.31 "scope": 2, 64.24/17.31 "term": "(p (d (e T48)) T49)" 64.24/17.31 }, 64.24/17.31 { 64.24/17.31 "clause": 2, 64.24/17.31 "scope": 2, 64.24/17.31 "term": "(p (d (e T48)) T49)" 64.24/17.31 }, 64.24/17.31 { 64.24/17.31 "clause": 3, 64.24/17.31 "scope": 2, 64.24/17.31 "term": "(p (d (e T48)) T49)" 64.24/17.31 }, 64.24/17.31 { 64.24/17.31 "clause": 4, 64.24/17.31 "scope": 2, 64.24/17.31 "term": "(p (d (e T48)) T49)" 64.24/17.31 } 64.24/17.31 ], 64.24/17.31 "kb": { 64.24/17.31 "nonunifying": [], 64.24/17.31 "intvars": {}, 64.24/17.31 "arithmetic": { 64.24/17.31 "type": "PlainIntegerRelationState", 64.24/17.31 "relations": [] 64.24/17.31 }, 64.24/17.31 "ground": [ 64.24/17.31 "T49", 64.24/17.31 "T48" 64.24/17.31 ], 64.24/17.31 "free": [], 64.24/17.31 "exprvars": [] 64.24/17.31 } 64.24/17.31 }, 64.24/17.31 "393": { 64.24/17.31 "goal": [{ 64.24/17.31 "clause": -1, 64.24/17.31 "scope": -1, 64.24/17.31 "term": "(true)" 64.24/17.31 }], 64.24/17.31 "kb": { 64.24/17.31 "nonunifying": [], 64.24/17.31 "intvars": {}, 64.24/17.31 "arithmetic": { 64.24/17.31 "type": "PlainIntegerRelationState", 64.24/17.31 "relations": [] 64.24/17.31 }, 64.24/17.31 "ground": [], 64.24/17.31 "free": [], 64.24/17.31 "exprvars": [] 64.24/17.31 } 64.24/17.31 }, 64.24/17.31 "394": { 64.24/17.31 "goal": [], 64.24/17.31 "kb": { 64.24/17.31 "nonunifying": [], 64.24/17.31 "intvars": {}, 64.24/17.31 "arithmetic": { 64.24/17.31 "type": "PlainIntegerRelationState", 64.24/17.31 "relations": [] 64.24/17.31 }, 64.24/17.31 "ground": [], 64.24/17.31 "free": [], 64.24/17.31 "exprvars": [] 64.24/17.31 } 64.24/17.31 }, 64.24/17.31 "395": { 64.24/17.31 "goal": [], 64.24/17.31 "kb": { 64.24/17.31 "nonunifying": [], 64.24/17.31 "intvars": {}, 64.24/17.31 "arithmetic": { 64.24/17.31 "type": "PlainIntegerRelationState", 64.24/17.31 "relations": [] 64.24/17.31 }, 64.24/17.31 "ground": [], 64.24/17.31 "free": [], 64.24/17.31 "exprvars": [] 64.24/17.31 } 64.24/17.31 }, 64.24/17.31 "396": { 64.24/17.31 "goal": [{ 64.24/17.31 "clause": 1, 64.24/17.31 "scope": 2, 64.24/17.31 "term": "(p (d (e T48)) T49)" 64.24/17.31 }], 64.24/17.31 "kb": { 64.24/17.31 "nonunifying": [], 64.24/17.31 "intvars": {}, 64.24/17.31 "arithmetic": { 64.24/17.31 "type": "PlainIntegerRelationState", 64.24/17.32 "relations": [] 64.24/17.32 }, 64.24/17.32 "ground": [ 64.24/17.32 "T49", 64.24/17.32 "T48" 64.24/17.32 ], 64.24/17.32 "free": [], 64.24/17.32 "exprvars": [] 64.24/17.32 } 64.24/17.32 }, 64.24/17.32 "397": { 64.24/17.32 "goal": [ 64.24/17.32 { 64.24/17.32 "clause": 2, 64.24/17.32 "scope": 2, 64.24/17.32 "term": "(p (d (e T48)) T49)" 64.24/17.32 }, 64.24/17.32 { 64.24/17.32 "clause": 3, 64.24/17.32 "scope": 2, 64.24/17.32 "term": "(p (d (e T48)) T49)" 64.24/17.32 }, 64.24/17.32 { 64.24/17.32 "clause": 4, 64.24/17.32 "scope": 2, 64.24/17.32 "term": "(p (d (e T48)) T49)" 64.24/17.32 } 64.24/17.32 ], 64.24/17.32 "kb": { 64.24/17.32 "nonunifying": [], 64.24/17.32 "intvars": {}, 64.24/17.32 "arithmetic": { 64.24/17.32 "type": "PlainIntegerRelationState", 64.24/17.32 "relations": [] 64.24/17.32 }, 64.24/17.32 "ground": [ 64.24/17.32 "T49", 64.24/17.32 "T48" 64.24/17.32 ], 64.24/17.32 "free": [], 64.24/17.32 "exprvars": [] 64.24/17.32 } 64.24/17.32 }, 64.24/17.32 "551": { 64.24/17.32 "goal": [{ 64.24/17.32 "clause": -1, 64.24/17.32 "scope": -1, 64.24/17.32 "term": "(p (d T138) X175)" 64.24/17.32 }], 64.24/17.32 "kb": { 64.24/17.32 "nonunifying": [], 64.24/17.32 "intvars": {}, 64.24/17.32 "arithmetic": { 64.24/17.32 "type": "PlainIntegerRelationState", 64.24/17.32 "relations": [] 64.24/17.32 }, 64.24/17.32 "ground": [], 64.24/17.32 "free": ["X175"], 64.24/17.32 "exprvars": [] 64.24/17.32 } 64.24/17.32 }, 64.24/17.32 "398": { 64.24/17.32 "goal": [{ 64.24/17.32 "clause": -1, 64.24/17.32 "scope": -1, 64.24/17.32 "term": "(true)" 64.24/17.32 }], 64.24/17.32 "kb": { 64.24/17.32 "nonunifying": [], 64.24/17.32 "intvars": {}, 64.24/17.32 "arithmetic": { 64.24/17.32 "type": "PlainIntegerRelationState", 64.24/17.32 "relations": [] 64.24/17.32 }, 64.24/17.32 "ground": [], 64.24/17.32 "free": [], 64.24/17.32 "exprvars": [] 64.24/17.32 } 64.24/17.32 }, 64.24/17.32 "552": { 64.24/17.32 "goal": [{ 64.24/17.32 "clause": -1, 64.24/17.32 "scope": -1, 64.24/17.32 "term": "(p (d (e T139)) X176)" 64.24/17.32 }], 64.24/17.32 "kb": { 64.24/17.32 "nonunifying": [], 64.24/17.32 "intvars": {}, 64.24/17.32 "arithmetic": { 64.24/17.32 "type": "PlainIntegerRelationState", 64.24/17.32 "relations": [] 64.24/17.32 }, 64.24/17.32 "ground": [], 64.24/17.32 "free": ["X176"], 64.24/17.32 "exprvars": [] 64.24/17.32 } 64.24/17.32 }, 64.24/17.32 "478": { 64.24/17.32 "goal": [{ 64.24/17.32 "clause": -1, 64.24/17.32 "scope": -1, 64.24/17.32 "term": "(',' (p (d (e T92)) T95) (p (d (e T93)) T94))" 64.24/17.32 }], 64.24/17.32 "kb": { 64.24/17.32 "nonunifying": [], 64.24/17.32 "intvars": {}, 64.24/17.32 "arithmetic": { 64.24/17.32 "type": "PlainIntegerRelationState", 64.24/17.32 "relations": [] 64.24/17.32 }, 64.24/17.32 "ground": [ 64.24/17.32 "T92", 64.24/17.32 "T93", 64.24/17.32 "T94", 64.24/17.32 "T95" 64.24/17.32 ], 64.24/17.32 "free": [], 64.24/17.32 "exprvars": [] 64.24/17.32 } 64.24/17.32 }, 64.24/17.32 "116": { 64.24/17.32 "goal": [], 64.24/17.32 "kb": { 64.24/17.32 "nonunifying": [], 64.24/17.32 "intvars": {}, 64.24/17.32 "arithmetic": { 64.24/17.32 "type": "PlainIntegerRelationState", 64.24/17.32 "relations": [] 64.24/17.32 }, 64.24/17.32 "ground": [], 64.24/17.32 "free": [], 64.24/17.32 "exprvars": [] 64.24/17.32 } 64.24/17.32 }, 64.24/17.32 "479": { 64.24/17.32 "goal": [], 64.24/17.32 "kb": { 64.24/17.32 "nonunifying": [], 64.24/17.32 "intvars": {}, 64.24/17.32 "arithmetic": { 64.24/17.32 "type": "PlainIntegerRelationState", 64.24/17.32 "relations": [] 64.24/17.32 }, 64.24/17.32 "ground": [], 64.24/17.32 "free": [], 64.24/17.32 "exprvars": [] 64.24/17.32 } 64.24/17.32 }, 64.24/17.32 "512": { 64.24/17.32 "goal": [{ 64.24/17.32 "clause": -1, 64.24/17.32 "scope": -1, 64.24/17.32 "term": "(',' (p (d (e T119)) X134) (p (d (e T120)) X135))" 64.24/17.32 }], 64.24/17.32 "kb": { 64.24/17.32 "nonunifying": [], 64.24/17.32 "intvars": {}, 64.24/17.32 "arithmetic": { 64.24/17.32 "type": "PlainIntegerRelationState", 64.24/17.32 "relations": [] 64.24/17.32 }, 64.24/17.32 "ground": [], 64.24/17.32 "free": [ 64.24/17.32 "X134", 64.24/17.32 "X135" 64.24/17.32 ], 64.24/17.32 "exprvars": [] 64.24/17.32 } 64.24/17.32 }, 64.24/17.32 "513": { 64.24/17.32 "goal": [], 64.24/17.32 "kb": { 64.24/17.32 "nonunifying": [], 64.24/17.32 "intvars": {}, 64.24/17.32 "arithmetic": { 64.24/17.32 "type": "PlainIntegerRelationState", 64.24/17.32 "relations": [] 64.24/17.32 }, 64.24/17.32 "ground": [], 64.24/17.32 "free": [], 64.24/17.32 "exprvars": [] 64.24/17.32 } 64.24/17.32 }, 64.24/17.32 "95": { 64.24/17.32 "goal": [], 64.24/17.32 "kb": { 64.24/17.32 "nonunifying": [], 64.24/17.32 "intvars": {}, 64.24/17.32 "arithmetic": { 64.24/17.32 "type": "PlainIntegerRelationState", 64.24/17.32 "relations": [] 64.24/17.32 }, 64.24/17.32 "ground": [], 64.24/17.32 "free": [], 64.24/17.32 "exprvars": [] 64.24/17.32 } 64.24/17.32 }, 64.24/17.32 "482": { 64.24/17.32 "goal": [], 64.24/17.32 "kb": { 64.24/17.32 "nonunifying": [], 64.24/17.32 "intvars": {}, 64.24/17.32 "arithmetic": { 64.24/17.32 "type": "PlainIntegerRelationState", 64.24/17.32 "relations": [] 64.24/17.32 }, 64.24/17.32 "ground": [], 64.24/17.32 "free": [], 64.24/17.32 "exprvars": [] 64.24/17.32 } 64.24/17.32 }, 64.24/17.32 "485": { 64.24/17.32 "goal": [{ 64.24/17.32 "clause": -1, 64.24/17.32 "scope": -1, 64.24/17.32 "term": "(',' (p (d T102) X100) (p (d (e X100)) T101))" 64.24/17.32 }], 64.24/17.32 "kb": { 64.24/17.32 "nonunifying": [], 64.24/17.32 "intvars": {}, 64.24/17.32 "arithmetic": { 64.24/17.32 "type": "PlainIntegerRelationState", 64.24/17.32 "relations": [] 64.24/17.32 }, 64.24/17.32 "ground": ["T101"], 64.24/17.32 "free": ["X100"], 64.24/17.32 "exprvars": [] 64.24/17.32 } 64.24/17.32 }, 64.24/17.32 "486": { 64.24/17.32 "goal": [], 64.24/17.32 "kb": { 64.24/17.32 "nonunifying": [], 64.24/17.32 "intvars": {}, 64.24/17.32 "arithmetic": { 64.24/17.32 "type": "PlainIntegerRelationState", 64.24/17.32 "relations": [] 64.24/17.32 }, 64.24/17.32 "ground": [], 64.24/17.32 "free": [], 64.24/17.32 "exprvars": [] 64.24/17.32 } 64.24/17.32 }, 64.24/17.32 "487": { 64.24/17.32 "goal": [{ 64.24/17.32 "clause": -1, 64.24/17.32 "scope": -1, 64.24/17.32 "term": "(p (d T102) X100)" 64.24/17.32 }], 64.24/17.32 "kb": { 64.24/17.32 "nonunifying": [], 64.24/17.32 "intvars": {}, 64.24/17.32 "arithmetic": { 64.24/17.32 "type": "PlainIntegerRelationState", 64.24/17.32 "relations": [] 64.24/17.32 }, 64.24/17.32 "ground": [], 64.24/17.32 "free": ["X100"], 64.24/17.32 "exprvars": [] 64.24/17.32 } 64.24/17.32 }, 64.24/17.32 "488": { 64.24/17.32 "goal": [{ 64.24/17.32 "clause": -1, 64.24/17.32 "scope": -1, 64.24/17.32 "term": "(p (d (e T103)) T101)" 64.24/17.32 }], 64.24/17.32 "kb": { 64.24/17.32 "nonunifying": [], 64.24/17.32 "intvars": {}, 64.24/17.32 "arithmetic": { 64.24/17.32 "type": "PlainIntegerRelationState", 64.24/17.32 "relations": [] 64.24/17.32 }, 64.24/17.32 "ground": ["T101"], 64.24/17.32 "free": [], 64.24/17.32 "exprvars": [] 64.24/17.32 } 64.24/17.32 }, 64.24/17.32 "445": { 64.24/17.32 "goal": [], 64.24/17.32 "kb": { 64.24/17.32 "nonunifying": [], 64.24/17.32 "intvars": {}, 64.24/17.32 "arithmetic": { 64.24/17.32 "type": "PlainIntegerRelationState", 64.24/17.32 "relations": [] 64.24/17.32 }, 64.24/17.32 "ground": [], 64.24/17.32 "free": [], 64.24/17.32 "exprvars": [] 64.24/17.32 } 64.24/17.32 }, 64.24/17.32 "489": { 64.24/17.32 "goal": [ 64.24/17.32 { 64.24/17.32 "clause": 0, 64.24/17.32 "scope": 3, 64.24/17.32 "term": "(p (d T102) X100)" 64.24/17.32 }, 64.24/17.32 { 64.24/17.32 "clause": 1, 64.24/17.32 "scope": 3, 64.24/17.32 "term": "(p (d T102) X100)" 64.24/17.32 }, 64.24/17.32 { 64.24/17.32 "clause": 2, 64.24/17.32 "scope": 3, 64.24/17.32 "term": "(p (d T102) X100)" 64.24/17.32 }, 64.24/17.32 { 64.24/17.32 "clause": 3, 64.24/17.32 "scope": 3, 64.24/17.32 "term": "(p (d T102) X100)" 64.24/17.32 }, 64.24/17.32 { 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[], 64.24/17.33 "free": [], 64.24/17.33 "exprvars": [] 64.24/17.33 } 64.24/17.33 }, 64.24/17.33 "386": { 64.24/17.33 "goal": [{ 64.24/17.33 "clause": -1, 64.24/17.33 "scope": -1, 64.24/17.33 "term": "(',' (p (d (e T47)) T50) (p (d (e T48)) T49))" 64.24/17.33 }], 64.24/17.33 "kb": { 64.24/17.33 "nonunifying": [], 64.24/17.33 "intvars": {}, 64.24/17.33 "arithmetic": { 64.24/17.33 "type": "PlainIntegerRelationState", 64.24/17.33 "relations": [] 64.24/17.33 }, 64.24/17.33 "ground": [ 64.24/17.33 "T47", 64.24/17.33 "T49", 64.24/17.33 "T48", 64.24/17.33 "T50" 64.24/17.33 ], 64.24/17.33 "free": [], 64.24/17.33 "exprvars": [] 64.24/17.33 } 64.24/17.33 }, 64.24/17.33 "463": { 64.24/17.33 "goal": [{ 64.24/17.33 "clause": 3, 64.24/17.33 "scope": 2, 64.24/17.33 "term": "(p (d (e T48)) T49)" 64.24/17.33 }], 64.24/17.33 "kb": { 64.24/17.33 "nonunifying": [], 64.24/17.33 "intvars": {}, 64.24/17.33 "arithmetic": { 64.24/17.33 "type": "PlainIntegerRelationState", 64.24/17.33 "relations": [] 64.24/17.33 }, 64.24/17.33 "ground": [ 64.24/17.33 "T49", 64.24/17.33 "T48" 64.24/17.33 ], 64.24/17.33 "free": [], 64.24/17.33 "exprvars": [] 64.24/17.33 } 64.24/17.33 }, 64.24/17.33 "540": { 64.24/17.33 "goal": [], 64.24/17.33 "kb": { 64.24/17.33 "nonunifying": [], 64.24/17.33 "intvars": {}, 64.24/17.33 "arithmetic": { 64.24/17.33 "type": "PlainIntegerRelationState", 64.24/17.33 "relations": [] 64.24/17.33 }, 64.24/17.33 "ground": [], 64.24/17.33 "free": [], 64.24/17.33 "exprvars": [] 64.24/17.33 } 64.24/17.33 }, 64.24/17.33 "387": { 64.24/17.33 "goal": [], 64.24/17.33 "kb": { 64.24/17.33 "nonunifying": [], 64.24/17.33 "intvars": {}, 64.24/17.33 "arithmetic": { 64.24/17.33 "type": "PlainIntegerRelationState", 64.24/17.33 "relations": [] 64.24/17.33 }, 64.24/17.33 "ground": [], 64.24/17.33 "free": [], 64.24/17.33 "exprvars": [] 64.24/17.33 } 64.24/17.33 }, 64.24/17.33 "464": { 64.24/17.33 "goal": [{ 64.24/17.33 "clause": 4, 64.24/17.33 "scope": 2, 64.24/17.33 "term": "(p (d (e T48)) T49)" 64.24/17.33 }], 64.24/17.33 "kb": { 64.24/17.33 "nonunifying": [], 64.24/17.33 "intvars": {}, 64.24/17.33 "arithmetic": { 64.24/17.33 "type": "PlainIntegerRelationState", 64.24/17.33 "relations": [] 64.24/17.33 }, 64.24/17.33 "ground": [ 64.24/17.33 "T49", 64.24/17.33 "T48" 64.24/17.33 ], 64.24/17.33 "free": [], 64.24/17.33 "exprvars": [] 64.24/17.33 } 64.24/17.33 }, 64.24/17.33 "541": { 64.24/17.33 "goal": [{ 64.24/17.33 "clause": -1, 64.24/17.33 "scope": -1, 64.24/17.33 "term": "(',' (p (d T138) X175) (p (d (e X175)) X176))" 64.24/17.33 }], 64.24/17.33 "kb": { 64.24/17.33 "nonunifying": [], 64.24/17.33 "intvars": {}, 64.24/17.33 "arithmetic": { 64.24/17.33 "type": "PlainIntegerRelationState", 64.24/17.33 "relations": [] 64.24/17.33 }, 64.24/17.33 "ground": [], 64.24/17.33 "free": [ 64.24/17.33 "X176", 64.24/17.33 "X175" 64.24/17.33 ], 64.24/17.33 "exprvars": [] 64.24/17.33 } 64.24/17.33 }, 64.24/17.33 "388": { 64.24/17.33 "goal": [{ 64.24/17.33 "clause": -1, 64.24/17.33 "scope": -1, 64.24/17.33 "term": "(p (d (e T47)) T50)" 64.24/17.33 }], 64.24/17.33 "kb": { 64.24/17.33 "nonunifying": [], 64.24/17.33 "intvars": {}, 64.24/17.33 "arithmetic": { 64.24/17.33 "type": "PlainIntegerRelationState", 64.24/17.33 "relations": [] 64.24/17.33 }, 64.24/17.33 "ground": [ 64.24/17.33 "T47", 64.24/17.33 "T50" 64.24/17.33 ], 64.24/17.33 "free": [], 64.24/17.33 "exprvars": [] 64.24/17.33 } 64.24/17.33 }, 64.24/17.33 "542": { 64.24/17.33 "goal": [], 64.24/17.33 "kb": { 64.24/17.33 "nonunifying": [], 64.24/17.33 "intvars": {}, 64.24/17.33 "arithmetic": { 64.24/17.33 "type": "PlainIntegerRelationState", 64.24/17.33 "relations": [] 64.24/17.33 }, 64.24/17.33 "ground": [], 64.24/17.33 "free": [], 64.24/17.33 "exprvars": [] 64.24/17.33 } 64.24/17.33 }, 64.24/17.33 "345": { 64.24/17.33 "goal": [{ 64.24/17.33 "clause": -1, 64.24/17.33 "scope": -1, 64.24/17.33 "term": "(p (d (e T28)) T26)" 64.24/17.33 }], 64.24/17.33 "kb": { 64.24/17.33 "nonunifying": [], 64.24/17.33 "intvars": {}, 64.24/17.33 "arithmetic": { 64.24/17.33 "type": "PlainIntegerRelationState", 64.24/17.33 "relations": [] 64.24/17.33 }, 64.24/17.33 "ground": ["T26"], 64.24/17.33 "free": [], 64.24/17.33 "exprvars": [] 64.24/17.33 } 64.24/17.33 }, 64.24/17.33 "389": { 64.24/17.33 "goal": [{ 64.24/17.33 "clause": -1, 64.24/17.33 "scope": -1, 64.24/17.33 "term": "(p (d (e T48)) T49)" 64.24/17.33 }], 64.24/17.33 "kb": { 64.24/17.33 "nonunifying": [], 64.24/17.33 "intvars": {}, 64.24/17.33 "arithmetic": { 64.24/17.33 "type": "PlainIntegerRelationState", 64.24/17.33 "relations": [] 64.24/17.33 }, 64.24/17.33 "ground": [ 64.24/17.33 "T49", 64.24/17.33 "T48" 64.24/17.33 ], 64.24/17.33 "free": [], 64.24/17.33 "exprvars": [] 64.24/17.33 } 64.24/17.33 }, 64.24/17.33 "346": { 64.24/17.33 "goal": [{ 64.24/17.33 "clause": -1, 64.24/17.33 "scope": -1, 64.24/17.33 "term": "(p (d (e T30)) T27)" 64.24/17.33 }], 64.24/17.33 "kb": { 64.24/17.33 "nonunifying": [], 64.24/17.33 "intvars": {}, 64.24/17.33 "arithmetic": { 64.24/17.33 "type": "PlainIntegerRelationState", 64.24/17.33 "relations": [] 64.24/17.33 }, 64.24/17.33 "ground": ["T27"], 64.24/17.33 "free": [], 64.24/17.33 "exprvars": [] 64.24/17.33 } 64.24/17.33 }, 64.24/17.33 "500": { 64.24/17.33 "goal": [], 64.24/17.33 "kb": { 64.24/17.33 "nonunifying": [], 64.24/17.33 "intvars": {}, 64.24/17.33 "arithmetic": { 64.24/17.33 "type": "PlainIntegerRelationState", 64.24/17.33 "relations": [] 64.24/17.33 }, 64.24/17.33 "ground": [], 64.24/17.33 "free": [], 64.24/17.33 "exprvars": [] 64.24/17.33 } 64.24/17.33 }, 64.24/17.33 "501": { 64.24/17.33 "goal": [], 64.24/17.33 "kb": { 64.24/17.33 "nonunifying": [], 64.24/17.33 "intvars": {}, 64.24/17.33 "arithmetic": { 64.24/17.33 "type": "PlainIntegerRelationState", 64.24/17.33 "relations": [] 64.24/17.33 }, 64.24/17.33 "ground": [], 64.24/17.33 "free": [], 64.24/17.33 "exprvars": [] 64.24/17.33 } 64.24/17.33 }, 64.24/17.33 "506": { 64.24/17.33 "goal": [{ 64.24/17.33 "clause": 2, 64.24/17.33 "scope": 3, 64.24/17.33 "term": "(p (d T102) X100)" 64.24/17.33 }], 64.24/17.33 "kb": { 64.24/17.33 "nonunifying": [], 64.24/17.33 "intvars": {}, 64.24/17.33 "arithmetic": { 64.24/17.33 "type": "PlainIntegerRelationState", 64.24/17.33 "relations": [] 64.24/17.33 }, 64.24/17.33 "ground": [], 64.24/17.33 "free": ["X100"], 64.24/17.33 "exprvars": [] 64.24/17.33 } 64.24/17.33 }, 64.24/17.33 "507": { 64.24/17.33 "goal": [ 64.24/17.33 { 64.24/17.33 "clause": 3, 64.24/17.33 "scope": 3, 64.24/17.33 "term": "(p (d T102) X100)" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "clause": 4, 64.24/17.33 "scope": 3, 64.24/17.33 "term": "(p (d T102) X100)" 64.24/17.33 } 64.24/17.33 ], 64.24/17.33 "kb": { 64.24/17.33 "nonunifying": [], 64.24/17.33 "intvars": {}, 64.24/17.33 "arithmetic": { 64.24/17.33 "type": "PlainIntegerRelationState", 64.24/17.33 "relations": [] 64.24/17.33 }, 64.24/17.33 "ground": [], 64.24/17.33 "free": ["X100"], 64.24/17.33 "exprvars": [] 64.24/17.33 } 64.24/17.33 } 64.24/17.33 }, 64.24/17.33 "edges": [ 64.24/17.33 { 64.24/17.33 "from": 27, 64.24/17.33 "to": 28, 64.24/17.33 "label": "CASE" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 28, 64.24/17.33 "to": 31, 64.24/17.33 "label": "PARALLEL" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 28, 64.24/17.33 "to": 32, 64.24/17.33 "label": "PARALLEL" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 31, 64.24/17.33 "to": 88, 64.24/17.33 "label": "EVAL with clause\np(d(e(t)), const(1)).\nand substitutionT1 -> d(e(t)),\nT2 -> const(1)" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 31, 64.24/17.33 "to": 95, 64.24/17.33 "label": "EVAL-BACKTRACK" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 32, 64.24/17.33 "to": 132, 64.24/17.33 "label": "PARALLEL" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 32, 64.24/17.33 "to": 133, 64.24/17.33 "label": "PARALLEL" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 88, 64.24/17.33 "to": 116, 64.24/17.33 "label": "SUCCESS" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 132, 64.24/17.33 "to": 134, 64.24/17.33 "label": "EVAL with clause\np(d(e(const(X5))), const(0)).\nand substitutionX5 -> T7,\nT1 -> d(e(const(T7))),\nT2 -> const(0)" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 132, 64.24/17.33 "to": 135, 64.24/17.33 "label": "EVAL-BACKTRACK" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 133, 64.24/17.33 "to": 248, 64.24/17.33 "label": "PARALLEL" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 133, 64.24/17.33 "to": 249, 64.24/17.33 "label": "PARALLEL" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 134, 64.24/17.33 "to": 136, 64.24/17.33 "label": "SUCCESS" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 248, 64.24/17.33 "to": 339, 64.24/17.33 "label": "EVAL with clause\np(d(e(+(X22, X23))), +(X24, X25)) :- ','(p(d(e(X22)), X24), p(d(e(X23)), X25)).\nand substitutionX22 -> T28,\nX23 -> T29,\nT1 -> d(e(+(T28, T29))),\nX24 -> T26,\nX25 -> T27,\nT2 -> +(T26, T27),\nT24 -> T28,\nT25 -> T29" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 248, 64.24/17.33 "to": 341, 64.24/17.33 "label": "EVAL-BACKTRACK" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 249, 64.24/17.33 "to": 372, 64.24/17.33 "label": "PARALLEL" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 249, 64.24/17.33 "to": 373, 64.24/17.33 "label": "PARALLEL" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 339, 64.24/17.33 "to": 345, 64.24/17.33 "label": "SPLIT 1" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 339, 64.24/17.33 "to": 346, 64.24/17.33 "label": "SPLIT 2\nnew knowledge:\nT26 is ground\nreplacements:T29 -> T30" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 345, 64.24/17.33 "to": 27, 64.24/17.33 "label": "INSTANCE with matching:\nT1 -> d(e(T28))\nT2 -> T26" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 346, 64.24/17.33 "to": 27, 64.24/17.33 "label": "INSTANCE with matching:\nT1 -> d(e(T30))\nT2 -> T27" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 372, 64.24/17.33 "to": 386, 64.24/17.33 "label": "EVAL with clause\np(d(e(*(X42, X43))), +(*(X42, X44), *(X43, X45))) :- ','(p(d(e(X42)), X45), p(d(e(X43)), X44)).\nand substitutionX42 -> T47,\nX43 -> T48,\nT1 -> d(e(*(T47, T48))),\nX44 -> T49,\nX45 -> T50,\nT2 -> +(*(T47, T49), *(T48, T50))" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 372, 64.24/17.33 "to": 387, 64.24/17.33 "label": "EVAL-BACKTRACK" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 373, 64.24/17.33 "to": 485, 64.24/17.33 "label": "EVAL with clause\np(d(d(X98)), X99) :- ','(p(d(X98), X100), p(d(e(X100)), X99)).\nand substitutionX98 -> T102,\nT1 -> d(d(T102)),\nT2 -> T101,\nX99 -> T101,\nT100 -> T102" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 373, 64.24/17.33 "to": 486, 64.24/17.33 "label": "EVAL-BACKTRACK" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 386, 64.24/17.33 "to": 388, 64.24/17.33 "label": "SPLIT 1" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 386, 64.24/17.33 "to": 389, 64.24/17.33 "label": "SPLIT 2\nnew knowledge:\nT47 is ground\nT50 is ground" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 388, 64.24/17.33 "to": 389, 64.24/17.33 "label": "INSTANCE with matching:\nT48 -> T47\nT49 -> T50" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 389, 64.24/17.33 "to": 390, 64.24/17.33 "label": "CASE" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 390, 64.24/17.33 "to": 391, 64.24/17.33 "label": "PARALLEL" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 390, 64.24/17.33 "to": 392, 64.24/17.33 "label": "PARALLEL" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 391, 64.24/17.33 "to": 393, 64.24/17.33 "label": "EVAL with clause\np(d(e(t)), const(1)).\nand substitutionT48 -> t,\nT49 -> const(1)" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 391, 64.24/17.33 "to": 394, 64.24/17.33 "label": "EVAL-BACKTRACK" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 392, 64.24/17.33 "to": 396, 64.24/17.33 "label": "PARALLEL" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 392, 64.24/17.33 "to": 397, 64.24/17.33 "label": "PARALLEL" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 393, 64.24/17.33 "to": 395, 64.24/17.33 "label": "SUCCESS" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 396, 64.24/17.33 "to": 398, 64.24/17.33 "label": "EVAL with clause\np(d(e(const(X50))), const(0)).\nand substitutionX50 -> T55,\nT48 -> const(T55),\nT49 -> const(0)" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 396, 64.24/17.33 "to": 445, 64.24/17.33 "label": "EVAL-BACKTRACK" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 397, 64.24/17.33 "to": 450, 64.24/17.33 "label": "PARALLEL" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 397, 64.24/17.33 "to": 451, 64.24/17.33 "label": "PARALLEL" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 398, 64.24/17.33 "to": 446, 64.24/17.33 "label": "SUCCESS" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 450, 64.24/17.33 "to": 455, 64.24/17.33 "label": "EVAL with clause\np(d(e(+(X67, X68))), +(X69, X70)) :- ','(p(d(e(X67)), X69), p(d(e(X68)), X70)).\nand substitutionX67 -> T72,\nX68 -> T73,\nT48 -> +(T72, T73),\nX69 -> T74,\nX70 -> T75,\nT49 -> +(T74, T75)" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 450, 64.24/17.33 "to": 456, 64.24/17.33 "label": "EVAL-BACKTRACK" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 451, 64.24/17.33 "to": 463, 64.24/17.33 "label": "PARALLEL" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 451, 64.24/17.33 "to": 464, 64.24/17.33 "label": "PARALLEL" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 455, 64.24/17.33 "to": 386, 64.24/17.33 "label": "INSTANCE with matching:\nT47 -> T72\nT50 -> T74\nT48 -> T73\nT49 -> T75" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 463, 64.24/17.33 "to": 478, 64.24/17.33 "label": "EVAL with clause\np(d(e(*(X87, X88))), +(*(X87, X89), *(X88, X90))) :- ','(p(d(e(X87)), X90), p(d(e(X88)), X89)).\nand substitutionX87 -> T92,\nX88 -> T93,\nT48 -> *(T92, T93),\nX89 -> T94,\nX90 -> T95,\nT49 -> +(*(T92, T94), *(T93, T95))" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 463, 64.24/17.33 "to": 479, 64.24/17.33 "label": "EVAL-BACKTRACK" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 464, 64.24/17.33 "to": 482, 64.24/17.33 "label": "BACKTRACK\nfor clause: p(d(d(X)), DDX) :- ','(p(d(X), DX), p(d(e(DX)), DDX))because of non-unification" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 478, 64.24/17.33 "to": 386, 64.24/17.33 "label": "INSTANCE with matching:\nT47 -> T92\nT50 -> T95\nT48 -> T93\nT49 -> T94" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 485, 64.24/17.33 "to": 487, 64.24/17.33 "label": "SPLIT 1" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 485, 64.24/17.33 "to": 488, 64.24/17.33 "label": "SPLIT 2\nreplacements:X100 -> T103" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 487, 64.24/17.33 "to": 489, 64.24/17.33 "label": "CASE" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 488, 64.24/17.33 "to": 27, 64.24/17.33 "label": "INSTANCE with matching:\nT1 -> d(e(T103))\nT2 -> T101" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 489, 64.24/17.33 "to": 490, 64.24/17.33 "label": "PARALLEL" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 489, 64.24/17.33 "to": 491, 64.24/17.33 "label": "PARALLEL" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 490, 64.24/17.33 "to": 492, 64.24/17.33 "label": "EVAL with clause\np(d(e(t)), const(1)).\nand substitutionT102 -> e(t),\nX100 -> const(1)" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 490, 64.24/17.33 "to": 493, 64.24/17.33 "label": "EVAL-BACKTRACK" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 491, 64.24/17.33 "to": 497, 64.24/17.33 "label": "PARALLEL" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 491, 64.24/17.33 "to": 498, 64.24/17.33 "label": "PARALLEL" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 492, 64.24/17.33 "to": 494, 64.24/17.33 "label": "SUCCESS" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 497, 64.24/17.33 "to": 499, 64.24/17.33 "label": "EVAL with clause\np(d(e(const(X105))), const(0)).\nand substitutionX105 -> T108,\nT102 -> e(const(T108)),\nX100 -> const(0)" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 497, 64.24/17.33 "to": 500, 64.24/17.33 "label": "EVAL-BACKTRACK" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 498, 64.24/17.33 "to": 506, 64.24/17.33 "label": "PARALLEL" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 498, 64.24/17.33 "to": 507, 64.24/17.33 "label": "PARALLEL" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 499, 64.24/17.33 "to": 501, 64.24/17.33 "label": "SUCCESS" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 506, 64.24/17.33 "to": 512, 64.24/17.33 "label": "EVAL with clause\np(d(e(+(X130, X131))), +(X132, X133)) :- ','(p(d(e(X130)), X132), p(d(e(X131)), X133)).\nand substitutionX130 -> T119,\nX131 -> T120,\nT102 -> e(+(T119, T120)),\nX132 -> X134,\nX133 -> X135,\nX100 -> +(X134, X135),\nT117 -> T119,\nT118 -> T120" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 506, 64.24/17.33 "to": 513, 64.24/17.33 "label": "EVAL-BACKTRACK" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 507, 64.24/17.33 "to": 533, 64.24/17.33 "label": "PARALLEL" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 507, 64.24/17.33 "to": 534, 64.24/17.33 "label": "PARALLEL" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 512, 64.24/17.33 "to": 529, 64.24/17.33 "label": "SPLIT 1" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 512, 64.24/17.33 "to": 530, 64.24/17.33 "label": "SPLIT 2\nreplacements:X134 -> T121,\nT120 -> T122" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 529, 64.24/17.33 "to": 487, 64.24/17.33 "label": "INSTANCE with matching:\nT102 -> e(T119)\nX100 -> X134" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 530, 64.24/17.33 "to": 487, 64.24/17.33 "label": "INSTANCE with matching:\nT102 -> e(T122)\nX100 -> X135" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 533, 64.24/17.33 "to": 538, 64.24/17.33 "label": "EVAL with clause\np(d(e(*(X160, X161))), +(*(X160, X162), *(X161, X163))) :- ','(p(d(e(X160)), X163), p(d(e(X161)), X162)).\nand substitutionX160 -> T133,\nX161 -> T134,\nT102 -> e(*(T133, T134)),\nX162 -> X164,\nX163 -> X165,\nX100 -> +(*(T133, X164), *(T134, X165)),\nT131 -> T133,\nT132 -> T134" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 533, 64.24/17.33 "to": 540, 64.24/17.33 "label": "EVAL-BACKTRACK" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 534, 64.24/17.33 "to": 541, 64.24/17.33 "label": "EVAL with clause\np(d(d(X173)), X174) :- ','(p(d(X173), X175), p(d(e(X175)), X174)).\nand substitutionX173 -> T138,\nT102 -> d(T138),\nX100 -> X176,\nX174 -> X176,\nT137 -> T138" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 534, 64.24/17.33 "to": 542, 64.24/17.33 "label": "EVAL-BACKTRACK" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 538, 64.24/17.33 "to": 512, 64.24/17.33 "label": "INSTANCE with matching:\nT119 -> T133\nX134 -> X165\nT120 -> T134\nX135 -> X164" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 541, 64.24/17.33 "to": 551, 64.24/17.33 "label": "SPLIT 1" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 541, 64.24/17.33 "to": 552, 64.24/17.33 "label": "SPLIT 2\nreplacements:X175 -> T139" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 551, 64.24/17.33 "to": 487, 64.24/17.33 "label": "INSTANCE with matching:\nT102 -> T138\nX100 -> X175" 64.24/17.33 }, 64.24/17.33 { 64.24/17.33 "from": 552, 64.24/17.33 "to": 487, 64.24/17.33 "label": "INSTANCE with matching:\nT102 -> e(T139)\nX100 -> X176" 64.24/17.33 } 64.24/17.33 ], 64.24/17.33 "type": "Graph" 64.24/17.33 } 64.24/17.33 } 64.24/17.33 64.24/17.33 ---------------------------------------- 64.24/17.33 64.24/17.33 (77) 64.24/17.33 Complex Obligation (AND) 64.24/17.33 64.24/17.33 ---------------------------------------- 64.24/17.33 64.24/17.33 (78) 64.24/17.33 Obligation: 64.24/17.33 Rules: 64.24/17.33 f491_in -> f497_in :|: TRUE 64.24/17.33 f498_out -> f491_out :|: TRUE 64.24/17.33 f491_in -> f498_in :|: TRUE 64.24/17.33 f497_out -> f491_out :|: TRUE 64.24/17.33 f512_out -> f538_out :|: TRUE 64.24/17.33 f538_in -> f512_in :|: TRUE 64.24/17.33 f541_out -> f534_out :|: TRUE 64.24/17.33 f542_out -> f534_out :|: TRUE 64.24/17.33 f534_in -> f542_in :|: TRUE 64.24/17.33 f534_in -> f541_in :|: TRUE 64.24/17.33 f498_in -> f507_in :|: TRUE 64.24/17.33 f498_in -> f506_in :|: TRUE 64.24/17.33 f506_out -> f498_out :|: TRUE 64.24/17.33 f507_out -> f498_out :|: TRUE 64.24/17.33 f533_in -> f538_in :|: TRUE 64.24/17.33 f540_out -> f533_out :|: TRUE 64.24/17.33 f533_in -> f540_in :|: TRUE 64.24/17.33 f538_out -> f533_out :|: TRUE 64.24/17.33 f551_out -> f552_in :|: TRUE 64.24/17.33 f541_in -> f551_in :|: TRUE 64.24/17.33 f552_out -> f541_out :|: TRUE 64.24/17.33 f529_out -> f530_in :|: TRUE 64.24/17.33 f512_in -> f529_in :|: TRUE 64.24/17.33 f530_out -> f512_out :|: TRUE 64.24/17.33 f487_out -> f552_out :|: TRUE 64.24/17.33 f552_in -> f487_in :|: TRUE 64.24/17.33 f551_in -> f487_in :|: TRUE 64.24/17.33 f487_out -> f551_out :|: TRUE 64.24/17.33 f490_out -> f489_out :|: TRUE 64.24/17.33 f491_out -> f489_out :|: TRUE 64.24/17.33 f489_in -> f491_in :|: TRUE 64.24/17.33 f489_in -> f490_in :|: TRUE 64.24/17.33 f512_out -> f506_out :|: TRUE 64.24/17.33 f513_out -> f506_out :|: TRUE 64.24/17.33 f506_in -> f512_in :|: TRUE 64.24/17.33 f506_in -> f513_in :|: TRUE 64.24/17.33 f487_in -> f489_in :|: TRUE 64.24/17.33 f489_out -> f487_out :|: TRUE 64.24/17.33 f533_out -> f507_out :|: TRUE 64.24/17.33 f507_in -> f533_in :|: TRUE 64.24/17.33 f507_in -> f534_in :|: TRUE 64.24/17.33 f534_out -> f507_out :|: TRUE 64.24/17.33 f529_in -> f487_in :|: TRUE 64.24/17.33 f487_out -> f529_out :|: TRUE 64.24/17.33 f487_out -> f530_out :|: TRUE 64.24/17.33 f530_in -> f487_in :|: TRUE 64.24/17.33 f28_out(T2) -> f27_out(T2) :|: TRUE 64.24/17.33 f27_in(x) -> f28_in(x) :|: TRUE 64.24/17.33 f31_out(x1) -> f28_out(x1) :|: TRUE 64.24/17.33 f28_in(x2) -> f32_in(x2) :|: TRUE 64.24/17.33 f32_out(x3) -> f28_out(x3) :|: TRUE 64.24/17.33 f28_in(x4) -> f31_in(x4) :|: TRUE 64.24/17.33 f32_in(x5) -> f133_in(x5) :|: TRUE 64.24/17.33 f32_in(x6) -> f132_in(x6) :|: TRUE 64.24/17.33 f132_out(x7) -> f32_out(x7) :|: TRUE 64.24/17.33 f133_out(x8) -> f32_out(x8) :|: TRUE 64.24/17.33 f133_in(x9) -> f248_in(x9) :|: TRUE 64.24/17.33 f249_out(x10) -> f133_out(x10) :|: TRUE 64.24/17.33 f133_in(x11) -> f249_in(x11) :|: TRUE 64.24/17.33 f248_out(x12) -> f133_out(x12) :|: TRUE 64.24/17.33 f373_out(x13) -> f249_out(x13) :|: TRUE 64.24/17.33 f372_out(x14) -> f249_out(x14) :|: TRUE 64.24/17.33 f249_in(x15) -> f372_in(x15) :|: TRUE 64.24/17.33 f249_in(x16) -> f373_in(x16) :|: TRUE 64.24/17.33 f373_in(x17) -> f486_in :|: TRUE 64.24/17.33 f485_out(T101) -> f373_out(T101) :|: TRUE 64.24/17.33 f486_out -> f373_out(x18) :|: TRUE 64.24/17.33 f373_in(x19) -> f485_in(x19) :|: TRUE 64.24/17.33 f488_out(x20) -> f485_out(x20) :|: TRUE 64.24/17.33 f487_out -> f488_in(x21) :|: TRUE 64.24/17.33 f485_in(x22) -> f487_in :|: TRUE 64.24/17.33 Start term: f27_in(T2) 64.24/17.33 64.24/17.33 ---------------------------------------- 64.24/17.33 64.24/17.33 (79) IRSwTSimpleDependencyGraphProof (EQUIVALENT) 64.24/17.33 Constructed simple dependency graph. 64.24/17.33 64.24/17.33 Simplified to the following IRSwTs: 64.24/17.33 64.24/17.33 intTRSProblem: 64.24/17.33 f491_in -> f498_in :|: TRUE 64.24/17.33 f538_in -> f512_in :|: TRUE 64.24/17.33 f534_in -> f541_in :|: TRUE 64.24/17.33 f498_in -> f507_in :|: TRUE 64.24/17.33 f498_in -> f506_in :|: TRUE 64.24/17.33 f533_in -> f538_in :|: TRUE 64.24/17.33 f541_in -> f551_in :|: TRUE 64.24/17.33 f512_in -> f529_in :|: TRUE 64.24/17.33 f551_in -> f487_in :|: TRUE 64.24/17.33 f489_in -> f491_in :|: TRUE 64.24/17.33 f506_in -> f512_in :|: TRUE 64.24/17.33 f487_in -> f489_in :|: TRUE 64.24/17.33 f507_in -> f533_in :|: TRUE 64.24/17.33 f507_in -> f534_in :|: TRUE 64.24/17.33 f529_in -> f487_in :|: TRUE 64.24/17.33 64.24/17.33 64.24/17.33 ---------------------------------------- 64.24/17.33 64.24/17.33 (80) 64.24/17.33 Obligation: 64.24/17.33 Rules: 64.24/17.33 f491_in -> f498_in :|: TRUE 64.24/17.33 f538_in -> f512_in :|: TRUE 64.24/17.33 f534_in -> f541_in :|: TRUE 64.24/17.33 f498_in -> f507_in :|: TRUE 64.24/17.33 f498_in -> f506_in :|: TRUE 64.24/17.33 f533_in -> f538_in :|: TRUE 64.24/17.33 f541_in -> f551_in :|: TRUE 64.24/17.33 f512_in -> f529_in :|: TRUE 64.24/17.33 f551_in -> f487_in :|: TRUE 64.24/17.33 f489_in -> f491_in :|: TRUE 64.24/17.33 f506_in -> f512_in :|: TRUE 64.24/17.33 f487_in -> f489_in :|: TRUE 64.24/17.33 f507_in -> f533_in :|: TRUE 64.24/17.33 f507_in -> f534_in :|: TRUE 64.24/17.33 f529_in -> f487_in :|: TRUE 64.24/17.33 64.24/17.33 ---------------------------------------- 64.24/17.33 64.24/17.33 (81) IntTRSCompressionProof (EQUIVALENT) 64.24/17.33 Compressed rules. 64.24/17.33 ---------------------------------------- 64.24/17.33 64.24/17.33 (82) 64.24/17.33 Obligation: 64.24/17.33 Rules: 64.24/17.33 f489_in -> f489_in :|: TRUE 64.24/17.33 64.24/17.33 ---------------------------------------- 64.24/17.33 64.24/17.33 (83) IRSFormatTransformerProof (EQUIVALENT) 64.24/17.33 Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). 64.24/17.33 ---------------------------------------- 64.24/17.33 64.24/17.33 (84) 64.24/17.33 Obligation: 64.24/17.33 Rules: 64.24/17.33 f489_in -> f489_in :|: TRUE 64.24/17.33 64.24/17.33 ---------------------------------------- 64.24/17.33 64.24/17.33 (85) IRSwTTerminationDigraphProof (EQUIVALENT) 64.24/17.33 Constructed termination digraph! 64.24/17.33 Nodes: 64.24/17.33 (1) f489_in -> f489_in :|: TRUE 64.24/17.33 64.24/17.33 Arcs: 64.24/17.33 (1) -> (1) 64.24/17.33 64.24/17.33 This digraph is fully evaluated! 64.24/17.33 ---------------------------------------- 64.24/17.33 64.24/17.33 (86) 64.24/17.33 Obligation: 64.24/17.33 64.24/17.33 Termination digraph: 64.24/17.33 Nodes: 64.24/17.33 (1) f489_in -> f489_in :|: TRUE 64.24/17.33 64.24/17.33 Arcs: 64.24/17.33 (1) -> (1) 64.24/17.33 64.24/17.33 This digraph is fully evaluated! 64.24/17.33 64.24/17.33 ---------------------------------------- 64.24/17.33 64.24/17.33 (87) FilterProof (EQUIVALENT) 64.24/17.33 Used the following sort dictionary for filtering: 64.24/17.33 f489_in() 64.24/17.33 Replaced non-predefined constructor symbols by 0. 64.24/17.33 ---------------------------------------- 64.24/17.33 64.24/17.33 (88) 64.24/17.33 Obligation: 64.24/17.33 Rules: 64.24/17.33 f489_in -> f489_in :|: TRUE 64.24/17.33 64.24/17.33 ---------------------------------------- 64.24/17.33 64.24/17.33 (89) IntTRSPeriodicNontermProof (COMPLETE) 64.24/17.33 Normalized system to the following form: 64.24/17.33 f(pc) -> f(1) :|: pc = 1 && TRUE 64.24/17.33 Witness term starting non-terminating reduction: f(1) 64.24/17.33 ---------------------------------------- 64.24/17.33 64.24/17.33 (90) 64.24/17.33 NO 64.24/17.33 64.24/17.33 ---------------------------------------- 64.24/17.33 64.24/17.33 (91) 64.24/17.33 Obligation: 64.24/17.33 Rules: 64.24/17.33 f388_in(T47, T50) -> f389_in(T47, T50) :|: TRUE 64.24/17.33 f389_out(x, x1) -> f388_out(x, x1) :|: TRUE 64.24/17.33 f392_out(T48, T49) -> f390_out(T48, T49) :|: TRUE 64.24/17.33 f391_out(x2, x3) -> f390_out(x2, x3) :|: TRUE 64.24/17.33 f390_in(x4, x5) -> f391_in(x4, x5) :|: TRUE 64.24/17.33 f390_in(x6, x7) -> f392_in(x6, x7) :|: TRUE 64.24/17.33 f450_out(x8, x9) -> f397_out(x8, x9) :|: TRUE 64.24/17.33 f451_out(x10, x11) -> f397_out(x10, x11) :|: TRUE 64.24/17.33 f397_in(x12, x13) -> f451_in(x12, x13) :|: TRUE 64.24/17.33 f397_in(x14, x15) -> f450_in(x14, x15) :|: TRUE 64.24/17.33 f478_out(T92, T95, T93, T94) -> f463_out(T92 * T93, T92 * T94 + T93 * T95) :|: TRUE 64.24/17.33 f463_in(x16, x17) -> f479_in :|: TRUE 64.24/17.33 f463_in(x18 * x19, x18 * x20 + x19 * x21) -> f478_in(x18, x21, x19, x20) :|: TRUE 64.24/17.33 f479_out -> f463_out(x22, x23) :|: TRUE 64.24/17.33 f397_out(x24, x25) -> f392_out(x24, x25) :|: TRUE 64.24/17.33 f396_out(x26, x27) -> f392_out(x26, x27) :|: TRUE 64.24/17.33 f392_in(x28, x29) -> f397_in(x28, x29) :|: TRUE 64.24/17.33 f392_in(x30, x31) -> f396_in(x30, x31) :|: TRUE 64.24/17.33 f390_out(x32, x33) -> f389_out(x32, x33) :|: TRUE 64.24/17.33 f389_in(x34, x35) -> f390_in(x34, x35) :|: TRUE 64.24/17.33 f386_in(x36, x37, x38, x39) -> f388_in(x36, x37) :|: TRUE 64.24/17.33 f388_out(x40, x41) -> f389_in(x42, x43) :|: TRUE 64.24/17.33 f389_out(x44, x45) -> f386_out(x46, x47, x44, x45) :|: TRUE 64.24/17.33 f478_in(x48, x49, x50, x51) -> f386_in(x48, x49, x50, x51) :|: TRUE 64.24/17.33 f386_out(x52, x53, x54, x55) -> f478_out(x52, x53, x54, x55) :|: TRUE 64.24/17.33 f455_out(T72, T74, T73, T75) -> f450_out(T72 + T73, T74 + T75) :|: TRUE 64.24/17.33 f450_in(x56 + x57, x58 + x59) -> f455_in(x56, x58, x57, x59) :|: TRUE 64.24/17.33 f450_in(x60, x61) -> f456_in :|: TRUE 64.24/17.33 f456_out -> f450_out(x62, x63) :|: TRUE 64.24/17.33 f463_out(x64, x65) -> f451_out(x64, x65) :|: TRUE 64.24/17.33 f464_out(x66, x67) -> f451_out(x66, x67) :|: TRUE 64.24/17.33 f451_in(x68, x69) -> f464_in(x68, x69) :|: TRUE 64.24/17.33 f451_in(x70, x71) -> f463_in(x70, x71) :|: TRUE 64.24/17.33 f455_in(x72, x73, x74, x75) -> f386_in(x72, x73, x74, x75) :|: TRUE 64.24/17.33 f386_out(x76, x77, x78, x79) -> f455_out(x76, x77, x78, x79) :|: TRUE 64.24/17.33 f28_out(T2) -> f27_out(T2) :|: TRUE 64.24/17.33 f27_in(x80) -> f28_in(x80) :|: TRUE 64.24/17.33 f31_out(x81) -> f28_out(x81) :|: TRUE 64.24/17.33 f28_in(x82) -> f32_in(x82) :|: TRUE 64.24/17.33 f32_out(x83) -> f28_out(x83) :|: TRUE 64.24/17.33 f28_in(x84) -> f31_in(x84) :|: TRUE 64.24/17.33 f32_in(x85) -> f133_in(x85) :|: TRUE 64.24/17.33 f32_in(x86) -> f132_in(x86) :|: TRUE 64.24/17.33 f132_out(x87) -> f32_out(x87) :|: TRUE 64.24/17.33 f133_out(x88) -> f32_out(x88) :|: TRUE 64.24/17.33 f133_in(x89) -> f248_in(x89) :|: TRUE 64.24/17.33 f249_out(x90) -> f133_out(x90) :|: TRUE 64.24/17.33 f133_in(x91) -> f249_in(x91) :|: TRUE 64.24/17.33 f248_out(x92) -> f133_out(x92) :|: TRUE 64.24/17.33 f373_out(x93) -> f249_out(x93) :|: TRUE 64.24/17.33 f372_out(x94) -> f249_out(x94) :|: TRUE 64.24/17.33 f249_in(x95) -> f372_in(x95) :|: TRUE 64.24/17.33 f249_in(x96) -> f373_in(x96) :|: TRUE 64.24/17.33 f386_out(x97, x98, x99, x100) -> f372_out(x97 * x100 + x99 * x98) :|: TRUE 64.24/17.33 f387_out -> f372_out(x101) :|: TRUE 64.24/17.33 f372_in(x102 * x103 + x104 * x105) -> f386_in(x102, x105, x104, x103) :|: TRUE 64.24/17.33 f372_in(x106) -> f387_in :|: TRUE 64.24/17.33 Start term: f27_in(T2) 64.24/17.33 64.24/17.33 ---------------------------------------- 64.24/17.33 64.24/17.33 (92) IRSwTSimpleDependencyGraphProof (EQUIVALENT) 64.24/17.33 Constructed simple dependency graph. 64.24/17.33 64.24/17.33 Simplified to the following IRSwTs: 64.24/17.33 64.24/17.33 intTRSProblem: 64.24/17.33 f388_in(T47, T50) -> f389_in(T47, T50) :|: TRUE 64.24/17.33 f390_in(x6, x7) -> f392_in(x6, x7) :|: TRUE 64.24/17.33 f397_in(x12, x13) -> f451_in(x12, x13) :|: TRUE 64.24/17.33 f397_in(x14, x15) -> f450_in(x14, x15) :|: TRUE 64.24/17.33 f463_in(x18 * x19, x18 * x20 + x19 * x21) -> f478_in(x18, x21, x19, x20) :|: TRUE 64.24/17.33 f392_in(x28, x29) -> f397_in(x28, x29) :|: TRUE 64.24/17.33 f389_in(x34, x35) -> f390_in(x34, x35) :|: TRUE 64.24/17.33 f386_in(x36, x37, x38, x39) -> f388_in(x36, x37) :|: TRUE 64.24/17.33 f478_in(x48, x49, x50, x51) -> f386_in(x48, x49, x50, x51) :|: TRUE 64.24/17.33 f450_in(x56 + x57, x58 + x59) -> f455_in(x56, x58, x57, x59) :|: TRUE 64.24/17.33 f451_in(x70, x71) -> f463_in(x70, x71) :|: TRUE 64.24/17.33 f455_in(x72, x73, x74, x75) -> f386_in(x72, x73, x74, x75) :|: TRUE 64.24/17.33 64.24/17.33 64.24/17.33 ---------------------------------------- 64.24/17.33 64.24/17.33 (93) 64.24/17.33 Obligation: 64.24/17.33 Rules: 64.24/17.33 f388_in(T47, T50) -> f389_in(T47, T50) :|: TRUE 64.24/17.33 f390_in(x6, x7) -> f392_in(x6, x7) :|: TRUE 64.24/17.33 f397_in(x12, x13) -> f451_in(x12, x13) :|: TRUE 64.24/17.33 f397_in(x14, x15) -> f450_in(x14, x15) :|: TRUE 64.24/17.33 f463_in(x18 * x19, x18 * x20 + x19 * x21) -> f478_in(x18, x21, x19, x20) :|: TRUE 64.24/17.33 f392_in(x28, x29) -> f397_in(x28, x29) :|: TRUE 64.24/17.33 f389_in(x34, x35) -> f390_in(x34, x35) :|: TRUE 64.24/17.36 f386_in(x36, x37, x38, x39) -> f388_in(x36, x37) :|: TRUE 64.24/17.36 f478_in(x48, x49, x50, x51) -> f386_in(x48, x49, x50, x51) :|: TRUE 64.24/17.36 f450_in(x56 + x57, x58 + x59) -> f455_in(x56, x58, x57, x59) :|: TRUE 64.24/17.36 f451_in(x70, x71) -> f463_in(x70, x71) :|: TRUE 64.24/17.36 f455_in(x72, x73, x74, x75) -> f386_in(x72, x73, x74, x75) :|: TRUE 64.24/17.36 64.24/17.36 ---------------------------------------- 64.24/17.36 64.24/17.36 (94) IntTRSCompressionProof (EQUIVALENT) 64.24/17.36 Compressed rules. 64.24/17.36 ---------------------------------------- 64.24/17.36 64.24/17.36 (95) 64.24/17.36 Obligation: 64.24/17.36 Rules: 64.24/17.36 f386_in(sum~x56:0~x57:0, sum~x58:0~x59:0, x38:0, x39:0) -> f386_in(x56:0, x58:0, x57:0, x59:0) :|: TRUE && sum~x56:0~x57:0 = x56:0 + x57:0 && sum~x58:0~x59:0 = x58:0 + x59:0 64.24/17.36 f386_in(x, x1, x2, x3) -> f386_in(x4, x5, x6, x7) :|: TRUE && x = x4 * x6 && x1 = x4 * x7 + x6 * x5 64.24/17.36 64.24/17.36 ---------------------------------------- 64.24/17.36 64.24/17.36 (96) IRSFormatTransformerProof (EQUIVALENT) 64.24/17.36 Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). 64.24/17.36 ---------------------------------------- 64.24/17.36 64.24/17.36 (97) 64.24/17.36 Obligation: 64.24/17.36 Rules: 64.24/17.36 f386_in(sum~x56:0~x57:0, sum~x58:0~x59:0, x38:0, x39:0) -> f386_in(x56:0, x58:0, x57:0, x59:0) :|: TRUE && sum~x56:0~x57:0 = x56:0 + x57:0 && sum~x58:0~x59:0 = x58:0 + x59:0 64.24/17.36 f386_in(x, x1, x2, x3) -> f386_in(x4, x5, x6, x7) :|: TRUE && x = x4 * x6 && x1 = x4 * x7 + x6 * x5 64.24/17.36 64.24/17.36 ---------------------------------------- 64.24/17.36 64.24/17.36 (98) IRSwTTerminationDigraphProof (EQUIVALENT) 64.24/17.36 Constructed termination digraph! 64.24/17.36 Nodes: 64.24/17.36 (1) f386_in(sum~x56:0~x57:0, sum~x58:0~x59:0, x38:0, x39:0) -> f386_in(x56:0, x58:0, x57:0, x59:0) :|: TRUE && sum~x56:0~x57:0 = x56:0 + x57:0 && sum~x58:0~x59:0 = x58:0 + x59:0 64.24/17.36 (2) f386_in(x, x1, x2, x3) -> f386_in(x4, x5, x6, x7) :|: TRUE && x = x4 * x6 && x1 = x4 * x7 + x6 * x5 64.24/17.36 64.24/17.36 Arcs: 64.24/17.36 (1) -> (1), (2) 64.24/17.36 (2) -> (1), (2) 64.24/17.36 64.24/17.36 This digraph is fully evaluated! 64.24/17.36 ---------------------------------------- 64.24/17.36 64.24/17.36 (99) 64.24/17.36 Obligation: 64.24/17.36 64.24/17.36 Termination digraph: 64.24/17.36 Nodes: 64.24/17.36 (1) f386_in(sum~x56:0~x57:0, sum~x58:0~x59:0, x38:0, x39:0) -> f386_in(x56:0, x58:0, x57:0, x59:0) :|: TRUE && sum~x56:0~x57:0 = x56:0 + x57:0 && sum~x58:0~x59:0 = x58:0 + x59:0 64.24/17.36 (2) f386_in(x, x1, x2, x3) -> f386_in(x4, x5, x6, x7) :|: TRUE && x = x4 * x6 && x1 = x4 * x7 + x6 * x5 64.24/17.36 64.24/17.36 Arcs: 64.24/17.36 (1) -> (1), (2) 64.24/17.36 (2) -> (1), (2) 64.24/17.36 64.24/17.36 This digraph is fully evaluated! 64.24/17.36 64.24/17.36 ---------------------------------------- 64.24/17.36 64.24/17.36 (100) IntTRSCompressionProof (EQUIVALENT) 64.24/17.36 Compressed rules. 64.24/17.36 ---------------------------------------- 64.24/17.36 64.24/17.36 (101) 64.24/17.36 Obligation: 64.24/17.36 Rules: 64.24/17.36 f386_in(times~x4:0~x6:0, sum~times~x4:0~x7:0~times~x6:0~x5:0, x2:0, x3:0) -> f386_in(x4:0, x5:0, x6:0, x7:0) :|: TRUE && times~x4:0~x6:0 = x4:0 * x6:0 && sum~times~x4:0~x7:0~times~x6:0~x5:0 = x4:0 * x7:0 + x6:0 * x5:0 64.24/17.36 f386_in(sum~x56:0:0~x57:0:0, sum~x58:0:0~x59:0:0, x38:0:0, x39:0:0) -> f386_in(x56:0:0, x58:0:0, x57:0:0, x59:0:0) :|: TRUE && sum~x56:0:0~x57:0:0 = x56:0:0 + x57:0:0 && sum~x58:0:0~x59:0:0 = x58:0:0 + x59:0:0 64.24/17.36 64.24/17.36 ---------------------------------------- 64.24/17.36 64.24/17.36 (102) IntTRSUnneededArgumentFilterProof (EQUIVALENT) 64.24/17.36 Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: 64.24/17.36 none 64.24/17.36 64.24/17.36 ---------------------------------------- 64.24/17.36 64.24/17.36 (103) 64.24/17.36 Obligation: 64.24/17.36 Rules: 64.24/17.36 f386_in(times~x4:0~x6:0, sum~times~x4:0~x7:0~times~x6:0~x5:0, x2:0, x3:0) -> f386_in(x4:0, x5:0, x6:0, x7:0) :|: TRUE && times~x4:0~x6:0 = x4:0 * x6:0 && sum~times~x4:0~x7:0~times~x6:0~x5:0 = x4:0 * x7:0 + x6:0 * x5:0 64.24/17.36 f386_in(sum~x56:0:0~x57:0:0, sum~x58:0:0~x59:0:0, x38:0:0, x39:0:0) -> f386_in(x56:0:0, x58:0:0, x57:0:0, x59:0:0) :|: TRUE && sum~x56:0:0~x57:0:0 = x56:0:0 + x57:0:0 && sum~x58:0:0~x59:0:0 = x58:0:0 + x59:0:0 64.24/17.36 64.24/17.36 ---------------------------------------- 64.24/17.36 64.24/17.36 (104) IRSwTToIntTRSProof (SOUND) 64.24/17.36 Applied path-length measure to transform intTRS with terms to intTRS. 64.24/17.36 ---------------------------------------- 64.24/17.36 64.24/17.36 (105) 64.24/17.36 Obligation: 64.24/17.36 Rules: 64.24/17.36 f386_in(times~x4~x6, sum~times~x4~x7~times~x6~x5, x2, x3) -> f386_in(x4, x5, x6, x7) :|: TRUE && times~x4~x6 = x4 * x6 && sum~times~x4~x7~times~x6~x5 = x4 * x7 + x6 * x5 64.24/17.36 f386_in(sum~x12~x14, sum~x13~x15, x10, x11) -> f386_in(x12, x13, x14, x15) :|: TRUE && sum~x12~x14 = x12 + x14 && sum~x13~x15 = x13 + x15 64.24/17.36 64.24/17.36 ---------------------------------------- 64.24/17.36 64.24/17.36 (106) IntTRSCompressionProof (EQUIVALENT) 64.24/17.36 Compressed rules. 64.24/17.36 ---------------------------------------- 64.24/17.36 64.24/17.36 (107) 64.24/17.36 Obligation: 64.24/17.36 Rules: 64.24/17.36 f386_in(times~x4:0~x6:0, sum~times~x4:0~x7:0~times~x6:0~x5:0, x2:0, x3:0) -> f386_in(x4:0, x5:0, x6:0, x7:0) :|: TRUE && times~x4:0~x6:0 = x4:0 * x6:0 && sum~times~x4:0~x7:0~times~x6:0~x5:0 = x4:0 * x7:0 + x6:0 * x5:0 64.24/17.36 f386_in(sum~x12:0~x14:0, sum~x13:0~x15:0, x10:0, x11:0) -> f386_in(x12:0, x13:0, x14:0, x15:0) :|: TRUE && sum~x12:0~x14:0 = x12:0 + x14:0 && sum~x13:0~x15:0 = x13:0 + x15:0 64.24/17.36 64.24/17.36 ---------------------------------------- 64.24/17.36 64.24/17.36 (108) IntTRSUnneededArgumentFilterProof (EQUIVALENT) 64.24/17.36 Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: 64.24/17.36 none 64.24/17.36 64.24/17.36 ---------------------------------------- 64.24/17.36 64.24/17.36 (109) 64.24/17.36 Obligation: 64.24/17.36 Rules: 64.24/17.36 f386_in(times~x4:0~x6:0, sum~times~x4:0~x7:0~times~x6:0~x5:0, x2:0, x3:0) -> f386_in(x4:0, x5:0, x6:0, x7:0) :|: TRUE && times~x4:0~x6:0 = x4:0 * x6:0 && sum~times~x4:0~x7:0~times~x6:0~x5:0 = x4:0 * x7:0 + x6:0 * x5:0 64.24/17.36 f386_in(sum~x12:0~x14:0, sum~x13:0~x15:0, x10:0, x11:0) -> f386_in(x12:0, x13:0, x14:0, x15:0) :|: TRUE && sum~x12:0~x14:0 = x12:0 + x14:0 && sum~x13:0~x15:0 = x13:0 + x15:0 64.24/17.36 64.24/17.36 ---------------------------------------- 64.24/17.36 64.24/17.36 (110) IntTRSPeriodicNontermProof (COMPLETE) 64.24/17.36 Normalized system to the following form: 64.24/17.36 f(pc, times~x4:0~x6:0, sum~times~x4:0~x7:0~times~x6:0~x5:0, x2:0, x3:0) -> f(1, x4:0, x5:0, x6:0, x7:0) :|: pc = 1 && (TRUE && times~x4:0~x6:0 = x4:0 * x6:0 && sum~times~x4:0~x7:0~times~x6:0~x5:0 = x4:0 * x7:0 + x6:0 * x5:0) 64.24/17.36 f(pc, sum~x12:0~x14:0, sum~x13:0~x15:0, x10:0, x11:0) -> f(1, x12:0, x13:0, x14:0, x15:0) :|: pc = 1 && (TRUE && sum~x12:0~x14:0 = x12:0 + x14:0 && sum~x13:0~x15:0 = x13:0 + x15:0) 64.24/17.36 Witness term starting non-terminating reduction: f(1, 0, 4, -3, -3) 64.24/17.36 ---------------------------------------- 64.24/17.36 64.24/17.36 (111) 64.24/17.36 NO 64.24/17.36 64.24/17.36 ---------------------------------------- 64.24/17.36 64.24/17.36 (112) 64.24/17.36 Obligation: 64.24/17.36 Rules: 64.24/17.36 f488_out(T101) -> f485_out(T101) :|: TRUE 64.24/17.36 f487_out -> f488_in(x) :|: TRUE 64.24/17.36 f485_in(x1) -> f487_in :|: TRUE 64.24/17.36 f491_in -> f497_in :|: TRUE 64.24/17.36 f498_out -> f491_out :|: TRUE 64.24/17.36 f491_in -> f498_in :|: TRUE 64.24/17.36 f497_out -> f491_out :|: TRUE 64.24/17.36 f541_out -> f534_out :|: TRUE 64.24/17.36 f542_out -> f534_out :|: TRUE 64.24/17.36 f534_in -> f542_in :|: TRUE 64.24/17.36 f534_in -> f541_in :|: TRUE 64.24/17.36 f373_out(T2) -> f249_out(T2) :|: TRUE 64.24/17.36 f372_out(x2) -> f249_out(x2) :|: TRUE 64.24/17.36 f249_in(x3) -> f372_in(x3) :|: TRUE 64.24/17.36 f249_in(x4) -> f373_in(x4) :|: TRUE 64.24/17.36 f498_in -> f507_in :|: TRUE 64.24/17.36 f498_in -> f506_in :|: TRUE 64.24/17.36 f506_out -> f498_out :|: TRUE 64.24/17.36 f507_out -> f498_out :|: TRUE 64.24/17.36 f373_in(x5) -> f486_in :|: TRUE 64.24/17.36 f485_out(x6) -> f373_out(x6) :|: TRUE 64.24/17.36 f486_out -> f373_out(x7) :|: TRUE 64.24/17.36 f373_in(x8) -> f485_in(x8) :|: TRUE 64.24/17.36 f533_in -> f538_in :|: TRUE 64.24/17.36 f540_out -> f533_out :|: TRUE 64.24/17.36 f533_in -> f540_in :|: TRUE 64.24/17.36 f538_out -> f533_out :|: TRUE 64.24/17.36 f32_in(x9) -> f133_in(x9) :|: TRUE 64.24/17.36 f32_in(x10) -> f132_in(x10) :|: TRUE 64.24/17.36 f132_out(x11) -> f32_out(x11) :|: TRUE 64.24/17.36 f133_out(x12) -> f32_out(x12) :|: TRUE 64.24/17.36 f31_out(x13) -> f28_out(x13) :|: TRUE 64.24/17.36 f28_in(x14) -> f32_in(x14) :|: TRUE 64.24/17.36 f32_out(x15) -> f28_out(x15) :|: TRUE 64.24/17.36 f28_in(x16) -> f31_in(x16) :|: TRUE 64.24/17.36 f529_out -> f530_in :|: TRUE 64.24/17.36 f512_in -> f529_in :|: TRUE 64.24/17.36 f530_out -> f512_out :|: TRUE 64.24/17.36 f345_out(T26) -> f346_in(T27) :|: TRUE 64.24/17.36 f339_in(x17, x18) -> f345_in(x17) :|: TRUE 64.24/17.36 f346_out(x19) -> f339_out(x20, x19) :|: TRUE 64.24/17.36 f487_in -> f489_in :|: TRUE 64.24/17.36 f489_out -> f487_out :|: TRUE 64.24/17.36 f490_out -> f489_out :|: TRUE 64.24/17.36 f491_out -> f489_out :|: TRUE 64.24/17.36 f489_in -> f491_in :|: TRUE 64.24/17.36 f489_in -> f490_in :|: TRUE 64.24/17.36 f512_out -> f506_out :|: TRUE 64.24/17.36 f513_out -> f506_out :|: TRUE 64.24/17.36 f506_in -> f512_in :|: TRUE 64.24/17.36 f506_in -> f513_in :|: TRUE 64.24/17.36 f533_out -> f507_out :|: TRUE 64.24/17.36 f507_in -> f533_in :|: TRUE 64.24/17.36 f507_in -> f534_in :|: TRUE 64.24/17.36 f534_out -> f507_out :|: TRUE 64.24/17.36 f529_in -> f487_in :|: TRUE 64.24/17.36 f487_out -> f529_out :|: TRUE 64.24/17.36 f487_out -> f530_out :|: TRUE 64.24/17.36 f530_in -> f487_in :|: TRUE 64.24/17.36 f500_out -> f497_out :|: TRUE 64.24/17.36 f497_in -> f500_in :|: TRUE 64.24/17.36 f499_out -> f497_out :|: TRUE 64.24/17.36 f497_in -> f499_in :|: TRUE 64.24/17.36 f248_in(x21 + x22) -> f339_in(x21, x22) :|: TRUE 64.24/17.36 f341_out -> f248_out(x23) :|: TRUE 64.24/17.36 f248_in(x24) -> f341_in :|: TRUE 64.24/17.36 f339_out(x25, x26) -> f248_out(x25 + x26) :|: TRUE 64.55/17.39 f345_in(x27) -> f27_in(x27) :|: TRUE 64.55/17.39 f27_out(x28) -> f345_out(x28) :|: TRUE 64.55/17.39 f512_out -> f538_out :|: TRUE 64.55/17.39 f538_in -> f512_in :|: TRUE 64.55/17.39 f28_out(x29) -> f27_out(x29) :|: TRUE 64.55/17.39 f27_in(x30) -> f28_in(x30) :|: TRUE 64.55/17.39 f492_out -> f490_out :|: TRUE 64.55/17.39 f490_in -> f493_in :|: TRUE 64.55/17.39 f493_out -> f490_out :|: TRUE 64.55/17.39 f490_in -> f492_in :|: TRUE 64.55/17.39 f551_out -> f552_in :|: TRUE 64.55/17.39 f541_in -> f551_in :|: TRUE 64.55/17.39 f552_out -> f541_out :|: TRUE 64.55/17.39 f133_in(x31) -> f248_in(x31) :|: TRUE 64.55/17.39 f249_out(x32) -> f133_out(x32) :|: TRUE 64.55/17.39 f133_in(x33) -> f249_in(x33) :|: TRUE 64.55/17.39 f248_out(x34) -> f133_out(x34) :|: TRUE 64.55/17.39 f27_out(x35) -> f346_out(x35) :|: TRUE 64.55/17.39 f346_in(x36) -> f27_in(x36) :|: TRUE 64.55/17.39 f487_out -> f552_out :|: TRUE 64.55/17.39 f552_in -> f487_in :|: TRUE 64.55/17.39 f499_in -> f499_out :|: TRUE 64.55/17.39 f27_out(x37) -> f488_out(x37) :|: TRUE 64.55/17.39 f488_in(x38) -> f27_in(x38) :|: TRUE 64.55/17.39 f551_in -> f487_in :|: TRUE 64.55/17.39 f487_out -> f551_out :|: TRUE 64.55/17.39 f492_in -> f492_out :|: TRUE 64.55/17.39 Start term: f27_in(T2) 64.55/17.39 64.55/17.39 ---------------------------------------- 64.55/17.39 64.55/17.39 (113) IRSwTSimpleDependencyGraphProof (EQUIVALENT) 64.55/17.39 Constructed simple dependency graph. 64.55/17.39 64.55/17.39 Simplified to the following IRSwTs: 64.55/17.39 64.55/17.39 intTRSProblem: 64.55/17.39 f487_out -> f488_in(x) :|: TRUE 64.55/17.39 f485_in(x1) -> f487_in :|: TRUE 64.55/17.39 f491_in -> f497_in :|: TRUE 64.55/17.39 f498_out -> f491_out :|: TRUE 64.55/17.39 f491_in -> f498_in :|: TRUE 64.55/17.39 f497_out -> f491_out :|: TRUE 64.55/17.39 f541_out -> f534_out :|: TRUE 64.55/17.39 f534_in -> f541_in :|: TRUE 64.55/17.39 f249_in(x4) -> f373_in(x4) :|: TRUE 64.55/17.39 f498_in -> f507_in :|: TRUE 64.55/17.39 f498_in -> f506_in :|: TRUE 64.55/17.39 f506_out -> f498_out :|: TRUE 64.55/17.39 f507_out -> f498_out :|: TRUE 64.55/17.39 f373_in(x8) -> f485_in(x8) :|: TRUE 64.55/17.39 f533_in -> f538_in :|: TRUE 64.55/17.39 f538_out -> f533_out :|: TRUE 64.55/17.39 f32_in(x9) -> f133_in(x9) :|: TRUE 64.55/17.39 f28_in(x14) -> f32_in(x14) :|: TRUE 64.55/17.39 f529_out -> f530_in :|: TRUE 64.55/17.39 f512_in -> f529_in :|: TRUE 64.55/17.39 f530_out -> f512_out :|: TRUE 64.55/17.39 f339_in(x17, x18) -> f345_in(x17) :|: TRUE 64.55/17.39 f487_in -> f489_in :|: TRUE 64.55/17.39 f489_out -> f487_out :|: TRUE 64.55/17.39 f490_out -> f489_out :|: TRUE 64.55/17.39 f491_out -> f489_out :|: TRUE 64.55/17.39 f489_in -> f491_in :|: TRUE 64.55/17.39 f489_in -> f490_in :|: TRUE 64.55/17.39 f512_out -> f506_out :|: TRUE 64.55/17.39 f506_in -> f512_in :|: TRUE 64.55/17.39 f533_out -> f507_out :|: TRUE 64.55/17.39 f507_in -> f533_in :|: TRUE 64.55/17.39 f507_in -> f534_in :|: TRUE 64.55/17.39 f534_out -> f507_out :|: TRUE 64.55/17.39 f529_in -> f487_in :|: TRUE 64.55/17.39 f487_out -> f529_out :|: TRUE 64.55/17.39 f487_out -> f530_out :|: TRUE 64.55/17.39 f530_in -> f487_in :|: TRUE 64.55/17.39 f499_out -> f497_out :|: TRUE 64.55/17.39 f497_in -> f499_in :|: TRUE 64.55/17.39 f248_in(x21 + x22) -> f339_in(x21, x22) :|: TRUE 64.55/17.39 f345_in(x27) -> f27_in(x27) :|: TRUE 64.55/17.39 f512_out -> f538_out :|: TRUE 64.55/17.39 f538_in -> f512_in :|: TRUE 64.55/17.39 f27_in(x30) -> f28_in(x30) :|: TRUE 64.55/17.39 f492_out -> f490_out :|: TRUE 64.55/17.39 f490_in -> f492_in :|: TRUE 64.55/17.39 f551_out -> f552_in :|: TRUE 64.55/17.39 f541_in -> f551_in :|: TRUE 64.55/17.39 f552_out -> f541_out :|: TRUE 64.55/17.39 f133_in(x31) -> f248_in(x31) :|: TRUE 64.55/17.39 f133_in(x33) -> f249_in(x33) :|: TRUE 64.55/17.39 f487_out -> f552_out :|: TRUE 64.55/17.39 f552_in -> f487_in :|: TRUE 64.55/17.39 f499_in -> f499_out :|: TRUE 64.55/17.39 f488_in(x38) -> f27_in(x38) :|: TRUE 64.55/17.39 f551_in -> f487_in :|: TRUE 64.55/17.39 f487_out -> f551_out :|: TRUE 64.55/17.39 f492_in -> f492_out :|: TRUE 64.55/17.39 64.55/17.39 64.55/17.39 ---------------------------------------- 64.55/17.39 64.55/17.39 (114) 64.55/17.39 Obligation: 64.55/17.39 Rules: 64.55/17.39 f487_out -> f488_in(x) :|: TRUE 64.55/17.39 f485_in(x1) -> f487_in :|: TRUE 64.55/17.39 f491_in -> f497_in :|: TRUE 64.55/17.39 f498_out -> f491_out :|: TRUE 64.55/17.39 f491_in -> f498_in :|: TRUE 64.55/17.39 f497_out -> f491_out :|: TRUE 64.55/17.39 f541_out -> f534_out :|: TRUE 64.55/17.39 f534_in -> f541_in :|: TRUE 64.55/17.39 f249_in(x4) -> f373_in(x4) :|: TRUE 64.55/17.39 f498_in -> f507_in :|: TRUE 64.55/17.39 f498_in -> f506_in :|: TRUE 64.55/17.39 f506_out -> f498_out :|: TRUE 64.55/17.39 f507_out -> f498_out :|: TRUE 64.55/17.39 f373_in(x8) -> f485_in(x8) :|: TRUE 64.55/17.39 f533_in -> f538_in :|: TRUE 64.55/17.39 f538_out -> f533_out :|: TRUE 64.55/17.39 f32_in(x9) -> f133_in(x9) :|: TRUE 64.55/17.39 f28_in(x14) -> f32_in(x14) :|: TRUE 64.55/17.39 f529_out -> f530_in :|: TRUE 64.55/17.39 f512_in -> f529_in :|: TRUE 64.55/17.39 f530_out -> f512_out :|: TRUE 64.55/17.39 f339_in(x17, x18) -> f345_in(x17) :|: TRUE 64.55/17.39 f487_in -> f489_in :|: TRUE 64.55/17.39 f489_out -> f487_out :|: TRUE 64.55/17.39 f490_out -> f489_out :|: TRUE 64.55/17.39 f491_out -> f489_out :|: TRUE 64.55/17.39 f489_in -> f491_in :|: TRUE 64.55/17.39 f489_in -> f490_in :|: TRUE 64.55/17.39 f512_out -> f506_out :|: TRUE 64.55/17.39 f506_in -> f512_in :|: TRUE 64.55/17.39 f533_out -> f507_out :|: TRUE 64.55/17.39 f507_in -> f533_in :|: TRUE 64.55/17.39 f507_in -> f534_in :|: TRUE 64.55/17.39 f534_out -> f507_out :|: TRUE 64.55/17.39 f529_in -> f487_in :|: TRUE 64.55/17.39 f487_out -> f529_out :|: TRUE 64.55/17.39 f487_out -> f530_out :|: TRUE 64.55/17.39 f530_in -> f487_in :|: TRUE 64.55/17.39 f499_out -> f497_out :|: TRUE 64.55/17.39 f497_in -> f499_in :|: TRUE 64.55/17.39 f248_in(x21 + x22) -> f339_in(x21, x22) :|: TRUE 64.55/17.39 f345_in(x27) -> f27_in(x27) :|: TRUE 64.55/17.39 f512_out -> f538_out :|: TRUE 64.55/17.39 f538_in -> f512_in :|: TRUE 64.55/17.39 f27_in(x30) -> f28_in(x30) :|: TRUE 64.55/17.39 f492_out -> f490_out :|: TRUE 64.55/17.39 f490_in -> f492_in :|: TRUE 64.55/17.39 f551_out -> f552_in :|: TRUE 64.55/17.39 f541_in -> f551_in :|: TRUE 64.55/17.39 f552_out -> f541_out :|: TRUE 64.55/17.39 f133_in(x31) -> f248_in(x31) :|: TRUE 64.55/17.39 f133_in(x33) -> f249_in(x33) :|: TRUE 64.55/17.39 f487_out -> f552_out :|: TRUE 64.55/17.39 f552_in -> f487_in :|: TRUE 64.55/17.39 f499_in -> f499_out :|: TRUE 64.55/17.39 f488_in(x38) -> f27_in(x38) :|: TRUE 64.55/17.39 f551_in -> f487_in :|: TRUE 64.55/17.39 f487_out -> f551_out :|: TRUE 64.55/17.39 f492_in -> f492_out :|: TRUE 64.55/17.39 64.55/17.39 ---------------------------------------- 64.55/17.39 64.55/17.39 (115) PrologToDTProblemTransformerProof (SOUND) 64.55/17.39 Built DT problem from termination graph DT10. 64.55/17.39 64.55/17.39 { 64.55/17.39 "root": 33, 64.55/17.39 "program": { 64.55/17.39 "directives": [], 64.55/17.39 "clauses": [ 64.55/17.39 [ 64.55/17.39 "(p (d (e (t))) (const (1)))", 64.55/17.39 null 64.55/17.39 ], 64.55/17.39 [ 64.55/17.39 "(p (d (e (const A))) (const (0)))", 64.55/17.39 null 64.55/17.39 ], 64.55/17.39 [ 64.55/17.39 "(p (d (e (+ X Y))) (+ DX DY))", 64.55/17.39 "(',' (p (d (e X)) DX) (p (d (e Y)) DY))" 64.55/17.39 ], 64.55/17.39 [ 64.55/17.39 "(p (d (e (* X Y))) (+ (* X DY) (* Y DX)))", 64.55/17.39 "(',' (p (d (e X)) DX) (p (d (e Y)) DY))" 64.55/17.39 ], 64.55/17.39 [ 64.55/17.39 "(p (d (d X)) DDX)", 64.55/17.39 "(',' (p (d X) DX) (p (d (e DX)) DDX))" 64.55/17.39 ] 64.55/17.39 ] 64.55/17.39 }, 64.55/17.39 "graph": { 64.55/17.39 "nodes": { 64.55/17.39 "473": { 64.55/17.39 "goal": [{ 64.55/17.39 "clause": -1, 64.55/17.39 "scope": -1, 64.55/17.39 "term": "(',' (',' (p (d (e T73)) X146) (p (d (e T74)) X145)) (p (d (e (+ (* T73 X145) (* T74 X146)))) (const (1))))" 64.55/17.39 }], 64.55/17.39 "kb": { 64.55/17.39 "nonunifying": [], 64.55/17.39 "intvars": {}, 64.55/17.39 "arithmetic": { 64.55/17.39 "type": "PlainIntegerRelationState", 64.55/17.39 "relations": [] 64.55/17.39 }, 64.55/17.39 "ground": [], 64.55/17.39 "free": [ 64.55/17.39 "X145", 64.55/17.39 "X146" 64.55/17.39 ], 64.55/17.39 "exprvars": [] 64.55/17.39 } 64.55/17.39 }, 64.55/17.39 "474": { 64.55/17.39 "goal": [], 64.55/17.39 "kb": { 64.55/17.39 "nonunifying": [], 64.55/17.39 "intvars": {}, 64.55/17.39 "arithmetic": { 64.55/17.39 "type": "PlainIntegerRelationState", 64.55/17.39 "relations": [] 64.55/17.39 }, 64.55/17.39 "ground": [], 64.55/17.39 "free": [], 64.55/17.39 "exprvars": [] 64.55/17.39 } 64.55/17.39 }, 64.55/17.39 "236": { 64.55/17.39 "goal": [{ 64.55/17.39 "clause": 2, 64.55/17.39 "scope": 2, 64.55/17.39 "term": "(',' (p (d T10) X14) (p (d (e X14)) (const (1))))" 64.55/17.39 }], 64.55/17.39 "kb": { 64.55/17.39 "nonunifying": [], 64.55/17.39 "intvars": {}, 64.55/17.39 "arithmetic": { 64.55/17.39 "type": "PlainIntegerRelationState", 64.55/17.39 "relations": [] 64.55/17.39 }, 64.55/17.39 "ground": [], 64.55/17.39 "free": ["X14"], 64.55/17.39 "exprvars": [] 64.55/17.39 } 64.55/17.39 }, 64.55/17.39 "238": { 64.55/17.39 "goal": [ 64.55/17.39 { 64.55/17.39 "clause": 3, 64.55/17.39 "scope": 2, 64.55/17.39 "term": "(',' (p (d T10) X14) (p (d (e X14)) (const (1))))" 64.55/17.39 }, 64.55/17.39 { 64.55/17.39 "clause": 4, 64.55/17.39 "scope": 2, 64.55/17.39 "term": "(',' (p (d T10) X14) (p (d (e X14)) (const (1))))" 64.55/17.39 } 64.55/17.39 ], 64.55/17.39 "kb": { 64.55/17.39 "nonunifying": [], 64.55/17.39 "intvars": {}, 64.55/17.39 "arithmetic": { 64.55/17.39 "type": "PlainIntegerRelationState", 64.55/17.39 "relations": [] 64.55/17.39 }, 64.55/17.39 "ground": [], 64.55/17.39 "free": ["X14"], 64.55/17.39 "exprvars": [] 64.55/17.39 } 64.55/17.39 }, 64.55/17.39 "480": { 64.55/17.39 "goal": [{ 64.55/17.39 "clause": -1, 64.55/17.39 "scope": -1, 64.55/17.39 "term": "(p (d (e T73)) X146)" 64.55/17.39 }], 64.55/17.39 "kb": { 64.55/17.39 "nonunifying": [], 64.55/17.39 "intvars": {}, 64.55/17.39 "arithmetic": { 64.55/17.39 "type": "PlainIntegerRelationState", 64.55/17.39 "relations": [] 64.55/17.39 }, 64.55/17.39 "ground": [], 64.55/17.39 "free": ["X146"], 64.55/17.39 "exprvars": [] 64.55/17.39 } 64.55/17.39 }, 64.55/17.39 "481": { 64.55/17.39 "goal": [{ 64.55/17.39 "clause": -1, 64.55/17.39 "scope": -1, 64.55/17.39 "term": "(',' (p (d (e T76)) X145) (p (d (e (+ (* T77 X145) (* T76 T75)))) (const (1))))" 64.55/17.39 }], 64.55/17.39 "kb": { 64.55/17.39 "nonunifying": [], 64.55/17.39 "intvars": {}, 64.55/17.39 "arithmetic": { 64.55/17.39 "type": "PlainIntegerRelationState", 64.55/17.39 "relations": [] 64.55/17.39 }, 64.55/17.39 "ground": [], 64.55/17.39 "free": ["X145"], 64.55/17.39 "exprvars": [] 64.55/17.39 } 64.55/17.39 }, 64.55/17.39 "815": { 64.55/17.39 "goal": [{ 64.55/17.39 "clause": -1, 64.55/17.39 "scope": -1, 64.55/17.39 "term": "(p (d (e (+ T365 T364))) T342)" 64.55/17.39 }], 64.55/17.39 "kb": { 64.55/17.39 "nonunifying": [ 64.55/17.39 [ 64.55/17.39 "(p T366 T342)", 64.55/17.39 "(p (d (e (t))) (const (1)))" 64.55/17.39 ], 64.55/17.39 [ 64.55/17.39 "(p T366 T342)", 64.55/17.39 "(p (d (e (const X235))) (const (0)))" 64.55/17.39 ], 64.55/17.39 [ 64.55/17.39 "(p T366 T342)", 64.55/17.39 "(p (d (e (+ X329 X330))) (+ X331 X332))" 64.55/17.39 ], 64.55/17.39 [ 64.55/17.39 "(p T366 T342)", 64.55/17.39 "(p (d (e (* X412 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64.55/17.43 }, 64.55/17.43 "221": { 64.55/17.43 "goal": [ 64.55/17.43 { 64.55/17.43 "clause": 2, 64.55/17.43 "scope": 2, 64.55/17.43 "term": "(',' (p (d T10) X14) (p (d (e X14)) (const (1))))" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "clause": 3, 64.55/17.43 "scope": 2, 64.55/17.43 "term": "(',' (p (d T10) X14) (p (d (e X14)) (const (1))))" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "clause": 4, 64.55/17.43 "scope": 2, 64.55/17.43 "term": "(',' (p (d T10) X14) (p (d (e X14)) (const (1))))" 64.55/17.43 } 64.55/17.43 ], 64.55/17.43 "kb": { 64.55/17.43 "nonunifying": [], 64.55/17.43 "intvars": {}, 64.55/17.43 "arithmetic": { 64.55/17.43 "type": "PlainIntegerRelationState", 64.55/17.43 "relations": [] 64.55/17.43 }, 64.55/17.43 "ground": [], 64.55/17.43 "free": ["X14"], 64.55/17.43 "exprvars": [] 64.55/17.43 } 64.55/17.43 }, 64.55/17.43 "343": { 64.55/17.43 "goal": [], 64.55/17.43 "kb": { 64.55/17.43 "nonunifying": [], 64.55/17.43 "intvars": {}, 64.55/17.43 "arithmetic": { 64.55/17.43 "type": "PlainIntegerRelationState", 64.55/17.43 "relations": [] 64.55/17.43 }, 64.55/17.43 "ground": [], 64.55/17.43 "free": [], 64.55/17.43 "exprvars": [] 64.55/17.43 } 64.55/17.43 }, 64.55/17.43 "226": { 64.55/17.43 "goal": [{ 64.55/17.43 "clause": -1, 64.55/17.43 "scope": -1, 64.55/17.43 "term": "(p (d (e (const (0)))) (const (1)))" 64.55/17.43 }], 64.55/17.43 "kb": { 64.55/17.43 "nonunifying": [], 64.55/17.43 "intvars": {}, 64.55/17.43 "arithmetic": { 64.55/17.43 "type": "PlainIntegerRelationState", 64.55/17.43 "relations": [] 64.55/17.43 }, 64.55/17.43 "ground": [], 64.55/17.43 "free": [], 64.55/17.43 "exprvars": [] 64.55/17.43 } 64.55/17.43 }, 64.55/17.43 "228": { 64.55/17.43 "goal": [], 64.55/17.43 "kb": { 64.55/17.43 "nonunifying": [], 64.55/17.43 "intvars": {}, 64.55/17.43 "arithmetic": { 64.55/17.43 "type": "PlainIntegerRelationState", 64.55/17.43 "relations": [] 64.55/17.43 }, 64.55/17.43 "ground": [], 64.55/17.43 "free": [], 64.55/17.43 "exprvars": [] 64.55/17.43 } 64.55/17.43 } 64.55/17.43 }, 64.55/17.43 "edges": [ 64.55/17.43 { 64.55/17.43 "from": 33, 64.55/17.43 "to": 36, 64.55/17.43 "label": "CASE" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 36, 64.55/17.43 "to": 168, 64.55/17.43 "label": "EVAL with clause\np(d(e(t)), const(1)).\nand substitutionT1 -> d(e(t)),\nT2 -> const(1)" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 36, 64.55/17.43 "to": 169, 64.55/17.43 "label": "EVAL-BACKTRACK" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 168, 64.55/17.43 "to": 170, 64.55/17.43 "label": "SUCCESS" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 169, 64.55/17.43 "to": 555, 64.55/17.43 "label": "EVAL with clause\np(d(e(const(X235))), const(0)).\nand substitutionX235 -> T122,\nT1 -> d(e(const(T122))),\nT2 -> const(0)" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 169, 64.55/17.43 "to": 604, 64.55/17.43 "label": "EVAL-BACKTRACK" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 170, 64.55/17.43 "to": 171, 64.55/17.43 "label": "BACKTRACK\nfor clause: p(d(e(const(A))), const(0))because of non-unification" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 171, 64.55/17.43 "to": 173, 64.55/17.43 "label": "BACKTRACK\nfor clause: p(d(e(+(X, Y))), +(DX, DY)) :- ','(p(d(e(X)), DX), p(d(e(Y)), DY))because of non-unification" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 173, 64.55/17.43 "to": 176, 64.55/17.43 "label": "BACKTRACK\nfor clause: p(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) :- ','(p(d(e(X)), DX), p(d(e(Y)), DY))because of non-unification" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 176, 64.55/17.43 "to": 183, 64.55/17.43 "label": "EVAL with clause\np(d(d(X12)), X13) :- ','(p(d(X12), X14), p(d(e(X14)), X13)).\nand substitutionX12 -> T10,\nT1 -> d(d(T10)),\nX13 -> const(1),\nT9 -> T10" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 176, 64.55/17.43 "to": 185, 64.55/17.43 "label": "EVAL-BACKTRACK" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 183, 64.55/17.43 "to": 188, 64.55/17.43 "label": "CASE" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 188, 64.55/17.43 "to": 191, 64.55/17.43 "label": "PARALLEL" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 188, 64.55/17.43 "to": 193, 64.55/17.43 "label": "PARALLEL" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 191, 64.55/17.43 "to": 197, 64.55/17.43 "label": "EVAL with clause\np(d(e(t)), const(1)).\nand substitutionT10 -> e(t),\nX14 -> const(1)" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 191, 64.55/17.43 "to": 199, 64.55/17.43 "label": "EVAL-BACKTRACK" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 193, 64.55/17.43 "to": 220, 64.55/17.43 "label": "PARALLEL" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 193, 64.55/17.43 "to": 221, 64.55/17.43 "label": "PARALLEL" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 197, 64.55/17.43 "to": 33, 64.55/17.43 "label": "INSTANCE with matching:\nT1 -> d(e(const(1)))\nT2 -> const(1)" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 220, 64.55/17.43 "to": 226, 64.55/17.43 "label": "EVAL with clause\np(d(e(const(X19))), const(0)).\nand substitutionX19 -> T15,\nT10 -> e(const(T15)),\nX14 -> const(0)" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 220, 64.55/17.43 "to": 228, 64.55/17.43 "label": "EVAL-BACKTRACK" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 221, 64.55/17.43 "to": 236, 64.55/17.43 "label": "PARALLEL" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 221, 64.55/17.43 "to": 238, 64.55/17.43 "label": "PARALLEL" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 226, 64.55/17.43 "to": 33, 64.55/17.43 "label": "INSTANCE with matching:\nT1 -> d(e(const(0)))\nT2 -> const(1)" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 236, 64.55/17.43 "to": 338, 64.55/17.43 "label": "EVAL with clause\np(d(e(+(X44, X45))), +(X46, X47)) :- ','(p(d(e(X44)), X46), p(d(e(X45)), X47)).\nand substitutionX44 -> T26,\nX45 -> T27,\nT10 -> e(+(T26, T27)),\nX46 -> X48,\nX47 -> X49,\nX14 -> +(X48, X49),\nT24 -> T26,\nT25 -> T27" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 236, 64.55/17.43 "to": 343, 64.55/17.43 "label": "EVAL-BACKTRACK" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 238, 64.55/17.43 "to": 459, 64.55/17.43 "label": "PARALLEL" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 238, 64.55/17.43 "to": 460, 64.55/17.43 "label": "PARALLEL" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 338, 64.55/17.43 "to": 399, 64.55/17.43 "label": "SPLIT 1" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 338, 64.55/17.43 "to": 400, 64.55/17.43 "label": "SPLIT 2\nreplacements:X48 -> T28,\nT27 -> T29" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 399, 64.55/17.43 "to": 403, 64.55/17.43 "label": "CASE" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 400, 64.55/17.43 "to": 452, 64.55/17.43 "label": "SPLIT 1" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 400, 64.55/17.43 "to": 453, 64.55/17.43 "label": "SPLIT 2\nreplacements:X49 -> T61,\nT28 -> T62" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 403, 64.55/17.43 "to": 404, 64.55/17.43 "label": "PARALLEL" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 403, 64.55/17.43 "to": 405, 64.55/17.43 "label": "PARALLEL" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 404, 64.55/17.43 "to": 406, 64.55/17.43 "label": "EVAL with clause\np(d(e(t)), const(1)).\nand substitutionT26 -> t,\nX48 -> const(1)" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 404, 64.55/17.43 "to": 407, 64.55/17.43 "label": "EVAL-BACKTRACK" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 405, 64.55/17.43 "to": 409, 64.55/17.43 "label": "PARALLEL" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 405, 64.55/17.43 "to": 410, 64.55/17.43 "label": "PARALLEL" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 406, 64.55/17.43 "to": 408, 64.55/17.43 "label": "SUCCESS" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 409, 64.55/17.43 "to": 413, 64.55/17.43 "label": "EVAL with clause\np(d(e(const(X54))), const(0)).\nand substitutionX54 -> T34,\nT26 -> const(T34),\nX48 -> const(0)" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 409, 64.55/17.43 "to": 414, 64.55/17.43 "label": "EVAL-BACKTRACK" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 410, 64.55/17.43 "to": 418, 64.55/17.43 "label": "PARALLEL" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 410, 64.55/17.43 "to": 419, 64.55/17.43 "label": "PARALLEL" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 413, 64.55/17.43 "to": 415, 64.55/17.43 "label": "SUCCESS" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 418, 64.55/17.43 "to": 426, 64.55/17.43 "label": "EVAL with clause\np(d(e(+(X79, X80))), +(X81, X82)) :- ','(p(d(e(X79)), X81), p(d(e(X80)), X82)).\nand substitutionX79 -> T45,\nX80 -> T46,\nT26 -> +(T45, T46),\nX81 -> X83,\nX82 -> X84,\nX48 -> +(X83, X84),\nT43 -> T45,\nT44 -> T46" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 418, 64.55/17.43 "to": 427, 64.55/17.43 "label": "EVAL-BACKTRACK" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 419, 64.55/17.43 "to": 439, 64.55/17.43 "label": "PARALLEL" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 419, 64.55/17.43 "to": 440, 64.55/17.43 "label": "PARALLEL" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 426, 64.55/17.43 "to": 431, 64.55/17.43 "label": "SPLIT 1" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 426, 64.55/17.43 "to": 432, 64.55/17.43 "label": "SPLIT 2\nreplacements:X83 -> T47,\nT46 -> T48" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 431, 64.55/17.43 "to": 399, 64.55/17.43 "label": "INSTANCE with matching:\nT26 -> T45\nX48 -> X83" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 432, 64.55/17.43 "to": 399, 64.55/17.43 "label": "INSTANCE with matching:\nT26 -> T48\nX48 -> X84" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 439, 64.55/17.43 "to": 443, 64.55/17.43 "label": "EVAL with clause\np(d(e(*(X109, X110))), +(*(X109, X111), *(X110, X112))) :- ','(p(d(e(X109)), X112), p(d(e(X110)), X111)).\nand substitutionX109 -> T59,\nX110 -> T60,\nT26 -> *(T59, T60),\nX111 -> X113,\nX112 -> X114,\nX48 -> +(*(T59, X113), *(T60, X114)),\nT57 -> T59,\nT58 -> T60" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 439, 64.55/17.43 "to": 444, 64.55/17.43 "label": "EVAL-BACKTRACK" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 440, 64.55/17.43 "to": 447, 64.55/17.43 "label": "BACKTRACK\nfor clause: p(d(d(X)), DDX) :- ','(p(d(X), DX), p(d(e(DX)), DDX))because of non-unification" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 443, 64.55/17.43 "to": 426, 64.55/17.43 "label": "INSTANCE with matching:\nT45 -> T59\nX83 -> X114\nT46 -> T60\nX84 -> X113" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 452, 64.55/17.43 "to": 399, 64.55/17.43 "label": "INSTANCE with matching:\nT26 -> T29\nX48 -> X49" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 453, 64.55/17.43 "to": 33, 64.55/17.43 "label": "INSTANCE with matching:\nT1 -> d(e(+(T62, T61)))\nT2 -> const(1)" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 459, 64.55/17.43 "to": 473, 64.55/17.43 "label": "EVAL with clause\np(d(e(*(X141, X142))), +(*(X141, X143), *(X142, X144))) :- ','(p(d(e(X141)), X144), p(d(e(X142)), X143)).\nand substitutionX141 -> T73,\nX142 -> T74,\nT10 -> e(*(T73, T74)),\nX143 -> X145,\nX144 -> X146,\nX14 -> +(*(T73, X145), *(T74, X146)),\nT71 -> T73,\nT72 -> T74" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 459, 64.55/17.43 "to": 474, 64.55/17.43 "label": "EVAL-BACKTRACK" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 460, 64.55/17.43 "to": 510, 64.55/17.43 "label": "EVAL with clause\np(d(d(X154)), X155) :- ','(p(d(X154), X156), p(d(e(X156)), X155)).\nand substitutionX154 -> T85,\nT10 -> d(T85),\nX14 -> X157,\nX155 -> X157,\nT84 -> T85" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 460, 64.55/17.43 "to": 511, 64.55/17.43 "label": "EVAL-BACKTRACK" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 473, 64.55/17.43 "to": 480, 64.55/17.43 "label": "SPLIT 1" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 473, 64.55/17.43 "to": 481, 64.55/17.43 "label": "SPLIT 2\nreplacements:X146 -> T75,\nT74 -> T76,\nT73 -> T77" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 480, 64.55/17.43 "to": 399, 64.55/17.43 "label": "INSTANCE with matching:\nT26 -> T73\nX48 -> X146" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 481, 64.55/17.43 "to": 503, 64.55/17.43 "label": "SPLIT 1" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 481, 64.55/17.43 "to": 505, 64.55/17.43 "label": "SPLIT 2\nreplacements:X145 -> T78,\nT77 -> T79,\nT76 -> T80,\nT75 -> T81" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 503, 64.55/17.43 "to": 399, 64.55/17.43 "label": "INSTANCE with matching:\nT26 -> T76\nX48 -> X145" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 505, 64.55/17.43 "to": 33, 64.55/17.43 "label": "INSTANCE with matching:\nT1 -> d(e(+(*(T79, T78), *(T80, T81))))\nT2 -> const(1)" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 510, 64.55/17.43 "to": 514, 64.55/17.43 "label": "SPLIT 1" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 510, 64.55/17.43 "to": 515, 64.55/17.43 "label": "SPLIT 2\nreplacements:X156 -> T86" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 514, 64.55/17.43 "to": 516, 64.55/17.43 "label": "CASE" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 515, 64.55/17.43 "to": 183, 64.55/17.43 "label": "INSTANCE with matching:\nT10 -> e(T86)\nX14 -> X157" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 516, 64.55/17.43 "to": 517, 64.55/17.43 "label": "PARALLEL" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 516, 64.55/17.43 "to": 518, 64.55/17.43 "label": "PARALLEL" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 517, 64.55/17.43 "to": 519, 64.55/17.43 "label": "EVAL with clause\np(d(e(t)), const(1)).\nand substitutionT85 -> e(t),\nX156 -> const(1)" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 517, 64.55/17.43 "to": 520, 64.55/17.43 "label": "EVAL-BACKTRACK" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 518, 64.55/17.43 "to": 524, 64.55/17.43 "label": "PARALLEL" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 518, 64.55/17.43 "to": 525, 64.55/17.43 "label": "PARALLEL" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 519, 64.55/17.43 "to": 521, 64.55/17.43 "label": "SUCCESS" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 524, 64.55/17.43 "to": 526, 64.55/17.43 "label": "EVAL with clause\np(d(e(const(X162))), const(0)).\nand substitutionX162 -> T91,\nT85 -> e(const(T91)),\nX156 -> const(0)" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 524, 64.55/17.43 "to": 527, 64.55/17.43 "label": "EVAL-BACKTRACK" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 525, 64.55/17.43 "to": 531, 64.55/17.43 "label": "PARALLEL" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 525, 64.55/17.43 "to": 532, 64.55/17.43 "label": "PARALLEL" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 526, 64.55/17.43 "to": 528, 64.55/17.43 "label": "SUCCESS" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 531, 64.55/17.43 "to": 535, 64.55/17.43 "label": "EVAL with clause\np(d(e(+(X187, X188))), +(X189, X190)) :- ','(p(d(e(X187)), X189), p(d(e(X188)), X190)).\nand substitutionX187 -> T102,\nX188 -> T103,\nT85 -> e(+(T102, T103)),\nX189 -> X191,\nX190 -> X192,\nX156 -> +(X191, X192),\nT100 -> T102,\nT101 -> T103" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 531, 64.55/17.43 "to": 536, 64.55/17.43 "label": "EVAL-BACKTRACK" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 532, 64.55/17.43 "to": 537, 64.55/17.43 "label": "PARALLEL" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 532, 64.55/17.43 "to": 539, 64.55/17.43 "label": "PARALLEL" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 535, 64.55/17.43 "to": 426, 64.55/17.43 "label": "INSTANCE with matching:\nT45 -> T102\nX83 -> X191\nT46 -> T103\nX84 -> X192" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 537, 64.55/17.43 "to": 543, 64.55/17.43 "label": "EVAL with clause\np(d(e(*(X217, X218))), +(*(X217, X219), *(X218, X220))) :- ','(p(d(e(X217)), X220), p(d(e(X218)), X219)).\nand substitutionX217 -> T114,\nX218 -> T115,\nT85 -> e(*(T114, T115)),\nX219 -> X221,\nX220 -> X222,\nX156 -> +(*(T114, X221), *(T115, X222)),\nT112 -> T114,\nT113 -> T115" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 537, 64.55/17.43 "to": 544, 64.55/17.43 "label": "EVAL-BACKTRACK" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 539, 64.55/17.43 "to": 549, 64.55/17.43 "label": "EVAL with clause\np(d(d(X230)), X231) :- ','(p(d(X230), X232), p(d(e(X232)), X231)).\nand substitutionX230 -> T119,\nT85 -> d(T119),\nX156 -> X233,\nX231 -> X233,\nT118 -> T119" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 539, 64.55/17.43 "to": 550, 64.55/17.43 "label": "EVAL-BACKTRACK" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 543, 64.55/17.43 "to": 426, 64.55/17.43 "label": "INSTANCE with matching:\nT45 -> T114\nX83 -> X222\nT46 -> T115\nX84 -> X221" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 549, 64.55/17.43 "to": 553, 64.55/17.43 "label": "SPLIT 1" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 549, 64.55/17.43 "to": 554, 64.55/17.43 "label": "SPLIT 2\nreplacements:X232 -> T120" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 553, 64.55/17.43 "to": 514, 64.55/17.43 "label": "INSTANCE with matching:\nT85 -> T119\nX156 -> X232" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 554, 64.55/17.43 "to": 399, 64.55/17.43 "label": "INSTANCE with matching:\nT26 -> T120\nX48 -> X233" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 555, 64.55/17.43 "to": 605, 64.55/17.43 "label": "SUCCESS" 64.55/17.43 }, 64.55/17.43 { 64.55/17.43 "from": 604, 64.55/17.43 "to": 687, 64.55/17.43 "label": "EVAL with clause\np(d(e(+(X329, X330))), +(X331, X332)) :- ','(p(d(e(X329)), X331), p(d(e(X330)), X332)).\nand substitutionX329 -> T183,\nX330 -> T184,\nT1 -> d(e(+(T183, T184))),\nX331 -> T181,\nX332 -> T182,\nT2 -> +(T181, T182),\nT179 -> T183,\nT180 -> T184" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 604, 64.55/17.44 "to": 688, 64.55/17.44 "label": "EVAL-BACKTRACK" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 605, 64.55/17.44 "to": 606, 64.55/17.44 "label": "BACKTRACK\nfor clause: p(d(e(+(X, Y))), +(DX, DY)) :- ','(p(d(e(X)), DX), p(d(e(Y)), DY))because of non-unification" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 606, 64.55/17.44 "to": 607, 64.55/17.44 "label": "BACKTRACK\nfor clause: p(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) :- ','(p(d(e(X)), DX), p(d(e(Y)), DY))because of non-unification" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 607, 64.55/17.44 "to": 608, 64.55/17.44 "label": "EVAL with clause\np(d(d(X246)), X247) :- ','(p(d(X246), X248), p(d(e(X248)), X247)).\nand substitutionX246 -> T129,\nT1 -> d(d(T129)),\nX247 -> const(0),\nT128 -> T129" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 607, 64.55/17.44 "to": 609, 64.55/17.44 "label": "EVAL-BACKTRACK" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 608, 64.55/17.44 "to": 610, 64.55/17.44 "label": "CASE" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 610, 64.55/17.44 "to": 611, 64.55/17.44 "label": "PARALLEL" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 610, 64.55/17.44 "to": 612, 64.55/17.44 "label": "PARALLEL" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 611, 64.55/17.44 "to": 613, 64.55/17.44 "label": "EVAL with clause\np(d(e(t)), const(1)).\nand substitutionT129 -> e(t),\nX248 -> const(1)" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 611, 64.55/17.44 "to": 614, 64.55/17.44 "label": "EVAL-BACKTRACK" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 612, 64.55/17.44 "to": 615, 64.55/17.44 "label": "PARALLEL" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 612, 64.55/17.44 "to": 616, 64.55/17.44 "label": "PARALLEL" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 613, 64.55/17.44 "to": 33, 64.55/17.44 "label": "INSTANCE with matching:\nT1 -> d(e(const(1)))\nT2 -> const(0)" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 615, 64.55/17.44 "to": 617, 64.55/17.44 "label": "EVAL with clause\np(d(e(const(X253))), const(0)).\nand substitutionX253 -> T134,\nT129 -> e(const(T134)),\nX248 -> const(0)" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 615, 64.55/17.44 "to": 618, 64.55/17.44 "label": "EVAL-BACKTRACK" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 616, 64.55/17.44 "to": 667, 64.55/17.44 "label": "PARALLEL" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 616, 64.55/17.44 "to": 668, 64.55/17.44 "label": "PARALLEL" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 617, 64.55/17.44 "to": 33, 64.55/17.44 "label": "INSTANCE with matching:\nT1 -> d(e(const(0)))\nT2 -> const(0)" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 667, 64.55/17.44 "to": 669, 64.55/17.44 "label": "EVAL with clause\np(d(e(+(X278, X279))), +(X280, X281)) :- ','(p(d(e(X278)), X280), p(d(e(X279)), X281)).\nand substitutionX278 -> T145,\nX279 -> T146,\nT129 -> e(+(T145, T146)),\nX280 -> X282,\nX281 -> X283,\nX248 -> +(X282, X283),\nT143 -> T145,\nT144 -> T146" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 667, 64.55/17.44 "to": 670, 64.55/17.44 "label": "EVAL-BACKTRACK" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 668, 64.55/17.44 "to": 675, 64.55/17.44 "label": "PARALLEL" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 668, 64.55/17.44 "to": 676, 64.55/17.44 "label": "PARALLEL" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 669, 64.55/17.44 "to": 671, 64.55/17.44 "label": "SPLIT 1" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 669, 64.55/17.44 "to": 672, 64.55/17.44 "label": "SPLIT 2\nreplacements:X282 -> T147,\nT146 -> T148" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 671, 64.55/17.44 "to": 399, 64.55/17.44 "label": "INSTANCE with matching:\nT26 -> T145\nX48 -> X282" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 672, 64.55/17.44 "to": 673, 64.55/17.44 "label": "SPLIT 1" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 672, 64.55/17.44 "to": 674, 64.55/17.44 "label": "SPLIT 2\nreplacements:X283 -> T149,\nT147 -> T150" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 673, 64.55/17.44 "to": 399, 64.55/17.44 "label": "INSTANCE with matching:\nT26 -> T148\nX48 -> X283" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 674, 64.55/17.44 "to": 33, 64.55/17.44 "label": "INSTANCE with matching:\nT1 -> d(e(+(T150, T149)))\nT2 -> const(0)" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 675, 64.55/17.44 "to": 677, 64.55/17.44 "label": "EVAL with clause\np(d(e(*(X308, X309))), +(*(X308, X310), *(X309, X311))) :- ','(p(d(e(X308)), X311), p(d(e(X309)), X310)).\nand substitutionX308 -> T161,\nX309 -> T162,\nT129 -> e(*(T161, T162)),\nX310 -> X312,\nX311 -> X313,\nX248 -> +(*(T161, X312), *(T162, X313)),\nT159 -> T161,\nT160 -> T162" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 675, 64.55/17.44 "to": 678, 64.55/17.44 "label": "EVAL-BACKTRACK" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 676, 64.55/17.44 "to": 683, 64.55/17.44 "label": "EVAL with clause\np(d(d(X321)), X322) :- ','(p(d(X321), X323), p(d(e(X323)), X322)).\nand substitutionX321 -> T173,\nT129 -> d(T173),\nX248 -> X324,\nX322 -> X324,\nT172 -> T173" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 676, 64.55/17.44 "to": 684, 64.55/17.44 "label": "EVAL-BACKTRACK" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 677, 64.55/17.44 "to": 679, 64.55/17.44 "label": "SPLIT 1" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 677, 64.55/17.44 "to": 680, 64.55/17.44 "label": "SPLIT 2\nreplacements:X313 -> T163,\nT162 -> T164,\nT161 -> T165" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 679, 64.55/17.44 "to": 399, 64.55/17.44 "label": "INSTANCE with matching:\nT26 -> T161\nX48 -> X313" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 680, 64.55/17.44 "to": 681, 64.55/17.44 "label": "SPLIT 1" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 680, 64.55/17.44 "to": 682, 64.55/17.44 "label": "SPLIT 2\nreplacements:X312 -> T166,\nT165 -> T167,\nT164 -> T168,\nT163 -> T169" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 681, 64.55/17.44 "to": 399, 64.55/17.44 "label": "INSTANCE with matching:\nT26 -> T164\nX48 -> X312" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 682, 64.55/17.44 "to": 33, 64.55/17.44 "label": "INSTANCE with matching:\nT1 -> d(e(+(*(T167, T166), *(T168, T169))))\nT2 -> const(0)" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 683, 64.55/17.44 "to": 685, 64.55/17.44 "label": "SPLIT 1" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 683, 64.55/17.44 "to": 686, 64.55/17.44 "label": "SPLIT 2\nreplacements:X323 -> T174" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 685, 64.55/17.44 "to": 514, 64.55/17.44 "label": "INSTANCE with matching:\nT85 -> T173\nX156 -> X323" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 686, 64.55/17.44 "to": 608, 64.55/17.44 "label": "INSTANCE with matching:\nT129 -> e(T174)\nX248 -> X324" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 687, 64.55/17.44 "to": 689, 64.55/17.44 "label": "CASE" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 688, 64.55/17.44 "to": 720, 64.55/17.44 "label": "EVAL with clause\np(d(e(*(X412, X413))), +(*(X412, X414), *(X413, X415))) :- ','(p(d(e(X412)), X415), p(d(e(X413)), X414)).\nand substitutionX412 -> T274,\nX413 -> T275,\nT1 -> d(e(*(T274, T275))),\nX414 -> T276,\nX415 -> T277,\nT2 -> +(*(T274, T276), *(T275, T277))" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 688, 64.55/17.44 "to": 721, 64.55/17.44 "label": "EVAL-BACKTRACK" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 689, 64.55/17.44 "to": 690, 64.55/17.44 "label": "PARALLEL" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 689, 64.55/17.44 "to": 691, 64.55/17.44 "label": "PARALLEL" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 690, 64.55/17.44 "to": 692, 64.55/17.44 "label": "EVAL with clause\np(d(e(t)), const(1)).\nand substitutionT183 -> t,\nT181 -> const(1),\nT184 -> T185" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 690, 64.55/17.44 "to": 693, 64.55/17.44 "label": "EVAL-BACKTRACK" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 691, 64.55/17.44 "to": 694, 64.55/17.44 "label": "PARALLEL" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 691, 64.55/17.44 "to": 695, 64.55/17.44 "label": "PARALLEL" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 692, 64.55/17.44 "to": 33, 64.55/17.44 "label": "INSTANCE with matching:\nT1 -> d(e(T185))\nT2 -> T182" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 694, 64.55/17.44 "to": 696, 64.55/17.44 "label": "EVAL with clause\np(d(e(const(X337))), const(0)).\nand substitutionX337 -> T190,\nT183 -> const(T190),\nT181 -> const(0),\nT184 -> T191" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 694, 64.55/17.44 "to": 697, 64.55/17.44 "label": "EVAL-BACKTRACK" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 695, 64.55/17.44 "to": 698, 64.55/17.44 "label": "PARALLEL" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 695, 64.55/17.44 "to": 699, 64.55/17.44 "label": "PARALLEL" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 696, 64.55/17.44 "to": 33, 64.55/17.44 "label": "INSTANCE with matching:\nT1 -> d(e(T191))\nT2 -> T182" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 698, 64.55/17.44 "to": 700, 64.55/17.44 "label": "EVAL with clause\np(d(e(+(X354, X355))), +(X356, X357)) :- ','(p(d(e(X354)), X356), p(d(e(X355)), X357)).\nand substitutionX354 -> T212,\nX355 -> T213,\nT183 -> +(T212, T213),\nX356 -> T210,\nX357 -> T211,\nT181 -> +(T210, T211),\nT208 -> T212,\nT209 -> T213,\nT184 -> T214" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 698, 64.55/17.44 "to": 701, 64.55/17.44 "label": "EVAL-BACKTRACK" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 699, 64.55/17.44 "to": 706, 64.55/17.44 "label": "PARALLEL" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 699, 64.55/17.44 "to": 707, 64.55/17.44 "label": "PARALLEL" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 700, 64.55/17.44 "to": 702, 64.55/17.44 "label": "SPLIT 1" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 700, 64.55/17.44 "to": 703, 64.55/17.44 "label": "SPLIT 2\nnew knowledge:\nT210 is ground\nreplacements:T213 -> T215,\nT214 -> T216" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 702, 64.55/17.44 "to": 33, 64.55/17.44 "label": "INSTANCE with matching:\nT1 -> d(e(T212))\nT2 -> T210" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 703, 64.55/17.44 "to": 704, 64.55/17.44 "label": "SPLIT 1" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 703, 64.55/17.44 "to": 705, 64.55/17.44 "label": "SPLIT 2\nnew knowledge:\nT211 is ground\nreplacements:T216 -> T217" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 704, 64.55/17.44 "to": 33, 64.55/17.44 "label": "INSTANCE with matching:\nT1 -> d(e(T215))\nT2 -> T211" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 705, 64.55/17.44 "to": 33, 64.55/17.44 "label": "INSTANCE with matching:\nT1 -> d(e(T217))\nT2 -> T182" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 706, 64.55/17.44 "to": 708, 64.55/17.44 "label": "EVAL with clause\np(d(e(*(X374, X375))), +(*(X374, X376), *(X375, X377))) :- ','(p(d(e(X374)), X377), p(d(e(X375)), X376)).\nand substitutionX374 -> T234,\nX375 -> T235,\nT183 -> *(T234, T235),\nX376 -> T236,\nX377 -> T237,\nT181 -> +(*(T234, T236), *(T235, T237)),\nT184 -> T238" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 706, 64.55/17.44 "to": 709, 64.55/17.44 "label": "EVAL-BACKTRACK" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 707, 64.55/17.44 "to": 710, 64.55/17.44 "label": "BACKTRACK\nfor clause: p(d(d(X)), DDX) :- ','(p(d(X), DX), p(d(e(DX)), DDX))because of non-unification" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 708, 64.55/17.44 "to": 700, 64.55/17.44 "label": "INSTANCE with matching:\nT212 -> T234\nT210 -> T237\nT213 -> T235\nT211 -> T236\nT214 -> T238" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 710, 64.55/17.44 "to": 711, 64.55/17.44 "label": "FAILURE" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 711, 64.55/17.44 "to": 712, 64.55/17.44 "label": "PARALLEL" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 711, 64.55/17.44 "to": 713, 64.55/17.44 "label": "PARALLEL" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 712, 64.55/17.44 "to": 714, 64.55/17.44 "label": "EVAL with clause\np(d(e(*(X396, X397))), +(*(X396, X398), *(X397, X399))) :- ','(p(d(e(X396)), X399), p(d(e(X397)), X398)).\nand substitutionX396 -> T255,\nX397 -> T256,\nT1 -> d(e(*(T255, T256))),\nX398 -> T257,\nT181 -> *(T255, T257),\nX399 -> T258,\nT182 -> *(T256, T258)" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 712, 64.55/17.44 "to": 715, 64.55/17.44 "label": "EVAL-BACKTRACK" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 713, 64.55/17.44 "to": 716, 64.55/17.44 "label": "EVAL with clause\np(d(d(X405)), X406) :- ','(p(d(X405), X407), p(d(e(X407)), X406)).\nand substitutionX405 -> T268,\nT1 -> d(d(T268)),\nT181 -> T266,\nT182 -> T267,\nX406 -> +(T266, T267),\nT265 -> T268" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 713, 64.55/17.44 "to": 717, 64.55/17.44 "label": "EVAL-BACKTRACK" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 714, 64.55/17.44 "to": 703, 64.55/17.44 "label": "INSTANCE with matching:\nT215 -> T255\nT211 -> T258\nT216 -> T256\nT182 -> T257" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 716, 64.55/17.44 "to": 718, 64.55/17.44 "label": "SPLIT 1" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 716, 64.55/17.44 "to": 719, 64.55/17.44 "label": "SPLIT 2\nreplacements:X407 -> T269" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 718, 64.55/17.44 "to": 514, 64.55/17.44 "label": "INSTANCE with matching:\nT85 -> T268\nX156 -> X407" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 719, 64.55/17.44 "to": 33, 64.55/17.44 "label": "INSTANCE with matching:\nT1 -> d(e(T269))\nT2 -> +(T266, T267)" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 720, 64.55/17.44 "to": 722, 64.55/17.44 "label": "CASE" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 721, 64.55/17.44 "to": 743, 64.55/17.44 "label": "EVAL with clause\np(d(d(X473)), X474) :- ','(p(d(X473), X475), p(d(e(X475)), X474)).\nand substitutionX473 -> T343,\nT1 -> d(d(T343)),\nT2 -> T342,\nX474 -> T342,\nT341 -> T343" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 721, 64.55/17.44 "to": 744, 64.55/17.44 "label": "EVAL-BACKTRACK" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 722, 64.55/17.44 "to": 723, 64.55/17.44 "label": "PARALLEL" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 722, 64.55/17.44 "to": 724, 64.55/17.44 "label": "PARALLEL" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 723, 64.55/17.44 "to": 725, 64.55/17.44 "label": "EVAL with clause\np(d(e(t)), const(1)).\nand substitutionT274 -> t,\nT277 -> const(1)" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 723, 64.55/17.44 "to": 726, 64.55/17.44 "label": "EVAL-BACKTRACK" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 724, 64.55/17.44 "to": 727, 64.55/17.44 "label": "PARALLEL" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 724, 64.55/17.44 "to": 728, 64.55/17.44 "label": "PARALLEL" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 725, 64.55/17.44 "to": 33, 64.55/17.44 "label": "INSTANCE with matching:\nT1 -> d(e(T275))\nT2 -> T276" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 727, 64.55/17.44 "to": 729, 64.55/17.44 "label": "EVAL with clause\np(d(e(const(X420))), const(0)).\nand substitutionX420 -> T282,\nT274 -> const(T282),\nT277 -> const(0)" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 727, 64.55/17.44 "to": 730, 64.55/17.44 "label": "EVAL-BACKTRACK" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 728, 64.55/17.44 "to": 731, 64.55/17.44 "label": "PARALLEL" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 728, 64.55/17.44 "to": 732, 64.55/17.44 "label": "PARALLEL" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 729, 64.55/17.44 "to": 33, 64.55/17.44 "label": "INSTANCE with matching:\nT1 -> d(e(T275))\nT2 -> T276" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 731, 64.55/17.44 "to": 733, 64.55/17.44 "label": "EVAL with clause\np(d(e(+(X437, X438))), +(X439, X440)) :- ','(p(d(e(X437)), X439), p(d(e(X438)), X440)).\nand substitutionX437 -> T299,\nX438 -> T300,\nT274 -> +(T299, T300),\nX439 -> T301,\nX440 -> T302,\nT277 -> +(T301, T302)" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 731, 64.55/17.44 "to": 734, 64.55/17.44 "label": "EVAL-BACKTRACK" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 732, 64.55/17.44 "to": 735, 64.55/17.44 "label": "PARALLEL" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 732, 64.55/17.44 "to": 736, 64.55/17.44 "label": "PARALLEL" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 733, 64.55/17.44 "to": 700, 64.55/17.44 "label": "INSTANCE with matching:\nT212 -> T299\nT210 -> T301\nT213 -> T300\nT211 -> T302\nT214 -> T275\nT182 -> T276" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 735, 64.55/17.44 "to": 737, 64.55/17.44 "label": "EVAL with clause\np(d(e(*(X457, X458))), +(*(X457, X459), *(X458, X460))) :- ','(p(d(e(X457)), X460), p(d(e(X458)), X459)).\nand substitutionX457 -> T319,\nX458 -> T320,\nT274 -> *(T319, T320),\nX459 -> T321,\nX460 -> T322,\nT277 -> +(*(T319, T321), *(T320, T322))" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 735, 64.55/17.44 "to": 738, 64.55/17.44 "label": "EVAL-BACKTRACK" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 736, 64.55/17.44 "to": 739, 64.55/17.44 "label": "BACKTRACK\nfor clause: p(d(d(X)), DDX) :- ','(p(d(X), DX), p(d(e(DX)), DDX))because of non-unification" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 737, 64.55/17.44 "to": 700, 64.55/17.44 "label": "INSTANCE with matching:\nT212 -> T319\nT210 -> T322\nT213 -> T320\nT211 -> T321\nT214 -> T275\nT182 -> T276" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 739, 64.55/17.44 "to": 740, 64.55/17.44 "label": "FAILURE" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 740, 64.55/17.44 "to": 741, 64.55/17.44 "label": "EVAL with clause\np(d(d(X468)), X469) :- ','(p(d(X468), X470), p(d(e(X470)), X469)).\nand substitutionX468 -> T338,\nT1 -> d(d(T338)),\nT274 -> T334,\nT276 -> T335,\nT275 -> T336,\nT277 -> T337,\nX469 -> +(*(T334, T335), *(T336, T337)),\nT333 -> T338" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 740, 64.55/17.44 "to": 742, 64.55/17.44 "label": "EVAL-BACKTRACK" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 741, 64.55/17.44 "to": 716, 64.55/17.44 "label": "INSTANCE with matching:\nT268 -> T338\nX407 -> X470\nT266 -> *(T334, T335)\nT267 -> *(T336, T337)" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 743, 64.55/17.44 "to": 745, 64.55/17.44 "label": "CASE" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 745, 64.55/17.44 "to": 746, 64.55/17.44 "label": "PARALLEL" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 745, 64.55/17.44 "to": 747, 64.55/17.44 "label": "PARALLEL" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 746, 64.55/17.44 "to": 748, 64.55/17.44 "label": "EVAL with clause\np(d(e(t)), const(1)).\nand substitutionT343 -> e(t),\nX475 -> const(1)" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 746, 64.55/17.44 "to": 749, 64.55/17.44 "label": "EVAL-BACKTRACK" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 747, 64.55/17.44 "to": 750, 64.55/17.44 "label": "PARALLEL" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 747, 64.55/17.44 "to": 751, 64.55/17.44 "label": "PARALLEL" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 748, 64.55/17.44 "to": 33, 64.55/17.44 "label": "INSTANCE with matching:\nT1 -> d(e(const(1)))\nT2 -> T342" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 750, 64.55/17.44 "to": 752, 64.55/17.44 "label": "EVAL with clause\np(d(e(const(X480))), const(0)).\nand substitutionX480 -> T348,\nT343 -> e(const(T348)),\nX475 -> const(0)" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 750, 64.55/17.44 "to": 753, 64.55/17.44 "label": "EVAL-BACKTRACK" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 751, 64.55/17.44 "to": 754, 64.55/17.44 "label": "PARALLEL" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 751, 64.55/17.44 "to": 755, 64.55/17.44 "label": "PARALLEL" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 752, 64.55/17.44 "to": 33, 64.55/17.44 "label": "INSTANCE with matching:\nT1 -> d(e(const(0)))\nT2 -> T342" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 754, 64.55/17.44 "to": 756, 64.55/17.44 "label": "EVAL with clause\np(d(e(+(X505, X506))), +(X507, X508)) :- ','(p(d(e(X505)), X507), p(d(e(X506)), X508)).\nand substitutionX505 -> T359,\nX506 -> T360,\nT343 -> e(+(T359, T360)),\nX507 -> X509,\nX508 -> X510,\nX475 -> +(X509, X510),\nT357 -> T359,\nT358 -> T360" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 754, 64.55/17.44 "to": 757, 64.55/17.44 "label": "EVAL-BACKTRACK" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 755, 64.55/17.44 "to": 816, 64.55/17.44 "label": "PARALLEL" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 755, 64.55/17.44 "to": 817, 64.55/17.44 "label": "PARALLEL" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 756, 64.55/17.44 "to": 758, 64.55/17.44 "label": "SPLIT 1" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 756, 64.55/17.44 "to": 759, 64.55/17.44 "label": "SPLIT 2\nreplacements:X509 -> T361,\nT360 -> T362,\nT1 -> T363" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 758, 64.55/17.44 "to": 399, 64.55/17.44 "label": "INSTANCE with matching:\nT26 -> T359\nX48 -> X509" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 759, 64.55/17.44 "to": 760, 64.55/17.44 "label": "SPLIT 1" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 759, 64.55/17.44 "to": 815, 64.55/17.44 "label": "SPLIT 2\nreplacements:X510 -> T364,\nT361 -> T365,\nT363 -> T366" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 760, 64.55/17.44 "to": 399, 64.55/17.44 "label": "INSTANCE with matching:\nT26 -> T362\nX48 -> X510" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 815, 64.55/17.44 "to": 33, 64.55/17.44 "label": "INSTANCE with matching:\nT1 -> d(e(+(T365, T364)))\nT2 -> T342" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 816, 64.55/17.44 "to": 818, 64.55/17.44 "label": "EVAL with clause\np(d(e(*(X535, X536))), +(*(X535, X537), *(X536, X538))) :- ','(p(d(e(X535)), X538), p(d(e(X536)), X537)).\nand substitutionX535 -> T377,\nX536 -> T378,\nT343 -> e(*(T377, T378)),\nX537 -> X539,\nX538 -> X540,\nX475 -> +(*(T377, X539), *(T378, X540)),\nT375 -> T377,\nT376 -> T378" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 816, 64.55/17.44 "to": 819, 64.55/17.44 "label": "EVAL-BACKTRACK" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 817, 64.55/17.44 "to": 824, 64.55/17.44 "label": "EVAL with clause\np(d(d(X548)), X549) :- ','(p(d(X548), X550), p(d(e(X550)), X549)).\nand substitutionX548 -> T391,\nT343 -> d(T391),\nX475 -> X551,\nX549 -> X551,\nT390 -> T391" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 817, 64.55/17.44 "to": 825, 64.55/17.44 "label": "EVAL-BACKTRACK" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 818, 64.55/17.44 "to": 820, 64.55/17.44 "label": "SPLIT 1" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 818, 64.55/17.44 "to": 821, 64.55/17.44 "label": "SPLIT 2\nreplacements:X540 -> T379,\nT378 -> T380,\nT377 -> T381,\nT1 -> T382" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 820, 64.55/17.44 "to": 399, 64.55/17.44 "label": "INSTANCE with matching:\nT26 -> T377\nX48 -> X540" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 821, 64.55/17.44 "to": 822, 64.55/17.44 "label": "SPLIT 1" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 821, 64.55/17.44 "to": 823, 64.55/17.44 "label": "SPLIT 2\nreplacements:X539 -> T383,\nT381 -> T384,\nT380 -> T385,\nT379 -> T386,\nT382 -> T387" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 822, 64.55/17.44 "to": 399, 64.55/17.44 "label": "INSTANCE with matching:\nT26 -> T380\nX48 -> X539" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 823, 64.55/17.44 "to": 33, 64.55/17.44 "label": "INSTANCE with matching:\nT1 -> d(e(+(*(T384, T383), *(T385, T386))))\nT2 -> T342" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 824, 64.55/17.44 "to": 826, 64.55/17.44 "label": "SPLIT 1" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 824, 64.55/17.44 "to": 827, 64.55/17.44 "label": "SPLIT 2\nreplacements:X550 -> T392,\nT1 -> T393" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 826, 64.55/17.44 "to": 514, 64.55/17.44 "label": "INSTANCE with matching:\nT85 -> T391\nX156 -> X550" 64.55/17.44 }, 64.55/17.44 { 64.55/17.44 "from": 827, 64.55/17.44 "to": 743, 64.55/17.44 "label": "INSTANCE with matching:\nT343 -> e(T392)\nX475 -> X551\nT1 -> T393" 64.55/17.44 } 64.55/17.44 ], 64.55/17.44 "type": "Graph" 64.55/17.44 } 64.55/17.44 } 64.55/17.44 64.55/17.44 ---------------------------------------- 64.55/17.44 64.55/17.44 (116) 64.55/17.44 Obligation: 64.55/17.44 Triples: 64.55/17.44 64.55/17.44 pH(+(X1, X2), +(X3, X4)) :- pI(X1, X3, X2, X4). 64.55/17.44 pH(*(X1, X2), +(*(X1, X3), *(X2, X4))) :- pI(X1, X4, X2, X3). 64.55/17.44 pI(X1, X2, X3, X4) :- pH(X1, X2). 64.55/17.44 pI(X1, X2, X3, X4) :- ','(pcH(X1, X2), pH(X3, X4)). 64.55/17.44 pB(e(t), const(1)) :- pA(d(e(const(1))), const(1)). 64.55/17.44 pB(e(const(X1)), const(0)) :- pA(d(e(const(0))), const(1)). 64.55/17.44 pB(e(+(X1, X2)), +(X3, X4)) :- pH(X1, X3). 64.55/17.44 pB(e(+(X1, X2)), +(X3, X4)) :- ','(pcH(X1, X3), pH(X2, X4)). 64.55/17.44 pB(e(+(X1, X2)), +(X3, X4)) :- ','(pcH(X1, X3), ','(pcH(X2, X4), pA(d(e(+(X3, X4))), const(1)))). 64.55/17.44 pB(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) :- pH(X1, X4). 64.55/17.44 pB(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) :- ','(pcH(X1, X4), pH(X2, X3)). 64.55/17.44 pB(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) :- ','(pcH(X1, X4), ','(pcH(X2, X3), pA(d(e(+(*(X1, X3), *(X2, X4)))), const(1)))). 64.55/17.44 pB(d(X1), X2) :- pJ(X1, X3). 64.55/17.44 pB(d(X1), X2) :- ','(pcJ(X1, X3), pB(e(X3), X2)). 64.55/17.44 pJ(e(+(X1, X2)), +(X3, X4)) :- pI(X1, X3, X2, X4). 64.55/17.44 pJ(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) :- pI(X1, X4, X2, X3). 64.55/17.44 pJ(d(X1), X2) :- pJ(X1, X3). 64.55/17.44 pJ(d(X1), X2) :- ','(pcJ(X1, X3), pH(X3, X2)). 64.55/17.44 pC(e(t), const(1)) :- pA(d(e(const(1))), const(0)). 64.55/17.44 pC(e(const(X1)), const(0)) :- pA(d(e(const(0))), const(0)). 64.55/17.44 pC(e(+(X1, X2)), +(X3, X4)) :- pH(X1, X3). 64.55/17.44 pC(e(+(X1, X2)), +(X3, X4)) :- ','(pcH(X1, X3), pH(X2, X4)). 64.55/17.44 pC(e(+(X1, X2)), +(X3, X4)) :- ','(pcH(X1, X3), ','(pcH(X2, X4), pA(d(e(+(X3, X4))), const(0)))). 64.55/17.44 pC(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) :- pH(X1, X4). 64.55/17.44 pC(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) :- ','(pcH(X1, X4), pH(X2, X3)). 64.55/17.44 pC(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) :- ','(pcH(X1, X4), ','(pcH(X2, X3), pA(d(e(+(*(X1, X3), *(X2, X4)))), const(0)))). 64.55/17.44 pC(d(X1), X2) :- pJ(X1, X3). 64.55/17.44 pC(d(X1), X2) :- ','(pcJ(X1, X3), pC(e(X3), X2)). 64.55/17.44 pD(X1, X2, X3, X4, X5, X6) :- pA(d(e(X1)), X2). 64.55/17.44 pD(X1, X2, X3, X4, X5, X6) :- ','(pcA(d(e(X1)), X2), pE(X3, X4, X5, X6)). 64.55/17.44 pE(X1, X2, X3, X4) :- pA(d(e(X1)), X2). 64.55/17.44 pE(X1, X2, X3, X4) :- ','(pcA(d(e(X1)), X2), pA(d(e(X3)), X4)). 64.55/17.44 pF(X1, X2, X3, X4) :- pJ(X1, X2). 64.55/17.44 pF(X1, X2, X3, X4) :- ','(pcJ(X1, X2), pA(d(e(X2)), +(X3, X4))). 64.55/17.44 pG(e(t), const(1), X1) :- pA(d(e(const(1))), X1). 64.55/17.44 pG(e(const(X1)), const(0), X2) :- pA(d(e(const(0))), X2). 64.55/17.44 pG(e(+(X1, X2)), +(X3, X4), X5) :- pH(X1, X3). 64.55/17.44 pG(e(+(X1, X2)), +(X3, X4), X5) :- ','(pcH(X1, X3), pH(X2, X4)). 64.55/17.44 pG(e(+(X1, X2)), +(X3, X4), X5) :- ','(pcH(X1, X3), ','(pcH(X2, X4), pA(d(e(+(X3, X4))), X5))). 64.55/17.44 pG(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) :- pH(X1, X4). 64.55/17.44 pG(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) :- ','(pcH(X1, X4), pH(X2, X3)). 64.55/17.44 pG(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) :- ','(pcH(X1, X4), ','(pcH(X2, X3), pA(d(e(+(*(X1, X3), *(X2, X4)))), X5))). 64.55/17.44 pG(d(X1), X2, X3) :- pJ(X1, X4). 64.55/17.44 pG(d(X1), X2, X3) :- ','(pcJ(X1, X4), pG(e(X4), X2, X3)). 64.55/17.44 pA(d(d(X1)), const(1)) :- pB(X1, X2). 64.55/17.44 pA(d(d(X1)), const(0)) :- pC(X1, X2). 64.55/17.44 pA(d(e(+(t, X1))), +(const(1), X2)) :- pA(d(e(X1)), X2). 64.55/17.44 pA(d(e(+(const(X1), X2))), +(const(0), X3)) :- pA(d(e(X2)), X3). 64.55/17.44 pA(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) :- pD(X1, X4, X2, X5, X3, X6). 64.55/17.44 pA(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) :- pD(X1, X5, X2, X4, X3, X6). 64.55/17.44 pA(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) :- pE(X1, X4, X2, X3). 64.55/17.44 pA(d(d(X1)), +(X2, X3)) :- pF(X1, X4, X2, X3). 64.55/17.44 pA(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) :- pA(d(e(X1)), X2). 64.55/17.44 pA(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) :- pA(d(e(X2)), X3). 64.55/17.44 pA(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) :- pD(X1, X5, X2, X6, X3, X4). 64.55/17.44 pA(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) :- pD(X1, X6, X2, X5, X3, X4). 64.55/17.44 pA(d(d(X1)), +(*(X2, X3), *(X4, X5))) :- pF(X1, X6, *(X2, X3), *(X4, X5)). 64.55/17.44 pA(d(d(X1)), X2) :- pG(X1, X3, X2). 64.55/17.44 64.55/17.44 Clauses: 64.55/17.44 64.55/17.44 pcA(d(e(t)), const(1)). 64.55/17.44 pcA(d(d(X1)), const(1)) :- qcB(X1, X2). 64.55/17.44 pcA(d(e(const(X1))), const(0)). 64.55/17.44 pcA(d(d(X1)), const(0)) :- qcC(X1, X2). 64.55/17.44 pcA(d(e(+(t, X1))), +(const(1), X2)) :- pcA(d(e(X1)), X2). 64.55/17.44 pcA(d(e(+(const(X1), X2))), +(const(0), X3)) :- pcA(d(e(X2)), X3). 64.55/17.44 pcA(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) :- qcD(X1, X4, X2, X5, X3, X6). 64.55/17.44 pcA(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) :- qcD(X1, X5, X2, X4, X3, X6). 64.55/17.44 pcA(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) :- qcE(X1, X4, X2, X3). 64.55/17.44 pcA(d(d(X1)), +(X2, X3)) :- qcF(X1, X4, X2, X3). 64.55/17.44 pcA(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) :- pcA(d(e(X1)), X2). 64.55/17.44 pcA(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) :- pcA(d(e(X2)), X3). 64.55/17.44 pcA(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) :- qcD(X1, X5, X2, X6, X3, X4). 64.55/17.44 pcA(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) :- qcD(X1, X6, X2, X5, X3, X4). 64.55/17.44 pcA(d(d(X1)), +(*(X2, X3), *(X4, X5))) :- qcF(X1, X6, *(X2, X3), *(X4, X5)). 64.55/17.44 pcA(d(d(X1)), X2) :- qcG(X1, X3, X2). 64.55/17.44 pcH(t, const(1)). 64.55/17.44 pcH(const(X1), const(0)). 64.55/17.44 pcH(+(X1, X2), +(X3, X4)) :- qcI(X1, X3, X2, X4). 64.55/17.44 pcH(*(X1, X2), +(*(X1, X3), *(X2, X4))) :- qcI(X1, X4, X2, X3). 64.55/17.44 qcI(X1, X2, X3, X4) :- ','(pcH(X1, X2), pcH(X3, X4)). 64.55/17.44 qcB(e(t), const(1)) :- pcA(d(e(const(1))), const(1)). 64.55/17.44 qcB(e(const(X1)), const(0)) :- pcA(d(e(const(0))), const(1)). 64.55/17.44 qcB(e(+(X1, X2)), +(X3, X4)) :- ','(pcH(X1, X3), ','(pcH(X2, X4), pcA(d(e(+(X3, X4))), const(1)))). 64.55/17.44 qcB(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) :- ','(pcH(X1, X4), ','(pcH(X2, X3), pcA(d(e(+(*(X1, X3), *(X2, X4)))), const(1)))). 64.55/17.44 qcB(d(X1), X2) :- ','(pcJ(X1, X3), qcB(e(X3), X2)). 64.55/17.44 pcJ(e(t), const(1)). 64.55/17.44 pcJ(e(const(X1)), const(0)). 64.55/17.44 pcJ(e(+(X1, X2)), +(X3, X4)) :- qcI(X1, X3, X2, X4). 64.55/17.44 pcJ(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) :- qcI(X1, X4, X2, X3). 64.55/17.44 pcJ(d(X1), X2) :- ','(pcJ(X1, X3), pcH(X3, X2)). 64.55/17.44 qcC(e(t), const(1)) :- pcA(d(e(const(1))), const(0)). 64.55/17.44 qcC(e(const(X1)), const(0)) :- pcA(d(e(const(0))), const(0)). 64.55/17.44 qcC(e(+(X1, X2)), +(X3, X4)) :- ','(pcH(X1, X3), ','(pcH(X2, X4), pcA(d(e(+(X3, X4))), const(0)))). 64.55/17.44 qcC(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) :- ','(pcH(X1, X4), ','(pcH(X2, X3), pcA(d(e(+(*(X1, X3), *(X2, X4)))), const(0)))). 64.55/17.44 qcC(d(X1), X2) :- ','(pcJ(X1, X3), qcC(e(X3), X2)). 64.55/17.44 qcD(X1, X2, X3, X4, X5, X6) :- ','(pcA(d(e(X1)), X2), qcE(X3, X4, X5, X6)). 64.55/17.44 qcE(X1, X2, X3, X4) :- ','(pcA(d(e(X1)), X2), pcA(d(e(X3)), X4)). 64.55/17.44 qcF(X1, X2, X3, X4) :- ','(pcJ(X1, X2), pcA(d(e(X2)), +(X3, X4))). 64.55/17.44 qcG(e(t), const(1), X1) :- pcA(d(e(const(1))), X1). 64.55/17.44 qcG(e(const(X1)), const(0), X2) :- pcA(d(e(const(0))), X2). 64.55/17.44 qcG(e(+(X1, X2)), +(X3, X4), X5) :- ','(pcH(X1, X3), ','(pcH(X2, X4), pcA(d(e(+(X3, X4))), X5))). 64.55/17.44 qcG(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) :- ','(pcH(X1, X4), ','(pcH(X2, X3), pcA(d(e(+(*(X1, X3), *(X2, X4)))), X5))). 64.55/17.44 qcG(d(X1), X2, X3) :- ','(pcJ(X1, X4), qcG(e(X4), X2, X3)). 64.55/17.44 64.55/17.44 Afs: 64.55/17.44 64.55/17.44 pA(x1, x2) = pA(x2) 64.55/17.44 64.55/17.44 64.55/17.44 ---------------------------------------- 64.55/17.44 64.55/17.44 (117) TriplesToPiDPProof (SOUND) 64.55/17.44 We use the technique of [DT09]. With regard to the inferred argument filtering the predicates were used in the following modes: 64.55/17.44 64.55/17.44 pA_in_2: (f,b) (b,b) 64.55/17.44 64.55/17.44 pB_in_2: (f,f) (b,f) 64.55/17.44 64.55/17.44 pC_in_2: (b,f) (f,f) 64.55/17.44 64.55/17.44 pD_in_6: (b,b,b,b,b,b) (f,b,f,b,f,b) (b,b,b,b,f,b) 64.55/17.44 64.55/17.44 pcA_in_2: (b,b) (f,b) 64.55/17.44 64.55/17.44 qcB_in_2: (b,f) (f,f) 64.55/17.44 64.55/17.44 qcC_in_2: (b,f) (f,f) 64.55/17.44 64.55/17.44 qcD_in_6: (b,b,b,b,b,b) (f,b,f,b,f,b) (b,b,b,b,f,b) 64.55/17.44 64.55/17.44 qcE_in_4: (b,b,b,b) (b,b,f,b) (f,b,f,b) 64.55/17.44 64.55/17.44 qcF_in_4: (b,f,b,b) (f,f,b,b) 64.55/17.44 64.55/17.44 pcJ_in_2: (b,f) (f,f) 64.55/17.44 64.55/17.44 qcI_in_4: (b,f,b,f) (f,f,f,f) 64.55/17.44 64.55/17.44 pcH_in_2: (b,f) (f,f) 64.55/17.44 64.55/17.44 qcG_in_3: (b,f,b) (f,f,b) 64.55/17.44 64.55/17.44 pE_in_4: (b,b,b,b) (b,b,f,b) (f,b,f,b) 64.55/17.44 64.55/17.44 pF_in_4: (b,f,b,b) (f,f,b,b) 64.55/17.44 64.55/17.44 pJ_in_2: (b,f) (f,f) 64.55/17.44 64.55/17.44 pI_in_4: (b,f,b,f) (f,f,f,f) 64.55/17.44 64.55/17.44 pH_in_2: (b,f) (f,f) 64.55/17.44 64.55/17.44 pG_in_3: (b,f,b) (f,f,b) 64.55/17.44 64.55/17.44 Transforming TRIPLES into the following Term Rewriting System: 64.55/17.44 64.55/17.44 Pi DP problem: 64.55/17.44 The TRS P consists of the following rules: 64.55/17.44 64.55/17.44 PA_IN_AG(d(d(X1)), const(1)) -> U65_AG(X1, pB_in_aa(X1, X2)) 64.55/17.44 PA_IN_AG(d(d(X1)), const(1)) -> PB_IN_AA(X1, X2) 64.55/17.44 PB_IN_AA(e(t), const(1)) -> U6_AA(pA_in_gg(d(e(const(1))), const(1))) 64.55/17.44 PB_IN_AA(e(t), const(1)) -> PA_IN_GG(d(e(const(1))), const(1)) 64.55/17.44 PA_IN_GG(d(d(X1)), const(1)) -> U65_GG(X1, pB_in_ga(X1, X2)) 64.55/17.44 PA_IN_GG(d(d(X1)), const(1)) -> PB_IN_GA(X1, X2) 64.55/17.44 PB_IN_GA(e(t), const(1)) -> U6_GA(pA_in_gg(d(e(const(1))), const(1))) 64.55/17.44 PB_IN_GA(e(t), const(1)) -> PA_IN_GG(d(e(const(1))), const(1)) 64.55/17.44 PA_IN_GG(d(d(X1)), const(0)) -> U66_GG(X1, pC_in_ga(X1, X2)) 64.55/17.44 PA_IN_GG(d(d(X1)), const(0)) -> PC_IN_GA(X1, X2) 64.55/17.44 PC_IN_GA(e(t), const(1)) -> U26_GA(pA_in_gg(d(e(const(1))), const(0))) 64.55/17.44 PC_IN_GA(e(t), const(1)) -> PA_IN_GG(d(e(const(1))), const(0)) 64.55/17.44 PA_IN_GG(d(e(+(t, X1))), +(const(1), X2)) -> U67_GG(X1, X2, pA_in_gg(d(e(X1)), X2)) 64.55/17.44 PA_IN_GG(d(e(+(t, X1))), +(const(1), X2)) -> PA_IN_GG(d(e(X1)), X2) 64.55/17.44 PA_IN_GG(d(e(+(const(X1), X2))), +(const(0), X3)) -> U68_GG(X1, X2, X3, pA_in_gg(d(e(X2)), X3)) 64.55/17.44 PA_IN_GG(d(e(+(const(X1), X2))), +(const(0), X3)) -> PA_IN_GG(d(e(X2)), X3) 64.55/17.44 PA_IN_GG(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) -> U69_GG(X1, X2, X3, X4, X5, X6, pD_in_gggggg(X1, X4, X2, X5, X3, X6)) 64.55/17.44 PA_IN_GG(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) -> PD_IN_GGGGGG(X1, X4, X2, X5, X3, X6) 64.55/17.44 PD_IN_GGGGGG(X1, X2, X3, X4, X5, X6) -> U41_GGGGGG(X1, X2, X3, X4, X5, X6, pA_in_gg(d(e(X1)), X2)) 64.55/17.44 PD_IN_GGGGGG(X1, X2, X3, X4, X5, X6) -> PA_IN_GG(d(e(X1)), X2) 64.55/17.44 PA_IN_GG(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) -> U70_GG(X1, X2, X3, X4, X5, X6, pD_in_gggggg(X1, X5, X2, X4, X3, X6)) 64.55/17.44 PA_IN_GG(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) -> PD_IN_GGGGGG(X1, X5, X2, X4, X3, X6) 64.55/17.44 PD_IN_GGGGGG(X1, X2, X3, X4, X5, X6) -> U42_GGGGGG(X1, X2, X3, X4, X5, X6, pcA_in_gg(d(e(X1)), X2)) 64.55/17.44 U42_GGGGGG(X1, X2, X3, X4, X5, X6, pcA_out_gg(d(e(X1)), X2)) -> U43_GGGGGG(X1, X2, X3, X4, X5, X6, pE_in_gggg(X3, X4, X5, X6)) 64.55/17.44 U42_GGGGGG(X1, X2, X3, X4, X5, X6, pcA_out_gg(d(e(X1)), X2)) -> PE_IN_GGGG(X3, X4, X5, X6) 64.55/17.44 PE_IN_GGGG(X1, X2, X3, X4) -> U44_GGGG(X1, X2, X3, X4, pA_in_gg(d(e(X1)), X2)) 64.55/17.44 PE_IN_GGGG(X1, X2, X3, X4) -> PA_IN_GG(d(e(X1)), X2) 64.55/17.44 PA_IN_GG(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) -> U71_GG(X1, X2, X3, X4, pE_in_gggg(X1, X4, X2, X3)) 64.55/17.44 PA_IN_GG(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) -> PE_IN_GGGG(X1, X4, X2, X3) 64.55/17.44 PE_IN_GGGG(X1, X2, X3, X4) -> U45_GGGG(X1, X2, X3, X4, pcA_in_gg(d(e(X1)), X2)) 64.55/17.44 U45_GGGG(X1, X2, X3, X4, pcA_out_gg(d(e(X1)), X2)) -> U46_GGGG(X1, X2, X3, X4, pA_in_gg(d(e(X3)), X4)) 64.55/17.44 U45_GGGG(X1, X2, X3, X4, pcA_out_gg(d(e(X1)), X2)) -> PA_IN_GG(d(e(X3)), X4) 64.55/17.44 PA_IN_GG(d(d(X1)), +(X2, X3)) -> U72_GG(X1, X2, X3, pF_in_gagg(X1, X4, X2, X3)) 64.55/17.44 PA_IN_GG(d(d(X1)), +(X2, X3)) -> PF_IN_GAGG(X1, X4, X2, X3) 64.55/17.44 PF_IN_GAGG(X1, X2, X3, X4) -> U47_GAGG(X1, X2, X3, X4, pJ_in_ga(X1, X2)) 64.55/17.44 PF_IN_GAGG(X1, X2, X3, X4) -> PJ_IN_GA(X1, X2) 64.55/17.44 PJ_IN_GA(e(+(X1, X2)), +(X3, X4)) -> U21_GA(X1, X2, X3, X4, pI_in_gaga(X1, X3, X2, X4)) 64.55/17.44 PJ_IN_GA(e(+(X1, X2)), +(X3, X4)) -> PI_IN_GAGA(X1, X3, X2, X4) 64.55/17.44 PI_IN_GAGA(X1, X2, X3, X4) -> U3_GAGA(X1, X2, X3, X4, pH_in_ga(X1, X2)) 64.55/17.44 PI_IN_GAGA(X1, X2, X3, X4) -> PH_IN_GA(X1, X2) 64.55/17.44 PH_IN_GA(+(X1, X2), +(X3, X4)) -> U1_GA(X1, X2, X3, X4, pI_in_gaga(X1, X3, X2, X4)) 64.55/17.44 PH_IN_GA(+(X1, X2), +(X3, X4)) -> PI_IN_GAGA(X1, X3, X2, X4) 64.55/17.44 PI_IN_GAGA(X1, X2, X3, X4) -> U4_GAGA(X1, X2, X3, X4, pcH_in_ga(X1, X2)) 64.55/17.44 U4_GAGA(X1, X2, X3, X4, pcH_out_ga(X1, X2)) -> U5_GAGA(X1, X2, X3, X4, pH_in_ga(X3, X4)) 64.55/17.44 U4_GAGA(X1, X2, X3, X4, pcH_out_ga(X1, X2)) -> PH_IN_GA(X3, X4) 64.55/17.44 PH_IN_GA(*(X1, X2), +(*(X1, X3), *(X2, X4))) -> U2_GA(X1, X2, X3, X4, pI_in_gaga(X1, X4, X2, X3)) 64.55/17.44 PH_IN_GA(*(X1, X2), +(*(X1, X3), *(X2, X4))) -> PI_IN_GAGA(X1, X4, X2, X3) 64.55/17.44 PJ_IN_GA(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U22_GA(X1, X2, X3, X4, pI_in_gaga(X1, X4, X2, X3)) 64.55/17.44 PJ_IN_GA(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> PI_IN_GAGA(X1, X4, X2, X3) 64.55/17.44 PJ_IN_GA(d(X1), X2) -> U23_GA(X1, X2, pJ_in_ga(X1, X3)) 64.55/17.44 PJ_IN_GA(d(X1), X2) -> PJ_IN_GA(X1, X3) 64.55/17.44 PJ_IN_GA(d(X1), X2) -> U24_GA(X1, X2, pcJ_in_ga(X1, X3)) 64.55/17.44 U24_GA(X1, X2, pcJ_out_ga(X1, X3)) -> U25_GA(X1, X2, pH_in_ga(X3, X2)) 64.55/17.44 U24_GA(X1, X2, pcJ_out_ga(X1, X3)) -> PH_IN_GA(X3, X2) 64.55/17.44 PF_IN_GAGG(X1, X2, X3, X4) -> U48_GAGG(X1, X2, X3, X4, pcJ_in_ga(X1, X2)) 64.55/17.44 U48_GAGG(X1, X2, X3, X4, pcJ_out_ga(X1, X2)) -> U49_GAGG(X1, X2, X3, X4, pA_in_gg(d(e(X2)), +(X3, X4))) 64.55/17.44 U48_GAGG(X1, X2, X3, X4, pcJ_out_ga(X1, X2)) -> PA_IN_GG(d(e(X2)), +(X3, X4)) 64.55/17.44 PA_IN_GG(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) -> U73_GG(X1, X2, pA_in_gg(d(e(X1)), X2)) 64.55/17.44 PA_IN_GG(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) -> PA_IN_GG(d(e(X1)), X2) 64.55/17.44 PA_IN_GG(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) -> U74_GG(X1, X2, X3, pA_in_gg(d(e(X2)), X3)) 64.55/17.44 PA_IN_GG(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) -> PA_IN_GG(d(e(X2)), X3) 64.55/17.44 PA_IN_GG(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) -> U75_GG(X1, X2, X3, X4, X5, X6, pD_in_gggggg(X1, X5, X2, X6, X3, X4)) 64.55/17.44 PA_IN_GG(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) -> PD_IN_GGGGGG(X1, X5, X2, X6, X3, X4) 64.55/17.44 PA_IN_GG(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) -> U76_GG(X1, X2, X3, X4, X5, X6, pD_in_gggggg(X1, X6, X2, X5, X3, X4)) 64.55/17.44 PA_IN_GG(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) -> PD_IN_GGGGGG(X1, X6, X2, X5, X3, X4) 64.55/17.44 PA_IN_GG(d(d(X1)), +(*(X2, X3), *(X4, X5))) -> U77_GG(X1, X2, X3, X4, X5, pF_in_gagg(X1, X6, *(X2, X3), *(X4, X5))) 64.55/17.44 PA_IN_GG(d(d(X1)), +(*(X2, X3), *(X4, X5))) -> PF_IN_GAGG(X1, X6, *(X2, X3), *(X4, X5)) 64.55/17.44 PA_IN_GG(d(d(X1)), X2) -> U78_GG(X1, X2, pG_in_gag(X1, X3, X2)) 64.55/17.44 PA_IN_GG(d(d(X1)), X2) -> PG_IN_GAG(X1, X3, X2) 64.55/17.44 PG_IN_GAG(e(t), const(1), X1) -> U50_GAG(X1, pA_in_gg(d(e(const(1))), X1)) 64.55/17.44 PG_IN_GAG(e(t), const(1), X1) -> PA_IN_GG(d(e(const(1))), X1) 64.55/17.44 PG_IN_GAG(e(const(X1)), const(0), X2) -> U51_GAG(X1, X2, pA_in_gg(d(e(const(0))), X2)) 64.55/17.44 PG_IN_GAG(e(const(X1)), const(0), X2) -> PA_IN_GG(d(e(const(0))), X2) 64.55/17.44 PG_IN_GAG(e(+(X1, X2)), +(X3, X4), X5) -> U52_GAG(X1, X2, X3, X4, X5, pH_in_ga(X1, X3)) 64.55/17.44 PG_IN_GAG(e(+(X1, X2)), +(X3, X4), X5) -> PH_IN_GA(X1, X3) 64.55/17.44 PG_IN_GAG(e(+(X1, X2)), +(X3, X4), X5) -> U53_GAG(X1, X2, X3, X4, X5, pcH_in_ga(X1, X3)) 64.55/17.44 U53_GAG(X1, X2, X3, X4, X5, pcH_out_ga(X1, X3)) -> U54_GAG(X1, X2, X3, X4, X5, pH_in_ga(X2, X4)) 64.55/17.44 U53_GAG(X1, X2, X3, X4, X5, pcH_out_ga(X1, X3)) -> PH_IN_GA(X2, X4) 64.55/17.44 U53_GAG(X1, X2, X3, X4, X5, pcH_out_ga(X1, X3)) -> U55_GAG(X1, X2, X3, X4, X5, pcH_in_ga(X2, X4)) 64.55/17.44 U55_GAG(X1, X2, X3, X4, X5, pcH_out_ga(X2, X4)) -> U56_GAG(X1, X2, X3, X4, X5, pA_in_gg(d(e(+(X3, X4))), X5)) 64.55/17.44 U55_GAG(X1, X2, X3, X4, X5, pcH_out_ga(X2, X4)) -> PA_IN_GG(d(e(+(X3, X4))), X5) 64.55/17.44 PG_IN_GAG(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) -> U57_GAG(X1, X2, X3, X4, X5, pH_in_ga(X1, X4)) 64.55/17.44 PG_IN_GAG(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) -> PH_IN_GA(X1, X4) 64.55/17.44 PG_IN_GAG(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) -> U58_GAG(X1, X2, X3, X4, X5, pcH_in_ga(X1, X4)) 64.55/17.44 U58_GAG(X1, X2, X3, X4, X5, pcH_out_ga(X1, X4)) -> U59_GAG(X1, X2, X3, X4, X5, pH_in_ga(X2, X3)) 64.55/17.44 U58_GAG(X1, X2, X3, X4, X5, pcH_out_ga(X1, X4)) -> PH_IN_GA(X2, X3) 64.55/17.44 U58_GAG(X1, X2, X3, X4, X5, pcH_out_ga(X1, X4)) -> U60_GAG(X1, X2, X3, X4, X5, pcH_in_ga(X2, X3)) 64.55/17.44 U60_GAG(X1, X2, X3, X4, X5, pcH_out_ga(X2, X3)) -> U61_GAG(X1, X2, X3, X4, X5, pA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), X5)) 64.55/17.44 U60_GAG(X1, X2, X3, X4, X5, pcH_out_ga(X2, X3)) -> PA_IN_GG(d(e(+(*(X1, X3), *(X2, X4)))), X5) 64.55/17.44 PG_IN_GAG(d(X1), X2, X3) -> U62_GAG(X1, X2, X3, pJ_in_ga(X1, X4)) 64.55/17.44 PG_IN_GAG(d(X1), X2, X3) -> PJ_IN_GA(X1, X4) 64.55/17.44 PG_IN_GAG(d(X1), X2, X3) -> U63_GAG(X1, X2, X3, pcJ_in_ga(X1, X4)) 64.55/17.44 U63_GAG(X1, X2, X3, pcJ_out_ga(X1, X4)) -> U64_GAG(X1, X2, X3, pG_in_gag(e(X4), X2, X3)) 64.55/17.44 U63_GAG(X1, X2, X3, pcJ_out_ga(X1, X4)) -> PG_IN_GAG(e(X4), X2, X3) 64.55/17.44 PC_IN_GA(e(const(X1)), const(0)) -> U27_GA(X1, pA_in_gg(d(e(const(0))), const(0))) 64.55/17.44 PC_IN_GA(e(const(X1)), const(0)) -> PA_IN_GG(d(e(const(0))), const(0)) 64.55/17.44 PC_IN_GA(e(+(X1, X2)), +(X3, X4)) -> U28_GA(X1, X2, X3, X4, pH_in_ga(X1, X3)) 64.55/17.44 PC_IN_GA(e(+(X1, X2)), +(X3, X4)) -> PH_IN_GA(X1, X3) 64.55/17.44 PC_IN_GA(e(+(X1, X2)), +(X3, X4)) -> U29_GA(X1, X2, X3, X4, pcH_in_ga(X1, X3)) 64.55/17.44 U29_GA(X1, X2, X3, X4, pcH_out_ga(X1, X3)) -> U30_GA(X1, X2, X3, X4, pH_in_ga(X2, X4)) 64.55/17.44 U29_GA(X1, X2, X3, X4, pcH_out_ga(X1, X3)) -> PH_IN_GA(X2, X4) 64.55/17.44 U29_GA(X1, X2, X3, X4, pcH_out_ga(X1, X3)) -> U31_GA(X1, X2, X3, X4, pcH_in_ga(X2, X4)) 64.55/17.44 U31_GA(X1, X2, X3, X4, pcH_out_ga(X2, X4)) -> U32_GA(X1, X2, X3, X4, pA_in_gg(d(e(+(X3, X4))), const(0))) 64.55/17.44 U31_GA(X1, X2, X3, X4, pcH_out_ga(X2, X4)) -> PA_IN_GG(d(e(+(X3, X4))), const(0)) 64.55/17.44 PC_IN_GA(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U33_GA(X1, X2, X3, X4, pH_in_ga(X1, X4)) 64.55/17.44 PC_IN_GA(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> PH_IN_GA(X1, X4) 64.55/17.44 PC_IN_GA(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U34_GA(X1, X2, X3, X4, pcH_in_ga(X1, X4)) 64.55/17.44 U34_GA(X1, X2, X3, X4, pcH_out_ga(X1, X4)) -> U35_GA(X1, X2, X3, X4, pH_in_ga(X2, X3)) 64.55/17.44 U34_GA(X1, X2, X3, X4, pcH_out_ga(X1, X4)) -> PH_IN_GA(X2, X3) 64.55/17.44 U34_GA(X1, X2, X3, X4, pcH_out_ga(X1, X4)) -> U36_GA(X1, X2, X3, X4, pcH_in_ga(X2, X3)) 64.55/17.44 U36_GA(X1, X2, X3, X4, pcH_out_ga(X2, X3)) -> U37_GA(X1, X2, X3, X4, pA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(0))) 64.55/17.44 U36_GA(X1, X2, X3, X4, pcH_out_ga(X2, X3)) -> PA_IN_GG(d(e(+(*(X1, X3), *(X2, X4)))), const(0)) 64.55/17.44 PC_IN_GA(d(X1), X2) -> U38_GA(X1, X2, pJ_in_ga(X1, X3)) 64.55/17.44 PC_IN_GA(d(X1), X2) -> PJ_IN_GA(X1, X3) 64.55/17.44 PC_IN_GA(d(X1), X2) -> U39_GA(X1, X2, pcJ_in_ga(X1, X3)) 64.55/17.44 U39_GA(X1, X2, pcJ_out_ga(X1, X3)) -> U40_GA(X1, X2, pC_in_ga(e(X3), X2)) 64.55/17.44 U39_GA(X1, X2, pcJ_out_ga(X1, X3)) -> PC_IN_GA(e(X3), X2) 64.55/17.44 PB_IN_GA(e(const(X1)), const(0)) -> U7_GA(X1, pA_in_gg(d(e(const(0))), const(1))) 64.55/17.44 PB_IN_GA(e(const(X1)), const(0)) -> PA_IN_GG(d(e(const(0))), const(1)) 64.55/17.44 PB_IN_GA(e(+(X1, X2)), +(X3, X4)) -> U8_GA(X1, X2, X3, X4, pH_in_ga(X1, X3)) 64.55/17.44 PB_IN_GA(e(+(X1, X2)), +(X3, X4)) -> PH_IN_GA(X1, X3) 64.55/17.44 PB_IN_GA(e(+(X1, X2)), +(X3, X4)) -> U9_GA(X1, X2, X3, X4, pcH_in_ga(X1, X3)) 64.55/17.44 U9_GA(X1, X2, X3, X4, pcH_out_ga(X1, X3)) -> U10_GA(X1, X2, X3, X4, pH_in_ga(X2, X4)) 64.55/17.44 U9_GA(X1, X2, X3, X4, pcH_out_ga(X1, X3)) -> PH_IN_GA(X2, X4) 64.55/17.44 U9_GA(X1, X2, X3, X4, pcH_out_ga(X1, X3)) -> U11_GA(X1, X2, X3, X4, pcH_in_ga(X2, X4)) 64.55/17.44 U11_GA(X1, X2, X3, X4, pcH_out_ga(X2, X4)) -> U12_GA(X1, X2, X3, X4, pA_in_gg(d(e(+(X3, X4))), const(1))) 64.55/17.44 U11_GA(X1, X2, X3, X4, pcH_out_ga(X2, X4)) -> PA_IN_GG(d(e(+(X3, X4))), const(1)) 64.55/17.44 PB_IN_GA(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U13_GA(X1, X2, X3, X4, pH_in_ga(X1, X4)) 64.55/17.44 PB_IN_GA(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> PH_IN_GA(X1, X4) 64.55/17.44 PB_IN_GA(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U14_GA(X1, X2, X3, X4, pcH_in_ga(X1, X4)) 64.55/17.44 U14_GA(X1, X2, X3, X4, pcH_out_ga(X1, X4)) -> U15_GA(X1, X2, X3, X4, pH_in_ga(X2, X3)) 64.55/17.44 U14_GA(X1, X2, X3, X4, pcH_out_ga(X1, X4)) -> PH_IN_GA(X2, X3) 64.55/17.44 U14_GA(X1, X2, X3, X4, pcH_out_ga(X1, X4)) -> U16_GA(X1, X2, X3, X4, pcH_in_ga(X2, X3)) 64.55/17.44 U16_GA(X1, X2, X3, X4, pcH_out_ga(X2, X3)) -> U17_GA(X1, X2, X3, X4, pA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(1))) 64.55/17.44 U16_GA(X1, X2, X3, X4, pcH_out_ga(X2, X3)) -> PA_IN_GG(d(e(+(*(X1, X3), *(X2, X4)))), const(1)) 64.55/17.44 PB_IN_GA(d(X1), X2) -> U18_GA(X1, X2, pJ_in_ga(X1, X3)) 64.55/17.44 PB_IN_GA(d(X1), X2) -> PJ_IN_GA(X1, X3) 64.55/17.44 PB_IN_GA(d(X1), X2) -> U19_GA(X1, X2, pcJ_in_ga(X1, X3)) 64.55/17.44 U19_GA(X1, X2, pcJ_out_ga(X1, X3)) -> U20_GA(X1, X2, pB_in_ga(e(X3), X2)) 64.55/17.44 U19_GA(X1, X2, pcJ_out_ga(X1, X3)) -> PB_IN_GA(e(X3), X2) 64.55/17.44 PB_IN_AA(e(const(X1)), const(0)) -> U7_AA(X1, pA_in_gg(d(e(const(0))), const(1))) 64.55/17.44 PB_IN_AA(e(const(X1)), const(0)) -> PA_IN_GG(d(e(const(0))), const(1)) 64.55/17.44 PB_IN_AA(e(+(X1, X2)), +(X3, X4)) -> U8_AA(X1, X2, X3, X4, pH_in_aa(X1, X3)) 64.55/17.44 PB_IN_AA(e(+(X1, X2)), +(X3, X4)) -> PH_IN_AA(X1, X3) 64.55/17.44 PH_IN_AA(+(X1, X2), +(X3, X4)) -> U1_AA(X1, X2, X3, X4, pI_in_aaaa(X1, X3, X2, X4)) 64.55/17.44 PH_IN_AA(+(X1, X2), +(X3, X4)) -> PI_IN_AAAA(X1, X3, X2, X4) 64.55/17.44 PI_IN_AAAA(X1, X2, X3, X4) -> U3_AAAA(X1, X2, X3, X4, pH_in_aa(X1, X2)) 64.55/17.44 PI_IN_AAAA(X1, X2, X3, X4) -> PH_IN_AA(X1, X2) 64.55/17.44 PH_IN_AA(*(X1, X2), +(*(X1, X3), *(X2, X4))) -> U2_AA(X1, X2, X3, X4, pI_in_aaaa(X1, X4, X2, X3)) 64.55/17.44 PH_IN_AA(*(X1, X2), +(*(X1, X3), *(X2, X4))) -> PI_IN_AAAA(X1, X4, X2, X3) 64.55/17.44 PI_IN_AAAA(X1, X2, X3, X4) -> U4_AAAA(X1, X2, X3, X4, pcH_in_aa(X1, X2)) 64.55/17.44 U4_AAAA(X1, X2, X3, X4, pcH_out_aa(X1, X2)) -> U5_AAAA(X1, X2, X3, X4, pH_in_aa(X3, X4)) 64.55/17.44 U4_AAAA(X1, X2, X3, X4, pcH_out_aa(X1, X2)) -> PH_IN_AA(X3, X4) 64.55/17.44 PB_IN_AA(e(+(X1, X2)), +(X3, X4)) -> U9_AA(X1, X2, X3, X4, pcH_in_aa(X1, X3)) 64.55/17.44 U9_AA(X1, X2, X3, X4, pcH_out_aa(X1, X3)) -> U10_AA(X1, X2, X3, X4, pH_in_aa(X2, X4)) 64.55/17.44 U9_AA(X1, X2, X3, X4, pcH_out_aa(X1, X3)) -> PH_IN_AA(X2, X4) 64.55/17.44 U9_AA(X1, X2, X3, X4, pcH_out_aa(X1, X3)) -> U11_AA(X1, X2, X3, X4, pcH_in_aa(X2, X4)) 64.55/17.44 U11_AA(X1, X2, X3, X4, pcH_out_aa(X2, X4)) -> U12_AA(X1, X2, X3, X4, pA_in_gg(d(e(+(X3, X4))), const(1))) 64.55/17.44 U11_AA(X1, X2, X3, X4, pcH_out_aa(X2, X4)) -> PA_IN_GG(d(e(+(X3, X4))), const(1)) 64.55/17.44 PB_IN_AA(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U13_AA(X1, X2, X3, X4, pH_in_aa(X1, X4)) 64.55/17.44 PB_IN_AA(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> PH_IN_AA(X1, X4) 64.55/17.44 PB_IN_AA(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U14_AA(X1, X2, X3, X4, pcH_in_aa(X1, X4)) 64.55/17.44 U14_AA(X1, X2, X3, X4, pcH_out_aa(X1, X4)) -> U15_AA(X1, X2, X3, X4, pH_in_aa(X2, X3)) 64.55/17.44 U14_AA(X1, X2, X3, X4, pcH_out_aa(X1, X4)) -> PH_IN_AA(X2, X3) 64.55/17.44 U14_AA(X1, X2, X3, X4, pcH_out_aa(X1, X4)) -> U16_AA(X1, X2, X3, X4, pcH_in_aa(X2, X3)) 64.55/17.44 U16_AA(X1, X2, X3, X4, pcH_out_aa(X2, X3)) -> U17_AA(X1, X2, X3, X4, pA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(1))) 64.55/17.44 U16_AA(X1, X2, X3, X4, pcH_out_aa(X2, X3)) -> PA_IN_GG(d(e(+(*(X1, X3), *(X2, X4)))), const(1)) 64.55/17.44 PB_IN_AA(d(X1), X2) -> U18_AA(X1, X2, pJ_in_aa(X1, X3)) 64.55/17.44 PB_IN_AA(d(X1), X2) -> PJ_IN_AA(X1, X3) 64.55/17.44 PJ_IN_AA(e(+(X1, X2)), +(X3, X4)) -> U21_AA(X1, X2, X3, X4, pI_in_aaaa(X1, X3, X2, X4)) 64.55/17.44 PJ_IN_AA(e(+(X1, X2)), +(X3, X4)) -> PI_IN_AAAA(X1, X3, X2, X4) 64.55/17.44 PJ_IN_AA(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U22_AA(X1, X2, X3, X4, pI_in_aaaa(X1, X4, X2, X3)) 64.55/17.44 PJ_IN_AA(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> PI_IN_AAAA(X1, X4, X2, X3) 64.55/17.44 PJ_IN_AA(d(X1), X2) -> U23_AA(X1, X2, pJ_in_aa(X1, X3)) 64.55/17.44 PJ_IN_AA(d(X1), X2) -> PJ_IN_AA(X1, X3) 64.55/17.44 PJ_IN_AA(d(X1), X2) -> U24_AA(X1, X2, pcJ_in_aa(X1, X3)) 64.55/17.44 U24_AA(X1, X2, pcJ_out_aa(X1, X3)) -> U25_AA(X1, X2, pH_in_ga(X3, X2)) 64.55/17.44 U24_AA(X1, X2, pcJ_out_aa(X1, X3)) -> PH_IN_GA(X3, X2) 64.55/17.44 PB_IN_AA(d(X1), X2) -> U19_AA(X1, X2, pcJ_in_aa(X1, X3)) 64.55/17.44 U19_AA(X1, X2, pcJ_out_aa(X1, X3)) -> U20_AA(X1, X2, pB_in_ga(e(X3), X2)) 64.55/17.44 U19_AA(X1, X2, pcJ_out_aa(X1, X3)) -> PB_IN_GA(e(X3), X2) 64.55/17.44 PA_IN_AG(d(d(X1)), const(0)) -> U66_AG(X1, pC_in_aa(X1, X2)) 64.55/17.44 PA_IN_AG(d(d(X1)), const(0)) -> PC_IN_AA(X1, X2) 64.55/17.44 PC_IN_AA(e(t), const(1)) -> U26_AA(pA_in_gg(d(e(const(1))), const(0))) 64.55/17.44 PC_IN_AA(e(t), const(1)) -> PA_IN_GG(d(e(const(1))), const(0)) 64.55/17.44 PC_IN_AA(e(const(X1)), const(0)) -> U27_AA(X1, pA_in_gg(d(e(const(0))), const(0))) 64.55/17.44 PC_IN_AA(e(const(X1)), const(0)) -> PA_IN_GG(d(e(const(0))), const(0)) 64.55/17.44 PC_IN_AA(e(+(X1, X2)), +(X3, X4)) -> U28_AA(X1, X2, X3, X4, pH_in_aa(X1, X3)) 64.55/17.44 PC_IN_AA(e(+(X1, X2)), +(X3, X4)) -> PH_IN_AA(X1, X3) 64.55/17.44 PC_IN_AA(e(+(X1, X2)), +(X3, X4)) -> U29_AA(X1, X2, X3, X4, pcH_in_aa(X1, X3)) 64.55/17.44 U29_AA(X1, X2, X3, X4, pcH_out_aa(X1, X3)) -> U30_AA(X1, X2, X3, X4, pH_in_aa(X2, X4)) 64.55/17.44 U29_AA(X1, X2, X3, X4, pcH_out_aa(X1, X3)) -> PH_IN_AA(X2, X4) 64.55/17.44 U29_AA(X1, X2, X3, X4, pcH_out_aa(X1, X3)) -> U31_AA(X1, X2, X3, X4, pcH_in_aa(X2, X4)) 64.55/17.44 U31_AA(X1, X2, X3, X4, pcH_out_aa(X2, X4)) -> U32_AA(X1, X2, X3, X4, pA_in_gg(d(e(+(X3, X4))), const(0))) 64.55/17.44 U31_AA(X1, X2, X3, X4, pcH_out_aa(X2, X4)) -> PA_IN_GG(d(e(+(X3, X4))), const(0)) 64.55/17.44 PC_IN_AA(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U33_AA(X1, X2, X3, X4, pH_in_aa(X1, X4)) 64.55/17.44 PC_IN_AA(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> PH_IN_AA(X1, X4) 64.55/17.44 PC_IN_AA(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U34_AA(X1, X2, X3, X4, pcH_in_aa(X1, X4)) 64.55/17.44 U34_AA(X1, X2, X3, X4, pcH_out_aa(X1, X4)) -> U35_AA(X1, X2, X3, X4, pH_in_aa(X2, X3)) 64.55/17.44 U34_AA(X1, X2, X3, X4, pcH_out_aa(X1, X4)) -> PH_IN_AA(X2, X3) 64.55/17.44 U34_AA(X1, X2, X3, X4, pcH_out_aa(X1, X4)) -> U36_AA(X1, X2, X3, X4, pcH_in_aa(X2, X3)) 64.55/17.44 U36_AA(X1, X2, X3, X4, pcH_out_aa(X2, X3)) -> U37_AA(X1, X2, X3, X4, pA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(0))) 64.55/17.44 U36_AA(X1, X2, X3, X4, pcH_out_aa(X2, X3)) -> PA_IN_GG(d(e(+(*(X1, X3), *(X2, X4)))), const(0)) 64.55/17.44 PC_IN_AA(d(X1), X2) -> U38_AA(X1, X2, pJ_in_aa(X1, X3)) 64.55/17.44 PC_IN_AA(d(X1), X2) -> PJ_IN_AA(X1, X3) 64.55/17.44 PC_IN_AA(d(X1), X2) -> U39_AA(X1, X2, pcJ_in_aa(X1, X3)) 64.55/17.44 U39_AA(X1, X2, pcJ_out_aa(X1, X3)) -> U40_AA(X1, X2, pC_in_ga(e(X3), X2)) 64.55/17.44 U39_AA(X1, X2, pcJ_out_aa(X1, X3)) -> PC_IN_GA(e(X3), X2) 64.55/17.44 PA_IN_AG(d(e(+(t, X1))), +(const(1), X2)) -> U67_AG(X1, X2, pA_in_ag(d(e(X1)), X2)) 64.55/17.44 PA_IN_AG(d(e(+(t, X1))), +(const(1), X2)) -> PA_IN_AG(d(e(X1)), X2) 64.55/17.44 PA_IN_AG(d(e(+(const(X1), X2))), +(const(0), X3)) -> U68_AG(X1, X2, X3, pA_in_ag(d(e(X2)), X3)) 64.55/17.44 PA_IN_AG(d(e(+(const(X1), X2))), +(const(0), X3)) -> PA_IN_AG(d(e(X2)), X3) 64.55/17.44 PA_IN_AG(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) -> U69_AG(X1, X2, X3, X4, X5, X6, pD_in_agagag(X1, X4, X2, X5, X3, X6)) 64.55/17.44 PA_IN_AG(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) -> PD_IN_AGAGAG(X1, X4, X2, X5, X3, X6) 64.55/17.44 PD_IN_AGAGAG(X1, X2, X3, X4, X5, X6) -> U41_AGAGAG(X1, X2, X3, X4, X5, X6, pA_in_ag(d(e(X1)), X2)) 64.55/17.44 PD_IN_AGAGAG(X1, X2, X3, X4, X5, X6) -> PA_IN_AG(d(e(X1)), X2) 64.55/17.44 PA_IN_AG(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) -> U70_AG(X1, X2, X3, X4, X5, X6, pD_in_ggggag(X1, X5, X2, X4, X3, X6)) 64.55/17.44 PA_IN_AG(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) -> PD_IN_GGGGAG(X1, X5, X2, X4, X3, X6) 64.55/17.44 PD_IN_GGGGAG(X1, X2, X3, X4, X5, X6) -> U41_GGGGAG(X1, X2, X3, X4, X5, X6, pA_in_gg(d(e(X1)), X2)) 64.55/17.44 PD_IN_GGGGAG(X1, X2, X3, X4, X5, X6) -> PA_IN_GG(d(e(X1)), X2) 64.55/17.44 PD_IN_GGGGAG(X1, X2, X3, X4, X5, X6) -> U42_GGGGAG(X1, X2, X3, X4, X5, X6, pcA_in_gg(d(e(X1)), X2)) 64.55/17.44 U42_GGGGAG(X1, X2, X3, X4, X5, X6, pcA_out_gg(d(e(X1)), X2)) -> U43_GGGGAG(X1, X2, X3, X4, X5, X6, pE_in_ggag(X3, X4, X5, X6)) 64.55/17.44 U42_GGGGAG(X1, X2, X3, X4, X5, X6, pcA_out_gg(d(e(X1)), X2)) -> PE_IN_GGAG(X3, X4, X5, X6) 64.55/17.44 PE_IN_GGAG(X1, X2, X3, X4) -> U44_GGAG(X1, X2, X3, X4, pA_in_gg(d(e(X1)), X2)) 64.55/17.44 PE_IN_GGAG(X1, X2, X3, X4) -> PA_IN_GG(d(e(X1)), X2) 64.55/17.44 PE_IN_GGAG(X1, X2, X3, X4) -> U45_GGAG(X1, X2, X3, X4, pcA_in_gg(d(e(X1)), X2)) 64.55/17.44 U45_GGAG(X1, X2, X3, X4, pcA_out_gg(d(e(X1)), X2)) -> U46_GGAG(X1, X2, X3, X4, pA_in_ag(d(e(X3)), X4)) 64.55/17.44 U45_GGAG(X1, X2, X3, X4, pcA_out_gg(d(e(X1)), X2)) -> PA_IN_AG(d(e(X3)), X4) 64.55/17.44 PA_IN_AG(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) -> U71_AG(X1, X2, X3, X4, pE_in_gggg(X1, X4, X2, X3)) 64.55/17.44 PA_IN_AG(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) -> PE_IN_GGGG(X1, X4, X2, X3) 64.55/17.44 PA_IN_AG(d(d(X1)), +(X2, X3)) -> U72_AG(X1, X2, X3, pF_in_aagg(X1, X4, X2, X3)) 64.55/17.44 PA_IN_AG(d(d(X1)), +(X2, X3)) -> PF_IN_AAGG(X1, X4, X2, X3) 64.55/17.44 PF_IN_AAGG(X1, X2, X3, X4) -> U47_AAGG(X1, X2, X3, X4, pJ_in_aa(X1, X2)) 64.55/17.44 PF_IN_AAGG(X1, X2, X3, X4) -> PJ_IN_AA(X1, X2) 64.55/17.44 PF_IN_AAGG(X1, X2, X3, X4) -> U48_AAGG(X1, X2, X3, X4, pcJ_in_aa(X1, X2)) 64.55/17.44 U48_AAGG(X1, X2, X3, X4, pcJ_out_aa(X1, X2)) -> U49_AAGG(X1, X2, X3, X4, pA_in_gg(d(e(X2)), +(X3, X4))) 64.55/17.44 U48_AAGG(X1, X2, X3, X4, pcJ_out_aa(X1, X2)) -> PA_IN_GG(d(e(X2)), +(X3, X4)) 64.55/17.44 PA_IN_AG(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) -> U73_AG(X1, X2, pA_in_gg(d(e(X1)), X2)) 64.55/17.44 PA_IN_AG(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) -> PA_IN_GG(d(e(X1)), X2) 64.55/17.44 PA_IN_AG(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) -> U74_AG(X1, X2, X3, pA_in_gg(d(e(X2)), X3)) 64.55/17.44 PA_IN_AG(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) -> PA_IN_GG(d(e(X2)), X3) 64.55/17.44 PA_IN_AG(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) -> U75_AG(X1, X2, X3, X4, X5, X6, pD_in_gggggg(X1, X5, X2, X6, X3, X4)) 64.55/17.44 PA_IN_AG(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) -> PD_IN_GGGGGG(X1, X5, X2, X6, X3, X4) 64.55/17.44 PA_IN_AG(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) -> U76_AG(X1, X2, X3, X4, X5, X6, pD_in_gggggg(X1, X6, X2, X5, X3, X4)) 64.55/17.44 PA_IN_AG(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) -> PD_IN_GGGGGG(X1, X6, X2, X5, X3, X4) 64.55/17.44 PA_IN_AG(d(d(X1)), +(*(X2, X3), *(X4, X5))) -> U77_AG(X1, X2, X3, X4, X5, pF_in_aagg(X1, X6, *(X2, X3), *(X4, X5))) 64.55/17.44 PA_IN_AG(d(d(X1)), +(*(X2, X3), *(X4, X5))) -> PF_IN_AAGG(X1, X6, *(X2, X3), *(X4, X5)) 64.55/17.44 PA_IN_AG(d(d(X1)), X2) -> U78_AG(X1, X2, pG_in_aag(X1, X3, X2)) 64.55/17.44 PA_IN_AG(d(d(X1)), X2) -> PG_IN_AAG(X1, X3, X2) 64.55/17.44 PG_IN_AAG(e(t), const(1), X1) -> U50_AAG(X1, pA_in_gg(d(e(const(1))), X1)) 64.55/17.44 PG_IN_AAG(e(t), const(1), X1) -> PA_IN_GG(d(e(const(1))), X1) 64.55/17.44 PG_IN_AAG(e(const(X1)), const(0), X2) -> U51_AAG(X1, X2, pA_in_gg(d(e(const(0))), X2)) 64.55/17.44 PG_IN_AAG(e(const(X1)), const(0), X2) -> PA_IN_GG(d(e(const(0))), X2) 64.55/17.44 PG_IN_AAG(e(+(X1, X2)), +(X3, X4), X5) -> U52_AAG(X1, X2, X3, X4, X5, pH_in_aa(X1, X3)) 64.55/17.44 PG_IN_AAG(e(+(X1, X2)), +(X3, X4), X5) -> PH_IN_AA(X1, X3) 64.55/17.44 PG_IN_AAG(e(+(X1, X2)), +(X3, X4), X5) -> U53_AAG(X1, X2, X3, X4, X5, pcH_in_aa(X1, X3)) 64.55/17.44 U53_AAG(X1, X2, X3, X4, X5, pcH_out_aa(X1, X3)) -> U54_AAG(X1, X2, X3, X4, X5, pH_in_aa(X2, X4)) 64.55/17.44 U53_AAG(X1, X2, X3, X4, X5, pcH_out_aa(X1, X3)) -> PH_IN_AA(X2, X4) 64.55/17.44 U53_AAG(X1, X2, X3, X4, X5, pcH_out_aa(X1, X3)) -> U55_AAG(X1, X2, X3, X4, X5, pcH_in_aa(X2, X4)) 64.55/17.44 U55_AAG(X1, X2, X3, X4, X5, pcH_out_aa(X2, X4)) -> U56_AAG(X1, X2, X3, X4, X5, pA_in_gg(d(e(+(X3, X4))), X5)) 64.55/17.44 U55_AAG(X1, X2, X3, X4, X5, pcH_out_aa(X2, X4)) -> PA_IN_GG(d(e(+(X3, X4))), X5) 64.55/17.44 PG_IN_AAG(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) -> U57_AAG(X1, X2, X3, X4, X5, pH_in_aa(X1, X4)) 64.55/17.44 PG_IN_AAG(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) -> PH_IN_AA(X1, X4) 64.55/17.44 PG_IN_AAG(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) -> U58_AAG(X1, X2, X3, X4, X5, pcH_in_aa(X1, X4)) 64.55/17.44 U58_AAG(X1, X2, X3, X4, X5, pcH_out_aa(X1, X4)) -> U59_AAG(X1, X2, X3, X4, X5, pH_in_aa(X2, X3)) 64.55/17.44 U58_AAG(X1, X2, X3, X4, X5, pcH_out_aa(X1, X4)) -> PH_IN_AA(X2, X3) 64.55/17.44 U58_AAG(X1, X2, X3, X4, X5, pcH_out_aa(X1, X4)) -> U60_AAG(X1, X2, X3, X4, X5, pcH_in_aa(X2, X3)) 64.55/17.44 U60_AAG(X1, X2, X3, X4, X5, pcH_out_aa(X2, X3)) -> U61_AAG(X1, X2, X3, X4, X5, pA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), X5)) 64.55/17.44 U60_AAG(X1, X2, X3, X4, X5, pcH_out_aa(X2, X3)) -> PA_IN_GG(d(e(+(*(X1, X3), *(X2, X4)))), X5) 64.55/17.44 PG_IN_AAG(d(X1), X2, X3) -> U62_AAG(X1, X2, X3, pJ_in_aa(X1, X4)) 64.55/17.44 PG_IN_AAG(d(X1), X2, X3) -> PJ_IN_AA(X1, X4) 64.55/17.44 PG_IN_AAG(d(X1), X2, X3) -> U63_AAG(X1, X2, X3, pcJ_in_aa(X1, X4)) 64.55/17.44 U63_AAG(X1, X2, X3, pcJ_out_aa(X1, X4)) -> U64_AAG(X1, X2, X3, pG_in_gag(e(X4), X2, X3)) 64.55/17.44 U63_AAG(X1, X2, X3, pcJ_out_aa(X1, X4)) -> PG_IN_GAG(e(X4), X2, X3) 64.55/17.44 PD_IN_AGAGAG(X1, X2, X3, X4, X5, X6) -> U42_AGAGAG(X1, X2, X3, X4, X5, X6, pcA_in_ag(d(e(X1)), X2)) 64.55/17.44 U42_AGAGAG(X1, X2, X3, X4, X5, X6, pcA_out_ag(d(e(X1)), X2)) -> U43_AGAGAG(X1, X2, X3, X4, X5, X6, pE_in_agag(X3, X4, X5, X6)) 64.55/17.44 U42_AGAGAG(X1, X2, X3, X4, X5, X6, pcA_out_ag(d(e(X1)), X2)) -> PE_IN_AGAG(X3, X4, X5, X6) 64.55/17.44 PE_IN_AGAG(X1, X2, X3, X4) -> U44_AGAG(X1, X2, X3, X4, pA_in_ag(d(e(X1)), X2)) 64.55/17.44 PE_IN_AGAG(X1, X2, X3, X4) -> PA_IN_AG(d(e(X1)), X2) 64.55/17.44 PE_IN_AGAG(X1, X2, X3, X4) -> U45_AGAG(X1, X2, X3, X4, pcA_in_ag(d(e(X1)), X2)) 64.55/17.44 U45_AGAG(X1, X2, X3, X4, pcA_out_ag(d(e(X1)), X2)) -> U46_AGAG(X1, X2, X3, X4, pA_in_ag(d(e(X3)), X4)) 64.55/17.44 U45_AGAG(X1, X2, X3, X4, pcA_out_ag(d(e(X1)), X2)) -> PA_IN_AG(d(e(X3)), X4) 64.55/17.44 64.55/17.44 The TRS R consists of the following rules: 64.55/17.44 64.55/17.44 pcA_in_gg(d(e(t)), const(1)) -> pcA_out_gg(d(e(t)), const(1)) 64.55/17.44 pcA_in_gg(d(d(X1)), const(1)) -> U80_gg(X1, qcB_in_ga(X1, X2)) 64.55/17.44 qcB_in_ga(e(t), const(1)) -> U98_ga(pcA_in_gg(d(e(const(1))), const(1))) 64.55/17.44 pcA_in_gg(d(e(const(X1))), const(0)) -> pcA_out_gg(d(e(const(X1))), const(0)) 64.55/17.44 pcA_in_gg(d(d(X1)), const(0)) -> U81_gg(X1, qcC_in_ga(X1, X2)) 64.55/17.44 qcC_in_ga(e(t), const(1)) -> U112_ga(pcA_in_gg(d(e(const(1))), const(0))) 64.55/17.44 pcA_in_gg(d(e(+(t, X1))), +(const(1), X2)) -> U82_gg(X1, X2, pcA_in_gg(d(e(X1)), X2)) 64.55/17.44 pcA_in_gg(d(e(+(const(X1), X2))), +(const(0), X3)) -> U83_gg(X1, X2, X3, pcA_in_gg(d(e(X2)), X3)) 64.55/17.44 pcA_in_gg(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) -> U84_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X4, X2, X5, X3, X6)) 64.55/17.44 qcD_in_gggggg(X1, X2, X3, X4, X5, X6) -> U122_gggggg(X1, X2, X3, X4, X5, X6, pcA_in_gg(d(e(X1)), X2)) 64.55/17.44 pcA_in_gg(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) -> U85_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X5, X2, X4, X3, X6)) 64.55/17.44 U85_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X5, X2, X4, X3, X6)) -> pcA_out_gg(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) 64.55/17.44 pcA_in_gg(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) -> U86_gg(X1, X2, X3, X4, qcE_in_gggg(X1, X4, X2, X3)) 64.55/17.44 qcE_in_gggg(X1, X2, X3, X4) -> U124_gggg(X1, X2, X3, X4, pcA_in_gg(d(e(X1)), X2)) 64.55/17.44 pcA_in_gg(d(d(X1)), +(X2, X3)) -> U87_gg(X1, X2, X3, qcF_in_gagg(X1, X4, X2, X3)) 64.55/17.44 qcF_in_gagg(X1, X2, X3, X4) -> U126_gagg(X1, X2, X3, X4, pcJ_in_ga(X1, X2)) 64.55/17.44 pcJ_in_ga(e(t), const(1)) -> pcJ_out_ga(e(t), const(1)) 64.55/17.44 pcJ_in_ga(e(const(X1)), const(0)) -> pcJ_out_ga(e(const(X1)), const(0)) 64.55/17.44 pcJ_in_ga(e(+(X1, X2)), +(X3, X4)) -> U108_ga(X1, X2, X3, X4, qcI_in_gaga(X1, X3, X2, X4)) 64.55/17.44 qcI_in_gaga(X1, X2, X3, X4) -> U96_gaga(X1, X2, X3, X4, pcH_in_ga(X1, X2)) 64.55/17.44 pcH_in_ga(t, const(1)) -> pcH_out_ga(t, const(1)) 64.55/17.44 pcH_in_ga(const(X1), const(0)) -> pcH_out_ga(const(X1), const(0)) 64.55/17.44 pcH_in_ga(+(X1, X2), +(X3, X4)) -> U94_ga(X1, X2, X3, X4, qcI_in_gaga(X1, X3, X2, X4)) 64.55/17.44 U94_ga(X1, X2, X3, X4, qcI_out_gaga(X1, X3, X2, X4)) -> pcH_out_ga(+(X1, X2), +(X3, X4)) 64.55/17.44 pcH_in_ga(*(X1, X2), +(*(X1, X3), *(X2, X4))) -> U95_ga(X1, X2, X3, X4, qcI_in_gaga(X1, X4, X2, X3)) 64.55/17.44 U95_ga(X1, X2, X3, X4, qcI_out_gaga(X1, X4, X2, X3)) -> pcH_out_ga(*(X1, X2), +(*(X1, X3), *(X2, X4))) 64.55/17.44 U96_gaga(X1, X2, X3, X4, pcH_out_ga(X1, X2)) -> U97_gaga(X1, X2, X3, X4, pcH_in_ga(X3, X4)) 64.55/17.44 U97_gaga(X1, X2, X3, X4, pcH_out_ga(X3, X4)) -> qcI_out_gaga(X1, X2, X3, X4) 64.55/17.44 U108_ga(X1, X2, X3, X4, qcI_out_gaga(X1, X3, X2, X4)) -> pcJ_out_ga(e(+(X1, X2)), +(X3, X4)) 64.55/17.44 pcJ_in_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U109_ga(X1, X2, X3, X4, qcI_in_gaga(X1, X4, X2, X3)) 64.55/17.44 U109_ga(X1, X2, X3, X4, qcI_out_gaga(X1, X4, X2, X3)) -> pcJ_out_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.55/17.44 pcJ_in_ga(d(X1), X2) -> U110_ga(X1, X2, pcJ_in_ga(X1, X3)) 64.55/17.44 U110_ga(X1, X2, pcJ_out_ga(X1, X3)) -> U111_ga(X1, X2, pcH_in_ga(X3, X2)) 64.55/17.44 U111_ga(X1, X2, pcH_out_ga(X3, X2)) -> pcJ_out_ga(d(X1), X2) 64.55/17.44 U126_gagg(X1, X2, X3, X4, pcJ_out_ga(X1, X2)) -> U127_gagg(X1, X2, X3, X4, pcA_in_gg(d(e(X2)), +(X3, X4))) 64.55/17.44 pcA_in_gg(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) -> U88_gg(X1, X2, pcA_in_gg(d(e(X1)), X2)) 64.55/17.44 pcA_in_gg(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) -> U89_gg(X1, X2, X3, pcA_in_gg(d(e(X2)), X3)) 64.55/17.44 pcA_in_gg(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) -> U90_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X5, X2, X6, X3, X4)) 64.55/17.44 U90_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X5, X2, X6, X3, X4)) -> pcA_out_gg(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) 64.55/17.44 pcA_in_gg(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) -> U91_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X6, X2, X5, X3, X4)) 64.55/17.44 U91_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X6, X2, X5, X3, X4)) -> pcA_out_gg(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) 64.55/17.44 pcA_in_gg(d(d(X1)), +(*(X2, X3), *(X4, X5))) -> U92_gg(X1, X2, X3, X4, X5, qcF_in_gagg(X1, X6, *(X2, X3), *(X4, X5))) 64.55/17.44 U92_gg(X1, X2, X3, X4, X5, qcF_out_gagg(X1, X6, *(X2, X3), *(X4, X5))) -> pcA_out_gg(d(d(X1)), +(*(X2, X3), *(X4, X5))) 64.55/17.44 pcA_in_gg(d(d(X1)), X2) -> U93_gg(X1, X2, qcG_in_gag(X1, X3, X2)) 64.55/17.44 qcG_in_gag(e(t), const(1), X1) -> U128_gag(X1, pcA_in_gg(d(e(const(1))), X1)) 64.55/17.44 U128_gag(X1, pcA_out_gg(d(e(const(1))), X1)) -> qcG_out_gag(e(t), const(1), X1) 64.55/17.44 qcG_in_gag(e(const(X1)), const(0), X2) -> U129_gag(X1, X2, pcA_in_gg(d(e(const(0))), X2)) 64.55/17.44 U129_gag(X1, X2, pcA_out_gg(d(e(const(0))), X2)) -> qcG_out_gag(e(const(X1)), const(0), X2) 64.55/17.44 qcG_in_gag(e(+(X1, X2)), +(X3, X4), X5) -> U130_gag(X1, X2, X3, X4, X5, pcH_in_ga(X1, X3)) 64.55/17.44 U130_gag(X1, X2, X3, X4, X5, pcH_out_ga(X1, X3)) -> U131_gag(X1, X2, X3, X4, X5, pcH_in_ga(X2, X4)) 64.55/17.44 U131_gag(X1, X2, X3, X4, X5, pcH_out_ga(X2, X4)) -> U132_gag(X1, X2, X3, X4, X5, pcA_in_gg(d(e(+(X3, X4))), X5)) 64.55/17.44 U132_gag(X1, X2, X3, X4, X5, pcA_out_gg(d(e(+(X3, X4))), X5)) -> qcG_out_gag(e(+(X1, X2)), +(X3, X4), X5) 64.55/17.44 qcG_in_gag(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) -> U133_gag(X1, X2, X3, X4, X5, pcH_in_ga(X1, X4)) 64.55/17.44 U133_gag(X1, X2, X3, X4, X5, pcH_out_ga(X1, X4)) -> U134_gag(X1, X2, X3, X4, X5, pcH_in_ga(X2, X3)) 64.55/17.44 U134_gag(X1, X2, X3, X4, X5, pcH_out_ga(X2, X3)) -> U135_gag(X1, X2, X3, X4, X5, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), X5)) 64.55/17.44 U135_gag(X1, X2, X3, X4, X5, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), X5)) -> qcG_out_gag(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) 64.55/17.44 qcG_in_gag(d(X1), X2, X3) -> U136_gag(X1, X2, X3, pcJ_in_ga(X1, X4)) 64.55/17.44 U136_gag(X1, X2, X3, pcJ_out_ga(X1, X4)) -> U137_gag(X1, X2, X3, qcG_in_gag(e(X4), X2, X3)) 64.55/17.44 U137_gag(X1, X2, X3, qcG_out_gag(e(X4), X2, X3)) -> qcG_out_gag(d(X1), X2, X3) 64.55/17.44 U93_gg(X1, X2, qcG_out_gag(X1, X3, X2)) -> pcA_out_gg(d(d(X1)), X2) 64.55/17.44 U89_gg(X1, X2, X3, pcA_out_gg(d(e(X2)), X3)) -> pcA_out_gg(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) 64.55/17.44 U88_gg(X1, X2, pcA_out_gg(d(e(X1)), X2)) -> pcA_out_gg(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) 64.55/17.44 U127_gagg(X1, X2, X3, X4, pcA_out_gg(d(e(X2)), +(X3, X4))) -> qcF_out_gagg(X1, X2, X3, X4) 64.55/17.44 U87_gg(X1, X2, X3, qcF_out_gagg(X1, X4, X2, X3)) -> pcA_out_gg(d(d(X1)), +(X2, X3)) 64.55/17.44 U124_gggg(X1, X2, X3, X4, pcA_out_gg(d(e(X1)), X2)) -> U125_gggg(X1, X2, X3, X4, pcA_in_gg(d(e(X3)), X4)) 64.55/17.44 U125_gggg(X1, X2, X3, X4, pcA_out_gg(d(e(X3)), X4)) -> qcE_out_gggg(X1, X2, X3, X4) 64.55/17.44 U86_gg(X1, X2, X3, X4, qcE_out_gggg(X1, X4, X2, X3)) -> pcA_out_gg(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) 64.55/17.44 U122_gggggg(X1, X2, X3, X4, X5, X6, pcA_out_gg(d(e(X1)), X2)) -> U123_gggggg(X1, X2, X3, X4, X5, X6, qcE_in_gggg(X3, X4, X5, X6)) 64.55/17.44 U123_gggggg(X1, X2, X3, X4, X5, X6, qcE_out_gggg(X3, X4, X5, X6)) -> qcD_out_gggggg(X1, X2, X3, X4, X5, X6) 64.55/17.44 U84_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X4, X2, X5, X3, X6)) -> pcA_out_gg(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) 64.55/17.44 U83_gg(X1, X2, X3, pcA_out_gg(d(e(X2)), X3)) -> pcA_out_gg(d(e(+(const(X1), X2))), +(const(0), X3)) 64.55/17.44 U82_gg(X1, X2, pcA_out_gg(d(e(X1)), X2)) -> pcA_out_gg(d(e(+(t, X1))), +(const(1), X2)) 64.55/17.44 U112_ga(pcA_out_gg(d(e(const(1))), const(0))) -> qcC_out_ga(e(t), const(1)) 64.55/17.44 qcC_in_ga(e(const(X1)), const(0)) -> U113_ga(X1, pcA_in_gg(d(e(const(0))), const(0))) 64.55/17.44 U113_ga(X1, pcA_out_gg(d(e(const(0))), const(0))) -> qcC_out_ga(e(const(X1)), const(0)) 64.55/17.44 qcC_in_ga(e(+(X1, X2)), +(X3, X4)) -> U114_ga(X1, X2, X3, X4, pcH_in_ga(X1, X3)) 64.55/17.44 U114_ga(X1, X2, X3, X4, pcH_out_ga(X1, X3)) -> U115_ga(X1, X2, X3, X4, pcH_in_ga(X2, X4)) 64.55/17.44 U115_ga(X1, X2, X3, X4, pcH_out_ga(X2, X4)) -> U116_ga(X1, X2, X3, X4, pcA_in_gg(d(e(+(X3, X4))), const(0))) 64.55/17.44 U116_ga(X1, X2, X3, X4, pcA_out_gg(d(e(+(X3, X4))), const(0))) -> qcC_out_ga(e(+(X1, X2)), +(X3, X4)) 64.55/17.44 qcC_in_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U117_ga(X1, X2, X3, X4, pcH_in_ga(X1, X4)) 64.55/17.44 U117_ga(X1, X2, X3, X4, pcH_out_ga(X1, X4)) -> U118_ga(X1, X2, X3, X4, pcH_in_ga(X2, X3)) 64.55/17.44 U118_ga(X1, X2, X3, X4, pcH_out_ga(X2, X3)) -> U119_ga(X1, X2, X3, X4, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(0))) 64.55/17.44 U119_ga(X1, X2, X3, X4, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(0))) -> qcC_out_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.55/17.44 qcC_in_ga(d(X1), X2) -> U120_ga(X1, X2, pcJ_in_ga(X1, X3)) 64.55/17.44 U120_ga(X1, X2, pcJ_out_ga(X1, X3)) -> U121_ga(X1, X2, qcC_in_ga(e(X3), X2)) 64.55/17.44 U121_ga(X1, X2, qcC_out_ga(e(X3), X2)) -> qcC_out_ga(d(X1), X2) 64.55/17.44 U81_gg(X1, qcC_out_ga(X1, X2)) -> pcA_out_gg(d(d(X1)), const(0)) 64.55/17.44 U98_ga(pcA_out_gg(d(e(const(1))), const(1))) -> qcB_out_ga(e(t), const(1)) 64.55/17.44 qcB_in_ga(e(const(X1)), const(0)) -> U99_ga(X1, pcA_in_gg(d(e(const(0))), const(1))) 64.55/17.44 U99_ga(X1, pcA_out_gg(d(e(const(0))), const(1))) -> qcB_out_ga(e(const(X1)), const(0)) 64.55/17.44 qcB_in_ga(e(+(X1, X2)), +(X3, X4)) -> U100_ga(X1, X2, X3, X4, pcH_in_ga(X1, X3)) 64.55/17.44 U100_ga(X1, X2, X3, X4, pcH_out_ga(X1, X3)) -> U101_ga(X1, X2, X3, X4, pcH_in_ga(X2, X4)) 64.55/17.44 U101_ga(X1, X2, X3, X4, pcH_out_ga(X2, X4)) -> U102_ga(X1, X2, X3, X4, pcA_in_gg(d(e(+(X3, X4))), const(1))) 64.55/17.44 U102_ga(X1, X2, X3, X4, pcA_out_gg(d(e(+(X3, X4))), const(1))) -> qcB_out_ga(e(+(X1, X2)), +(X3, X4)) 64.55/17.44 qcB_in_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U103_ga(X1, X2, X3, X4, pcH_in_ga(X1, X4)) 64.55/17.44 U103_ga(X1, X2, X3, X4, pcH_out_ga(X1, X4)) -> U104_ga(X1, X2, X3, X4, pcH_in_ga(X2, X3)) 64.55/17.44 U104_ga(X1, X2, X3, X4, pcH_out_ga(X2, X3)) -> U105_ga(X1, X2, X3, X4, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(1))) 64.55/17.44 U105_ga(X1, X2, X3, X4, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(1))) -> qcB_out_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.55/17.44 qcB_in_ga(d(X1), X2) -> U106_ga(X1, X2, pcJ_in_ga(X1, X3)) 64.55/17.44 U106_ga(X1, X2, pcJ_out_ga(X1, X3)) -> U107_ga(X1, X2, qcB_in_ga(e(X3), X2)) 64.55/17.44 U107_ga(X1, X2, qcB_out_ga(e(X3), X2)) -> qcB_out_ga(d(X1), X2) 64.55/17.44 U80_gg(X1, qcB_out_ga(X1, X2)) -> pcA_out_gg(d(d(X1)), const(1)) 64.55/17.44 pcH_in_aa(t, const(1)) -> pcH_out_aa(t, const(1)) 64.55/17.44 pcH_in_aa(const(X1), const(0)) -> pcH_out_aa(const(X1), const(0)) 64.55/17.44 pcH_in_aa(+(X1, X2), +(X3, X4)) -> U94_aa(X1, X2, X3, X4, qcI_in_aaaa(X1, X3, X2, X4)) 64.55/17.44 qcI_in_aaaa(X1, X2, X3, X4) -> U96_aaaa(X1, X2, X3, X4, pcH_in_aa(X1, X2)) 64.55/17.44 pcH_in_aa(*(X1, X2), +(*(X1, X3), *(X2, X4))) -> U95_aa(X1, X2, X3, X4, qcI_in_aaaa(X1, X4, X2, X3)) 64.55/17.44 U95_aa(X1, X2, X3, X4, qcI_out_aaaa(X1, X4, X2, X3)) -> pcH_out_aa(*(X1, X2), +(*(X1, X3), *(X2, X4))) 64.55/17.44 U96_aaaa(X1, X2, X3, X4, pcH_out_aa(X1, X2)) -> U97_aaaa(X1, X2, X3, X4, pcH_in_aa(X3, X4)) 64.55/17.44 U97_aaaa(X1, X2, X3, X4, pcH_out_aa(X3, X4)) -> qcI_out_aaaa(X1, X2, X3, X4) 64.55/17.44 U94_aa(X1, X2, X3, X4, qcI_out_aaaa(X1, X3, X2, X4)) -> pcH_out_aa(+(X1, X2), +(X3, X4)) 64.55/17.44 pcJ_in_aa(e(t), const(1)) -> pcJ_out_aa(e(t), const(1)) 64.55/17.44 pcJ_in_aa(e(const(X1)), const(0)) -> pcJ_out_aa(e(const(X1)), const(0)) 64.55/17.44 pcJ_in_aa(e(+(X1, X2)), +(X3, X4)) -> U108_aa(X1, X2, X3, X4, qcI_in_aaaa(X1, X3, X2, X4)) 64.55/17.44 U108_aa(X1, X2, X3, X4, qcI_out_aaaa(X1, X3, X2, X4)) -> pcJ_out_aa(e(+(X1, X2)), +(X3, X4)) 64.55/17.44 pcJ_in_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U109_aa(X1, X2, X3, X4, qcI_in_aaaa(X1, X4, X2, X3)) 64.55/17.44 U109_aa(X1, X2, X3, X4, qcI_out_aaaa(X1, X4, X2, X3)) -> pcJ_out_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.55/17.44 pcJ_in_aa(d(X1), X2) -> U110_aa(X1, X2, pcJ_in_aa(X1, X3)) 64.55/17.44 U110_aa(X1, X2, pcJ_out_aa(X1, X3)) -> U111_aa(X1, X2, pcH_in_ga(X3, X2)) 64.55/17.44 U111_aa(X1, X2, pcH_out_ga(X3, X2)) -> pcJ_out_aa(d(X1), X2) 64.55/17.44 pcA_in_ag(d(e(t)), const(1)) -> pcA_out_ag(d(e(t)), const(1)) 64.55/17.44 pcA_in_ag(d(d(X1)), const(1)) -> U80_ag(X1, qcB_in_aa(X1, X2)) 64.55/17.44 qcB_in_aa(e(t), const(1)) -> U98_aa(pcA_in_gg(d(e(const(1))), const(1))) 64.55/17.44 U98_aa(pcA_out_gg(d(e(const(1))), const(1))) -> qcB_out_aa(e(t), const(1)) 64.55/17.44 qcB_in_aa(e(const(X1)), const(0)) -> U99_aa(X1, pcA_in_gg(d(e(const(0))), const(1))) 64.55/17.44 U99_aa(X1, pcA_out_gg(d(e(const(0))), const(1))) -> qcB_out_aa(e(const(X1)), const(0)) 64.55/17.44 qcB_in_aa(e(+(X1, X2)), +(X3, X4)) -> U100_aa(X1, X2, X3, X4, pcH_in_aa(X1, X3)) 64.55/17.44 U100_aa(X1, X2, X3, X4, pcH_out_aa(X1, X3)) -> U101_aa(X1, X2, X3, X4, pcH_in_aa(X2, X4)) 64.55/17.44 U101_aa(X1, X2, X3, X4, pcH_out_aa(X2, X4)) -> U102_aa(X1, X2, X3, X4, pcA_in_gg(d(e(+(X3, X4))), const(1))) 64.55/17.44 U102_aa(X1, X2, X3, X4, pcA_out_gg(d(e(+(X3, X4))), const(1))) -> qcB_out_aa(e(+(X1, X2)), +(X3, X4)) 64.55/17.44 qcB_in_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U103_aa(X1, X2, X3, X4, pcH_in_aa(X1, X4)) 64.55/17.44 U103_aa(X1, X2, X3, X4, pcH_out_aa(X1, X4)) -> U104_aa(X1, X2, X3, X4, pcH_in_aa(X2, X3)) 64.55/17.44 U104_aa(X1, X2, X3, X4, pcH_out_aa(X2, X3)) -> U105_aa(X1, X2, X3, X4, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(1))) 64.55/17.44 U105_aa(X1, X2, X3, X4, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(1))) -> qcB_out_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.55/17.44 qcB_in_aa(d(X1), X2) -> U106_aa(X1, X2, pcJ_in_aa(X1, X3)) 64.55/17.44 U106_aa(X1, X2, pcJ_out_aa(X1, X3)) -> U107_aa(X1, X2, qcB_in_ga(e(X3), X2)) 64.55/17.44 U107_aa(X1, X2, qcB_out_ga(e(X3), X2)) -> qcB_out_aa(d(X1), X2) 64.55/17.44 U80_ag(X1, qcB_out_aa(X1, X2)) -> pcA_out_ag(d(d(X1)), const(1)) 64.55/17.44 pcA_in_ag(d(e(const(X1))), const(0)) -> pcA_out_ag(d(e(const(X1))), const(0)) 64.55/17.44 pcA_in_ag(d(d(X1)), const(0)) -> U81_ag(X1, qcC_in_aa(X1, X2)) 64.55/17.44 qcC_in_aa(e(t), const(1)) -> U112_aa(pcA_in_gg(d(e(const(1))), const(0))) 64.55/17.44 U112_aa(pcA_out_gg(d(e(const(1))), const(0))) -> qcC_out_aa(e(t), const(1)) 64.55/17.44 qcC_in_aa(e(const(X1)), const(0)) -> U113_aa(X1, pcA_in_gg(d(e(const(0))), const(0))) 64.55/17.44 U113_aa(X1, pcA_out_gg(d(e(const(0))), const(0))) -> qcC_out_aa(e(const(X1)), const(0)) 64.55/17.44 qcC_in_aa(e(+(X1, X2)), +(X3, X4)) -> U114_aa(X1, X2, X3, X4, pcH_in_aa(X1, X3)) 64.55/17.44 U114_aa(X1, X2, X3, X4, pcH_out_aa(X1, X3)) -> U115_aa(X1, X2, X3, X4, pcH_in_aa(X2, X4)) 64.55/17.44 U115_aa(X1, X2, X3, X4, pcH_out_aa(X2, X4)) -> U116_aa(X1, X2, X3, X4, pcA_in_gg(d(e(+(X3, X4))), const(0))) 64.55/17.44 U116_aa(X1, X2, X3, X4, pcA_out_gg(d(e(+(X3, X4))), const(0))) -> qcC_out_aa(e(+(X1, X2)), +(X3, X4)) 64.55/17.44 qcC_in_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U117_aa(X1, X2, X3, X4, pcH_in_aa(X1, X4)) 64.55/17.44 U117_aa(X1, X2, X3, X4, pcH_out_aa(X1, X4)) -> U118_aa(X1, X2, X3, X4, pcH_in_aa(X2, X3)) 64.55/17.44 U118_aa(X1, X2, X3, X4, pcH_out_aa(X2, X3)) -> U119_aa(X1, X2, X3, X4, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(0))) 64.55/17.44 U119_aa(X1, X2, X3, X4, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(0))) -> qcC_out_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.55/17.44 qcC_in_aa(d(X1), X2) -> U120_aa(X1, X2, pcJ_in_aa(X1, X3)) 64.55/17.44 U120_aa(X1, X2, pcJ_out_aa(X1, X3)) -> U121_aa(X1, X2, qcC_in_ga(e(X3), X2)) 64.55/17.44 U121_aa(X1, X2, qcC_out_ga(e(X3), X2)) -> qcC_out_aa(d(X1), X2) 64.55/17.44 U81_ag(X1, qcC_out_aa(X1, X2)) -> pcA_out_ag(d(d(X1)), const(0)) 64.55/17.44 pcA_in_ag(d(e(+(t, X1))), +(const(1), X2)) -> U82_ag(X1, X2, pcA_in_ag(d(e(X1)), X2)) 64.55/17.44 pcA_in_ag(d(e(+(const(X1), X2))), +(const(0), X3)) -> U83_ag(X1, X2, X3, pcA_in_ag(d(e(X2)), X3)) 64.55/17.44 pcA_in_ag(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) -> U84_ag(X1, X2, X3, X4, X5, X6, qcD_in_agagag(X1, X4, X2, X5, X3, X6)) 64.55/17.44 qcD_in_agagag(X1, X2, X3, X4, X5, X6) -> U122_agagag(X1, X2, X3, X4, X5, X6, pcA_in_ag(d(e(X1)), X2)) 64.55/17.44 pcA_in_ag(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) -> U85_ag(X1, X2, X3, X4, X5, X6, qcD_in_ggggag(X1, X5, X2, X4, X3, X6)) 64.55/17.44 qcD_in_ggggag(X1, X2, X3, X4, X5, X6) -> U122_ggggag(X1, X2, X3, X4, X5, X6, pcA_in_gg(d(e(X1)), X2)) 64.55/17.44 U122_ggggag(X1, X2, X3, X4, X5, X6, pcA_out_gg(d(e(X1)), X2)) -> U123_ggggag(X1, X2, X3, X4, X5, X6, qcE_in_ggag(X3, X4, X5, X6)) 64.55/17.44 qcE_in_ggag(X1, X2, X3, X4) -> U124_ggag(X1, X2, X3, X4, pcA_in_gg(d(e(X1)), X2)) 64.55/17.44 U124_ggag(X1, X2, X3, X4, pcA_out_gg(d(e(X1)), X2)) -> U125_ggag(X1, X2, X3, X4, pcA_in_ag(d(e(X3)), X4)) 64.55/17.44 pcA_in_ag(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) -> U86_ag(X1, X2, X3, X4, qcE_in_gggg(X1, X4, X2, X3)) 64.55/17.44 U86_ag(X1, X2, X3, X4, qcE_out_gggg(X1, X4, X2, X3)) -> pcA_out_ag(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) 64.55/17.44 pcA_in_ag(d(d(X1)), +(X2, X3)) -> U87_ag(X1, X2, X3, qcF_in_aagg(X1, X4, X2, X3)) 64.55/17.44 qcF_in_aagg(X1, X2, X3, X4) -> U126_aagg(X1, X2, X3, X4, pcJ_in_aa(X1, X2)) 64.55/17.44 U126_aagg(X1, X2, X3, X4, pcJ_out_aa(X1, X2)) -> U127_aagg(X1, X2, X3, X4, pcA_in_gg(d(e(X2)), +(X3, X4))) 64.55/17.44 U127_aagg(X1, X2, X3, X4, pcA_out_gg(d(e(X2)), +(X3, X4))) -> qcF_out_aagg(X1, X2, X3, X4) 64.55/17.44 U87_ag(X1, X2, X3, qcF_out_aagg(X1, X4, X2, X3)) -> pcA_out_ag(d(d(X1)), +(X2, X3)) 64.55/17.44 pcA_in_ag(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) -> U88_ag(X1, X2, pcA_in_gg(d(e(X1)), X2)) 64.55/17.44 U88_ag(X1, X2, pcA_out_gg(d(e(X1)), X2)) -> pcA_out_ag(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) 64.55/17.44 pcA_in_ag(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) -> U89_ag(X1, X2, X3, pcA_in_gg(d(e(X2)), X3)) 64.55/17.44 U89_ag(X1, X2, X3, pcA_out_gg(d(e(X2)), X3)) -> pcA_out_ag(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) 64.55/17.44 pcA_in_ag(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) -> U90_ag(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X5, X2, X6, X3, X4)) 64.55/17.44 U90_ag(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X5, X2, X6, X3, X4)) -> pcA_out_ag(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) 64.55/17.44 pcA_in_ag(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) -> U91_ag(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X6, X2, X5, X3, X4)) 64.55/17.44 U91_ag(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X6, X2, X5, X3, X4)) -> pcA_out_ag(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) 64.55/17.44 pcA_in_ag(d(d(X1)), +(*(X2, X3), *(X4, X5))) -> U92_ag(X1, X2, X3, X4, X5, qcF_in_aagg(X1, X6, *(X2, X3), *(X4, X5))) 64.55/17.44 U92_ag(X1, X2, X3, X4, X5, qcF_out_aagg(X1, X6, *(X2, X3), *(X4, X5))) -> pcA_out_ag(d(d(X1)), +(*(X2, X3), *(X4, X5))) 64.55/17.44 pcA_in_ag(d(d(X1)), X2) -> U93_ag(X1, X2, qcG_in_aag(X1, X3, X2)) 64.55/17.44 qcG_in_aag(e(t), const(1), X1) -> U128_aag(X1, pcA_in_gg(d(e(const(1))), X1)) 64.55/17.44 U128_aag(X1, pcA_out_gg(d(e(const(1))), X1)) -> qcG_out_aag(e(t), const(1), X1) 64.55/17.44 qcG_in_aag(e(const(X1)), const(0), X2) -> U129_aag(X1, X2, pcA_in_gg(d(e(const(0))), X2)) 64.55/17.44 U129_aag(X1, X2, pcA_out_gg(d(e(const(0))), X2)) -> qcG_out_aag(e(const(X1)), const(0), X2) 64.55/17.44 qcG_in_aag(e(+(X1, X2)), +(X3, X4), X5) -> U130_aag(X1, X2, X3, X4, X5, pcH_in_aa(X1, X3)) 64.55/17.44 U130_aag(X1, X2, X3, X4, X5, pcH_out_aa(X1, X3)) -> U131_aag(X1, X2, X3, X4, X5, pcH_in_aa(X2, X4)) 64.55/17.44 U131_aag(X1, X2, X3, X4, X5, pcH_out_aa(X2, X4)) -> U132_aag(X1, X2, X3, X4, X5, pcA_in_gg(d(e(+(X3, X4))), X5)) 64.55/17.44 U132_aag(X1, X2, X3, X4, X5, pcA_out_gg(d(e(+(X3, X4))), X5)) -> qcG_out_aag(e(+(X1, X2)), +(X3, X4), X5) 64.55/17.44 qcG_in_aag(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) -> U133_aag(X1, X2, X3, X4, X5, pcH_in_aa(X1, X4)) 64.55/17.44 U133_aag(X1, X2, X3, X4, X5, pcH_out_aa(X1, X4)) -> U134_aag(X1, X2, X3, X4, X5, pcH_in_aa(X2, X3)) 64.55/17.44 U134_aag(X1, X2, X3, X4, X5, pcH_out_aa(X2, X3)) -> U135_aag(X1, X2, X3, X4, X5, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), X5)) 64.55/17.44 U135_aag(X1, X2, X3, X4, X5, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), X5)) -> qcG_out_aag(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) 64.55/17.44 qcG_in_aag(d(X1), X2, X3) -> U136_aag(X1, X2, X3, pcJ_in_aa(X1, X4)) 64.55/17.44 U136_aag(X1, X2, X3, pcJ_out_aa(X1, X4)) -> U137_aag(X1, X2, X3, qcG_in_gag(e(X4), X2, X3)) 64.55/17.44 U137_aag(X1, X2, X3, qcG_out_gag(e(X4), X2, X3)) -> qcG_out_aag(d(X1), X2, X3) 64.55/17.44 U93_ag(X1, X2, qcG_out_aag(X1, X3, X2)) -> pcA_out_ag(d(d(X1)), X2) 64.55/17.44 U125_ggag(X1, X2, X3, X4, pcA_out_ag(d(e(X3)), X4)) -> qcE_out_ggag(X1, X2, X3, X4) 64.55/17.44 U123_ggggag(X1, X2, X3, X4, X5, X6, qcE_out_ggag(X3, X4, X5, X6)) -> qcD_out_ggggag(X1, X2, X3, X4, X5, X6) 64.55/17.44 U85_ag(X1, X2, X3, X4, X5, X6, qcD_out_ggggag(X1, X5, X2, X4, X3, X6)) -> pcA_out_ag(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) 64.55/17.44 U122_agagag(X1, X2, X3, X4, X5, X6, pcA_out_ag(d(e(X1)), X2)) -> U123_agagag(X1, X2, X3, X4, X5, X6, qcE_in_agag(X3, X4, X5, X6)) 64.55/17.44 qcE_in_agag(X1, X2, X3, X4) -> U124_agag(X1, X2, X3, X4, pcA_in_ag(d(e(X1)), X2)) 64.55/17.44 U124_agag(X1, X2, X3, X4, pcA_out_ag(d(e(X1)), X2)) -> U125_agag(X1, X2, X3, X4, pcA_in_ag(d(e(X3)), X4)) 64.55/17.44 U125_agag(X1, X2, X3, X4, pcA_out_ag(d(e(X3)), X4)) -> qcE_out_agag(X1, X2, X3, X4) 64.55/17.44 U123_agagag(X1, X2, X3, X4, X5, X6, qcE_out_agag(X3, X4, X5, X6)) -> qcD_out_agagag(X1, X2, X3, X4, X5, X6) 64.55/17.44 U84_ag(X1, X2, X3, X4, X5, X6, qcD_out_agagag(X1, X4, X2, X5, X3, X6)) -> pcA_out_ag(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) 64.55/17.44 U83_ag(X1, X2, X3, pcA_out_ag(d(e(X2)), X3)) -> pcA_out_ag(d(e(+(const(X1), X2))), +(const(0), X3)) 64.55/17.44 U82_ag(X1, X2, pcA_out_ag(d(e(X1)), X2)) -> pcA_out_ag(d(e(+(t, X1))), +(const(1), X2)) 64.55/17.44 64.55/17.44 The argument filtering Pi contains the following mapping: 64.55/17.44 pA_in_ag(x1, x2) = pA_in_ag(x2) 64.55/17.44 64.55/17.44 const(x1) = const 64.55/17.44 64.55/17.44 1 = 1 64.55/17.44 64.55/17.44 pB_in_aa(x1, x2) = pB_in_aa 64.55/17.44 64.55/17.44 pA_in_gg(x1, x2) = pA_in_gg(x1, x2) 64.55/17.44 64.55/17.44 d(x1) = d(x1) 64.55/17.44 64.55/17.44 pB_in_ga(x1, x2) = pB_in_ga(x1) 64.55/17.44 64.55/17.44 e(x1) = e(x1) 64.55/17.44 64.55/17.44 t = t 64.55/17.44 64.55/17.44 0 = 0 64.55/17.44 64.55/17.44 pC_in_ga(x1, x2) = pC_in_ga(x1) 64.55/17.44 64.55/17.44 +(x1, x2) = +(x1, x2) 64.55/17.44 64.55/17.44 pD_in_gggggg(x1, x2, x3, x4, x5, x6) = pD_in_gggggg(x1, x2, x3, x4, x5, x6) 64.55/17.44 64.55/17.44 *(x1, x2) = *(x1, x2) 64.55/17.44 64.55/17.44 pcA_in_gg(x1, x2) = pcA_in_gg(x1, x2) 64.55/17.44 64.55/17.44 pcA_out_gg(x1, x2) = pcA_out_gg(x1, x2) 64.55/17.44 64.55/17.44 U80_gg(x1, x2) = U80_gg(x1, x2) 64.55/17.44 64.55/17.44 qcB_in_ga(x1, x2) = qcB_in_ga(x1) 64.55/17.44 64.55/17.44 U98_ga(x1) = U98_ga(x1) 64.55/17.44 64.55/17.44 U81_gg(x1, x2) = U81_gg(x1, x2) 64.55/17.44 64.55/17.44 qcC_in_ga(x1, x2) = qcC_in_ga(x1) 64.55/17.44 64.55/17.44 U112_ga(x1) = U112_ga(x1) 64.55/17.44 64.55/17.44 U82_gg(x1, x2, x3) = U82_gg(x1, x2, x3) 64.55/17.44 64.55/17.44 U83_gg(x1, x2, x3, x4) = U83_gg(x2, x3, x4) 64.55/17.44 64.55/17.44 U84_gg(x1, x2, x3, x4, x5, x6, x7) = U84_gg(x1, x2, x3, x4, x5, x6, x7) 64.55/17.44 64.55/17.44 qcD_in_gggggg(x1, x2, x3, x4, x5, x6) = qcD_in_gggggg(x1, x2, x3, x4, x5, x6) 64.55/17.44 64.55/17.44 U122_gggggg(x1, x2, x3, x4, x5, x6, x7) = U122_gggggg(x1, x2, x3, x4, x5, x6, x7) 64.55/17.44 64.55/17.44 U85_gg(x1, x2, x3, x4, x5, x6, x7) = U85_gg(x1, x2, x3, x4, x5, x6, x7) 64.55/17.44 64.55/17.44 qcD_out_gggggg(x1, x2, x3, x4, x5, x6) = qcD_out_gggggg(x1, x2, x3, x4, x5, x6) 64.55/17.44 64.55/17.44 U86_gg(x1, x2, x3, x4, x5) = U86_gg(x1, x2, x3, x4, x5) 64.55/17.44 64.55/17.44 qcE_in_gggg(x1, x2, x3, x4) = qcE_in_gggg(x1, x2, x3, x4) 64.55/17.44 64.55/17.44 U124_gggg(x1, x2, x3, x4, x5) = U124_gggg(x1, x2, x3, x4, x5) 64.55/17.44 64.55/17.44 U87_gg(x1, x2, x3, x4) = U87_gg(x1, x2, x3, x4) 64.55/17.44 64.55/17.44 qcF_in_gagg(x1, x2, x3, x4) = qcF_in_gagg(x1, x3, x4) 64.55/17.44 64.55/17.44 U126_gagg(x1, x2, x3, x4, x5) = U126_gagg(x1, x3, x4, x5) 64.55/17.44 64.55/17.44 pcJ_in_ga(x1, x2) = pcJ_in_ga(x1) 64.55/17.44 64.55/17.44 pcJ_out_ga(x1, x2) = pcJ_out_ga(x1, x2) 64.55/17.44 64.55/17.44 U108_ga(x1, x2, x3, x4, x5) = U108_ga(x1, x2, x5) 64.55/17.44 64.55/17.44 qcI_in_gaga(x1, x2, x3, x4) = qcI_in_gaga(x1, x3) 64.55/17.44 64.55/17.44 U96_gaga(x1, x2, x3, x4, x5) = U96_gaga(x1, x3, x5) 64.55/17.44 64.55/17.44 pcH_in_ga(x1, x2) = pcH_in_ga(x1) 64.55/17.44 64.55/17.44 pcH_out_ga(x1, x2) = pcH_out_ga(x1, x2) 64.55/17.44 64.55/17.44 U94_ga(x1, x2, x3, x4, x5) = U94_ga(x1, x2, x5) 64.55/17.44 64.55/17.44 qcI_out_gaga(x1, x2, x3, x4) = qcI_out_gaga(x1, x2, x3, x4) 64.55/17.44 64.55/17.44 U95_ga(x1, x2, x3, x4, x5) = U95_ga(x1, x2, x5) 64.55/17.44 64.55/17.44 U97_gaga(x1, x2, x3, x4, x5) = U97_gaga(x1, x2, x3, x5) 64.55/17.44 64.55/17.44 U109_ga(x1, x2, x3, x4, x5) = U109_ga(x1, x2, x5) 64.55/17.44 64.55/17.44 U110_ga(x1, x2, x3) = U110_ga(x1, x3) 64.55/17.44 64.55/17.44 U111_ga(x1, x2, x3) = U111_ga(x1, x3) 64.55/17.44 64.55/17.44 U127_gagg(x1, x2, x3, x4, x5) = U127_gagg(x1, x2, x3, x4, x5) 64.55/17.44 64.55/17.44 U88_gg(x1, x2, x3) = U88_gg(x1, x2, x3) 64.55/17.44 64.55/17.44 U89_gg(x1, x2, x3, x4) = U89_gg(x2, x3, x4) 64.55/17.44 64.55/17.44 U90_gg(x1, x2, x3, x4, x5, x6, x7) = U90_gg(x1, x2, x3, x4, x5, x6, x7) 64.55/17.44 64.55/17.44 U91_gg(x1, x2, x3, x4, x5, x6, x7) = U91_gg(x1, x2, x3, x4, x5, x6, x7) 64.55/17.44 64.55/17.44 U92_gg(x1, x2, x3, x4, x5, x6) = U92_gg(x1, x2, x3, x4, x5, x6) 64.55/17.44 64.55/17.44 qcF_out_gagg(x1, x2, x3, x4) = qcF_out_gagg(x1, x2, x3, x4) 64.55/17.44 64.55/17.44 U93_gg(x1, x2, x3) = U93_gg(x1, x2, x3) 64.55/17.44 64.55/17.44 qcG_in_gag(x1, x2, x3) = qcG_in_gag(x1, x3) 64.55/17.44 64.55/17.44 U128_gag(x1, x2) = U128_gag(x1, x2) 64.55/17.44 64.55/17.44 qcG_out_gag(x1, x2, x3) = qcG_out_gag(x1, x2, x3) 64.55/17.44 64.55/17.44 U129_gag(x1, x2, x3) = U129_gag(x2, x3) 64.55/17.44 64.55/17.44 U130_gag(x1, x2, x3, x4, x5, x6) = U130_gag(x1, x2, x5, x6) 64.55/17.44 64.55/17.44 U131_gag(x1, x2, x3, x4, x5, x6) = U131_gag(x1, x2, x3, x5, x6) 64.55/17.44 64.55/17.44 U132_gag(x1, x2, x3, x4, x5, x6) = U132_gag(x1, x2, x3, x4, x5, x6) 64.55/17.44 64.55/17.44 U133_gag(x1, x2, x3, x4, x5, x6) = U133_gag(x1, x2, x5, x6) 64.55/17.44 64.55/17.44 U134_gag(x1, x2, x3, x4, x5, x6) = U134_gag(x1, x2, x4, x5, x6) 64.55/17.44 64.55/17.44 U135_gag(x1, x2, x3, x4, x5, x6) = U135_gag(x1, x2, x3, x4, x5, x6) 64.55/17.44 64.55/17.44 U136_gag(x1, x2, x3, x4) = U136_gag(x1, x3, x4) 64.55/17.44 64.55/17.44 U137_gag(x1, x2, x3, x4) = U137_gag(x1, x3, x4) 64.55/17.44 64.55/17.44 U125_gggg(x1, x2, x3, x4, x5) = U125_gggg(x1, x2, x3, x4, x5) 64.55/17.44 64.55/17.44 qcE_out_gggg(x1, x2, x3, x4) = qcE_out_gggg(x1, x2, x3, x4) 64.55/17.44 64.55/17.44 U123_gggggg(x1, x2, x3, x4, x5, x6, x7) = U123_gggggg(x1, x2, x3, x4, x5, x6, x7) 64.55/17.44 64.55/17.44 qcC_out_ga(x1, x2) = qcC_out_ga(x1, x2) 64.55/17.44 64.55/17.44 U113_ga(x1, x2) = U113_ga(x2) 64.55/17.44 64.55/17.44 U114_ga(x1, x2, x3, x4, x5) = U114_ga(x1, x2, x5) 64.55/17.44 64.55/17.44 U115_ga(x1, x2, x3, x4, x5) = U115_ga(x1, x2, x3, x5) 64.55/17.44 64.55/17.44 U116_ga(x1, x2, x3, x4, x5) = U116_ga(x1, x2, x3, x4, x5) 64.55/17.44 64.55/17.44 U117_ga(x1, x2, x3, x4, x5) = U117_ga(x1, x2, x5) 64.55/17.44 64.55/17.44 U118_ga(x1, x2, x3, x4, x5) = U118_ga(x1, x2, x4, x5) 64.55/17.44 64.55/17.44 U119_ga(x1, x2, x3, x4, x5) = U119_ga(x1, x2, x3, x4, x5) 64.55/17.44 64.55/17.44 U120_ga(x1, x2, x3) = U120_ga(x1, x3) 64.55/17.44 64.55/17.44 U121_ga(x1, x2, x3) = U121_ga(x1, x3) 64.55/17.44 64.55/17.44 qcB_out_ga(x1, x2) = qcB_out_ga(x1, x2) 64.55/17.44 64.55/17.44 U99_ga(x1, x2) = U99_ga(x2) 64.55/17.44 64.55/17.44 U100_ga(x1, x2, x3, x4, x5) = U100_ga(x1, x2, x5) 64.55/17.44 64.55/17.44 U101_ga(x1, x2, x3, x4, x5) = U101_ga(x1, x2, x3, x5) 64.55/17.44 64.55/17.44 U102_ga(x1, x2, x3, x4, x5) = U102_ga(x1, x2, x3, x4, x5) 64.55/17.44 64.55/17.44 U103_ga(x1, x2, x3, x4, x5) = U103_ga(x1, x2, x5) 64.55/17.44 64.55/17.44 U104_ga(x1, x2, x3, x4, x5) = U104_ga(x1, x2, x4, x5) 64.55/17.44 64.55/17.44 U105_ga(x1, x2, x3, x4, x5) = U105_ga(x1, x2, x3, x4, x5) 64.55/17.44 64.55/17.44 U106_ga(x1, x2, x3) = U106_ga(x1, x3) 64.55/17.44 64.55/17.44 U107_ga(x1, x2, x3) = U107_ga(x1, x3) 64.55/17.44 64.55/17.44 pE_in_gggg(x1, x2, x3, x4) = pE_in_gggg(x1, x2, x3, x4) 64.55/17.44 64.55/17.44 pF_in_gagg(x1, x2, x3, x4) = pF_in_gagg(x1, x3, x4) 64.55/17.44 64.55/17.44 pJ_in_ga(x1, x2) = pJ_in_ga(x1) 64.55/17.44 64.55/17.44 pI_in_gaga(x1, x2, x3, x4) = pI_in_gaga(x1, x3) 64.55/17.44 64.55/17.44 pH_in_ga(x1, x2) = pH_in_ga(x1) 64.55/17.44 64.55/17.44 pG_in_gag(x1, x2, x3) = pG_in_gag(x1, x3) 64.55/17.44 64.55/17.44 pH_in_aa(x1, x2) = pH_in_aa 64.55/17.44 64.55/17.44 pI_in_aaaa(x1, x2, x3, x4) = pI_in_aaaa 64.55/17.44 64.55/17.44 pcH_in_aa(x1, x2) = pcH_in_aa 64.55/17.44 64.55/17.44 pcH_out_aa(x1, x2) = pcH_out_aa(x1, x2) 64.55/17.44 64.55/17.44 U94_aa(x1, x2, x3, x4, x5) = U94_aa(x5) 64.55/17.44 64.55/17.44 qcI_in_aaaa(x1, x2, x3, x4) = qcI_in_aaaa 64.55/17.44 64.55/17.44 U96_aaaa(x1, x2, x3, x4, x5) = U96_aaaa(x5) 64.55/17.44 64.55/17.44 U95_aa(x1, x2, x3, x4, x5) = U95_aa(x5) 64.55/17.44 64.55/17.44 qcI_out_aaaa(x1, x2, x3, x4) = qcI_out_aaaa(x1, x2, x3, x4) 64.55/17.44 64.55/17.44 U97_aaaa(x1, x2, x3, x4, x5) = U97_aaaa(x1, x2, x5) 64.55/17.44 64.55/17.44 pJ_in_aa(x1, x2) = pJ_in_aa 64.55/17.44 64.55/17.44 pcJ_in_aa(x1, x2) = pcJ_in_aa 64.55/17.44 64.55/17.44 pcJ_out_aa(x1, x2) = pcJ_out_aa(x1, x2) 64.55/17.44 64.55/17.44 U108_aa(x1, x2, x3, x4, x5) = U108_aa(x5) 64.55/17.44 64.55/17.44 U109_aa(x1, x2, x3, x4, x5) = U109_aa(x5) 64.55/17.44 64.55/17.44 U110_aa(x1, x2, x3) = U110_aa(x3) 64.55/17.44 64.55/17.44 U111_aa(x1, x2, x3) = U111_aa(x1, x3) 64.55/17.44 64.55/17.44 pC_in_aa(x1, x2) = pC_in_aa 64.55/17.44 64.55/17.44 pD_in_agagag(x1, x2, x3, x4, x5, x6) = pD_in_agagag(x2, x4, x6) 64.55/17.44 64.55/17.44 pD_in_ggggag(x1, x2, x3, x4, x5, x6) = pD_in_ggggag(x1, x2, x3, x4, x6) 64.55/17.44 64.55/17.44 pE_in_ggag(x1, x2, x3, x4) = pE_in_ggag(x1, x2, x4) 64.55/17.44 64.55/17.44 pF_in_aagg(x1, x2, x3, x4) = pF_in_aagg(x3, x4) 64.55/17.44 64.55/17.44 pG_in_aag(x1, x2, x3) = pG_in_aag(x3) 64.55/17.44 64.55/17.44 pcA_in_ag(x1, x2) = pcA_in_ag(x2) 64.55/17.44 64.55/17.44 pcA_out_ag(x1, x2) = pcA_out_ag(x1, x2) 64.55/17.44 64.55/17.44 U80_ag(x1, x2) = U80_ag(x2) 64.55/17.44 64.55/17.44 qcB_in_aa(x1, x2) = qcB_in_aa 64.55/17.44 64.55/17.44 U98_aa(x1) = U98_aa(x1) 64.55/17.44 64.55/17.44 qcB_out_aa(x1, x2) = qcB_out_aa(x1, x2) 64.55/17.44 64.55/17.44 U99_aa(x1, x2) = U99_aa(x2) 64.55/17.44 64.55/17.44 U100_aa(x1, x2, x3, x4, x5) = U100_aa(x5) 64.55/17.44 64.55/17.44 U101_aa(x1, x2, x3, x4, x5) = U101_aa(x1, x3, x5) 64.55/17.44 64.55/17.44 U102_aa(x1, x2, x3, x4, x5) = U102_aa(x1, x2, x3, x4, x5) 64.55/17.44 64.55/17.44 U103_aa(x1, x2, x3, x4, x5) = U103_aa(x5) 64.55/17.44 64.55/17.44 U104_aa(x1, x2, x3, x4, x5) = U104_aa(x1, x4, x5) 64.55/17.44 64.55/17.44 U105_aa(x1, x2, x3, x4, x5) = U105_aa(x1, x2, x3, x4, x5) 64.55/17.44 64.55/17.44 U106_aa(x1, x2, x3) = U106_aa(x3) 64.55/17.44 64.55/17.44 U107_aa(x1, x2, x3) = U107_aa(x1, x3) 64.55/17.44 64.55/17.44 U81_ag(x1, x2) = U81_ag(x2) 64.55/17.44 64.55/17.44 qcC_in_aa(x1, x2) = qcC_in_aa 64.55/17.44 64.55/17.44 U112_aa(x1) = U112_aa(x1) 64.55/17.44 64.55/17.44 qcC_out_aa(x1, x2) = qcC_out_aa(x1, x2) 64.55/17.44 64.55/17.44 U113_aa(x1, x2) = U113_aa(x2) 64.55/17.44 64.55/17.44 U114_aa(x1, x2, x3, x4, x5) = U114_aa(x5) 64.55/17.44 64.55/17.44 U115_aa(x1, x2, x3, x4, x5) = U115_aa(x1, x3, x5) 64.55/17.44 64.55/17.44 U116_aa(x1, x2, x3, x4, x5) = U116_aa(x1, x2, x3, x4, x5) 64.55/17.44 64.55/17.44 U117_aa(x1, x2, x3, x4, x5) = U117_aa(x5) 64.55/17.44 64.55/17.44 U118_aa(x1, x2, x3, x4, x5) = U118_aa(x1, x4, x5) 64.55/17.44 64.55/17.44 U119_aa(x1, x2, x3, x4, x5) = U119_aa(x1, x2, x3, x4, x5) 64.55/17.44 64.55/17.44 U120_aa(x1, x2, x3) = U120_aa(x3) 64.55/17.44 64.55/17.44 U121_aa(x1, x2, x3) = U121_aa(x1, x3) 64.55/17.44 64.55/17.44 U82_ag(x1, x2, x3) = U82_ag(x2, x3) 64.55/17.44 64.55/17.44 U83_ag(x1, x2, x3, x4) = U83_ag(x3, x4) 64.55/17.44 64.55/17.44 U84_ag(x1, x2, x3, x4, x5, x6, x7) = U84_ag(x4, x5, x6, x7) 64.55/17.44 64.55/17.44 qcD_in_agagag(x1, x2, x3, x4, x5, x6) = qcD_in_agagag(x2, x4, x6) 64.55/17.44 64.55/17.44 U122_agagag(x1, x2, x3, x4, x5, x6, x7) = U122_agagag(x2, x4, x6, x7) 64.55/17.44 64.55/17.44 U85_ag(x1, x2, x3, x4, x5, x6, x7) = U85_ag(x1, x2, x4, x5, x6, x7) 64.55/17.44 64.55/17.44 qcD_in_ggggag(x1, x2, x3, x4, x5, x6) = qcD_in_ggggag(x1, x2, x3, x4, x6) 64.55/17.44 64.55/17.44 U122_ggggag(x1, x2, x3, x4, x5, x6, x7) = U122_ggggag(x1, x2, x3, x4, x6, x7) 64.55/17.44 64.55/17.44 U123_ggggag(x1, x2, x3, x4, x5, x6, x7) = U123_ggggag(x1, x2, x3, x4, x6, x7) 64.55/17.44 64.55/17.44 qcE_in_ggag(x1, x2, x3, x4) = qcE_in_ggag(x1, x2, x4) 64.55/17.44 64.55/17.44 U124_ggag(x1, x2, x3, x4, x5) = U124_ggag(x1, x2, x4, x5) 64.55/17.44 64.55/17.44 U125_ggag(x1, x2, x3, x4, x5) = U125_ggag(x1, x2, x4, x5) 64.55/17.44 64.55/17.44 U86_ag(x1, x2, x3, x4, x5) = U86_ag(x1, x2, x3, x4, x5) 64.55/17.44 64.55/17.44 U87_ag(x1, x2, x3, x4) = U87_ag(x2, x3, x4) 64.55/17.44 64.55/17.44 qcF_in_aagg(x1, x2, x3, x4) = qcF_in_aagg(x3, x4) 64.55/17.44 64.55/17.44 U126_aagg(x1, x2, x3, x4, x5) = U126_aagg(x3, x4, x5) 64.55/17.44 64.55/17.44 U127_aagg(x1, x2, x3, x4, x5) = U127_aagg(x1, x2, x3, x4, x5) 64.55/17.44 64.55/17.44 qcF_out_aagg(x1, x2, x3, x4) = qcF_out_aagg(x1, x2, x3, x4) 64.55/17.44 64.55/17.44 U88_ag(x1, x2, x3) = U88_ag(x1, x2, x3) 64.55/17.44 64.55/17.44 U89_ag(x1, x2, x3, x4) = U89_ag(x2, x3, x4) 64.55/17.44 64.55/17.44 U90_ag(x1, x2, x3, x4, x5, x6, x7) = U90_ag(x1, x2, x3, x4, x5, x6, x7) 64.55/17.44 64.55/17.44 U91_ag(x1, x2, x3, x4, x5, x6, x7) = U91_ag(x1, x2, x3, x4, x5, x6, x7) 64.55/17.44 64.55/17.44 U92_ag(x1, x2, x3, x4, x5, x6) = U92_ag(x2, x3, x4, x5, x6) 64.55/17.44 64.55/17.44 U93_ag(x1, x2, x3) = U93_ag(x2, x3) 64.55/17.44 64.55/17.44 qcG_in_aag(x1, x2, x3) = qcG_in_aag(x3) 64.55/17.44 64.55/17.44 U128_aag(x1, x2) = U128_aag(x1, x2) 64.55/17.44 64.55/17.44 qcG_out_aag(x1, x2, x3) = qcG_out_aag(x1, x2, x3) 64.55/17.44 64.55/17.44 U129_aag(x1, x2, x3) = U129_aag(x2, x3) 64.55/17.44 64.55/17.44 U130_aag(x1, x2, x3, x4, x5, x6) = U130_aag(x5, x6) 64.55/17.44 64.55/17.44 U131_aag(x1, x2, x3, x4, x5, x6) = U131_aag(x1, x3, x5, x6) 64.55/17.44 64.55/17.44 U132_aag(x1, x2, x3, x4, x5, x6) = U132_aag(x1, x2, x3, x4, x5, x6) 64.55/17.44 64.55/17.44 U133_aag(x1, x2, x3, x4, x5, x6) = U133_aag(x5, x6) 64.55/17.44 64.55/17.44 U134_aag(x1, x2, x3, x4, x5, x6) = U134_aag(x1, x4, x5, x6) 64.55/17.44 64.55/17.44 U135_aag(x1, x2, x3, x4, x5, x6) = U135_aag(x1, x2, x3, x4, x5, x6) 64.55/17.44 64.55/17.44 U136_aag(x1, x2, x3, x4) = U136_aag(x3, x4) 64.55/17.44 64.55/17.44 U137_aag(x1, x2, x3, x4) = U137_aag(x1, x3, x4) 64.55/17.44 64.55/17.44 qcE_out_ggag(x1, x2, x3, x4) = qcE_out_ggag(x1, x2, x3, x4) 64.55/17.44 64.55/17.44 qcD_out_ggggag(x1, x2, x3, x4, x5, x6) = qcD_out_ggggag(x1, x2, x3, x4, x5, x6) 64.55/17.44 64.55/17.44 U123_agagag(x1, x2, x3, x4, x5, x6, x7) = U123_agagag(x1, x2, x4, x6, x7) 64.55/17.44 64.55/17.44 qcE_in_agag(x1, x2, x3, x4) = qcE_in_agag(x2, x4) 64.55/17.44 64.55/17.44 U124_agag(x1, x2, x3, x4, x5) = U124_agag(x2, x4, x5) 64.55/17.44 64.55/17.44 U125_agag(x1, x2, x3, x4, x5) = U125_agag(x1, x2, x4, x5) 64.55/17.44 64.55/17.44 qcE_out_agag(x1, x2, x3, x4) = qcE_out_agag(x1, x2, x3, x4) 64.55/17.44 64.55/17.44 qcD_out_agagag(x1, x2, x3, x4, x5, x6) = qcD_out_agagag(x1, x2, x3, x4, x5, x6) 64.55/17.44 64.55/17.44 pE_in_agag(x1, x2, x3, x4) = pE_in_agag(x2, x4) 64.55/17.44 64.55/17.44 PA_IN_AG(x1, x2) = PA_IN_AG(x2) 64.55/17.44 64.55/17.44 U65_AG(x1, x2) = U65_AG(x2) 64.55/17.44 64.55/17.44 PB_IN_AA(x1, x2) = PB_IN_AA 64.55/17.44 64.55/17.44 U6_AA(x1) = U6_AA(x1) 64.55/17.44 64.55/17.44 PA_IN_GG(x1, x2) = PA_IN_GG(x1, x2) 64.55/17.44 64.55/17.44 U65_GG(x1, x2) = U65_GG(x1, x2) 64.55/17.45 64.55/17.45 PB_IN_GA(x1, x2) = PB_IN_GA(x1) 64.55/17.45 64.55/17.45 U6_GA(x1) = U6_GA(x1) 64.55/17.45 64.55/17.45 U66_GG(x1, x2) = U66_GG(x1, x2) 64.55/17.45 64.55/17.45 PC_IN_GA(x1, x2) = PC_IN_GA(x1) 64.55/17.45 64.55/17.45 U26_GA(x1) = U26_GA(x1) 64.55/17.45 64.55/17.45 U67_GG(x1, x2, x3) = U67_GG(x1, x2, x3) 64.55/17.45 64.55/17.45 U68_GG(x1, x2, x3, x4) = U68_GG(x2, x3, x4) 64.55/17.45 64.55/17.45 U69_GG(x1, x2, x3, x4, x5, x6, x7) = U69_GG(x1, x2, x3, x4, x5, x6, x7) 64.55/17.45 64.55/17.45 PD_IN_GGGGGG(x1, x2, x3, x4, x5, x6) = PD_IN_GGGGGG(x1, x2, x3, x4, x5, x6) 64.55/17.45 64.55/17.45 U41_GGGGGG(x1, x2, x3, x4, x5, x6, x7) = U41_GGGGGG(x1, x2, x3, x4, x5, x6, x7) 64.55/17.45 64.55/17.45 U70_GG(x1, x2, x3, x4, x5, x6, x7) = U70_GG(x1, x2, x3, x4, x5, x6, x7) 64.55/17.45 64.55/17.45 U42_GGGGGG(x1, x2, x3, x4, x5, x6, x7) = U42_GGGGGG(x1, x2, x3, x4, x5, x6, x7) 64.55/17.45 64.55/17.45 U43_GGGGGG(x1, x2, x3, x4, x5, x6, x7) = U43_GGGGGG(x1, x2, x3, x4, x5, x6, x7) 64.55/17.45 64.55/17.45 PE_IN_GGGG(x1, x2, x3, x4) = PE_IN_GGGG(x1, x2, x3, x4) 64.55/17.45 64.55/17.45 U44_GGGG(x1, x2, x3, x4, x5) = U44_GGGG(x1, x2, x3, x4, x5) 64.55/17.45 64.55/17.45 U71_GG(x1, x2, x3, x4, x5) = U71_GG(x1, x2, x3, x4, x5) 64.55/17.45 64.55/17.45 U45_GGGG(x1, x2, x3, x4, x5) = U45_GGGG(x1, x2, x3, x4, x5) 64.55/17.45 64.55/17.45 U46_GGGG(x1, x2, x3, x4, x5) = U46_GGGG(x1, x2, x3, x4, x5) 64.55/17.45 64.55/17.45 U72_GG(x1, x2, x3, x4) = U72_GG(x1, x2, x3, x4) 64.55/17.45 64.55/17.45 PF_IN_GAGG(x1, x2, x3, x4) = PF_IN_GAGG(x1, x3, x4) 64.55/17.45 64.55/17.45 U47_GAGG(x1, x2, x3, x4, x5) = U47_GAGG(x1, x3, x4, x5) 64.55/17.45 64.55/17.45 PJ_IN_GA(x1, x2) = PJ_IN_GA(x1) 64.55/17.45 64.55/17.45 U21_GA(x1, x2, x3, x4, x5) = U21_GA(x1, x2, x5) 64.55/17.45 64.55/17.45 PI_IN_GAGA(x1, x2, x3, x4) = PI_IN_GAGA(x1, x3) 64.55/17.45 64.55/17.45 U3_GAGA(x1, x2, x3, x4, x5) = U3_GAGA(x1, x3, x5) 64.55/17.45 64.55/17.45 PH_IN_GA(x1, x2) = PH_IN_GA(x1) 64.55/17.45 64.55/17.45 U1_GA(x1, x2, x3, x4, x5) = U1_GA(x1, x2, x5) 64.55/17.45 64.55/17.45 U4_GAGA(x1, x2, x3, x4, x5) = U4_GAGA(x1, x3, x5) 64.55/17.45 64.55/17.45 U5_GAGA(x1, x2, x3, x4, x5) = U5_GAGA(x1, x3, x5) 64.55/17.45 64.55/17.45 U2_GA(x1, x2, x3, x4, x5) = U2_GA(x1, x2, x5) 64.55/17.45 64.55/17.45 U22_GA(x1, x2, x3, x4, x5) = U22_GA(x1, x2, x5) 64.55/17.45 64.55/17.45 U23_GA(x1, x2, x3) = U23_GA(x1, x3) 64.55/17.45 64.55/17.45 U24_GA(x1, x2, x3) = U24_GA(x1, x3) 64.55/17.45 64.55/17.45 U25_GA(x1, x2, x3) = U25_GA(x1, x3) 64.55/17.45 64.55/17.45 U48_GAGG(x1, x2, x3, x4, x5) = U48_GAGG(x1, x3, x4, x5) 64.55/17.45 64.55/17.45 U49_GAGG(x1, x2, x3, x4, x5) = U49_GAGG(x1, x3, x4, x5) 64.55/17.45 64.55/17.45 U73_GG(x1, x2, x3) = U73_GG(x1, x2, x3) 64.55/17.45 64.55/17.45 U74_GG(x1, x2, x3, x4) = U74_GG(x2, x3, x4) 64.55/17.45 64.55/17.45 U75_GG(x1, x2, x3, x4, x5, x6, x7) = U75_GG(x1, x2, x3, x4, x5, x6, x7) 64.55/17.45 64.55/17.45 U76_GG(x1, x2, x3, x4, x5, x6, x7) = U76_GG(x1, x2, x3, x4, x5, x6, x7) 64.55/17.45 64.55/17.45 U77_GG(x1, x2, x3, x4, x5, x6) = U77_GG(x1, x2, x3, x4, x5, x6) 64.55/17.45 64.55/17.45 U78_GG(x1, x2, x3) = U78_GG(x1, x2, x3) 64.55/17.45 64.55/17.45 PG_IN_GAG(x1, x2, x3) = PG_IN_GAG(x1, x3) 64.55/17.45 64.55/17.45 U50_GAG(x1, x2) = U50_GAG(x1, x2) 64.55/17.45 64.55/17.45 U51_GAG(x1, x2, x3) = U51_GAG(x2, x3) 64.55/17.45 64.55/17.45 U52_GAG(x1, x2, x3, x4, x5, x6) = U52_GAG(x1, x2, x5, x6) 64.55/17.45 64.55/17.45 U53_GAG(x1, x2, x3, x4, x5, x6) = U53_GAG(x1, x2, x5, x6) 64.55/17.45 64.55/17.45 U54_GAG(x1, x2, x3, x4, x5, x6) = U54_GAG(x1, x2, x5, x6) 64.55/17.45 64.55/17.45 U55_GAG(x1, x2, x3, x4, x5, x6) = U55_GAG(x1, x2, x3, x5, x6) 64.55/17.45 64.55/17.45 U56_GAG(x1, x2, x3, x4, x5, x6) = U56_GAG(x1, x2, x5, x6) 64.55/17.45 64.55/17.45 U57_GAG(x1, x2, x3, x4, x5, x6) = U57_GAG(x1, x2, x5, x6) 64.55/17.45 64.55/17.45 U58_GAG(x1, x2, x3, x4, x5, x6) = U58_GAG(x1, x2, x5, x6) 64.55/17.45 64.55/17.45 U59_GAG(x1, x2, x3, x4, x5, x6) = U59_GAG(x1, x2, x5, x6) 64.55/17.45 64.55/17.45 U60_GAG(x1, x2, x3, x4, x5, x6) = U60_GAG(x1, x2, x4, x5, x6) 64.55/17.45 64.55/17.45 U61_GAG(x1, x2, x3, x4, x5, x6) = U61_GAG(x1, x2, x5, x6) 64.55/17.45 64.55/17.45 U62_GAG(x1, x2, x3, x4) = U62_GAG(x1, x3, x4) 64.55/17.45 64.55/17.45 U63_GAG(x1, x2, x3, x4) = U63_GAG(x1, x3, x4) 64.55/17.45 64.55/17.45 U64_GAG(x1, x2, x3, x4) = U64_GAG(x1, x3, x4) 64.55/17.45 64.55/17.45 U27_GA(x1, x2) = U27_GA(x2) 64.55/17.45 64.55/17.45 U28_GA(x1, x2, x3, x4, x5) = U28_GA(x1, x2, x5) 64.55/17.45 64.55/17.45 U29_GA(x1, x2, x3, x4, x5) = U29_GA(x1, x2, x5) 64.55/17.45 64.55/17.45 U30_GA(x1, x2, x3, x4, x5) = U30_GA(x1, x2, x5) 64.55/17.45 64.55/17.45 U31_GA(x1, x2, x3, x4, x5) = U31_GA(x1, x2, x3, x5) 64.55/17.45 64.55/17.45 U32_GA(x1, x2, x3, x4, x5) = U32_GA(x1, x2, x5) 64.55/17.45 64.55/17.45 U33_GA(x1, x2, x3, x4, x5) = U33_GA(x1, x2, x5) 64.55/17.45 64.55/17.45 U34_GA(x1, x2, x3, x4, x5) = U34_GA(x1, x2, x5) 64.55/17.45 64.55/17.45 U35_GA(x1, x2, x3, x4, x5) = U35_GA(x1, x2, x5) 64.55/17.45 64.55/17.45 U36_GA(x1, x2, x3, x4, x5) = U36_GA(x1, x2, x4, x5) 64.55/17.45 64.55/17.45 U37_GA(x1, x2, x3, x4, x5) = U37_GA(x1, x2, x5) 64.55/17.45 64.55/17.45 U38_GA(x1, x2, x3) = U38_GA(x1, x3) 64.55/17.45 64.55/17.45 U39_GA(x1, x2, x3) = U39_GA(x1, x3) 64.55/17.45 64.55/17.45 U40_GA(x1, x2, x3) = U40_GA(x1, x3) 64.55/17.45 64.55/17.45 U7_GA(x1, x2) = U7_GA(x2) 64.55/17.45 64.55/17.45 U8_GA(x1, x2, x3, x4, x5) = U8_GA(x1, x2, x5) 64.55/17.45 64.55/17.45 U9_GA(x1, x2, x3, x4, x5) = U9_GA(x1, x2, x5) 64.55/17.45 64.55/17.45 U10_GA(x1, x2, x3, x4, x5) = U10_GA(x1, x2, x5) 64.55/17.45 64.55/17.45 U11_GA(x1, x2, x3, x4, x5) = U11_GA(x1, x2, x3, x5) 64.55/17.45 64.55/17.45 U12_GA(x1, x2, x3, x4, x5) = U12_GA(x1, x2, x5) 64.55/17.45 64.55/17.45 U13_GA(x1, x2, x3, x4, x5) = U13_GA(x1, x2, x5) 64.55/17.45 64.55/17.45 U14_GA(x1, x2, x3, x4, x5) = U14_GA(x1, x2, x5) 64.55/17.45 64.55/17.45 U15_GA(x1, x2, x3, x4, x5) = U15_GA(x1, x2, x5) 64.55/17.45 64.55/17.45 U16_GA(x1, x2, x3, x4, x5) = U16_GA(x1, x2, x4, x5) 64.55/17.45 64.55/17.45 U17_GA(x1, x2, x3, x4, x5) = U17_GA(x1, x2, x5) 64.55/17.45 64.55/17.45 U18_GA(x1, x2, x3) = U18_GA(x1, x3) 64.55/17.45 64.55/17.45 U19_GA(x1, x2, x3) = U19_GA(x1, x3) 64.55/17.45 64.55/17.45 U20_GA(x1, x2, x3) = U20_GA(x1, x3) 64.55/17.45 64.55/17.45 U7_AA(x1, x2) = U7_AA(x2) 64.55/17.45 64.55/17.45 U8_AA(x1, x2, x3, x4, x5) = U8_AA(x5) 64.55/17.45 64.55/17.45 PH_IN_AA(x1, x2) = PH_IN_AA 64.55/17.45 64.55/17.45 U1_AA(x1, x2, x3, x4, x5) = U1_AA(x5) 64.55/17.45 64.55/17.45 PI_IN_AAAA(x1, x2, x3, x4) = PI_IN_AAAA 64.55/17.45 64.55/17.45 U3_AAAA(x1, x2, x3, x4, x5) = U3_AAAA(x5) 64.55/17.45 64.55/17.45 U2_AA(x1, x2, x3, x4, x5) = U2_AA(x5) 64.55/17.45 64.55/17.45 U4_AAAA(x1, x2, x3, x4, x5) = U4_AAAA(x5) 64.55/17.45 64.55/17.45 U5_AAAA(x1, x2, x3, x4, x5) = U5_AAAA(x5) 64.55/17.45 64.55/17.45 U9_AA(x1, x2, x3, x4, x5) = U9_AA(x5) 64.55/17.45 64.55/17.45 U10_AA(x1, x2, x3, x4, x5) = U10_AA(x5) 64.55/17.45 64.55/17.45 U11_AA(x1, x2, x3, x4, x5) = U11_AA(x3, x5) 64.55/17.45 64.55/17.45 U12_AA(x1, x2, x3, x4, x5) = U12_AA(x5) 64.55/17.45 64.55/17.45 U13_AA(x1, x2, x3, x4, x5) = U13_AA(x5) 64.55/17.45 64.55/17.45 U14_AA(x1, x2, x3, x4, x5) = U14_AA(x5) 64.55/17.45 64.55/17.45 U15_AA(x1, x2, x3, x4, x5) = U15_AA(x5) 64.55/17.45 64.55/17.45 U16_AA(x1, x2, x3, x4, x5) = U16_AA(x1, x4, x5) 64.55/17.45 64.55/17.45 U17_AA(x1, x2, x3, x4, x5) = U17_AA(x5) 64.55/17.45 64.55/17.45 U18_AA(x1, x2, x3) = U18_AA(x3) 64.55/17.45 64.55/17.45 PJ_IN_AA(x1, x2) = PJ_IN_AA 64.55/17.45 64.55/17.45 U21_AA(x1, x2, x3, x4, x5) = U21_AA(x5) 64.55/17.45 64.55/17.45 U22_AA(x1, x2, x3, x4, x5) = U22_AA(x5) 64.55/17.45 64.55/17.45 U23_AA(x1, x2, x3) = U23_AA(x3) 64.55/17.45 64.55/17.45 U24_AA(x1, x2, x3) = U24_AA(x3) 64.55/17.45 64.55/17.45 U25_AA(x1, x2, x3) = U25_AA(x3) 64.55/17.45 64.55/17.45 U19_AA(x1, x2, x3) = U19_AA(x3) 64.55/17.45 64.55/17.45 U20_AA(x1, x2, x3) = U20_AA(x3) 64.55/17.45 64.55/17.45 U66_AG(x1, x2) = U66_AG(x2) 64.55/17.45 64.55/17.45 PC_IN_AA(x1, x2) = PC_IN_AA 64.55/17.45 64.55/17.45 U26_AA(x1) = U26_AA(x1) 64.55/17.45 64.55/17.45 U27_AA(x1, x2) = U27_AA(x2) 64.55/17.45 64.55/17.45 U28_AA(x1, x2, x3, x4, x5) = U28_AA(x5) 64.55/17.45 64.55/17.45 U29_AA(x1, x2, x3, x4, x5) = U29_AA(x5) 64.55/17.45 64.55/17.45 U30_AA(x1, x2, x3, x4, x5) = U30_AA(x5) 64.55/17.45 64.55/17.45 U31_AA(x1, x2, x3, x4, x5) = U31_AA(x3, x5) 64.55/17.45 64.55/17.45 U32_AA(x1, x2, x3, x4, x5) = U32_AA(x5) 64.55/17.45 64.55/17.45 U33_AA(x1, x2, x3, x4, x5) = U33_AA(x5) 64.55/17.45 64.55/17.45 U34_AA(x1, x2, x3, x4, x5) = U34_AA(x5) 64.55/17.45 64.55/17.45 U35_AA(x1, x2, x3, x4, x5) = U35_AA(x5) 64.55/17.45 64.55/17.45 U36_AA(x1, x2, x3, x4, x5) = U36_AA(x1, x4, x5) 64.55/17.45 64.55/17.45 U37_AA(x1, x2, x3, x4, x5) = U37_AA(x5) 64.55/17.45 64.55/17.45 U38_AA(x1, x2, x3) = U38_AA(x3) 64.55/17.45 64.55/17.45 U39_AA(x1, x2, x3) = U39_AA(x3) 64.55/17.45 64.55/17.45 U40_AA(x1, x2, x3) = U40_AA(x3) 64.55/17.45 64.55/17.45 U67_AG(x1, x2, x3) = U67_AG(x2, x3) 64.55/17.45 64.55/17.45 U68_AG(x1, x2, x3, x4) = U68_AG(x3, x4) 64.55/17.45 64.55/17.45 U69_AG(x1, x2, x3, x4, x5, x6, x7) = U69_AG(x4, x5, x6, x7) 64.55/17.45 64.55/17.45 PD_IN_AGAGAG(x1, x2, x3, x4, x5, x6) = PD_IN_AGAGAG(x2, x4, x6) 64.55/17.45 64.55/17.45 U41_AGAGAG(x1, x2, x3, x4, x5, x6, x7) = U41_AGAGAG(x2, x4, x6, x7) 64.55/17.45 64.55/17.45 U70_AG(x1, x2, x3, x4, x5, x6, x7) = U70_AG(x1, x2, x4, x5, x6, x7) 64.55/17.45 64.55/17.45 PD_IN_GGGGAG(x1, x2, x3, x4, x5, x6) = PD_IN_GGGGAG(x1, x2, x3, x4, x6) 64.55/17.45 64.55/17.45 U41_GGGGAG(x1, x2, x3, x4, x5, x6, x7) = U41_GGGGAG(x1, x2, x3, x4, x6, x7) 64.55/17.45 64.55/17.45 U42_GGGGAG(x1, x2, x3, x4, x5, x6, x7) = U42_GGGGAG(x1, x2, x3, x4, x6, x7) 64.55/17.45 64.55/17.45 U43_GGGGAG(x1, x2, x3, x4, x5, x6, x7) = U43_GGGGAG(x1, x2, x3, x4, x6, x7) 64.55/17.45 64.55/17.45 PE_IN_GGAG(x1, x2, x3, x4) = PE_IN_GGAG(x1, x2, x4) 64.55/17.45 64.55/17.45 U44_GGAG(x1, x2, x3, x4, x5) = U44_GGAG(x1, x2, x4, x5) 64.55/17.45 64.55/17.45 U45_GGAG(x1, x2, x3, x4, x5) = U45_GGAG(x1, x2, x4, x5) 64.55/17.45 64.55/17.45 U46_GGAG(x1, x2, x3, x4, x5) = U46_GGAG(x1, x2, x4, x5) 64.55/17.45 64.55/17.45 U71_AG(x1, x2, x3, x4, x5) = U71_AG(x1, x2, x3, x4, x5) 64.55/17.45 64.55/17.45 U72_AG(x1, x2, x3, x4) = U72_AG(x2, x3, x4) 64.55/17.45 64.55/17.45 PF_IN_AAGG(x1, x2, x3, x4) = PF_IN_AAGG(x3, x4) 64.55/17.45 64.55/17.45 U47_AAGG(x1, x2, x3, x4, x5) = U47_AAGG(x3, x4, x5) 64.55/17.45 64.55/17.45 U48_AAGG(x1, x2, x3, x4, x5) = U48_AAGG(x3, x4, x5) 64.55/17.45 64.55/17.45 U49_AAGG(x1, x2, x3, x4, x5) = U49_AAGG(x3, x4, x5) 64.55/17.45 64.55/17.45 U73_AG(x1, x2, x3) = U73_AG(x1, x2, x3) 64.55/17.45 64.55/17.45 U74_AG(x1, x2, x3, x4) = U74_AG(x2, x3, x4) 64.55/17.45 64.55/17.45 U75_AG(x1, x2, x3, x4, x5, x6, x7) = U75_AG(x1, x2, x3, x4, x5, x6, x7) 64.55/17.45 64.55/17.45 U76_AG(x1, x2, x3, x4, x5, x6, x7) = U76_AG(x1, x2, x3, x4, x5, x6, x7) 64.55/17.45 64.55/17.45 U77_AG(x1, x2, x3, x4, x5, x6) = U77_AG(x2, x3, x4, x5, x6) 64.55/17.45 64.55/17.45 U78_AG(x1, x2, x3) = U78_AG(x2, x3) 64.55/17.45 64.55/17.45 PG_IN_AAG(x1, x2, x3) = PG_IN_AAG(x3) 64.55/17.45 64.55/17.45 U50_AAG(x1, x2) = U50_AAG(x1, x2) 64.55/17.45 64.55/17.45 U51_AAG(x1, x2, x3) = U51_AAG(x2, x3) 64.55/17.45 64.55/17.45 U52_AAG(x1, x2, x3, x4, x5, x6) = U52_AAG(x5, x6) 64.55/17.45 64.55/17.45 U53_AAG(x1, x2, x3, x4, x5, x6) = U53_AAG(x5, x6) 64.55/17.45 64.55/17.45 U54_AAG(x1, x2, x3, x4, x5, x6) = U54_AAG(x5, x6) 64.55/17.45 64.55/17.45 U55_AAG(x1, x2, x3, x4, x5, x6) = U55_AAG(x3, x5, x6) 64.55/17.45 64.55/17.45 U56_AAG(x1, x2, x3, x4, x5, x6) = U56_AAG(x5, x6) 64.55/17.46 64.55/17.46 U57_AAG(x1, x2, x3, x4, x5, x6) = U57_AAG(x5, x6) 64.55/17.46 64.55/17.46 U58_AAG(x1, x2, x3, x4, x5, x6) = U58_AAG(x5, x6) 64.55/17.46 64.55/17.46 U59_AAG(x1, x2, x3, x4, x5, x6) = U59_AAG(x5, x6) 64.55/17.46 64.55/17.46 U60_AAG(x1, x2, x3, x4, x5, x6) = U60_AAG(x1, x4, x5, x6) 64.55/17.46 64.55/17.46 U61_AAG(x1, x2, x3, x4, x5, x6) = U61_AAG(x5, x6) 64.55/17.46 64.55/17.46 U62_AAG(x1, x2, x3, x4) = U62_AAG(x3, x4) 64.55/17.46 64.55/17.46 U63_AAG(x1, x2, x3, x4) = U63_AAG(x3, x4) 64.55/17.46 64.55/17.46 U64_AAG(x1, x2, x3, x4) = U64_AAG(x3, x4) 64.55/17.46 64.55/17.46 U42_AGAGAG(x1, x2, x3, x4, x5, x6, x7) = U42_AGAGAG(x2, x4, x6, x7) 64.55/17.46 64.55/17.46 U43_AGAGAG(x1, x2, x3, x4, x5, x6, x7) = U43_AGAGAG(x2, x4, x6, x7) 64.55/17.46 64.55/17.46 PE_IN_AGAG(x1, x2, x3, x4) = PE_IN_AGAG(x2, x4) 64.55/17.46 64.55/17.46 U44_AGAG(x1, x2, x3, x4, x5) = U44_AGAG(x2, x4, x5) 64.55/17.46 64.55/17.46 U45_AGAG(x1, x2, x3, x4, x5) = U45_AGAG(x2, x4, x5) 64.55/17.46 64.55/17.46 U46_AGAG(x1, x2, x3, x4, x5) = U46_AGAG(x2, x4, x5) 64.55/17.46 64.55/17.46 64.55/17.46 We have to consider all (P,R,Pi)-chains 64.55/17.46 64.55/17.46 64.55/17.46 Infinitary Constructor Rewriting Termination of PiDP implies Termination of TRIPLES 64.55/17.46 64.55/17.46 64.55/17.46 64.55/17.46 ---------------------------------------- 64.55/17.46 64.55/17.46 (118) 64.55/17.46 Obligation: 64.55/17.46 Pi DP problem: 64.55/17.46 The TRS P consists of the following rules: 64.55/17.46 64.55/17.46 PA_IN_AG(d(d(X1)), const(1)) -> U65_AG(X1, pB_in_aa(X1, X2)) 64.55/17.46 PA_IN_AG(d(d(X1)), const(1)) -> PB_IN_AA(X1, X2) 64.55/17.46 PB_IN_AA(e(t), const(1)) -> U6_AA(pA_in_gg(d(e(const(1))), const(1))) 64.55/17.46 PB_IN_AA(e(t), const(1)) -> PA_IN_GG(d(e(const(1))), const(1)) 64.55/17.46 PA_IN_GG(d(d(X1)), const(1)) -> U65_GG(X1, pB_in_ga(X1, X2)) 64.55/17.46 PA_IN_GG(d(d(X1)), const(1)) -> PB_IN_GA(X1, X2) 64.55/17.46 PB_IN_GA(e(t), const(1)) -> U6_GA(pA_in_gg(d(e(const(1))), const(1))) 64.55/17.46 PB_IN_GA(e(t), const(1)) -> PA_IN_GG(d(e(const(1))), const(1)) 64.55/17.46 PA_IN_GG(d(d(X1)), const(0)) -> U66_GG(X1, pC_in_ga(X1, X2)) 64.55/17.46 PA_IN_GG(d(d(X1)), const(0)) -> PC_IN_GA(X1, X2) 64.55/17.46 PC_IN_GA(e(t), const(1)) -> U26_GA(pA_in_gg(d(e(const(1))), const(0))) 64.55/17.46 PC_IN_GA(e(t), const(1)) -> PA_IN_GG(d(e(const(1))), const(0)) 64.55/17.46 PA_IN_GG(d(e(+(t, X1))), +(const(1), X2)) -> U67_GG(X1, X2, pA_in_gg(d(e(X1)), X2)) 64.55/17.46 PA_IN_GG(d(e(+(t, X1))), +(const(1), X2)) -> PA_IN_GG(d(e(X1)), X2) 64.55/17.46 PA_IN_GG(d(e(+(const(X1), X2))), +(const(0), X3)) -> U68_GG(X1, X2, X3, pA_in_gg(d(e(X2)), X3)) 64.55/17.46 PA_IN_GG(d(e(+(const(X1), X2))), +(const(0), X3)) -> PA_IN_GG(d(e(X2)), X3) 64.55/17.46 PA_IN_GG(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) -> U69_GG(X1, X2, X3, X4, X5, X6, pD_in_gggggg(X1, X4, X2, X5, X3, X6)) 64.55/17.46 PA_IN_GG(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) -> PD_IN_GGGGGG(X1, X4, X2, X5, X3, X6) 64.55/17.46 PD_IN_GGGGGG(X1, X2, X3, X4, X5, X6) -> U41_GGGGGG(X1, X2, X3, X4, X5, X6, pA_in_gg(d(e(X1)), X2)) 64.55/17.46 PD_IN_GGGGGG(X1, X2, X3, X4, X5, X6) -> PA_IN_GG(d(e(X1)), X2) 64.55/17.46 PA_IN_GG(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) -> U70_GG(X1, X2, X3, X4, X5, X6, pD_in_gggggg(X1, X5, X2, X4, X3, X6)) 64.55/17.46 PA_IN_GG(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) -> PD_IN_GGGGGG(X1, X5, X2, X4, X3, X6) 64.55/17.46 PD_IN_GGGGGG(X1, X2, X3, X4, X5, X6) -> U42_GGGGGG(X1, X2, X3, X4, X5, X6, pcA_in_gg(d(e(X1)), X2)) 64.55/17.46 U42_GGGGGG(X1, X2, X3, X4, X5, X6, pcA_out_gg(d(e(X1)), X2)) -> U43_GGGGGG(X1, X2, X3, X4, X5, X6, pE_in_gggg(X3, X4, X5, X6)) 64.55/17.46 U42_GGGGGG(X1, X2, X3, X4, X5, X6, pcA_out_gg(d(e(X1)), X2)) -> PE_IN_GGGG(X3, X4, X5, X6) 64.55/17.46 PE_IN_GGGG(X1, X2, X3, X4) -> U44_GGGG(X1, X2, X3, X4, pA_in_gg(d(e(X1)), X2)) 64.55/17.46 PE_IN_GGGG(X1, X2, X3, X4) -> PA_IN_GG(d(e(X1)), X2) 64.55/17.46 PA_IN_GG(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) -> U71_GG(X1, X2, X3, X4, pE_in_gggg(X1, X4, X2, X3)) 64.55/17.46 PA_IN_GG(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) -> PE_IN_GGGG(X1, X4, X2, X3) 64.55/17.46 PE_IN_GGGG(X1, X2, X3, X4) -> U45_GGGG(X1, X2, X3, X4, pcA_in_gg(d(e(X1)), X2)) 64.55/17.46 U45_GGGG(X1, X2, X3, X4, pcA_out_gg(d(e(X1)), X2)) -> U46_GGGG(X1, X2, X3, X4, pA_in_gg(d(e(X3)), X4)) 64.55/17.46 U45_GGGG(X1, X2, X3, X4, pcA_out_gg(d(e(X1)), X2)) -> PA_IN_GG(d(e(X3)), X4) 64.55/17.46 PA_IN_GG(d(d(X1)), +(X2, X3)) -> U72_GG(X1, X2, X3, pF_in_gagg(X1, X4, X2, X3)) 64.55/17.46 PA_IN_GG(d(d(X1)), +(X2, X3)) -> PF_IN_GAGG(X1, X4, X2, X3) 64.55/17.46 PF_IN_GAGG(X1, X2, X3, X4) -> U47_GAGG(X1, X2, X3, X4, pJ_in_ga(X1, X2)) 64.55/17.46 PF_IN_GAGG(X1, X2, X3, X4) -> PJ_IN_GA(X1, X2) 64.55/17.46 PJ_IN_GA(e(+(X1, X2)), +(X3, X4)) -> U21_GA(X1, X2, X3, X4, pI_in_gaga(X1, X3, X2, X4)) 64.55/17.46 PJ_IN_GA(e(+(X1, X2)), +(X3, X4)) -> PI_IN_GAGA(X1, X3, X2, X4) 64.55/17.46 PI_IN_GAGA(X1, X2, X3, X4) -> U3_GAGA(X1, X2, X3, X4, pH_in_ga(X1, X2)) 64.55/17.46 PI_IN_GAGA(X1, X2, X3, X4) -> PH_IN_GA(X1, X2) 64.55/17.46 PH_IN_GA(+(X1, X2), +(X3, X4)) -> U1_GA(X1, X2, X3, X4, pI_in_gaga(X1, X3, X2, X4)) 64.55/17.46 PH_IN_GA(+(X1, X2), +(X3, X4)) -> PI_IN_GAGA(X1, X3, X2, X4) 64.55/17.46 PI_IN_GAGA(X1, X2, X3, X4) -> U4_GAGA(X1, X2, X3, X4, pcH_in_ga(X1, X2)) 64.55/17.46 U4_GAGA(X1, X2, X3, X4, pcH_out_ga(X1, X2)) -> U5_GAGA(X1, X2, X3, X4, pH_in_ga(X3, X4)) 64.55/17.46 U4_GAGA(X1, X2, X3, X4, pcH_out_ga(X1, X2)) -> PH_IN_GA(X3, X4) 64.55/17.46 PH_IN_GA(*(X1, X2), +(*(X1, X3), *(X2, X4))) -> U2_GA(X1, X2, X3, X4, pI_in_gaga(X1, X4, X2, X3)) 64.55/17.46 PH_IN_GA(*(X1, X2), +(*(X1, X3), *(X2, X4))) -> PI_IN_GAGA(X1, X4, X2, X3) 64.55/17.46 PJ_IN_GA(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U22_GA(X1, X2, X3, X4, pI_in_gaga(X1, X4, X2, X3)) 64.55/17.46 PJ_IN_GA(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> PI_IN_GAGA(X1, X4, X2, X3) 64.55/17.46 PJ_IN_GA(d(X1), X2) -> U23_GA(X1, X2, pJ_in_ga(X1, X3)) 64.55/17.46 PJ_IN_GA(d(X1), X2) -> PJ_IN_GA(X1, X3) 64.55/17.46 PJ_IN_GA(d(X1), X2) -> U24_GA(X1, X2, pcJ_in_ga(X1, X3)) 64.55/17.46 U24_GA(X1, X2, pcJ_out_ga(X1, X3)) -> U25_GA(X1, X2, pH_in_ga(X3, X2)) 64.55/17.46 U24_GA(X1, X2, pcJ_out_ga(X1, X3)) -> PH_IN_GA(X3, X2) 64.55/17.46 PF_IN_GAGG(X1, X2, X3, X4) -> U48_GAGG(X1, X2, X3, X4, pcJ_in_ga(X1, X2)) 64.55/17.46 U48_GAGG(X1, X2, X3, X4, pcJ_out_ga(X1, X2)) -> U49_GAGG(X1, X2, X3, X4, pA_in_gg(d(e(X2)), +(X3, X4))) 64.55/17.46 U48_GAGG(X1, X2, X3, X4, pcJ_out_ga(X1, X2)) -> PA_IN_GG(d(e(X2)), +(X3, X4)) 64.55/17.46 PA_IN_GG(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) -> U73_GG(X1, X2, pA_in_gg(d(e(X1)), X2)) 64.55/17.46 PA_IN_GG(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) -> PA_IN_GG(d(e(X1)), X2) 64.55/17.46 PA_IN_GG(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) -> U74_GG(X1, X2, X3, pA_in_gg(d(e(X2)), X3)) 64.55/17.46 PA_IN_GG(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) -> PA_IN_GG(d(e(X2)), X3) 64.55/17.46 PA_IN_GG(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) -> U75_GG(X1, X2, X3, X4, X5, X6, pD_in_gggggg(X1, X5, X2, X6, X3, X4)) 64.55/17.46 PA_IN_GG(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) -> PD_IN_GGGGGG(X1, X5, X2, X6, X3, X4) 64.55/17.46 PA_IN_GG(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) -> U76_GG(X1, X2, X3, X4, X5, X6, pD_in_gggggg(X1, X6, X2, X5, X3, X4)) 64.55/17.46 PA_IN_GG(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) -> PD_IN_GGGGGG(X1, X6, X2, X5, X3, X4) 64.55/17.46 PA_IN_GG(d(d(X1)), +(*(X2, X3), *(X4, X5))) -> U77_GG(X1, X2, X3, X4, X5, pF_in_gagg(X1, X6, *(X2, X3), *(X4, X5))) 64.55/17.46 PA_IN_GG(d(d(X1)), +(*(X2, X3), *(X4, X5))) -> PF_IN_GAGG(X1, X6, *(X2, X3), *(X4, X5)) 64.55/17.46 PA_IN_GG(d(d(X1)), X2) -> U78_GG(X1, X2, pG_in_gag(X1, X3, X2)) 64.55/17.46 PA_IN_GG(d(d(X1)), X2) -> PG_IN_GAG(X1, X3, X2) 64.55/17.46 PG_IN_GAG(e(t), const(1), X1) -> U50_GAG(X1, pA_in_gg(d(e(const(1))), X1)) 64.55/17.46 PG_IN_GAG(e(t), const(1), X1) -> PA_IN_GG(d(e(const(1))), X1) 64.55/17.46 PG_IN_GAG(e(const(X1)), const(0), X2) -> U51_GAG(X1, X2, pA_in_gg(d(e(const(0))), X2)) 64.55/17.46 PG_IN_GAG(e(const(X1)), const(0), X2) -> PA_IN_GG(d(e(const(0))), X2) 64.55/17.46 PG_IN_GAG(e(+(X1, X2)), +(X3, X4), X5) -> U52_GAG(X1, X2, X3, X4, X5, pH_in_ga(X1, X3)) 64.55/17.46 PG_IN_GAG(e(+(X1, X2)), +(X3, X4), X5) -> PH_IN_GA(X1, X3) 64.55/17.46 PG_IN_GAG(e(+(X1, X2)), +(X3, X4), X5) -> U53_GAG(X1, X2, X3, X4, X5, pcH_in_ga(X1, X3)) 64.55/17.46 U53_GAG(X1, X2, X3, X4, X5, pcH_out_ga(X1, X3)) -> U54_GAG(X1, X2, X3, X4, X5, pH_in_ga(X2, X4)) 64.55/17.46 U53_GAG(X1, X2, X3, X4, X5, pcH_out_ga(X1, X3)) -> PH_IN_GA(X2, X4) 64.55/17.46 U53_GAG(X1, X2, X3, X4, X5, pcH_out_ga(X1, X3)) -> U55_GAG(X1, X2, X3, X4, X5, pcH_in_ga(X2, X4)) 64.55/17.46 U55_GAG(X1, X2, X3, X4, X5, pcH_out_ga(X2, X4)) -> U56_GAG(X1, X2, X3, X4, X5, pA_in_gg(d(e(+(X3, X4))), X5)) 64.55/17.46 U55_GAG(X1, X2, X3, X4, X5, pcH_out_ga(X2, X4)) -> PA_IN_GG(d(e(+(X3, X4))), X5) 64.55/17.46 PG_IN_GAG(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) -> U57_GAG(X1, X2, X3, X4, X5, pH_in_ga(X1, X4)) 64.55/17.46 PG_IN_GAG(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) -> PH_IN_GA(X1, X4) 64.55/17.46 PG_IN_GAG(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) -> U58_GAG(X1, X2, X3, X4, X5, pcH_in_ga(X1, X4)) 64.55/17.46 U58_GAG(X1, X2, X3, X4, X5, pcH_out_ga(X1, X4)) -> U59_GAG(X1, X2, X3, X4, X5, pH_in_ga(X2, X3)) 64.55/17.46 U58_GAG(X1, X2, X3, X4, X5, pcH_out_ga(X1, X4)) -> PH_IN_GA(X2, X3) 64.55/17.46 U58_GAG(X1, X2, X3, X4, X5, pcH_out_ga(X1, X4)) -> U60_GAG(X1, X2, X3, X4, X5, pcH_in_ga(X2, X3)) 64.55/17.46 U60_GAG(X1, X2, X3, X4, X5, pcH_out_ga(X2, X3)) -> U61_GAG(X1, X2, X3, X4, X5, pA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), X5)) 64.55/17.46 U60_GAG(X1, X2, X3, X4, X5, pcH_out_ga(X2, X3)) -> PA_IN_GG(d(e(+(*(X1, X3), *(X2, X4)))), X5) 64.55/17.46 PG_IN_GAG(d(X1), X2, X3) -> U62_GAG(X1, X2, X3, pJ_in_ga(X1, X4)) 64.55/17.46 PG_IN_GAG(d(X1), X2, X3) -> PJ_IN_GA(X1, X4) 64.55/17.46 PG_IN_GAG(d(X1), X2, X3) -> U63_GAG(X1, X2, X3, pcJ_in_ga(X1, X4)) 64.55/17.46 U63_GAG(X1, X2, X3, pcJ_out_ga(X1, X4)) -> U64_GAG(X1, X2, X3, pG_in_gag(e(X4), X2, X3)) 64.55/17.46 U63_GAG(X1, X2, X3, pcJ_out_ga(X1, X4)) -> PG_IN_GAG(e(X4), X2, X3) 64.55/17.46 PC_IN_GA(e(const(X1)), const(0)) -> U27_GA(X1, pA_in_gg(d(e(const(0))), const(0))) 64.55/17.46 PC_IN_GA(e(const(X1)), const(0)) -> PA_IN_GG(d(e(const(0))), const(0)) 64.55/17.46 PC_IN_GA(e(+(X1, X2)), +(X3, X4)) -> U28_GA(X1, X2, X3, X4, pH_in_ga(X1, X3)) 64.55/17.46 PC_IN_GA(e(+(X1, X2)), +(X3, X4)) -> PH_IN_GA(X1, X3) 64.55/17.46 PC_IN_GA(e(+(X1, X2)), +(X3, X4)) -> U29_GA(X1, X2, X3, X4, pcH_in_ga(X1, X3)) 64.55/17.46 U29_GA(X1, X2, X3, X4, pcH_out_ga(X1, X3)) -> U30_GA(X1, X2, X3, X4, pH_in_ga(X2, X4)) 64.55/17.46 U29_GA(X1, X2, X3, X4, pcH_out_ga(X1, X3)) -> PH_IN_GA(X2, X4) 64.55/17.46 U29_GA(X1, X2, X3, X4, pcH_out_ga(X1, X3)) -> U31_GA(X1, X2, X3, X4, pcH_in_ga(X2, X4)) 64.55/17.46 U31_GA(X1, X2, X3, X4, pcH_out_ga(X2, X4)) -> U32_GA(X1, X2, X3, X4, pA_in_gg(d(e(+(X3, X4))), const(0))) 64.55/17.46 U31_GA(X1, X2, X3, X4, pcH_out_ga(X2, X4)) -> PA_IN_GG(d(e(+(X3, X4))), const(0)) 64.55/17.46 PC_IN_GA(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U33_GA(X1, X2, X3, X4, pH_in_ga(X1, X4)) 64.55/17.46 PC_IN_GA(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> PH_IN_GA(X1, X4) 64.55/17.46 PC_IN_GA(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U34_GA(X1, X2, X3, X4, pcH_in_ga(X1, X4)) 64.55/17.46 U34_GA(X1, X2, X3, X4, pcH_out_ga(X1, X4)) -> U35_GA(X1, X2, X3, X4, pH_in_ga(X2, X3)) 64.55/17.46 U34_GA(X1, X2, X3, X4, pcH_out_ga(X1, X4)) -> PH_IN_GA(X2, X3) 64.55/17.46 U34_GA(X1, X2, X3, X4, pcH_out_ga(X1, X4)) -> U36_GA(X1, X2, X3, X4, pcH_in_ga(X2, X3)) 64.55/17.46 U36_GA(X1, X2, X3, X4, pcH_out_ga(X2, X3)) -> U37_GA(X1, X2, X3, X4, pA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(0))) 64.55/17.46 U36_GA(X1, X2, X3, X4, pcH_out_ga(X2, X3)) -> PA_IN_GG(d(e(+(*(X1, X3), *(X2, X4)))), const(0)) 64.55/17.46 PC_IN_GA(d(X1), X2) -> U38_GA(X1, X2, pJ_in_ga(X1, X3)) 64.55/17.46 PC_IN_GA(d(X1), X2) -> PJ_IN_GA(X1, X3) 64.55/17.46 PC_IN_GA(d(X1), X2) -> U39_GA(X1, X2, pcJ_in_ga(X1, X3)) 64.55/17.46 U39_GA(X1, X2, pcJ_out_ga(X1, X3)) -> U40_GA(X1, X2, pC_in_ga(e(X3), X2)) 64.55/17.46 U39_GA(X1, X2, pcJ_out_ga(X1, X3)) -> PC_IN_GA(e(X3), X2) 64.55/17.46 PB_IN_GA(e(const(X1)), const(0)) -> U7_GA(X1, pA_in_gg(d(e(const(0))), const(1))) 64.55/17.46 PB_IN_GA(e(const(X1)), const(0)) -> PA_IN_GG(d(e(const(0))), const(1)) 64.55/17.46 PB_IN_GA(e(+(X1, X2)), +(X3, X4)) -> U8_GA(X1, X2, X3, X4, pH_in_ga(X1, X3)) 64.55/17.46 PB_IN_GA(e(+(X1, X2)), +(X3, X4)) -> PH_IN_GA(X1, X3) 64.55/17.46 PB_IN_GA(e(+(X1, X2)), +(X3, X4)) -> U9_GA(X1, X2, X3, X4, pcH_in_ga(X1, X3)) 64.55/17.46 U9_GA(X1, X2, X3, X4, pcH_out_ga(X1, X3)) -> U10_GA(X1, X2, X3, X4, pH_in_ga(X2, X4)) 64.55/17.46 U9_GA(X1, X2, X3, X4, pcH_out_ga(X1, X3)) -> PH_IN_GA(X2, X4) 64.55/17.46 U9_GA(X1, X2, X3, X4, pcH_out_ga(X1, X3)) -> U11_GA(X1, X2, X3, X4, pcH_in_ga(X2, X4)) 64.55/17.46 U11_GA(X1, X2, X3, X4, pcH_out_ga(X2, X4)) -> U12_GA(X1, X2, X3, X4, pA_in_gg(d(e(+(X3, X4))), const(1))) 64.55/17.46 U11_GA(X1, X2, X3, X4, pcH_out_ga(X2, X4)) -> PA_IN_GG(d(e(+(X3, X4))), const(1)) 64.55/17.46 PB_IN_GA(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U13_GA(X1, X2, X3, X4, pH_in_ga(X1, X4)) 64.55/17.46 PB_IN_GA(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> PH_IN_GA(X1, X4) 64.55/17.46 PB_IN_GA(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U14_GA(X1, X2, X3, X4, pcH_in_ga(X1, X4)) 64.55/17.46 U14_GA(X1, X2, X3, X4, pcH_out_ga(X1, X4)) -> U15_GA(X1, X2, X3, X4, pH_in_ga(X2, X3)) 64.55/17.46 U14_GA(X1, X2, X3, X4, pcH_out_ga(X1, X4)) -> PH_IN_GA(X2, X3) 64.55/17.46 U14_GA(X1, X2, X3, X4, pcH_out_ga(X1, X4)) -> U16_GA(X1, X2, X3, X4, pcH_in_ga(X2, X3)) 64.55/17.46 U16_GA(X1, X2, X3, X4, pcH_out_ga(X2, X3)) -> U17_GA(X1, X2, X3, X4, pA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(1))) 64.55/17.46 U16_GA(X1, X2, X3, X4, pcH_out_ga(X2, X3)) -> PA_IN_GG(d(e(+(*(X1, X3), *(X2, X4)))), const(1)) 64.55/17.46 PB_IN_GA(d(X1), X2) -> U18_GA(X1, X2, pJ_in_ga(X1, X3)) 64.55/17.46 PB_IN_GA(d(X1), X2) -> PJ_IN_GA(X1, X3) 64.55/17.46 PB_IN_GA(d(X1), X2) -> U19_GA(X1, X2, pcJ_in_ga(X1, X3)) 64.55/17.46 U19_GA(X1, X2, pcJ_out_ga(X1, X3)) -> U20_GA(X1, X2, pB_in_ga(e(X3), X2)) 64.55/17.46 U19_GA(X1, X2, pcJ_out_ga(X1, X3)) -> PB_IN_GA(e(X3), X2) 64.55/17.46 PB_IN_AA(e(const(X1)), const(0)) -> U7_AA(X1, pA_in_gg(d(e(const(0))), const(1))) 64.55/17.46 PB_IN_AA(e(const(X1)), const(0)) -> PA_IN_GG(d(e(const(0))), const(1)) 64.55/17.46 PB_IN_AA(e(+(X1, X2)), +(X3, X4)) -> U8_AA(X1, X2, X3, X4, pH_in_aa(X1, X3)) 64.55/17.46 PB_IN_AA(e(+(X1, X2)), +(X3, X4)) -> PH_IN_AA(X1, X3) 64.55/17.46 PH_IN_AA(+(X1, X2), +(X3, X4)) -> U1_AA(X1, X2, X3, X4, pI_in_aaaa(X1, X3, X2, X4)) 64.55/17.46 PH_IN_AA(+(X1, X2), +(X3, X4)) -> PI_IN_AAAA(X1, X3, X2, X4) 64.55/17.46 PI_IN_AAAA(X1, X2, X3, X4) -> U3_AAAA(X1, X2, X3, X4, pH_in_aa(X1, X2)) 64.55/17.46 PI_IN_AAAA(X1, X2, X3, X4) -> PH_IN_AA(X1, X2) 64.55/17.46 PH_IN_AA(*(X1, X2), +(*(X1, X3), *(X2, X4))) -> U2_AA(X1, X2, X3, X4, pI_in_aaaa(X1, X4, X2, X3)) 64.55/17.46 PH_IN_AA(*(X1, X2), +(*(X1, X3), *(X2, X4))) -> PI_IN_AAAA(X1, X4, X2, X3) 64.55/17.46 PI_IN_AAAA(X1, X2, X3, X4) -> U4_AAAA(X1, X2, X3, X4, pcH_in_aa(X1, X2)) 64.55/17.46 U4_AAAA(X1, X2, X3, X4, pcH_out_aa(X1, X2)) -> U5_AAAA(X1, X2, X3, X4, pH_in_aa(X3, X4)) 64.55/17.46 U4_AAAA(X1, X2, X3, X4, pcH_out_aa(X1, X2)) -> PH_IN_AA(X3, X4) 64.55/17.46 PB_IN_AA(e(+(X1, X2)), +(X3, X4)) -> U9_AA(X1, X2, X3, X4, pcH_in_aa(X1, X3)) 64.55/17.46 U9_AA(X1, X2, X3, X4, pcH_out_aa(X1, X3)) -> U10_AA(X1, X2, X3, X4, pH_in_aa(X2, X4)) 64.55/17.46 U9_AA(X1, X2, X3, X4, pcH_out_aa(X1, X3)) -> PH_IN_AA(X2, X4) 64.55/17.46 U9_AA(X1, X2, X3, X4, pcH_out_aa(X1, X3)) -> U11_AA(X1, X2, X3, X4, pcH_in_aa(X2, X4)) 64.55/17.46 U11_AA(X1, X2, X3, X4, pcH_out_aa(X2, X4)) -> U12_AA(X1, X2, X3, X4, pA_in_gg(d(e(+(X3, X4))), const(1))) 64.55/17.46 U11_AA(X1, X2, X3, X4, pcH_out_aa(X2, X4)) -> PA_IN_GG(d(e(+(X3, X4))), const(1)) 64.55/17.46 PB_IN_AA(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U13_AA(X1, X2, X3, X4, pH_in_aa(X1, X4)) 64.55/17.46 PB_IN_AA(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> PH_IN_AA(X1, X4) 64.55/17.46 PB_IN_AA(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U14_AA(X1, X2, X3, X4, pcH_in_aa(X1, X4)) 64.55/17.46 U14_AA(X1, X2, X3, X4, pcH_out_aa(X1, X4)) -> U15_AA(X1, X2, X3, X4, pH_in_aa(X2, X3)) 64.55/17.46 U14_AA(X1, X2, X3, X4, pcH_out_aa(X1, X4)) -> PH_IN_AA(X2, X3) 64.55/17.46 U14_AA(X1, X2, X3, X4, pcH_out_aa(X1, X4)) -> U16_AA(X1, X2, X3, X4, pcH_in_aa(X2, X3)) 64.55/17.46 U16_AA(X1, X2, X3, X4, pcH_out_aa(X2, X3)) -> U17_AA(X1, X2, X3, X4, pA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(1))) 64.55/17.46 U16_AA(X1, X2, X3, X4, pcH_out_aa(X2, X3)) -> PA_IN_GG(d(e(+(*(X1, X3), *(X2, X4)))), const(1)) 64.55/17.46 PB_IN_AA(d(X1), X2) -> U18_AA(X1, X2, pJ_in_aa(X1, X3)) 64.55/17.46 PB_IN_AA(d(X1), X2) -> PJ_IN_AA(X1, X3) 64.55/17.46 PJ_IN_AA(e(+(X1, X2)), +(X3, X4)) -> U21_AA(X1, X2, X3, X4, pI_in_aaaa(X1, X3, X2, X4)) 64.55/17.46 PJ_IN_AA(e(+(X1, X2)), +(X3, X4)) -> PI_IN_AAAA(X1, X3, X2, X4) 64.55/17.46 PJ_IN_AA(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U22_AA(X1, X2, X3, X4, pI_in_aaaa(X1, X4, X2, X3)) 64.55/17.46 PJ_IN_AA(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> PI_IN_AAAA(X1, X4, X2, X3) 64.55/17.46 PJ_IN_AA(d(X1), X2) -> U23_AA(X1, X2, pJ_in_aa(X1, X3)) 64.55/17.46 PJ_IN_AA(d(X1), X2) -> PJ_IN_AA(X1, X3) 64.55/17.46 PJ_IN_AA(d(X1), X2) -> U24_AA(X1, X2, pcJ_in_aa(X1, X3)) 64.55/17.46 U24_AA(X1, X2, pcJ_out_aa(X1, X3)) -> U25_AA(X1, X2, pH_in_ga(X3, X2)) 64.55/17.46 U24_AA(X1, X2, pcJ_out_aa(X1, X3)) -> PH_IN_GA(X3, X2) 64.55/17.46 PB_IN_AA(d(X1), X2) -> U19_AA(X1, X2, pcJ_in_aa(X1, X3)) 64.55/17.46 U19_AA(X1, X2, pcJ_out_aa(X1, X3)) -> U20_AA(X1, X2, pB_in_ga(e(X3), X2)) 64.55/17.46 U19_AA(X1, X2, pcJ_out_aa(X1, X3)) -> PB_IN_GA(e(X3), X2) 64.55/17.46 PA_IN_AG(d(d(X1)), const(0)) -> U66_AG(X1, pC_in_aa(X1, X2)) 64.55/17.46 PA_IN_AG(d(d(X1)), const(0)) -> PC_IN_AA(X1, X2) 64.55/17.46 PC_IN_AA(e(t), const(1)) -> U26_AA(pA_in_gg(d(e(const(1))), const(0))) 64.55/17.46 PC_IN_AA(e(t), const(1)) -> PA_IN_GG(d(e(const(1))), const(0)) 64.55/17.46 PC_IN_AA(e(const(X1)), const(0)) -> U27_AA(X1, pA_in_gg(d(e(const(0))), const(0))) 64.55/17.46 PC_IN_AA(e(const(X1)), const(0)) -> PA_IN_GG(d(e(const(0))), const(0)) 64.55/17.46 PC_IN_AA(e(+(X1, X2)), +(X3, X4)) -> U28_AA(X1, X2, X3, X4, pH_in_aa(X1, X3)) 64.55/17.46 PC_IN_AA(e(+(X1, X2)), +(X3, X4)) -> PH_IN_AA(X1, X3) 64.55/17.46 PC_IN_AA(e(+(X1, X2)), +(X3, X4)) -> U29_AA(X1, X2, X3, X4, pcH_in_aa(X1, X3)) 64.55/17.46 U29_AA(X1, X2, X3, X4, pcH_out_aa(X1, X3)) -> U30_AA(X1, X2, X3, X4, pH_in_aa(X2, X4)) 64.55/17.46 U29_AA(X1, X2, X3, X4, pcH_out_aa(X1, X3)) -> PH_IN_AA(X2, X4) 64.55/17.46 U29_AA(X1, X2, X3, X4, pcH_out_aa(X1, X3)) -> U31_AA(X1, X2, X3, X4, pcH_in_aa(X2, X4)) 64.55/17.46 U31_AA(X1, X2, X3, X4, pcH_out_aa(X2, X4)) -> U32_AA(X1, X2, X3, X4, pA_in_gg(d(e(+(X3, X4))), const(0))) 64.55/17.46 U31_AA(X1, X2, X3, X4, pcH_out_aa(X2, X4)) -> PA_IN_GG(d(e(+(X3, X4))), const(0)) 64.55/17.46 PC_IN_AA(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U33_AA(X1, X2, X3, X4, pH_in_aa(X1, X4)) 64.55/17.46 PC_IN_AA(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> PH_IN_AA(X1, X4) 64.55/17.46 PC_IN_AA(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U34_AA(X1, X2, X3, X4, pcH_in_aa(X1, X4)) 64.55/17.46 U34_AA(X1, X2, X3, X4, pcH_out_aa(X1, X4)) -> U35_AA(X1, X2, X3, X4, pH_in_aa(X2, X3)) 64.55/17.46 U34_AA(X1, X2, X3, X4, pcH_out_aa(X1, X4)) -> PH_IN_AA(X2, X3) 64.55/17.46 U34_AA(X1, X2, X3, X4, pcH_out_aa(X1, X4)) -> U36_AA(X1, X2, X3, X4, pcH_in_aa(X2, X3)) 64.55/17.46 U36_AA(X1, X2, X3, X4, pcH_out_aa(X2, X3)) -> U37_AA(X1, X2, X3, X4, pA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(0))) 64.55/17.46 U36_AA(X1, X2, X3, X4, pcH_out_aa(X2, X3)) -> PA_IN_GG(d(e(+(*(X1, X3), *(X2, X4)))), const(0)) 64.55/17.46 PC_IN_AA(d(X1), X2) -> U38_AA(X1, X2, pJ_in_aa(X1, X3)) 64.55/17.46 PC_IN_AA(d(X1), X2) -> PJ_IN_AA(X1, X3) 64.55/17.46 PC_IN_AA(d(X1), X2) -> U39_AA(X1, X2, pcJ_in_aa(X1, X3)) 64.55/17.46 U39_AA(X1, X2, pcJ_out_aa(X1, X3)) -> U40_AA(X1, X2, pC_in_ga(e(X3), X2)) 64.55/17.46 U39_AA(X1, X2, pcJ_out_aa(X1, X3)) -> PC_IN_GA(e(X3), X2) 64.55/17.46 PA_IN_AG(d(e(+(t, X1))), +(const(1), X2)) -> U67_AG(X1, X2, pA_in_ag(d(e(X1)), X2)) 64.55/17.46 PA_IN_AG(d(e(+(t, X1))), +(const(1), X2)) -> PA_IN_AG(d(e(X1)), X2) 64.55/17.46 PA_IN_AG(d(e(+(const(X1), X2))), +(const(0), X3)) -> U68_AG(X1, X2, X3, pA_in_ag(d(e(X2)), X3)) 64.55/17.46 PA_IN_AG(d(e(+(const(X1), X2))), +(const(0), X3)) -> PA_IN_AG(d(e(X2)), X3) 64.55/17.46 PA_IN_AG(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) -> U69_AG(X1, X2, X3, X4, X5, X6, pD_in_agagag(X1, X4, X2, X5, X3, X6)) 64.55/17.46 PA_IN_AG(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) -> PD_IN_AGAGAG(X1, X4, X2, X5, X3, X6) 64.55/17.46 PD_IN_AGAGAG(X1, X2, X3, X4, X5, X6) -> U41_AGAGAG(X1, X2, X3, X4, X5, X6, pA_in_ag(d(e(X1)), X2)) 64.55/17.46 PD_IN_AGAGAG(X1, X2, X3, X4, X5, X6) -> PA_IN_AG(d(e(X1)), X2) 64.55/17.46 PA_IN_AG(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) -> U70_AG(X1, X2, X3, X4, X5, X6, pD_in_ggggag(X1, X5, X2, X4, X3, X6)) 64.55/17.46 PA_IN_AG(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) -> PD_IN_GGGGAG(X1, X5, X2, X4, X3, X6) 64.55/17.46 PD_IN_GGGGAG(X1, X2, X3, X4, X5, X6) -> U41_GGGGAG(X1, X2, X3, X4, X5, X6, pA_in_gg(d(e(X1)), X2)) 64.55/17.46 PD_IN_GGGGAG(X1, X2, X3, X4, X5, X6) -> PA_IN_GG(d(e(X1)), X2) 64.55/17.46 PD_IN_GGGGAG(X1, X2, X3, X4, X5, X6) -> U42_GGGGAG(X1, X2, X3, X4, X5, X6, pcA_in_gg(d(e(X1)), X2)) 64.55/17.46 U42_GGGGAG(X1, X2, X3, X4, X5, X6, pcA_out_gg(d(e(X1)), X2)) -> U43_GGGGAG(X1, X2, X3, X4, X5, X6, pE_in_ggag(X3, X4, X5, X6)) 64.55/17.46 U42_GGGGAG(X1, X2, X3, X4, X5, X6, pcA_out_gg(d(e(X1)), X2)) -> PE_IN_GGAG(X3, X4, X5, X6) 64.55/17.46 PE_IN_GGAG(X1, X2, X3, X4) -> U44_GGAG(X1, X2, X3, X4, pA_in_gg(d(e(X1)), X2)) 64.55/17.46 PE_IN_GGAG(X1, X2, X3, X4) -> PA_IN_GG(d(e(X1)), X2) 64.55/17.46 PE_IN_GGAG(X1, X2, X3, X4) -> U45_GGAG(X1, X2, X3, X4, pcA_in_gg(d(e(X1)), X2)) 64.55/17.46 U45_GGAG(X1, X2, X3, X4, pcA_out_gg(d(e(X1)), X2)) -> U46_GGAG(X1, X2, X3, X4, pA_in_ag(d(e(X3)), X4)) 64.55/17.46 U45_GGAG(X1, X2, X3, X4, pcA_out_gg(d(e(X1)), X2)) -> PA_IN_AG(d(e(X3)), X4) 64.55/17.46 PA_IN_AG(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) -> U71_AG(X1, X2, X3, X4, pE_in_gggg(X1, X4, X2, X3)) 64.55/17.46 PA_IN_AG(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) -> PE_IN_GGGG(X1, X4, X2, X3) 64.55/17.46 PA_IN_AG(d(d(X1)), +(X2, X3)) -> U72_AG(X1, X2, X3, pF_in_aagg(X1, X4, X2, X3)) 64.55/17.46 PA_IN_AG(d(d(X1)), +(X2, X3)) -> PF_IN_AAGG(X1, X4, X2, X3) 64.55/17.46 PF_IN_AAGG(X1, X2, X3, X4) -> U47_AAGG(X1, X2, X3, X4, pJ_in_aa(X1, X2)) 64.55/17.46 PF_IN_AAGG(X1, X2, X3, X4) -> PJ_IN_AA(X1, X2) 64.55/17.46 PF_IN_AAGG(X1, X2, X3, X4) -> U48_AAGG(X1, X2, X3, X4, pcJ_in_aa(X1, X2)) 64.55/17.46 U48_AAGG(X1, X2, X3, X4, pcJ_out_aa(X1, X2)) -> U49_AAGG(X1, X2, X3, X4, pA_in_gg(d(e(X2)), +(X3, X4))) 64.55/17.46 U48_AAGG(X1, X2, X3, X4, pcJ_out_aa(X1, X2)) -> PA_IN_GG(d(e(X2)), +(X3, X4)) 64.55/17.46 PA_IN_AG(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) -> U73_AG(X1, X2, pA_in_gg(d(e(X1)), X2)) 64.55/17.46 PA_IN_AG(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) -> PA_IN_GG(d(e(X1)), X2) 64.55/17.46 PA_IN_AG(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) -> U74_AG(X1, X2, X3, pA_in_gg(d(e(X2)), X3)) 64.55/17.46 PA_IN_AG(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) -> PA_IN_GG(d(e(X2)), X3) 64.55/17.46 PA_IN_AG(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) -> U75_AG(X1, X2, X3, X4, X5, X6, pD_in_gggggg(X1, X5, X2, X6, X3, X4)) 64.55/17.46 PA_IN_AG(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) -> PD_IN_GGGGGG(X1, X5, X2, X6, X3, X4) 64.55/17.46 PA_IN_AG(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) -> U76_AG(X1, X2, X3, X4, X5, X6, pD_in_gggggg(X1, X6, X2, X5, X3, X4)) 64.55/17.46 PA_IN_AG(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) -> PD_IN_GGGGGG(X1, X6, X2, X5, X3, X4) 64.55/17.46 PA_IN_AG(d(d(X1)), +(*(X2, X3), *(X4, X5))) -> U77_AG(X1, X2, X3, X4, X5, pF_in_aagg(X1, X6, *(X2, X3), *(X4, X5))) 64.55/17.46 PA_IN_AG(d(d(X1)), +(*(X2, X3), *(X4, X5))) -> PF_IN_AAGG(X1, X6, *(X2, X3), *(X4, X5)) 64.55/17.46 PA_IN_AG(d(d(X1)), X2) -> U78_AG(X1, X2, pG_in_aag(X1, X3, X2)) 64.55/17.46 PA_IN_AG(d(d(X1)), X2) -> PG_IN_AAG(X1, X3, X2) 64.55/17.46 PG_IN_AAG(e(t), const(1), X1) -> U50_AAG(X1, pA_in_gg(d(e(const(1))), X1)) 64.55/17.46 PG_IN_AAG(e(t), const(1), X1) -> PA_IN_GG(d(e(const(1))), X1) 64.55/17.46 PG_IN_AAG(e(const(X1)), const(0), X2) -> U51_AAG(X1, X2, pA_in_gg(d(e(const(0))), X2)) 64.55/17.46 PG_IN_AAG(e(const(X1)), const(0), X2) -> PA_IN_GG(d(e(const(0))), X2) 64.55/17.46 PG_IN_AAG(e(+(X1, X2)), +(X3, X4), X5) -> U52_AAG(X1, X2, X3, X4, X5, pH_in_aa(X1, X3)) 64.55/17.46 PG_IN_AAG(e(+(X1, X2)), +(X3, X4), X5) -> PH_IN_AA(X1, X3) 64.55/17.46 PG_IN_AAG(e(+(X1, X2)), +(X3, X4), X5) -> U53_AAG(X1, X2, X3, X4, X5, pcH_in_aa(X1, X3)) 64.55/17.46 U53_AAG(X1, X2, X3, X4, X5, pcH_out_aa(X1, X3)) -> U54_AAG(X1, X2, X3, X4, X5, pH_in_aa(X2, X4)) 64.55/17.46 U53_AAG(X1, X2, X3, X4, X5, pcH_out_aa(X1, X3)) -> PH_IN_AA(X2, X4) 64.55/17.46 U53_AAG(X1, X2, X3, X4, X5, pcH_out_aa(X1, X3)) -> U55_AAG(X1, X2, X3, X4, X5, pcH_in_aa(X2, X4)) 64.55/17.46 U55_AAG(X1, X2, X3, X4, X5, pcH_out_aa(X2, X4)) -> U56_AAG(X1, X2, X3, X4, X5, pA_in_gg(d(e(+(X3, X4))), X5)) 64.55/17.46 U55_AAG(X1, X2, X3, X4, X5, pcH_out_aa(X2, X4)) -> PA_IN_GG(d(e(+(X3, X4))), X5) 64.55/17.46 PG_IN_AAG(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) -> U57_AAG(X1, X2, X3, X4, X5, pH_in_aa(X1, X4)) 64.55/17.46 PG_IN_AAG(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) -> PH_IN_AA(X1, X4) 64.55/17.46 PG_IN_AAG(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) -> U58_AAG(X1, X2, X3, X4, X5, pcH_in_aa(X1, X4)) 64.55/17.46 U58_AAG(X1, X2, X3, X4, X5, pcH_out_aa(X1, X4)) -> U59_AAG(X1, X2, X3, X4, X5, pH_in_aa(X2, X3)) 64.55/17.46 U58_AAG(X1, X2, X3, X4, X5, pcH_out_aa(X1, X4)) -> PH_IN_AA(X2, X3) 64.55/17.46 U58_AAG(X1, X2, X3, X4, X5, pcH_out_aa(X1, X4)) -> U60_AAG(X1, X2, X3, X4, X5, pcH_in_aa(X2, X3)) 64.55/17.46 U60_AAG(X1, X2, X3, X4, X5, pcH_out_aa(X2, X3)) -> U61_AAG(X1, X2, X3, X4, X5, pA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), X5)) 64.55/17.46 U60_AAG(X1, X2, X3, X4, X5, pcH_out_aa(X2, X3)) -> PA_IN_GG(d(e(+(*(X1, X3), *(X2, X4)))), X5) 64.55/17.46 PG_IN_AAG(d(X1), X2, X3) -> U62_AAG(X1, X2, X3, pJ_in_aa(X1, X4)) 64.55/17.46 PG_IN_AAG(d(X1), X2, X3) -> PJ_IN_AA(X1, X4) 64.55/17.46 PG_IN_AAG(d(X1), X2, X3) -> U63_AAG(X1, X2, X3, pcJ_in_aa(X1, X4)) 64.55/17.46 U63_AAG(X1, X2, X3, pcJ_out_aa(X1, X4)) -> U64_AAG(X1, X2, X3, pG_in_gag(e(X4), X2, X3)) 64.55/17.46 U63_AAG(X1, X2, X3, pcJ_out_aa(X1, X4)) -> PG_IN_GAG(e(X4), X2, X3) 64.55/17.46 PD_IN_AGAGAG(X1, X2, X3, X4, X5, X6) -> U42_AGAGAG(X1, X2, X3, X4, X5, X6, pcA_in_ag(d(e(X1)), X2)) 64.55/17.46 U42_AGAGAG(X1, X2, X3, X4, X5, X6, pcA_out_ag(d(e(X1)), X2)) -> U43_AGAGAG(X1, X2, X3, X4, X5, X6, pE_in_agag(X3, X4, X5, X6)) 64.55/17.46 U42_AGAGAG(X1, X2, X3, X4, X5, X6, pcA_out_ag(d(e(X1)), X2)) -> PE_IN_AGAG(X3, X4, X5, X6) 64.55/17.46 PE_IN_AGAG(X1, X2, X3, X4) -> U44_AGAG(X1, X2, X3, X4, pA_in_ag(d(e(X1)), X2)) 64.55/17.46 PE_IN_AGAG(X1, X2, X3, X4) -> PA_IN_AG(d(e(X1)), X2) 64.55/17.46 PE_IN_AGAG(X1, X2, X3, X4) -> U45_AGAG(X1, X2, X3, X4, pcA_in_ag(d(e(X1)), X2)) 64.55/17.46 U45_AGAG(X1, X2, X3, X4, pcA_out_ag(d(e(X1)), X2)) -> U46_AGAG(X1, X2, X3, X4, pA_in_ag(d(e(X3)), X4)) 64.55/17.46 U45_AGAG(X1, X2, X3, X4, pcA_out_ag(d(e(X1)), X2)) -> PA_IN_AG(d(e(X3)), X4) 64.55/17.46 64.55/17.46 The TRS R consists of the following rules: 64.55/17.46 64.55/17.46 pcA_in_gg(d(e(t)), const(1)) -> pcA_out_gg(d(e(t)), const(1)) 64.55/17.46 pcA_in_gg(d(d(X1)), const(1)) -> U80_gg(X1, qcB_in_ga(X1, X2)) 64.55/17.46 qcB_in_ga(e(t), const(1)) -> U98_ga(pcA_in_gg(d(e(const(1))), const(1))) 64.55/17.46 pcA_in_gg(d(e(const(X1))), const(0)) -> pcA_out_gg(d(e(const(X1))), const(0)) 64.55/17.46 pcA_in_gg(d(d(X1)), const(0)) -> U81_gg(X1, qcC_in_ga(X1, X2)) 64.55/17.46 qcC_in_ga(e(t), const(1)) -> U112_ga(pcA_in_gg(d(e(const(1))), const(0))) 64.55/17.46 pcA_in_gg(d(e(+(t, X1))), +(const(1), X2)) -> U82_gg(X1, X2, pcA_in_gg(d(e(X1)), X2)) 64.55/17.46 pcA_in_gg(d(e(+(const(X1), X2))), +(const(0), X3)) -> U83_gg(X1, X2, X3, pcA_in_gg(d(e(X2)), X3)) 64.55/17.46 pcA_in_gg(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) -> U84_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X4, X2, X5, X3, X6)) 64.55/17.46 qcD_in_gggggg(X1, X2, X3, X4, X5, X6) -> U122_gggggg(X1, X2, X3, X4, X5, X6, pcA_in_gg(d(e(X1)), X2)) 64.55/17.46 pcA_in_gg(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) -> U85_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X5, X2, X4, X3, X6)) 64.55/17.46 U85_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X5, X2, X4, X3, X6)) -> pcA_out_gg(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) 64.55/17.46 pcA_in_gg(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) -> U86_gg(X1, X2, X3, X4, qcE_in_gggg(X1, X4, X2, X3)) 64.55/17.46 qcE_in_gggg(X1, X2, X3, X4) -> U124_gggg(X1, X2, X3, X4, pcA_in_gg(d(e(X1)), X2)) 64.55/17.46 pcA_in_gg(d(d(X1)), +(X2, X3)) -> U87_gg(X1, X2, X3, qcF_in_gagg(X1, X4, X2, X3)) 64.55/17.46 qcF_in_gagg(X1, X2, X3, X4) -> U126_gagg(X1, X2, X3, X4, pcJ_in_ga(X1, X2)) 64.55/17.46 pcJ_in_ga(e(t), const(1)) -> pcJ_out_ga(e(t), const(1)) 64.55/17.46 pcJ_in_ga(e(const(X1)), const(0)) -> pcJ_out_ga(e(const(X1)), const(0)) 64.55/17.46 pcJ_in_ga(e(+(X1, X2)), +(X3, X4)) -> U108_ga(X1, X2, X3, X4, qcI_in_gaga(X1, X3, X2, X4)) 64.55/17.46 qcI_in_gaga(X1, X2, X3, X4) -> U96_gaga(X1, X2, X3, X4, pcH_in_ga(X1, X2)) 64.55/17.46 pcH_in_ga(t, const(1)) -> pcH_out_ga(t, const(1)) 64.55/17.46 pcH_in_ga(const(X1), const(0)) -> pcH_out_ga(const(X1), const(0)) 64.55/17.46 pcH_in_ga(+(X1, X2), +(X3, X4)) -> U94_ga(X1, X2, X3, X4, qcI_in_gaga(X1, X3, X2, X4)) 64.55/17.46 U94_ga(X1, X2, X3, X4, qcI_out_gaga(X1, X3, X2, X4)) -> pcH_out_ga(+(X1, X2), +(X3, X4)) 64.55/17.46 pcH_in_ga(*(X1, X2), +(*(X1, X3), *(X2, X4))) -> U95_ga(X1, X2, X3, X4, qcI_in_gaga(X1, X4, X2, X3)) 64.55/17.46 U95_ga(X1, X2, X3, X4, qcI_out_gaga(X1, X4, X2, X3)) -> pcH_out_ga(*(X1, X2), +(*(X1, X3), *(X2, X4))) 64.55/17.46 U96_gaga(X1, X2, X3, X4, pcH_out_ga(X1, X2)) -> U97_gaga(X1, X2, X3, X4, pcH_in_ga(X3, X4)) 64.55/17.46 U97_gaga(X1, X2, X3, X4, pcH_out_ga(X3, X4)) -> qcI_out_gaga(X1, X2, X3, X4) 64.55/17.46 U108_ga(X1, X2, X3, X4, qcI_out_gaga(X1, X3, X2, X4)) -> pcJ_out_ga(e(+(X1, X2)), +(X3, X4)) 64.55/17.46 pcJ_in_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U109_ga(X1, X2, X3, X4, qcI_in_gaga(X1, X4, X2, X3)) 64.55/17.46 U109_ga(X1, X2, X3, X4, qcI_out_gaga(X1, X4, X2, X3)) -> pcJ_out_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.55/17.46 pcJ_in_ga(d(X1), X2) -> U110_ga(X1, X2, pcJ_in_ga(X1, X3)) 64.55/17.46 U110_ga(X1, X2, pcJ_out_ga(X1, X3)) -> U111_ga(X1, X2, pcH_in_ga(X3, X2)) 64.55/17.46 U111_ga(X1, X2, pcH_out_ga(X3, X2)) -> pcJ_out_ga(d(X1), X2) 64.55/17.46 U126_gagg(X1, X2, X3, X4, pcJ_out_ga(X1, X2)) -> U127_gagg(X1, X2, X3, X4, pcA_in_gg(d(e(X2)), +(X3, X4))) 64.55/17.46 pcA_in_gg(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) -> U88_gg(X1, X2, pcA_in_gg(d(e(X1)), X2)) 64.55/17.46 pcA_in_gg(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) -> U89_gg(X1, X2, X3, pcA_in_gg(d(e(X2)), X3)) 64.55/17.46 pcA_in_gg(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) -> U90_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X5, X2, X6, X3, X4)) 64.55/17.46 U90_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X5, X2, X6, X3, X4)) -> pcA_out_gg(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) 64.55/17.46 pcA_in_gg(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) -> U91_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X6, X2, X5, X3, X4)) 64.55/17.46 U91_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X6, X2, X5, X3, X4)) -> pcA_out_gg(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) 64.55/17.46 pcA_in_gg(d(d(X1)), +(*(X2, X3), *(X4, X5))) -> U92_gg(X1, X2, X3, X4, X5, qcF_in_gagg(X1, X6, *(X2, X3), *(X4, X5))) 64.55/17.46 U92_gg(X1, X2, X3, X4, X5, qcF_out_gagg(X1, X6, *(X2, X3), *(X4, X5))) -> pcA_out_gg(d(d(X1)), +(*(X2, X3), *(X4, X5))) 64.55/17.46 pcA_in_gg(d(d(X1)), X2) -> U93_gg(X1, X2, qcG_in_gag(X1, X3, X2)) 64.55/17.46 qcG_in_gag(e(t), const(1), X1) -> U128_gag(X1, pcA_in_gg(d(e(const(1))), X1)) 64.55/17.46 U128_gag(X1, pcA_out_gg(d(e(const(1))), X1)) -> qcG_out_gag(e(t), const(1), X1) 64.55/17.46 qcG_in_gag(e(const(X1)), const(0), X2) -> U129_gag(X1, X2, pcA_in_gg(d(e(const(0))), X2)) 64.55/17.46 U129_gag(X1, X2, pcA_out_gg(d(e(const(0))), X2)) -> qcG_out_gag(e(const(X1)), const(0), X2) 64.55/17.46 qcG_in_gag(e(+(X1, X2)), +(X3, X4), X5) -> U130_gag(X1, X2, X3, X4, X5, pcH_in_ga(X1, X3)) 64.55/17.46 U130_gag(X1, X2, X3, X4, X5, pcH_out_ga(X1, X3)) -> U131_gag(X1, X2, X3, X4, X5, pcH_in_ga(X2, X4)) 64.55/17.46 U131_gag(X1, X2, X3, X4, X5, pcH_out_ga(X2, X4)) -> U132_gag(X1, X2, X3, X4, X5, pcA_in_gg(d(e(+(X3, X4))), X5)) 64.55/17.46 U132_gag(X1, X2, X3, X4, X5, pcA_out_gg(d(e(+(X3, X4))), X5)) -> qcG_out_gag(e(+(X1, X2)), +(X3, X4), X5) 64.55/17.46 qcG_in_gag(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) -> U133_gag(X1, X2, X3, X4, X5, pcH_in_ga(X1, X4)) 64.55/17.46 U133_gag(X1, X2, X3, X4, X5, pcH_out_ga(X1, X4)) -> U134_gag(X1, X2, X3, X4, X5, pcH_in_ga(X2, X3)) 64.55/17.46 U134_gag(X1, X2, X3, X4, X5, pcH_out_ga(X2, X3)) -> U135_gag(X1, X2, X3, X4, X5, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), X5)) 64.55/17.46 U135_gag(X1, X2, X3, X4, X5, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), X5)) -> qcG_out_gag(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) 64.55/17.46 qcG_in_gag(d(X1), X2, X3) -> U136_gag(X1, X2, X3, pcJ_in_ga(X1, X4)) 64.55/17.46 U136_gag(X1, X2, X3, pcJ_out_ga(X1, X4)) -> U137_gag(X1, X2, X3, qcG_in_gag(e(X4), X2, X3)) 64.55/17.46 U137_gag(X1, X2, X3, qcG_out_gag(e(X4), X2, X3)) -> qcG_out_gag(d(X1), X2, X3) 64.55/17.46 U93_gg(X1, X2, qcG_out_gag(X1, X3, X2)) -> pcA_out_gg(d(d(X1)), X2) 64.55/17.46 U89_gg(X1, X2, X3, pcA_out_gg(d(e(X2)), X3)) -> pcA_out_gg(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) 64.55/17.46 U88_gg(X1, X2, pcA_out_gg(d(e(X1)), X2)) -> pcA_out_gg(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) 64.55/17.46 U127_gagg(X1, X2, X3, X4, pcA_out_gg(d(e(X2)), +(X3, X4))) -> qcF_out_gagg(X1, X2, X3, X4) 64.55/17.46 U87_gg(X1, X2, X3, qcF_out_gagg(X1, X4, X2, X3)) -> pcA_out_gg(d(d(X1)), +(X2, X3)) 64.55/17.46 U124_gggg(X1, X2, X3, X4, pcA_out_gg(d(e(X1)), X2)) -> U125_gggg(X1, X2, X3, X4, pcA_in_gg(d(e(X3)), X4)) 64.55/17.46 U125_gggg(X1, X2, X3, X4, pcA_out_gg(d(e(X3)), X4)) -> qcE_out_gggg(X1, X2, X3, X4) 64.55/17.46 U86_gg(X1, X2, X3, X4, qcE_out_gggg(X1, X4, X2, X3)) -> pcA_out_gg(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) 64.55/17.46 U122_gggggg(X1, X2, X3, X4, X5, X6, pcA_out_gg(d(e(X1)), X2)) -> U123_gggggg(X1, X2, X3, X4, X5, X6, qcE_in_gggg(X3, X4, X5, X6)) 64.55/17.46 U123_gggggg(X1, X2, X3, X4, X5, X6, qcE_out_gggg(X3, X4, X5, X6)) -> qcD_out_gggggg(X1, X2, X3, X4, X5, X6) 64.55/17.46 U84_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X4, X2, X5, X3, X6)) -> pcA_out_gg(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) 64.55/17.46 U83_gg(X1, X2, X3, pcA_out_gg(d(e(X2)), X3)) -> pcA_out_gg(d(e(+(const(X1), X2))), +(const(0), X3)) 64.55/17.46 U82_gg(X1, X2, pcA_out_gg(d(e(X1)), X2)) -> pcA_out_gg(d(e(+(t, X1))), +(const(1), X2)) 64.55/17.46 U112_ga(pcA_out_gg(d(e(const(1))), const(0))) -> qcC_out_ga(e(t), const(1)) 64.55/17.46 qcC_in_ga(e(const(X1)), const(0)) -> U113_ga(X1, pcA_in_gg(d(e(const(0))), const(0))) 64.55/17.46 U113_ga(X1, pcA_out_gg(d(e(const(0))), const(0))) -> qcC_out_ga(e(const(X1)), const(0)) 64.55/17.46 qcC_in_ga(e(+(X1, X2)), +(X3, X4)) -> U114_ga(X1, X2, X3, X4, pcH_in_ga(X1, X3)) 64.55/17.46 U114_ga(X1, X2, X3, X4, pcH_out_ga(X1, X3)) -> U115_ga(X1, X2, X3, X4, pcH_in_ga(X2, X4)) 64.55/17.46 U115_ga(X1, X2, X3, X4, pcH_out_ga(X2, X4)) -> U116_ga(X1, X2, X3, X4, pcA_in_gg(d(e(+(X3, X4))), const(0))) 64.55/17.46 U116_ga(X1, X2, X3, X4, pcA_out_gg(d(e(+(X3, X4))), const(0))) -> qcC_out_ga(e(+(X1, X2)), +(X3, X4)) 64.55/17.46 qcC_in_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U117_ga(X1, X2, X3, X4, pcH_in_ga(X1, X4)) 64.55/17.46 U117_ga(X1, X2, X3, X4, pcH_out_ga(X1, X4)) -> U118_ga(X1, X2, X3, X4, pcH_in_ga(X2, X3)) 64.55/17.46 U118_ga(X1, X2, X3, X4, pcH_out_ga(X2, X3)) -> U119_ga(X1, X2, X3, X4, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(0))) 64.55/17.46 U119_ga(X1, X2, X3, X4, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(0))) -> qcC_out_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.55/17.46 qcC_in_ga(d(X1), X2) -> U120_ga(X1, X2, pcJ_in_ga(X1, X3)) 64.55/17.46 U120_ga(X1, X2, pcJ_out_ga(X1, X3)) -> U121_ga(X1, X2, qcC_in_ga(e(X3), X2)) 64.55/17.46 U121_ga(X1, X2, qcC_out_ga(e(X3), X2)) -> qcC_out_ga(d(X1), X2) 64.55/17.46 U81_gg(X1, qcC_out_ga(X1, X2)) -> pcA_out_gg(d(d(X1)), const(0)) 64.55/17.46 U98_ga(pcA_out_gg(d(e(const(1))), const(1))) -> qcB_out_ga(e(t), const(1)) 64.55/17.46 qcB_in_ga(e(const(X1)), const(0)) -> U99_ga(X1, pcA_in_gg(d(e(const(0))), const(1))) 64.55/17.46 U99_ga(X1, pcA_out_gg(d(e(const(0))), const(1))) -> qcB_out_ga(e(const(X1)), const(0)) 64.55/17.46 qcB_in_ga(e(+(X1, X2)), +(X3, X4)) -> U100_ga(X1, X2, X3, X4, pcH_in_ga(X1, X3)) 64.55/17.46 U100_ga(X1, X2, X3, X4, pcH_out_ga(X1, X3)) -> U101_ga(X1, X2, X3, X4, pcH_in_ga(X2, X4)) 64.55/17.46 U101_ga(X1, X2, X3, X4, pcH_out_ga(X2, X4)) -> U102_ga(X1, X2, X3, X4, pcA_in_gg(d(e(+(X3, X4))), const(1))) 64.55/17.46 U102_ga(X1, X2, X3, X4, pcA_out_gg(d(e(+(X3, X4))), const(1))) -> qcB_out_ga(e(+(X1, X2)), +(X3, X4)) 64.55/17.46 qcB_in_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U103_ga(X1, X2, X3, X4, pcH_in_ga(X1, X4)) 64.55/17.46 U103_ga(X1, X2, X3, X4, pcH_out_ga(X1, X4)) -> U104_ga(X1, X2, X3, X4, pcH_in_ga(X2, X3)) 64.55/17.46 U104_ga(X1, X2, X3, X4, pcH_out_ga(X2, X3)) -> U105_ga(X1, X2, X3, X4, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(1))) 64.55/17.46 U105_ga(X1, X2, X3, X4, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(1))) -> qcB_out_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.55/17.46 qcB_in_ga(d(X1), X2) -> U106_ga(X1, X2, pcJ_in_ga(X1, X3)) 64.55/17.46 U106_ga(X1, X2, pcJ_out_ga(X1, X3)) -> U107_ga(X1, X2, qcB_in_ga(e(X3), X2)) 64.55/17.46 U107_ga(X1, X2, qcB_out_ga(e(X3), X2)) -> qcB_out_ga(d(X1), X2) 64.55/17.46 U80_gg(X1, qcB_out_ga(X1, X2)) -> pcA_out_gg(d(d(X1)), const(1)) 64.55/17.46 pcH_in_aa(t, const(1)) -> pcH_out_aa(t, const(1)) 64.55/17.46 pcH_in_aa(const(X1), const(0)) -> pcH_out_aa(const(X1), const(0)) 64.55/17.46 pcH_in_aa(+(X1, X2), +(X3, X4)) -> U94_aa(X1, X2, X3, X4, qcI_in_aaaa(X1, X3, X2, X4)) 64.55/17.46 qcI_in_aaaa(X1, X2, X3, X4) -> U96_aaaa(X1, X2, X3, X4, pcH_in_aa(X1, X2)) 64.55/17.46 pcH_in_aa(*(X1, X2), +(*(X1, X3), *(X2, X4))) -> U95_aa(X1, X2, X3, X4, qcI_in_aaaa(X1, X4, X2, X3)) 64.55/17.46 U95_aa(X1, X2, X3, X4, qcI_out_aaaa(X1, X4, X2, X3)) -> pcH_out_aa(*(X1, X2), +(*(X1, X3), *(X2, X4))) 64.55/17.46 U96_aaaa(X1, X2, X3, X4, pcH_out_aa(X1, X2)) -> U97_aaaa(X1, X2, X3, X4, pcH_in_aa(X3, X4)) 64.55/17.46 U97_aaaa(X1, X2, X3, X4, pcH_out_aa(X3, X4)) -> qcI_out_aaaa(X1, X2, X3, X4) 64.55/17.46 U94_aa(X1, X2, X3, X4, qcI_out_aaaa(X1, X3, X2, X4)) -> pcH_out_aa(+(X1, X2), +(X3, X4)) 64.55/17.46 pcJ_in_aa(e(t), const(1)) -> pcJ_out_aa(e(t), const(1)) 64.55/17.46 pcJ_in_aa(e(const(X1)), const(0)) -> pcJ_out_aa(e(const(X1)), const(0)) 64.55/17.46 pcJ_in_aa(e(+(X1, X2)), +(X3, X4)) -> U108_aa(X1, X2, X3, X4, qcI_in_aaaa(X1, X3, X2, X4)) 64.55/17.46 U108_aa(X1, X2, X3, X4, qcI_out_aaaa(X1, X3, X2, X4)) -> pcJ_out_aa(e(+(X1, X2)), +(X3, X4)) 64.55/17.46 pcJ_in_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U109_aa(X1, X2, X3, X4, qcI_in_aaaa(X1, X4, X2, X3)) 64.55/17.46 U109_aa(X1, X2, X3, X4, qcI_out_aaaa(X1, X4, X2, X3)) -> pcJ_out_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.55/17.46 pcJ_in_aa(d(X1), X2) -> U110_aa(X1, X2, pcJ_in_aa(X1, X3)) 64.55/17.46 U110_aa(X1, X2, pcJ_out_aa(X1, X3)) -> U111_aa(X1, X2, pcH_in_ga(X3, X2)) 64.55/17.46 U111_aa(X1, X2, pcH_out_ga(X3, X2)) -> pcJ_out_aa(d(X1), X2) 64.55/17.46 pcA_in_ag(d(e(t)), const(1)) -> pcA_out_ag(d(e(t)), const(1)) 64.55/17.46 pcA_in_ag(d(d(X1)), const(1)) -> U80_ag(X1, qcB_in_aa(X1, X2)) 64.55/17.46 qcB_in_aa(e(t), const(1)) -> U98_aa(pcA_in_gg(d(e(const(1))), const(1))) 64.55/17.46 U98_aa(pcA_out_gg(d(e(const(1))), const(1))) -> qcB_out_aa(e(t), const(1)) 64.55/17.46 qcB_in_aa(e(const(X1)), const(0)) -> U99_aa(X1, pcA_in_gg(d(e(const(0))), const(1))) 64.55/17.46 U99_aa(X1, pcA_out_gg(d(e(const(0))), const(1))) -> qcB_out_aa(e(const(X1)), const(0)) 64.55/17.46 qcB_in_aa(e(+(X1, X2)), +(X3, X4)) -> U100_aa(X1, X2, X3, X4, pcH_in_aa(X1, X3)) 64.55/17.46 U100_aa(X1, X2, X3, X4, pcH_out_aa(X1, X3)) -> U101_aa(X1, X2, X3, X4, pcH_in_aa(X2, X4)) 64.55/17.46 U101_aa(X1, X2, X3, X4, pcH_out_aa(X2, X4)) -> U102_aa(X1, X2, X3, X4, pcA_in_gg(d(e(+(X3, X4))), const(1))) 64.55/17.46 U102_aa(X1, X2, X3, X4, pcA_out_gg(d(e(+(X3, X4))), const(1))) -> qcB_out_aa(e(+(X1, X2)), +(X3, X4)) 64.55/17.46 qcB_in_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U103_aa(X1, X2, X3, X4, pcH_in_aa(X1, X4)) 64.55/17.46 U103_aa(X1, X2, X3, X4, pcH_out_aa(X1, X4)) -> U104_aa(X1, X2, X3, X4, pcH_in_aa(X2, X3)) 64.55/17.46 U104_aa(X1, X2, X3, X4, pcH_out_aa(X2, X3)) -> U105_aa(X1, X2, X3, X4, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(1))) 64.55/17.46 U105_aa(X1, X2, X3, X4, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(1))) -> qcB_out_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.55/17.46 qcB_in_aa(d(X1), X2) -> U106_aa(X1, X2, pcJ_in_aa(X1, X3)) 64.55/17.46 U106_aa(X1, X2, pcJ_out_aa(X1, X3)) -> U107_aa(X1, X2, qcB_in_ga(e(X3), X2)) 64.55/17.46 U107_aa(X1, X2, qcB_out_ga(e(X3), X2)) -> qcB_out_aa(d(X1), X2) 64.55/17.46 U80_ag(X1, qcB_out_aa(X1, X2)) -> pcA_out_ag(d(d(X1)), const(1)) 64.55/17.46 pcA_in_ag(d(e(const(X1))), const(0)) -> pcA_out_ag(d(e(const(X1))), const(0)) 64.55/17.46 pcA_in_ag(d(d(X1)), const(0)) -> U81_ag(X1, qcC_in_aa(X1, X2)) 64.55/17.46 qcC_in_aa(e(t), const(1)) -> U112_aa(pcA_in_gg(d(e(const(1))), const(0))) 64.55/17.46 U112_aa(pcA_out_gg(d(e(const(1))), const(0))) -> qcC_out_aa(e(t), const(1)) 64.55/17.46 qcC_in_aa(e(const(X1)), const(0)) -> U113_aa(X1, pcA_in_gg(d(e(const(0))), const(0))) 64.55/17.46 U113_aa(X1, pcA_out_gg(d(e(const(0))), const(0))) -> qcC_out_aa(e(const(X1)), const(0)) 64.55/17.46 qcC_in_aa(e(+(X1, X2)), +(X3, X4)) -> U114_aa(X1, X2, X3, X4, pcH_in_aa(X1, X3)) 64.55/17.46 U114_aa(X1, X2, X3, X4, pcH_out_aa(X1, X3)) -> U115_aa(X1, X2, X3, X4, pcH_in_aa(X2, X4)) 64.55/17.46 U115_aa(X1, X2, X3, X4, pcH_out_aa(X2, X4)) -> U116_aa(X1, X2, X3, X4, pcA_in_gg(d(e(+(X3, X4))), const(0))) 64.55/17.46 U116_aa(X1, X2, X3, X4, pcA_out_gg(d(e(+(X3, X4))), const(0))) -> qcC_out_aa(e(+(X1, X2)), +(X3, X4)) 64.55/17.46 qcC_in_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U117_aa(X1, X2, X3, X4, pcH_in_aa(X1, X4)) 64.55/17.46 U117_aa(X1, X2, X3, X4, pcH_out_aa(X1, X4)) -> U118_aa(X1, X2, X3, X4, pcH_in_aa(X2, X3)) 64.55/17.46 U118_aa(X1, X2, X3, X4, pcH_out_aa(X2, X3)) -> U119_aa(X1, X2, X3, X4, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(0))) 64.55/17.46 U119_aa(X1, X2, X3, X4, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(0))) -> qcC_out_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.55/17.46 qcC_in_aa(d(X1), X2) -> U120_aa(X1, X2, pcJ_in_aa(X1, X3)) 64.55/17.46 U120_aa(X1, X2, pcJ_out_aa(X1, X3)) -> U121_aa(X1, X2, qcC_in_ga(e(X3), X2)) 64.55/17.46 U121_aa(X1, X2, qcC_out_ga(e(X3), X2)) -> qcC_out_aa(d(X1), X2) 64.55/17.46 U81_ag(X1, qcC_out_aa(X1, X2)) -> pcA_out_ag(d(d(X1)), const(0)) 64.55/17.46 pcA_in_ag(d(e(+(t, X1))), +(const(1), X2)) -> U82_ag(X1, X2, pcA_in_ag(d(e(X1)), X2)) 64.55/17.46 pcA_in_ag(d(e(+(const(X1), X2))), +(const(0), X3)) -> U83_ag(X1, X2, X3, pcA_in_ag(d(e(X2)), X3)) 64.55/17.46 pcA_in_ag(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) -> U84_ag(X1, X2, X3, X4, X5, X6, qcD_in_agagag(X1, X4, X2, X5, X3, X6)) 64.55/17.46 qcD_in_agagag(X1, X2, X3, X4, X5, X6) -> U122_agagag(X1, X2, X3, X4, X5, X6, pcA_in_ag(d(e(X1)), X2)) 64.55/17.46 pcA_in_ag(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) -> U85_ag(X1, X2, X3, X4, X5, X6, qcD_in_ggggag(X1, X5, X2, X4, X3, X6)) 64.55/17.46 qcD_in_ggggag(X1, X2, X3, X4, X5, X6) -> U122_ggggag(X1, X2, X3, X4, X5, X6, pcA_in_gg(d(e(X1)), X2)) 64.55/17.46 U122_ggggag(X1, X2, X3, X4, X5, X6, pcA_out_gg(d(e(X1)), X2)) -> U123_ggggag(X1, X2, X3, X4, X5, X6, qcE_in_ggag(X3, X4, X5, X6)) 64.55/17.46 qcE_in_ggag(X1, X2, X3, X4) -> U124_ggag(X1, X2, X3, X4, pcA_in_gg(d(e(X1)), X2)) 64.55/17.46 U124_ggag(X1, X2, X3, X4, pcA_out_gg(d(e(X1)), X2)) -> U125_ggag(X1, X2, X3, X4, pcA_in_ag(d(e(X3)), X4)) 64.55/17.46 pcA_in_ag(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) -> U86_ag(X1, X2, X3, X4, qcE_in_gggg(X1, X4, X2, X3)) 64.55/17.46 U86_ag(X1, X2, X3, X4, qcE_out_gggg(X1, X4, X2, X3)) -> pcA_out_ag(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) 64.55/17.46 pcA_in_ag(d(d(X1)), +(X2, X3)) -> U87_ag(X1, X2, X3, qcF_in_aagg(X1, X4, X2, X3)) 64.55/17.46 qcF_in_aagg(X1, X2, X3, X4) -> U126_aagg(X1, X2, X3, X4, pcJ_in_aa(X1, X2)) 64.55/17.46 U126_aagg(X1, X2, X3, X4, pcJ_out_aa(X1, X2)) -> U127_aagg(X1, X2, X3, X4, pcA_in_gg(d(e(X2)), +(X3, X4))) 64.55/17.46 U127_aagg(X1, X2, X3, X4, pcA_out_gg(d(e(X2)), +(X3, X4))) -> qcF_out_aagg(X1, X2, X3, X4) 64.55/17.46 U87_ag(X1, X2, X3, qcF_out_aagg(X1, X4, X2, X3)) -> pcA_out_ag(d(d(X1)), +(X2, X3)) 64.55/17.46 pcA_in_ag(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) -> U88_ag(X1, X2, pcA_in_gg(d(e(X1)), X2)) 64.55/17.46 U88_ag(X1, X2, pcA_out_gg(d(e(X1)), X2)) -> pcA_out_ag(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) 64.55/17.46 pcA_in_ag(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) -> U89_ag(X1, X2, X3, pcA_in_gg(d(e(X2)), X3)) 64.55/17.46 U89_ag(X1, X2, X3, pcA_out_gg(d(e(X2)), X3)) -> pcA_out_ag(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) 64.55/17.46 pcA_in_ag(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) -> U90_ag(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X5, X2, X6, X3, X4)) 64.55/17.46 U90_ag(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X5, X2, X6, X3, X4)) -> pcA_out_ag(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) 64.55/17.46 pcA_in_ag(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) -> U91_ag(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X6, X2, X5, X3, X4)) 64.55/17.46 U91_ag(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X6, X2, X5, X3, X4)) -> pcA_out_ag(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) 64.55/17.46 pcA_in_ag(d(d(X1)), +(*(X2, X3), *(X4, X5))) -> U92_ag(X1, X2, X3, X4, X5, qcF_in_aagg(X1, X6, *(X2, X3), *(X4, X5))) 64.55/17.46 U92_ag(X1, X2, X3, X4, X5, qcF_out_aagg(X1, X6, *(X2, X3), *(X4, X5))) -> pcA_out_ag(d(d(X1)), +(*(X2, X3), *(X4, X5))) 64.55/17.46 pcA_in_ag(d(d(X1)), X2) -> U93_ag(X1, X2, qcG_in_aag(X1, X3, X2)) 64.55/17.46 qcG_in_aag(e(t), const(1), X1) -> U128_aag(X1, pcA_in_gg(d(e(const(1))), X1)) 64.55/17.46 U128_aag(X1, pcA_out_gg(d(e(const(1))), X1)) -> qcG_out_aag(e(t), const(1), X1) 64.55/17.46 qcG_in_aag(e(const(X1)), const(0), X2) -> U129_aag(X1, X2, pcA_in_gg(d(e(const(0))), X2)) 64.55/17.46 U129_aag(X1, X2, pcA_out_gg(d(e(const(0))), X2)) -> qcG_out_aag(e(const(X1)), const(0), X2) 64.55/17.46 qcG_in_aag(e(+(X1, X2)), +(X3, X4), X5) -> U130_aag(X1, X2, X3, X4, X5, pcH_in_aa(X1, X3)) 64.55/17.46 U130_aag(X1, X2, X3, X4, X5, pcH_out_aa(X1, X3)) -> U131_aag(X1, X2, X3, X4, X5, pcH_in_aa(X2, X4)) 64.55/17.46 U131_aag(X1, X2, X3, X4, X5, pcH_out_aa(X2, X4)) -> U132_aag(X1, X2, X3, X4, X5, pcA_in_gg(d(e(+(X3, X4))), X5)) 64.55/17.46 U132_aag(X1, X2, X3, X4, X5, pcA_out_gg(d(e(+(X3, X4))), X5)) -> qcG_out_aag(e(+(X1, X2)), +(X3, X4), X5) 64.55/17.46 qcG_in_aag(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) -> U133_aag(X1, X2, X3, X4, X5, pcH_in_aa(X1, X4)) 64.55/17.46 U133_aag(X1, X2, X3, X4, X5, pcH_out_aa(X1, X4)) -> U134_aag(X1, X2, X3, X4, X5, pcH_in_aa(X2, X3)) 64.55/17.46 U134_aag(X1, X2, X3, X4, X5, pcH_out_aa(X2, X3)) -> U135_aag(X1, X2, X3, X4, X5, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), X5)) 64.55/17.46 U135_aag(X1, X2, X3, X4, X5, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), X5)) -> qcG_out_aag(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) 64.55/17.46 qcG_in_aag(d(X1), X2, X3) -> U136_aag(X1, X2, X3, pcJ_in_aa(X1, X4)) 64.55/17.46 U136_aag(X1, X2, X3, pcJ_out_aa(X1, X4)) -> U137_aag(X1, X2, X3, qcG_in_gag(e(X4), X2, X3)) 64.55/17.46 U137_aag(X1, X2, X3, qcG_out_gag(e(X4), X2, X3)) -> qcG_out_aag(d(X1), X2, X3) 64.55/17.46 U93_ag(X1, X2, qcG_out_aag(X1, X3, X2)) -> pcA_out_ag(d(d(X1)), X2) 64.55/17.46 U125_ggag(X1, X2, X3, X4, pcA_out_ag(d(e(X3)), X4)) -> qcE_out_ggag(X1, X2, X3, X4) 64.55/17.46 U123_ggggag(X1, X2, X3, X4, X5, X6, qcE_out_ggag(X3, X4, X5, X6)) -> qcD_out_ggggag(X1, X2, X3, X4, X5, X6) 64.55/17.46 U85_ag(X1, X2, X3, X4, X5, X6, qcD_out_ggggag(X1, X5, X2, X4, X3, X6)) -> pcA_out_ag(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) 64.55/17.46 U122_agagag(X1, X2, X3, X4, X5, X6, pcA_out_ag(d(e(X1)), X2)) -> U123_agagag(X1, X2, X3, X4, X5, X6, qcE_in_agag(X3, X4, X5, X6)) 64.55/17.46 qcE_in_agag(X1, X2, X3, X4) -> U124_agag(X1, X2, X3, X4, pcA_in_ag(d(e(X1)), X2)) 64.55/17.46 U124_agag(X1, X2, X3, X4, pcA_out_ag(d(e(X1)), X2)) -> U125_agag(X1, X2, X3, X4, pcA_in_ag(d(e(X3)), X4)) 64.55/17.46 U125_agag(X1, X2, X3, X4, pcA_out_ag(d(e(X3)), X4)) -> qcE_out_agag(X1, X2, X3, X4) 64.55/17.46 U123_agagag(X1, X2, X3, X4, X5, X6, qcE_out_agag(X3, X4, X5, X6)) -> qcD_out_agagag(X1, X2, X3, X4, X5, X6) 64.55/17.46 U84_ag(X1, X2, X3, X4, X5, X6, qcD_out_agagag(X1, X4, X2, X5, X3, X6)) -> pcA_out_ag(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) 64.55/17.46 U83_ag(X1, X2, X3, pcA_out_ag(d(e(X2)), X3)) -> pcA_out_ag(d(e(+(const(X1), X2))), +(const(0), X3)) 64.55/17.46 U82_ag(X1, X2, pcA_out_ag(d(e(X1)), X2)) -> pcA_out_ag(d(e(+(t, X1))), +(const(1), X2)) 64.55/17.46 64.55/17.46 The argument filtering Pi contains the following mapping: 64.55/17.46 pA_in_ag(x1, x2) = pA_in_ag(x2) 64.55/17.46 64.55/17.46 const(x1) = const 64.55/17.46 64.55/17.46 1 = 1 64.55/17.46 64.55/17.46 pB_in_aa(x1, x2) = pB_in_aa 64.55/17.46 64.55/17.46 pA_in_gg(x1, x2) = pA_in_gg(x1, x2) 64.55/17.46 64.55/17.46 d(x1) = d(x1) 64.55/17.46 64.55/17.46 pB_in_ga(x1, x2) = pB_in_ga(x1) 64.55/17.46 64.55/17.46 e(x1) = e(x1) 64.55/17.46 64.55/17.46 t = t 64.55/17.46 64.55/17.46 0 = 0 64.55/17.46 64.55/17.46 pC_in_ga(x1, x2) = pC_in_ga(x1) 64.55/17.46 64.55/17.46 +(x1, x2) = +(x1, x2) 64.55/17.46 64.55/17.46 pD_in_gggggg(x1, x2, x3, x4, x5, x6) = pD_in_gggggg(x1, x2, x3, x4, x5, x6) 64.55/17.46 64.55/17.46 *(x1, x2) = *(x1, x2) 64.55/17.46 64.55/17.46 pcA_in_gg(x1, x2) = pcA_in_gg(x1, x2) 64.55/17.46 64.55/17.46 pcA_out_gg(x1, x2) = pcA_out_gg(x1, x2) 64.55/17.46 64.55/17.46 U80_gg(x1, x2) = U80_gg(x1, x2) 64.55/17.46 64.55/17.46 qcB_in_ga(x1, x2) = qcB_in_ga(x1) 64.55/17.46 64.55/17.46 U98_ga(x1) = U98_ga(x1) 64.55/17.46 64.55/17.46 U81_gg(x1, x2) = U81_gg(x1, x2) 64.55/17.46 64.55/17.46 qcC_in_ga(x1, x2) = qcC_in_ga(x1) 64.55/17.46 64.55/17.46 U112_ga(x1) = U112_ga(x1) 64.55/17.46 64.55/17.46 U82_gg(x1, x2, x3) = U82_gg(x1, x2, x3) 64.55/17.46 64.55/17.46 U83_gg(x1, x2, x3, x4) = U83_gg(x2, x3, x4) 64.55/17.46 64.55/17.46 U84_gg(x1, x2, x3, x4, x5, x6, x7) = U84_gg(x1, x2, x3, x4, x5, x6, x7) 64.55/17.46 64.55/17.46 qcD_in_gggggg(x1, x2, x3, x4, x5, x6) = qcD_in_gggggg(x1, x2, x3, x4, x5, x6) 64.55/17.46 64.55/17.46 U122_gggggg(x1, x2, x3, x4, x5, x6, x7) = U122_gggggg(x1, x2, x3, x4, x5, x6, x7) 64.55/17.46 64.55/17.46 U85_gg(x1, x2, x3, x4, x5, x6, x7) = U85_gg(x1, x2, x3, x4, x5, x6, x7) 64.55/17.46 64.55/17.46 qcD_out_gggggg(x1, x2, x3, x4, x5, x6) = qcD_out_gggggg(x1, x2, x3, x4, x5, x6) 64.55/17.46 64.55/17.46 U86_gg(x1, x2, x3, x4, x5) = U86_gg(x1, x2, x3, x4, x5) 64.55/17.46 64.55/17.46 qcE_in_gggg(x1, x2, x3, x4) = qcE_in_gggg(x1, x2, x3, x4) 64.55/17.46 64.55/17.46 U124_gggg(x1, x2, x3, x4, x5) = U124_gggg(x1, x2, x3, x4, x5) 64.55/17.46 64.55/17.46 U87_gg(x1, x2, x3, x4) = U87_gg(x1, x2, x3, x4) 64.55/17.46 64.55/17.46 qcF_in_gagg(x1, x2, x3, x4) = qcF_in_gagg(x1, x3, x4) 64.55/17.46 64.55/17.46 U126_gagg(x1, x2, x3, x4, x5) = U126_gagg(x1, x3, x4, x5) 64.55/17.46 64.55/17.46 pcJ_in_ga(x1, x2) = pcJ_in_ga(x1) 64.55/17.46 64.55/17.46 pcJ_out_ga(x1, x2) = pcJ_out_ga(x1, x2) 64.55/17.46 64.55/17.46 U108_ga(x1, x2, x3, x4, x5) = U108_ga(x1, x2, x5) 64.55/17.46 64.55/17.46 qcI_in_gaga(x1, x2, x3, x4) = qcI_in_gaga(x1, x3) 64.55/17.46 64.55/17.46 U96_gaga(x1, x2, x3, x4, x5) = U96_gaga(x1, x3, x5) 64.55/17.46 64.55/17.46 pcH_in_ga(x1, x2) = pcH_in_ga(x1) 64.55/17.46 64.55/17.46 pcH_out_ga(x1, x2) = pcH_out_ga(x1, x2) 64.55/17.46 64.55/17.46 U94_ga(x1, x2, x3, x4, x5) = U94_ga(x1, x2, x5) 64.55/17.46 64.55/17.46 qcI_out_gaga(x1, x2, x3, x4) = qcI_out_gaga(x1, x2, x3, x4) 64.55/17.46 64.55/17.46 U95_ga(x1, x2, x3, x4, x5) = U95_ga(x1, x2, x5) 64.55/17.46 64.55/17.46 U97_gaga(x1, x2, x3, x4, x5) = U97_gaga(x1, x2, x3, x5) 64.55/17.46 64.55/17.46 U109_ga(x1, x2, x3, x4, x5) = U109_ga(x1, x2, x5) 64.55/17.46 64.55/17.46 U110_ga(x1, x2, x3) = U110_ga(x1, x3) 64.55/17.46 64.55/17.46 U111_ga(x1, x2, x3) = U111_ga(x1, x3) 64.55/17.46 64.55/17.46 U127_gagg(x1, x2, x3, x4, x5) = U127_gagg(x1, x2, x3, x4, x5) 64.55/17.46 64.55/17.46 U88_gg(x1, x2, x3) = U88_gg(x1, x2, x3) 64.55/17.46 64.55/17.46 U89_gg(x1, x2, x3, x4) = U89_gg(x2, x3, x4) 64.55/17.46 64.55/17.46 U90_gg(x1, x2, x3, x4, x5, x6, x7) = U90_gg(x1, x2, x3, x4, x5, x6, x7) 64.55/17.46 64.55/17.46 U91_gg(x1, x2, x3, x4, x5, x6, x7) = U91_gg(x1, x2, x3, x4, x5, x6, x7) 64.55/17.46 64.55/17.46 U92_gg(x1, x2, x3, x4, x5, x6) = U92_gg(x1, x2, x3, x4, x5, x6) 64.55/17.46 64.55/17.46 qcF_out_gagg(x1, x2, x3, x4) = qcF_out_gagg(x1, x2, x3, x4) 64.55/17.46 64.55/17.46 U93_gg(x1, x2, x3) = U93_gg(x1, x2, x3) 64.55/17.46 64.55/17.46 qcG_in_gag(x1, x2, x3) = qcG_in_gag(x1, x3) 64.55/17.46 64.55/17.46 U128_gag(x1, x2) = U128_gag(x1, x2) 64.55/17.46 64.55/17.46 qcG_out_gag(x1, x2, x3) = qcG_out_gag(x1, x2, x3) 64.55/17.46 64.55/17.46 U129_gag(x1, x2, x3) = U129_gag(x2, x3) 64.55/17.46 64.55/17.46 U130_gag(x1, x2, x3, x4, x5, x6) = U130_gag(x1, x2, x5, x6) 64.55/17.46 64.55/17.46 U131_gag(x1, x2, x3, x4, x5, x6) = U131_gag(x1, x2, x3, x5, x6) 64.55/17.46 64.55/17.46 U132_gag(x1, x2, x3, x4, x5, x6) = U132_gag(x1, x2, x3, x4, x5, x6) 64.55/17.46 64.55/17.46 U133_gag(x1, x2, x3, x4, x5, x6) = U133_gag(x1, x2, x5, x6) 64.55/17.46 64.55/17.46 U134_gag(x1, x2, x3, x4, x5, x6) = U134_gag(x1, x2, x4, x5, x6) 64.55/17.46 64.55/17.46 U135_gag(x1, x2, x3, x4, x5, x6) = U135_gag(x1, x2, x3, x4, x5, x6) 64.55/17.46 64.55/17.46 U136_gag(x1, x2, x3, x4) = U136_gag(x1, x3, x4) 64.55/17.46 64.55/17.46 U137_gag(x1, x2, x3, x4) = U137_gag(x1, x3, x4) 64.55/17.46 64.55/17.46 U125_gggg(x1, x2, x3, x4, x5) = U125_gggg(x1, x2, x3, x4, x5) 64.55/17.46 64.55/17.46 qcE_out_gggg(x1, x2, x3, x4) = qcE_out_gggg(x1, x2, x3, x4) 64.55/17.46 64.55/17.46 U123_gggggg(x1, x2, x3, x4, x5, x6, x7) = U123_gggggg(x1, x2, x3, x4, x5, x6, x7) 64.55/17.46 64.55/17.46 qcC_out_ga(x1, x2) = qcC_out_ga(x1, x2) 64.55/17.46 64.55/17.46 U113_ga(x1, x2) = U113_ga(x2) 64.55/17.46 64.55/17.46 U114_ga(x1, x2, x3, x4, x5) = U114_ga(x1, x2, x5) 64.55/17.46 64.55/17.46 U115_ga(x1, x2, x3, x4, x5) = U115_ga(x1, x2, x3, x5) 64.55/17.46 64.55/17.46 U116_ga(x1, x2, x3, x4, x5) = U116_ga(x1, x2, x3, x4, x5) 64.55/17.46 64.55/17.46 U117_ga(x1, x2, x3, x4, x5) = U117_ga(x1, x2, x5) 64.55/17.46 64.55/17.46 U118_ga(x1, x2, x3, x4, x5) = U118_ga(x1, x2, x4, x5) 64.55/17.46 64.55/17.46 U119_ga(x1, x2, x3, x4, x5) = U119_ga(x1, x2, x3, x4, x5) 64.55/17.46 64.55/17.46 U120_ga(x1, x2, x3) = U120_ga(x1, x3) 64.55/17.46 64.55/17.46 U121_ga(x1, x2, x3) = U121_ga(x1, x3) 64.55/17.46 64.55/17.46 qcB_out_ga(x1, x2) = qcB_out_ga(x1, x2) 64.55/17.46 64.55/17.46 U99_ga(x1, x2) = U99_ga(x2) 64.55/17.46 64.55/17.46 U100_ga(x1, x2, x3, x4, x5) = U100_ga(x1, x2, x5) 64.55/17.46 64.55/17.46 U101_ga(x1, x2, x3, x4, x5) = U101_ga(x1, x2, x3, x5) 64.55/17.46 64.55/17.46 U102_ga(x1, x2, x3, x4, x5) = U102_ga(x1, x2, x3, x4, x5) 64.55/17.46 64.55/17.46 U103_ga(x1, x2, x3, x4, x5) = U103_ga(x1, x2, x5) 64.55/17.46 64.55/17.46 U104_ga(x1, x2, x3, x4, x5) = U104_ga(x1, x2, x4, x5) 64.55/17.46 64.55/17.46 U105_ga(x1, x2, x3, x4, x5) = U105_ga(x1, x2, x3, x4, x5) 64.55/17.46 64.55/17.46 U106_ga(x1, x2, x3) = U106_ga(x1, x3) 64.55/17.46 64.55/17.46 U107_ga(x1, x2, x3) = U107_ga(x1, x3) 64.55/17.46 64.55/17.46 pE_in_gggg(x1, x2, x3, x4) = pE_in_gggg(x1, x2, x3, x4) 64.55/17.46 64.55/17.46 pF_in_gagg(x1, x2, x3, x4) = pF_in_gagg(x1, x3, x4) 64.55/17.46 64.55/17.46 pJ_in_ga(x1, x2) = pJ_in_ga(x1) 64.55/17.46 64.55/17.46 pI_in_gaga(x1, x2, x3, x4) = pI_in_gaga(x1, x3) 64.55/17.46 64.55/17.46 pH_in_ga(x1, x2) = pH_in_ga(x1) 64.55/17.46 64.55/17.46 pG_in_gag(x1, x2, x3) = pG_in_gag(x1, x3) 64.55/17.46 64.55/17.46 pH_in_aa(x1, x2) = pH_in_aa 64.55/17.46 64.55/17.46 pI_in_aaaa(x1, x2, x3, x4) = pI_in_aaaa 64.55/17.46 64.55/17.46 pcH_in_aa(x1, x2) = pcH_in_aa 64.55/17.46 64.55/17.46 pcH_out_aa(x1, x2) = pcH_out_aa(x1, x2) 64.55/17.46 64.55/17.46 U94_aa(x1, x2, x3, x4, x5) = U94_aa(x5) 64.55/17.46 64.55/17.46 qcI_in_aaaa(x1, x2, x3, x4) = qcI_in_aaaa 64.55/17.46 64.55/17.46 U96_aaaa(x1, x2, x3, x4, x5) = U96_aaaa(x5) 64.55/17.46 64.55/17.46 U95_aa(x1, x2, x3, x4, x5) = U95_aa(x5) 64.55/17.46 64.55/17.46 qcI_out_aaaa(x1, x2, x3, x4) = qcI_out_aaaa(x1, x2, x3, x4) 64.55/17.46 64.55/17.46 U97_aaaa(x1, x2, x3, x4, x5) = U97_aaaa(x1, x2, x5) 64.55/17.46 64.55/17.46 pJ_in_aa(x1, x2) = pJ_in_aa 64.55/17.46 64.55/17.46 pcJ_in_aa(x1, x2) = pcJ_in_aa 64.55/17.46 64.55/17.46 pcJ_out_aa(x1, x2) = pcJ_out_aa(x1, x2) 64.55/17.46 64.55/17.46 U108_aa(x1, x2, x3, x4, x5) = U108_aa(x5) 64.55/17.46 64.55/17.46 U109_aa(x1, x2, x3, x4, x5) = U109_aa(x5) 64.55/17.46 64.55/17.46 U110_aa(x1, x2, x3) = U110_aa(x3) 64.55/17.46 64.55/17.46 U111_aa(x1, x2, x3) = U111_aa(x1, x3) 64.55/17.46 64.55/17.46 pC_in_aa(x1, x2) = pC_in_aa 64.55/17.46 64.55/17.46 pD_in_agagag(x1, x2, x3, x4, x5, x6) = pD_in_agagag(x2, x4, x6) 64.55/17.46 64.55/17.46 pD_in_ggggag(x1, x2, x3, x4, x5, x6) = pD_in_ggggag(x1, x2, x3, x4, x6) 64.55/17.46 64.55/17.46 pE_in_ggag(x1, x2, x3, x4) = pE_in_ggag(x1, x2, x4) 64.55/17.46 64.55/17.46 pF_in_aagg(x1, x2, x3, x4) = pF_in_aagg(x3, x4) 64.55/17.46 64.55/17.46 pG_in_aag(x1, x2, x3) = pG_in_aag(x3) 64.55/17.46 64.55/17.46 pcA_in_ag(x1, x2) = pcA_in_ag(x2) 64.55/17.46 64.55/17.46 pcA_out_ag(x1, x2) = pcA_out_ag(x1, x2) 64.55/17.46 64.55/17.46 U80_ag(x1, x2) = U80_ag(x2) 64.55/17.46 64.55/17.46 qcB_in_aa(x1, x2) = qcB_in_aa 64.55/17.46 64.55/17.46 U98_aa(x1) = U98_aa(x1) 64.55/17.46 64.55/17.46 qcB_out_aa(x1, x2) = qcB_out_aa(x1, x2) 64.55/17.46 64.55/17.46 U99_aa(x1, x2) = U99_aa(x2) 64.55/17.46 64.55/17.46 U100_aa(x1, x2, x3, x4, x5) = U100_aa(x5) 64.55/17.46 64.55/17.46 U101_aa(x1, x2, x3, x4, x5) = U101_aa(x1, x3, x5) 64.55/17.46 64.55/17.46 U102_aa(x1, x2, x3, x4, x5) = U102_aa(x1, x2, x3, x4, x5) 64.55/17.46 64.55/17.46 U103_aa(x1, x2, x3, x4, x5) = U103_aa(x5) 64.55/17.46 64.55/17.46 U104_aa(x1, x2, x3, x4, x5) = U104_aa(x1, x4, x5) 64.55/17.46 64.55/17.46 U105_aa(x1, x2, x3, x4, x5) = U105_aa(x1, x2, x3, x4, x5) 64.55/17.46 64.55/17.46 U106_aa(x1, x2, x3) = U106_aa(x3) 64.55/17.46 64.55/17.46 U107_aa(x1, x2, x3) = U107_aa(x1, x3) 64.55/17.46 64.55/17.46 U81_ag(x1, x2) = U81_ag(x2) 64.55/17.46 64.55/17.46 qcC_in_aa(x1, x2) = qcC_in_aa 64.55/17.46 64.55/17.46 U112_aa(x1) = U112_aa(x1) 64.55/17.46 64.55/17.46 qcC_out_aa(x1, x2) = qcC_out_aa(x1, x2) 64.55/17.46 64.55/17.46 U113_aa(x1, x2) = U113_aa(x2) 64.55/17.46 64.55/17.46 U114_aa(x1, x2, x3, x4, x5) = U114_aa(x5) 64.55/17.46 64.55/17.46 U115_aa(x1, x2, x3, x4, x5) = U115_aa(x1, x3, x5) 64.55/17.46 64.55/17.46 U116_aa(x1, x2, x3, x4, x5) = U116_aa(x1, x2, x3, x4, x5) 64.55/17.46 64.55/17.46 U117_aa(x1, x2, x3, x4, x5) = U117_aa(x5) 64.55/17.46 64.55/17.46 U118_aa(x1, x2, x3, x4, x5) = U118_aa(x1, x4, x5) 64.55/17.46 64.55/17.46 U119_aa(x1, x2, x3, x4, x5) = U119_aa(x1, x2, x3, x4, x5) 64.55/17.46 64.55/17.46 U120_aa(x1, x2, x3) = U120_aa(x3) 64.55/17.46 64.55/17.46 U121_aa(x1, x2, x3) = U121_aa(x1, x3) 64.55/17.46 64.55/17.46 U82_ag(x1, x2, x3) = U82_ag(x2, x3) 64.55/17.46 64.55/17.46 U83_ag(x1, x2, x3, x4) = U83_ag(x3, x4) 64.55/17.46 64.55/17.46 U84_ag(x1, x2, x3, x4, x5, x6, x7) = U84_ag(x4, x5, x6, x7) 64.55/17.46 64.55/17.46 qcD_in_agagag(x1, x2, x3, x4, x5, x6) = qcD_in_agagag(x2, x4, x6) 64.55/17.46 64.55/17.46 U122_agagag(x1, x2, x3, x4, x5, x6, x7) = U122_agagag(x2, x4, x6, x7) 64.55/17.46 64.55/17.46 U85_ag(x1, x2, x3, x4, x5, x6, x7) = U85_ag(x1, x2, x4, x5, x6, x7) 64.55/17.46 64.55/17.46 qcD_in_ggggag(x1, x2, x3, x4, x5, x6) = qcD_in_ggggag(x1, x2, x3, x4, x6) 64.55/17.46 64.55/17.46 U122_ggggag(x1, x2, x3, x4, x5, x6, x7) = U122_ggggag(x1, x2, x3, x4, x6, x7) 64.55/17.46 64.55/17.46 U123_ggggag(x1, x2, x3, x4, x5, x6, x7) = U123_ggggag(x1, x2, x3, x4, x6, x7) 64.55/17.46 64.55/17.46 qcE_in_ggag(x1, x2, x3, x4) = qcE_in_ggag(x1, x2, x4) 64.55/17.46 64.55/17.46 U124_ggag(x1, x2, x3, x4, x5) = U124_ggag(x1, x2, x4, x5) 64.55/17.46 64.55/17.46 U125_ggag(x1, x2, x3, x4, x5) = U125_ggag(x1, x2, x4, x5) 64.55/17.46 64.55/17.46 U86_ag(x1, x2, x3, x4, x5) = U86_ag(x1, x2, x3, x4, x5) 64.55/17.46 64.55/17.46 U87_ag(x1, x2, x3, x4) = U87_ag(x2, x3, x4) 64.55/17.46 64.55/17.46 qcF_in_aagg(x1, x2, x3, x4) = qcF_in_aagg(x3, x4) 64.55/17.46 64.55/17.46 U126_aagg(x1, x2, x3, x4, x5) = U126_aagg(x3, x4, x5) 64.55/17.46 64.55/17.46 U127_aagg(x1, x2, x3, x4, x5) = U127_aagg(x1, x2, x3, x4, x5) 64.55/17.46 64.55/17.46 qcF_out_aagg(x1, x2, x3, x4) = qcF_out_aagg(x1, x2, x3, x4) 64.55/17.46 64.55/17.46 U88_ag(x1, x2, x3) = U88_ag(x1, x2, x3) 64.55/17.46 64.55/17.46 U89_ag(x1, x2, x3, x4) = U89_ag(x2, x3, x4) 64.55/17.46 64.55/17.46 U90_ag(x1, x2, x3, x4, x5, x6, x7) = U90_ag(x1, x2, x3, x4, x5, x6, x7) 64.55/17.46 64.55/17.46 U91_ag(x1, x2, x3, x4, x5, x6, x7) = U91_ag(x1, x2, x3, x4, x5, x6, x7) 64.55/17.46 64.55/17.46 U92_ag(x1, x2, x3, x4, x5, x6) = U92_ag(x2, x3, x4, x5, x6) 64.55/17.46 64.55/17.46 U93_ag(x1, x2, x3) = U93_ag(x2, x3) 64.55/17.46 64.55/17.46 qcG_in_aag(x1, x2, x3) = qcG_in_aag(x3) 64.55/17.46 64.55/17.46 U128_aag(x1, x2) = U128_aag(x1, x2) 64.55/17.46 64.55/17.46 qcG_out_aag(x1, x2, x3) = qcG_out_aag(x1, x2, x3) 64.55/17.46 64.55/17.46 U129_aag(x1, x2, x3) = U129_aag(x2, x3) 64.55/17.46 64.55/17.46 U130_aag(x1, x2, x3, x4, x5, x6) = U130_aag(x5, x6) 64.55/17.46 64.55/17.46 U131_aag(x1, x2, x3, x4, x5, x6) = U131_aag(x1, x3, x5, x6) 64.55/17.46 64.55/17.46 U132_aag(x1, x2, x3, x4, x5, x6) = U132_aag(x1, x2, x3, x4, x5, x6) 64.55/17.46 64.55/17.46 U133_aag(x1, x2, x3, x4, x5, x6) = U133_aag(x5, x6) 64.55/17.46 64.55/17.46 U134_aag(x1, x2, x3, x4, x5, x6) = U134_aag(x1, x4, x5, x6) 64.55/17.47 64.55/17.47 U135_aag(x1, x2, x3, x4, x5, x6) = U135_aag(x1, x2, x3, x4, x5, x6) 64.55/17.47 64.55/17.47 U136_aag(x1, x2, x3, x4) = U136_aag(x3, x4) 64.55/17.47 64.55/17.47 U137_aag(x1, x2, x3, x4) = U137_aag(x1, x3, x4) 64.55/17.47 64.55/17.47 qcE_out_ggag(x1, x2, x3, x4) = qcE_out_ggag(x1, x2, x3, x4) 64.55/17.47 64.55/17.47 qcD_out_ggggag(x1, x2, x3, x4, x5, x6) = qcD_out_ggggag(x1, x2, x3, x4, x5, x6) 64.55/17.47 64.55/17.47 U123_agagag(x1, x2, x3, x4, x5, x6, x7) = U123_agagag(x1, x2, x4, x6, x7) 64.55/17.47 64.55/17.47 qcE_in_agag(x1, x2, x3, x4) = qcE_in_agag(x2, x4) 64.55/17.47 64.55/17.47 U124_agag(x1, x2, x3, x4, x5) = U124_agag(x2, x4, x5) 64.55/17.47 64.55/17.47 U125_agag(x1, x2, x3, x4, x5) = U125_agag(x1, x2, x4, x5) 64.55/17.47 64.55/17.47 qcE_out_agag(x1, x2, x3, x4) = qcE_out_agag(x1, x2, x3, x4) 64.55/17.47 64.55/17.47 qcD_out_agagag(x1, x2, x3, x4, x5, x6) = qcD_out_agagag(x1, x2, x3, x4, x5, x6) 64.55/17.47 64.55/17.47 pE_in_agag(x1, x2, x3, x4) = pE_in_agag(x2, x4) 64.55/17.47 64.55/17.47 PA_IN_AG(x1, x2) = PA_IN_AG(x2) 64.55/17.47 64.55/17.47 U65_AG(x1, x2) = U65_AG(x2) 64.55/17.47 64.55/17.47 PB_IN_AA(x1, x2) = PB_IN_AA 64.55/17.47 64.55/17.47 U6_AA(x1) = U6_AA(x1) 64.55/17.47 64.55/17.47 PA_IN_GG(x1, x2) = PA_IN_GG(x1, x2) 64.55/17.47 64.55/17.47 U65_GG(x1, x2) = U65_GG(x1, x2) 64.55/17.47 64.55/17.47 PB_IN_GA(x1, x2) = PB_IN_GA(x1) 64.55/17.47 64.55/17.47 U6_GA(x1) = U6_GA(x1) 64.55/17.47 64.55/17.47 U66_GG(x1, x2) = U66_GG(x1, x2) 64.55/17.47 64.55/17.47 PC_IN_GA(x1, x2) = PC_IN_GA(x1) 64.55/17.47 64.55/17.47 U26_GA(x1) = U26_GA(x1) 64.55/17.47 64.55/17.47 U67_GG(x1, x2, x3) = U67_GG(x1, x2, x3) 64.55/17.47 64.55/17.47 U68_GG(x1, x2, x3, x4) = U68_GG(x2, x3, x4) 64.55/17.47 64.55/17.47 U69_GG(x1, x2, x3, x4, x5, x6, x7) = U69_GG(x1, x2, x3, x4, x5, x6, x7) 64.55/17.47 64.55/17.47 PD_IN_GGGGGG(x1, x2, x3, x4, x5, x6) = PD_IN_GGGGGG(x1, x2, x3, x4, x5, x6) 64.55/17.47 64.55/17.47 U41_GGGGGG(x1, x2, x3, x4, x5, x6, x7) = U41_GGGGGG(x1, x2, x3, x4, x5, x6, x7) 64.55/17.47 64.55/17.47 U70_GG(x1, x2, x3, x4, x5, x6, x7) = U70_GG(x1, x2, x3, x4, x5, x6, x7) 64.55/17.47 64.55/17.47 U42_GGGGGG(x1, x2, x3, x4, x5, x6, x7) = U42_GGGGGG(x1, x2, x3, x4, x5, x6, x7) 64.55/17.47 64.55/17.47 U43_GGGGGG(x1, x2, x3, x4, x5, x6, x7) = U43_GGGGGG(x1, x2, x3, x4, x5, x6, x7) 64.55/17.47 64.55/17.47 PE_IN_GGGG(x1, x2, x3, x4) = PE_IN_GGGG(x1, x2, x3, x4) 64.55/17.47 64.55/17.47 U44_GGGG(x1, x2, x3, x4, x5) = U44_GGGG(x1, x2, x3, x4, x5) 64.55/17.47 64.55/17.47 U71_GG(x1, x2, x3, x4, x5) = U71_GG(x1, x2, x3, x4, x5) 64.55/17.47 64.55/17.47 U45_GGGG(x1, x2, x3, x4, x5) = U45_GGGG(x1, x2, x3, x4, x5) 64.55/17.47 64.55/17.47 U46_GGGG(x1, x2, x3, x4, x5) = U46_GGGG(x1, x2, x3, x4, x5) 64.55/17.47 64.55/17.47 U72_GG(x1, x2, x3, x4) = U72_GG(x1, x2, x3, x4) 64.55/17.47 64.55/17.47 PF_IN_GAGG(x1, x2, x3, x4) = PF_IN_GAGG(x1, x3, x4) 64.55/17.47 64.55/17.47 U47_GAGG(x1, x2, x3, x4, x5) = U47_GAGG(x1, x3, x4, x5) 64.55/17.47 64.55/17.47 PJ_IN_GA(x1, x2) = PJ_IN_GA(x1) 64.55/17.47 64.55/17.47 U21_GA(x1, x2, x3, x4, x5) = U21_GA(x1, x2, x5) 64.55/17.47 64.55/17.47 PI_IN_GAGA(x1, x2, x3, x4) = PI_IN_GAGA(x1, x3) 64.55/17.47 64.55/17.47 U3_GAGA(x1, x2, x3, x4, x5) = U3_GAGA(x1, x3, x5) 64.55/17.47 64.55/17.47 PH_IN_GA(x1, x2) = PH_IN_GA(x1) 64.55/17.47 64.55/17.47 U1_GA(x1, x2, x3, x4, x5) = U1_GA(x1, x2, x5) 64.55/17.47 64.55/17.47 U4_GAGA(x1, x2, x3, x4, x5) = U4_GAGA(x1, x3, x5) 64.55/17.47 64.55/17.47 U5_GAGA(x1, x2, x3, x4, x5) = U5_GAGA(x1, x3, x5) 64.55/17.47 64.55/17.47 U2_GA(x1, x2, x3, x4, x5) = U2_GA(x1, x2, x5) 64.55/17.47 64.55/17.47 U22_GA(x1, x2, x3, x4, x5) = U22_GA(x1, x2, x5) 64.55/17.47 64.55/17.47 U23_GA(x1, x2, x3) = U23_GA(x1, x3) 64.55/17.47 64.55/17.47 U24_GA(x1, x2, x3) = U24_GA(x1, x3) 64.55/17.47 64.55/17.47 U25_GA(x1, x2, x3) = U25_GA(x1, x3) 64.55/17.47 64.55/17.47 U48_GAGG(x1, x2, x3, x4, x5) = U48_GAGG(x1, x3, x4, x5) 64.55/17.47 64.55/17.47 U49_GAGG(x1, x2, x3, x4, x5) = U49_GAGG(x1, x3, x4, x5) 64.55/17.47 64.55/17.47 U73_GG(x1, x2, x3) = U73_GG(x1, x2, x3) 64.55/17.47 64.55/17.47 U74_GG(x1, x2, x3, x4) = U74_GG(x2, x3, x4) 64.55/17.47 64.55/17.47 U75_GG(x1, x2, x3, x4, x5, x6, x7) = U75_GG(x1, x2, x3, x4, x5, x6, x7) 64.55/17.47 64.55/17.47 U76_GG(x1, x2, x3, x4, x5, x6, x7) = U76_GG(x1, x2, x3, x4, x5, x6, x7) 64.55/17.47 64.55/17.47 U77_GG(x1, x2, x3, x4, x5, x6) = U77_GG(x1, x2, x3, x4, x5, x6) 64.55/17.47 64.55/17.47 U78_GG(x1, x2, x3) = U78_GG(x1, x2, x3) 64.55/17.47 64.55/17.47 PG_IN_GAG(x1, x2, x3) = PG_IN_GAG(x1, x3) 64.55/17.47 64.55/17.47 U50_GAG(x1, x2) = U50_GAG(x1, x2) 64.55/17.47 64.55/17.47 U51_GAG(x1, x2, x3) = U51_GAG(x2, x3) 64.55/17.47 64.55/17.47 U52_GAG(x1, x2, x3, x4, x5, x6) = U52_GAG(x1, x2, x5, x6) 64.55/17.47 64.55/17.47 U53_GAG(x1, x2, x3, x4, x5, x6) = U53_GAG(x1, x2, x5, x6) 64.55/17.47 64.55/17.47 U54_GAG(x1, x2, x3, x4, x5, x6) = U54_GAG(x1, x2, x5, x6) 64.55/17.47 64.55/17.47 U55_GAG(x1, x2, x3, x4, x5, x6) = U55_GAG(x1, x2, x3, x5, x6) 64.55/17.47 64.55/17.47 U56_GAG(x1, x2, x3, x4, x5, x6) = U56_GAG(x1, x2, x5, x6) 64.55/17.47 64.55/17.47 U57_GAG(x1, x2, x3, x4, x5, x6) = U57_GAG(x1, x2, x5, x6) 64.55/17.47 64.55/17.47 U58_GAG(x1, x2, x3, x4, x5, x6) = U58_GAG(x1, x2, x5, x6) 64.55/17.47 64.55/17.47 U59_GAG(x1, x2, x3, x4, x5, x6) = U59_GAG(x1, x2, x5, x6) 64.55/17.47 64.55/17.47 U60_GAG(x1, x2, x3, x4, x5, x6) = U60_GAG(x1, x2, x4, x5, x6) 64.55/17.47 64.55/17.47 U61_GAG(x1, x2, x3, x4, x5, x6) = U61_GAG(x1, x2, x5, x6) 64.55/17.47 64.55/17.47 U62_GAG(x1, x2, x3, x4) = U62_GAG(x1, x3, x4) 64.55/17.47 64.55/17.47 U63_GAG(x1, x2, x3, x4) = U63_GAG(x1, x3, x4) 64.55/17.47 64.55/17.47 U64_GAG(x1, x2, x3, x4) = U64_GAG(x1, x3, x4) 64.55/17.47 64.55/17.47 U27_GA(x1, x2) = U27_GA(x2) 64.55/17.47 64.55/17.47 U28_GA(x1, x2, x3, x4, x5) = U28_GA(x1, x2, x5) 64.55/17.47 64.55/17.47 U29_GA(x1, x2, x3, x4, x5) = U29_GA(x1, x2, x5) 64.55/17.47 64.55/17.47 U30_GA(x1, x2, x3, x4, x5) = U30_GA(x1, x2, x5) 64.55/17.47 64.55/17.47 U31_GA(x1, x2, x3, x4, x5) = U31_GA(x1, x2, x3, x5) 64.55/17.47 64.55/17.47 U32_GA(x1, x2, x3, x4, x5) = U32_GA(x1, x2, x5) 64.55/17.47 64.55/17.47 U33_GA(x1, x2, x3, x4, x5) = U33_GA(x1, x2, x5) 64.55/17.47 64.55/17.47 U34_GA(x1, x2, x3, x4, x5) = U34_GA(x1, x2, x5) 64.55/17.47 64.55/17.47 U35_GA(x1, x2, x3, x4, x5) = U35_GA(x1, x2, x5) 64.55/17.47 64.55/17.47 U36_GA(x1, x2, x3, x4, x5) = U36_GA(x1, x2, x4, x5) 64.55/17.47 64.55/17.47 U37_GA(x1, x2, x3, x4, x5) = U37_GA(x1, x2, x5) 64.55/17.47 64.55/17.47 U38_GA(x1, x2, x3) = U38_GA(x1, x3) 64.55/17.47 64.55/17.47 U39_GA(x1, x2, x3) = U39_GA(x1, x3) 64.55/17.47 64.55/17.47 U40_GA(x1, x2, x3) = U40_GA(x1, x3) 64.55/17.47 64.55/17.47 U7_GA(x1, x2) = U7_GA(x2) 64.55/17.47 64.55/17.47 U8_GA(x1, x2, x3, x4, x5) = U8_GA(x1, x2, x5) 64.55/17.47 64.55/17.47 U9_GA(x1, x2, x3, x4, x5) = U9_GA(x1, x2, x5) 64.55/17.47 64.55/17.47 U10_GA(x1, x2, x3, x4, x5) = U10_GA(x1, x2, x5) 64.55/17.47 64.55/17.47 U11_GA(x1, x2, x3, x4, x5) = U11_GA(x1, x2, x3, x5) 64.55/17.47 64.55/17.47 U12_GA(x1, x2, x3, x4, x5) = U12_GA(x1, x2, x5) 64.55/17.47 64.55/17.47 U13_GA(x1, x2, x3, x4, x5) = U13_GA(x1, x2, x5) 64.55/17.47 64.55/17.47 U14_GA(x1, x2, x3, x4, x5) = U14_GA(x1, x2, x5) 64.55/17.47 64.55/17.47 U15_GA(x1, x2, x3, x4, x5) = U15_GA(x1, x2, x5) 64.55/17.47 64.55/17.47 U16_GA(x1, x2, x3, x4, x5) = U16_GA(x1, x2, x4, x5) 64.55/17.47 64.55/17.47 U17_GA(x1, x2, x3, x4, x5) = U17_GA(x1, x2, x5) 64.55/17.47 64.55/17.47 U18_GA(x1, x2, x3) = U18_GA(x1, x3) 64.55/17.47 64.55/17.47 U19_GA(x1, x2, x3) = U19_GA(x1, x3) 64.55/17.47 64.55/17.47 U20_GA(x1, x2, x3) = U20_GA(x1, x3) 64.55/17.47 64.55/17.47 U7_AA(x1, x2) = U7_AA(x2) 64.55/17.47 64.55/17.47 U8_AA(x1, x2, x3, x4, x5) = U8_AA(x5) 64.55/17.47 64.55/17.47 PH_IN_AA(x1, x2) = PH_IN_AA 64.55/17.47 64.55/17.47 U1_AA(x1, x2, x3, x4, x5) = U1_AA(x5) 64.55/17.47 64.55/17.47 PI_IN_AAAA(x1, x2, x3, x4) = PI_IN_AAAA 64.55/17.47 64.55/17.47 U3_AAAA(x1, x2, x3, x4, x5) = U3_AAAA(x5) 64.55/17.47 64.55/17.47 U2_AA(x1, x2, x3, x4, x5) = U2_AA(x5) 64.55/17.47 64.55/17.47 U4_AAAA(x1, x2, x3, x4, x5) = U4_AAAA(x5) 64.55/17.47 64.55/17.47 U5_AAAA(x1, x2, x3, x4, x5) = U5_AAAA(x5) 64.55/17.47 64.55/17.47 U9_AA(x1, x2, x3, x4, x5) = U9_AA(x5) 64.55/17.47 64.55/17.47 U10_AA(x1, x2, x3, x4, x5) = U10_AA(x5) 64.55/17.47 64.55/17.47 U11_AA(x1, x2, x3, x4, x5) = U11_AA(x3, x5) 64.55/17.47 64.55/17.47 U12_AA(x1, x2, x3, x4, x5) = U12_AA(x5) 64.55/17.47 64.55/17.47 U13_AA(x1, x2, x3, x4, x5) = U13_AA(x5) 64.55/17.47 64.55/17.47 U14_AA(x1, x2, x3, x4, x5) = U14_AA(x5) 64.55/17.47 64.55/17.47 U15_AA(x1, x2, x3, x4, x5) = U15_AA(x5) 64.55/17.47 64.55/17.47 U16_AA(x1, x2, x3, x4, x5) = U16_AA(x1, x4, x5) 64.55/17.47 64.55/17.47 U17_AA(x1, x2, x3, x4, x5) = U17_AA(x5) 64.55/17.47 64.55/17.47 U18_AA(x1, x2, x3) = U18_AA(x3) 64.55/17.47 64.55/17.47 PJ_IN_AA(x1, x2) = PJ_IN_AA 64.55/17.47 64.55/17.47 U21_AA(x1, x2, x3, x4, x5) = U21_AA(x5) 64.55/17.47 64.55/17.47 U22_AA(x1, x2, x3, x4, x5) = U22_AA(x5) 64.55/17.47 64.55/17.47 U23_AA(x1, x2, x3) = U23_AA(x3) 64.55/17.47 64.55/17.47 U24_AA(x1, x2, x3) = U24_AA(x3) 64.55/17.47 64.55/17.47 U25_AA(x1, x2, x3) = U25_AA(x3) 64.55/17.47 64.55/17.47 U19_AA(x1, x2, x3) = U19_AA(x3) 64.55/17.47 64.55/17.47 U20_AA(x1, x2, x3) = U20_AA(x3) 64.55/17.47 64.55/17.47 U66_AG(x1, x2) = U66_AG(x2) 64.55/17.47 64.55/17.47 PC_IN_AA(x1, x2) = PC_IN_AA 64.55/17.47 64.55/17.47 U26_AA(x1) = U26_AA(x1) 64.55/17.47 64.55/17.47 U27_AA(x1, x2) = U27_AA(x2) 64.55/17.47 64.55/17.47 U28_AA(x1, x2, x3, x4, x5) = U28_AA(x5) 64.55/17.47 64.55/17.47 U29_AA(x1, x2, x3, x4, x5) = U29_AA(x5) 64.55/17.47 64.55/17.47 U30_AA(x1, x2, x3, x4, x5) = U30_AA(x5) 64.55/17.47 64.55/17.47 U31_AA(x1, x2, x3, x4, x5) = U31_AA(x3, x5) 64.55/17.47 64.55/17.47 U32_AA(x1, x2, x3, x4, x5) = U32_AA(x5) 64.55/17.47 64.55/17.47 U33_AA(x1, x2, x3, x4, x5) = U33_AA(x5) 64.55/17.47 64.55/17.47 U34_AA(x1, x2, x3, x4, x5) = U34_AA(x5) 64.55/17.47 64.55/17.47 U35_AA(x1, x2, x3, x4, x5) = U35_AA(x5) 64.55/17.47 64.55/17.47 U36_AA(x1, x2, x3, x4, x5) = U36_AA(x1, x4, x5) 64.55/17.47 64.55/17.47 U37_AA(x1, x2, x3, x4, x5) = U37_AA(x5) 64.55/17.47 64.55/17.47 U38_AA(x1, x2, x3) = U38_AA(x3) 64.55/17.47 64.55/17.47 U39_AA(x1, x2, x3) = U39_AA(x3) 64.55/17.47 64.55/17.47 U40_AA(x1, x2, x3) = U40_AA(x3) 64.55/17.47 64.55/17.47 U67_AG(x1, x2, x3) = U67_AG(x2, x3) 64.55/17.47 64.55/17.47 U68_AG(x1, x2, x3, x4) = U68_AG(x3, x4) 64.55/17.47 64.55/17.47 U69_AG(x1, x2, x3, x4, x5, x6, x7) = U69_AG(x4, x5, x6, x7) 64.55/17.47 64.55/17.47 PD_IN_AGAGAG(x1, x2, x3, x4, x5, x6) = PD_IN_AGAGAG(x2, x4, x6) 64.55/17.47 64.55/17.47 U41_AGAGAG(x1, x2, x3, x4, x5, x6, x7) = U41_AGAGAG(x2, x4, x6, x7) 64.55/17.47 64.55/17.47 U70_AG(x1, x2, x3, x4, x5, x6, x7) = U70_AG(x1, x2, x4, x5, x6, x7) 64.55/17.47 64.55/17.47 PD_IN_GGGGAG(x1, x2, x3, x4, x5, x6) = PD_IN_GGGGAG(x1, x2, x3, x4, x6) 64.55/17.47 64.55/17.47 U41_GGGGAG(x1, x2, x3, x4, x5, x6, x7) = U41_GGGGAG(x1, x2, x3, x4, x6, x7) 64.55/17.47 64.55/17.47 U42_GGGGAG(x1, x2, x3, x4, x5, x6, x7) = U42_GGGGAG(x1, x2, x3, x4, x6, x7) 64.55/17.47 64.55/17.47 U43_GGGGAG(x1, x2, x3, x4, x5, x6, x7) = U43_GGGGAG(x1, x2, x3, x4, x6, x7) 64.55/17.47 64.55/17.47 PE_IN_GGAG(x1, x2, x3, x4) = PE_IN_GGAG(x1, x2, x4) 64.55/17.47 64.55/17.47 U44_GGAG(x1, x2, x3, x4, x5) = U44_GGAG(x1, x2, x4, x5) 64.55/17.47 64.55/17.47 U45_GGAG(x1, x2, x3, x4, x5) = U45_GGAG(x1, x2, x4, x5) 64.55/17.47 64.55/17.47 U46_GGAG(x1, x2, x3, x4, x5) = U46_GGAG(x1, x2, x4, x5) 64.55/17.47 64.55/17.47 U71_AG(x1, x2, x3, x4, x5) = U71_AG(x1, x2, x3, x4, x5) 64.55/17.47 64.55/17.47 U72_AG(x1, x2, x3, x4) = U72_AG(x2, x3, x4) 64.55/17.47 64.55/17.47 PF_IN_AAGG(x1, x2, x3, x4) = PF_IN_AAGG(x3, x4) 64.55/17.47 64.55/17.47 U47_AAGG(x1, x2, x3, x4, x5) = U47_AAGG(x3, x4, x5) 64.55/17.47 64.55/17.47 U48_AAGG(x1, x2, x3, x4, x5) = U48_AAGG(x3, x4, x5) 64.55/17.47 64.55/17.47 U49_AAGG(x1, x2, x3, x4, x5) = U49_AAGG(x3, x4, x5) 64.55/17.47 64.55/17.47 U73_AG(x1, x2, x3) = U73_AG(x1, x2, x3) 64.55/17.47 64.55/17.47 U74_AG(x1, x2, x3, x4) = U74_AG(x2, x3, x4) 64.55/17.47 64.55/17.47 U75_AG(x1, x2, x3, x4, x5, x6, x7) = U75_AG(x1, x2, x3, x4, x5, x6, x7) 64.55/17.47 64.55/17.47 U76_AG(x1, x2, x3, x4, x5, x6, x7) = U76_AG(x1, x2, x3, x4, x5, x6, x7) 64.55/17.47 64.55/17.47 U77_AG(x1, x2, x3, x4, x5, x6) = U77_AG(x2, x3, x4, x5, x6) 64.55/17.47 64.55/17.47 U78_AG(x1, x2, x3) = U78_AG(x2, x3) 64.55/17.47 64.55/17.47 PG_IN_AAG(x1, x2, x3) = PG_IN_AAG(x3) 64.55/17.47 64.55/17.47 U50_AAG(x1, x2) = U50_AAG(x1, x2) 64.55/17.47 64.55/17.47 U51_AAG(x1, x2, x3) = U51_AAG(x2, x3) 64.55/17.47 64.55/17.47 U52_AAG(x1, x2, x3, x4, x5, x6) = U52_AAG(x5, x6) 64.55/17.47 64.55/17.47 U53_AAG(x1, x2, x3, x4, x5, x6) = U53_AAG(x5, x6) 64.55/17.47 64.55/17.47 U54_AAG(x1, x2, x3, x4, x5, x6) = U54_AAG(x5, x6) 64.55/17.47 64.55/17.47 U55_AAG(x1, x2, x3, x4, x5, x6) = U55_AAG(x3, x5, x6) 64.55/17.47 64.55/17.47 U56_AAG(x1, x2, x3, x4, x5, x6) = U56_AAG(x5, x6) 64.55/17.47 64.55/17.47 U57_AAG(x1, x2, x3, x4, x5, x6) = U57_AAG(x5, x6) 64.55/17.47 64.55/17.47 U58_AAG(x1, x2, x3, x4, x5, x6) = U58_AAG(x5, x6) 64.55/17.47 64.55/17.47 U59_AAG(x1, x2, x3, x4, x5, x6) = U59_AAG(x5, x6) 64.55/17.47 64.55/17.47 U60_AAG(x1, x2, x3, x4, x5, x6) = U60_AAG(x1, x4, x5, x6) 64.55/17.47 64.55/17.47 U61_AAG(x1, x2, x3, x4, x5, x6) = U61_AAG(x5, x6) 64.55/17.47 64.55/17.47 U62_AAG(x1, x2, x3, x4) = U62_AAG(x3, x4) 64.55/17.47 64.55/17.47 U63_AAG(x1, x2, x3, x4) = U63_AAG(x3, x4) 64.55/17.47 64.55/17.47 U64_AAG(x1, x2, x3, x4) = U64_AAG(x3, x4) 64.55/17.47 64.55/17.47 U42_AGAGAG(x1, x2, x3, x4, x5, x6, x7) = U42_AGAGAG(x2, x4, x6, x7) 64.55/17.47 64.55/17.47 U43_AGAGAG(x1, x2, x3, x4, x5, x6, x7) = U43_AGAGAG(x2, x4, x6, x7) 64.55/17.47 64.55/17.47 PE_IN_AGAG(x1, x2, x3, x4) = PE_IN_AGAG(x2, x4) 64.55/17.47 64.55/17.47 U44_AGAG(x1, x2, x3, x4, x5) = U44_AGAG(x2, x4, x5) 64.55/17.47 64.55/17.47 U45_AGAG(x1, x2, x3, x4, x5) = U45_AGAG(x2, x4, x5) 64.55/17.47 64.55/17.47 U46_AGAG(x1, x2, x3, x4, x5) = U46_AGAG(x2, x4, x5) 64.55/17.47 64.55/17.47 64.55/17.47 We have to consider all (P,R,Pi)-chains 64.55/17.47 ---------------------------------------- 64.55/17.47 64.55/17.47 (119) DependencyGraphProof (EQUIVALENT) 64.55/17.47 The approximation of the Dependency Graph [LOPSTR] contains 6 SCCs with 241 less nodes. 64.55/17.47 ---------------------------------------- 64.55/17.47 64.55/17.47 (120) 64.55/17.47 Complex Obligation (AND) 64.55/17.47 64.55/17.47 ---------------------------------------- 64.55/17.47 64.55/17.47 (121) 64.55/17.47 Obligation: 64.55/17.47 Pi DP problem: 64.55/17.47 The TRS P consists of the following rules: 64.55/17.47 64.55/17.47 PH_IN_AA(+(X1, X2), +(X3, X4)) -> PI_IN_AAAA(X1, X3, X2, X4) 64.55/17.47 PI_IN_AAAA(X1, X2, X3, X4) -> PH_IN_AA(X1, X2) 64.55/17.47 PH_IN_AA(*(X1, X2), +(*(X1, X3), *(X2, X4))) -> PI_IN_AAAA(X1, X4, X2, X3) 64.55/17.47 PI_IN_AAAA(X1, X2, X3, X4) -> U4_AAAA(X1, X2, X3, X4, pcH_in_aa(X1, X2)) 64.55/17.47 U4_AAAA(X1, X2, X3, X4, pcH_out_aa(X1, X2)) -> PH_IN_AA(X3, X4) 64.55/17.47 64.55/17.47 The TRS R consists of the following rules: 64.55/17.47 64.55/17.47 pcA_in_gg(d(e(t)), const(1)) -> pcA_out_gg(d(e(t)), const(1)) 64.55/17.47 pcA_in_gg(d(d(X1)), const(1)) -> U80_gg(X1, qcB_in_ga(X1, X2)) 64.55/17.47 qcB_in_ga(e(t), const(1)) -> U98_ga(pcA_in_gg(d(e(const(1))), const(1))) 64.55/17.47 pcA_in_gg(d(e(const(X1))), const(0)) -> pcA_out_gg(d(e(const(X1))), const(0)) 64.55/17.47 pcA_in_gg(d(d(X1)), const(0)) -> U81_gg(X1, qcC_in_ga(X1, X2)) 64.55/17.47 qcC_in_ga(e(t), const(1)) -> U112_ga(pcA_in_gg(d(e(const(1))), const(0))) 64.55/17.47 pcA_in_gg(d(e(+(t, X1))), +(const(1), X2)) -> U82_gg(X1, X2, pcA_in_gg(d(e(X1)), X2)) 64.55/17.47 pcA_in_gg(d(e(+(const(X1), X2))), +(const(0), X3)) -> U83_gg(X1, X2, X3, pcA_in_gg(d(e(X2)), X3)) 64.55/17.47 pcA_in_gg(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) -> U84_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X4, X2, X5, X3, X6)) 64.55/17.47 qcD_in_gggggg(X1, X2, X3, X4, X5, X6) -> U122_gggggg(X1, X2, X3, X4, X5, X6, pcA_in_gg(d(e(X1)), X2)) 64.55/17.47 pcA_in_gg(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) -> U85_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X5, X2, X4, X3, X6)) 64.55/17.47 U85_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X5, X2, X4, X3, X6)) -> pcA_out_gg(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) 64.55/17.47 pcA_in_gg(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) -> U86_gg(X1, X2, X3, X4, qcE_in_gggg(X1, X4, X2, X3)) 64.55/17.47 qcE_in_gggg(X1, X2, X3, X4) -> U124_gggg(X1, X2, X3, X4, pcA_in_gg(d(e(X1)), X2)) 64.55/17.47 pcA_in_gg(d(d(X1)), +(X2, X3)) -> U87_gg(X1, X2, X3, qcF_in_gagg(X1, X4, X2, X3)) 64.55/17.47 qcF_in_gagg(X1, X2, X3, X4) -> U126_gagg(X1, X2, X3, X4, pcJ_in_ga(X1, X2)) 64.55/17.47 pcJ_in_ga(e(t), const(1)) -> pcJ_out_ga(e(t), const(1)) 64.55/17.47 pcJ_in_ga(e(const(X1)), const(0)) -> pcJ_out_ga(e(const(X1)), const(0)) 64.55/17.47 pcJ_in_ga(e(+(X1, X2)), +(X3, X4)) -> U108_ga(X1, X2, X3, X4, qcI_in_gaga(X1, X3, X2, X4)) 64.55/17.47 qcI_in_gaga(X1, X2, X3, X4) -> U96_gaga(X1, X2, X3, X4, pcH_in_ga(X1, X2)) 64.55/17.47 pcH_in_ga(t, const(1)) -> pcH_out_ga(t, const(1)) 64.55/17.47 pcH_in_ga(const(X1), const(0)) -> pcH_out_ga(const(X1), const(0)) 64.55/17.47 pcH_in_ga(+(X1, X2), +(X3, X4)) -> U94_ga(X1, X2, X3, X4, qcI_in_gaga(X1, X3, X2, X4)) 64.55/17.47 U94_ga(X1, X2, X3, X4, qcI_out_gaga(X1, X3, X2, X4)) -> pcH_out_ga(+(X1, X2), +(X3, X4)) 64.55/17.47 pcH_in_ga(*(X1, X2), +(*(X1, X3), *(X2, X4))) -> U95_ga(X1, X2, X3, X4, qcI_in_gaga(X1, X4, X2, X3)) 64.55/17.47 U95_ga(X1, X2, X3, X4, qcI_out_gaga(X1, X4, X2, X3)) -> pcH_out_ga(*(X1, X2), +(*(X1, X3), *(X2, X4))) 64.55/17.47 U96_gaga(X1, X2, X3, X4, pcH_out_ga(X1, X2)) -> U97_gaga(X1, X2, X3, X4, pcH_in_ga(X3, X4)) 64.55/17.47 U97_gaga(X1, X2, X3, X4, pcH_out_ga(X3, X4)) -> qcI_out_gaga(X1, X2, X3, X4) 64.55/17.47 U108_ga(X1, X2, X3, X4, qcI_out_gaga(X1, X3, X2, X4)) -> pcJ_out_ga(e(+(X1, X2)), +(X3, X4)) 64.55/17.47 pcJ_in_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U109_ga(X1, X2, X3, X4, qcI_in_gaga(X1, X4, X2, X3)) 64.55/17.47 U109_ga(X1, X2, X3, X4, qcI_out_gaga(X1, X4, X2, X3)) -> pcJ_out_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.55/17.47 pcJ_in_ga(d(X1), X2) -> U110_ga(X1, X2, pcJ_in_ga(X1, X3)) 64.55/17.47 U110_ga(X1, X2, pcJ_out_ga(X1, X3)) -> U111_ga(X1, X2, pcH_in_ga(X3, X2)) 64.55/17.47 U111_ga(X1, X2, pcH_out_ga(X3, X2)) -> pcJ_out_ga(d(X1), X2) 64.55/17.47 U126_gagg(X1, X2, X3, X4, pcJ_out_ga(X1, X2)) -> U127_gagg(X1, X2, X3, X4, pcA_in_gg(d(e(X2)), +(X3, X4))) 64.55/17.47 pcA_in_gg(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) -> U88_gg(X1, X2, pcA_in_gg(d(e(X1)), X2)) 64.55/17.47 pcA_in_gg(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) -> U89_gg(X1, X2, X3, pcA_in_gg(d(e(X2)), X3)) 64.55/17.47 pcA_in_gg(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) -> U90_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X5, X2, X6, X3, X4)) 64.55/17.47 U90_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X5, X2, X6, X3, X4)) -> pcA_out_gg(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) 64.55/17.47 pcA_in_gg(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) -> U91_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X6, X2, X5, X3, X4)) 64.55/17.47 U91_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X6, X2, X5, X3, X4)) -> pcA_out_gg(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) 64.55/17.47 pcA_in_gg(d(d(X1)), +(*(X2, X3), *(X4, X5))) -> U92_gg(X1, X2, X3, X4, X5, qcF_in_gagg(X1, X6, *(X2, X3), *(X4, X5))) 64.55/17.47 U92_gg(X1, X2, X3, X4, X5, qcF_out_gagg(X1, X6, *(X2, X3), *(X4, X5))) -> pcA_out_gg(d(d(X1)), +(*(X2, X3), *(X4, X5))) 64.55/17.47 pcA_in_gg(d(d(X1)), X2) -> U93_gg(X1, X2, qcG_in_gag(X1, X3, X2)) 64.55/17.47 qcG_in_gag(e(t), const(1), X1) -> U128_gag(X1, pcA_in_gg(d(e(const(1))), X1)) 64.55/17.47 U128_gag(X1, pcA_out_gg(d(e(const(1))), X1)) -> qcG_out_gag(e(t), const(1), X1) 64.55/17.47 qcG_in_gag(e(const(X1)), const(0), X2) -> U129_gag(X1, X2, pcA_in_gg(d(e(const(0))), X2)) 64.55/17.47 U129_gag(X1, X2, pcA_out_gg(d(e(const(0))), X2)) -> qcG_out_gag(e(const(X1)), const(0), X2) 64.55/17.47 qcG_in_gag(e(+(X1, X2)), +(X3, X4), X5) -> U130_gag(X1, X2, X3, X4, X5, pcH_in_ga(X1, X3)) 64.55/17.47 U130_gag(X1, X2, X3, X4, X5, pcH_out_ga(X1, X3)) -> U131_gag(X1, X2, X3, X4, X5, pcH_in_ga(X2, X4)) 64.55/17.47 U131_gag(X1, X2, X3, X4, X5, pcH_out_ga(X2, X4)) -> U132_gag(X1, X2, X3, X4, X5, pcA_in_gg(d(e(+(X3, X4))), X5)) 64.55/17.47 U132_gag(X1, X2, X3, X4, X5, pcA_out_gg(d(e(+(X3, X4))), X5)) -> qcG_out_gag(e(+(X1, X2)), +(X3, X4), X5) 64.55/17.47 qcG_in_gag(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) -> U133_gag(X1, X2, X3, X4, X5, pcH_in_ga(X1, X4)) 64.55/17.47 U133_gag(X1, X2, X3, X4, X5, pcH_out_ga(X1, X4)) -> U134_gag(X1, X2, X3, X4, X5, pcH_in_ga(X2, X3)) 64.55/17.47 U134_gag(X1, X2, X3, X4, X5, pcH_out_ga(X2, X3)) -> U135_gag(X1, X2, X3, X4, X5, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), X5)) 64.55/17.47 U135_gag(X1, X2, X3, X4, X5, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), X5)) -> qcG_out_gag(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) 64.55/17.47 qcG_in_gag(d(X1), X2, X3) -> U136_gag(X1, X2, X3, pcJ_in_ga(X1, X4)) 64.55/17.47 U136_gag(X1, X2, X3, pcJ_out_ga(X1, X4)) -> U137_gag(X1, X2, X3, qcG_in_gag(e(X4), X2, X3)) 64.55/17.47 U137_gag(X1, X2, X3, qcG_out_gag(e(X4), X2, X3)) -> qcG_out_gag(d(X1), X2, X3) 64.55/17.47 U93_gg(X1, X2, qcG_out_gag(X1, X3, X2)) -> pcA_out_gg(d(d(X1)), X2) 64.55/17.47 U89_gg(X1, X2, X3, pcA_out_gg(d(e(X2)), X3)) -> pcA_out_gg(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) 64.55/17.47 U88_gg(X1, X2, pcA_out_gg(d(e(X1)), X2)) -> pcA_out_gg(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) 64.55/17.47 U127_gagg(X1, X2, X3, X4, pcA_out_gg(d(e(X2)), +(X3, X4))) -> qcF_out_gagg(X1, X2, X3, X4) 64.55/17.47 U87_gg(X1, X2, X3, qcF_out_gagg(X1, X4, X2, X3)) -> pcA_out_gg(d(d(X1)), +(X2, X3)) 64.55/17.47 U124_gggg(X1, X2, X3, X4, pcA_out_gg(d(e(X1)), X2)) -> U125_gggg(X1, X2, X3, X4, pcA_in_gg(d(e(X3)), X4)) 64.55/17.47 U125_gggg(X1, X2, X3, X4, pcA_out_gg(d(e(X3)), X4)) -> qcE_out_gggg(X1, X2, X3, X4) 64.55/17.47 U86_gg(X1, X2, X3, X4, qcE_out_gggg(X1, X4, X2, X3)) -> pcA_out_gg(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) 64.55/17.47 U122_gggggg(X1, X2, X3, X4, X5, X6, pcA_out_gg(d(e(X1)), X2)) -> U123_gggggg(X1, X2, X3, X4, X5, X6, qcE_in_gggg(X3, X4, X5, X6)) 64.55/17.47 U123_gggggg(X1, X2, X3, X4, X5, X6, qcE_out_gggg(X3, X4, X5, X6)) -> qcD_out_gggggg(X1, X2, X3, X4, X5, X6) 64.55/17.47 U84_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X4, X2, X5, X3, X6)) -> pcA_out_gg(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) 64.55/17.47 U83_gg(X1, X2, X3, pcA_out_gg(d(e(X2)), X3)) -> pcA_out_gg(d(e(+(const(X1), X2))), +(const(0), X3)) 64.55/17.47 U82_gg(X1, X2, pcA_out_gg(d(e(X1)), X2)) -> pcA_out_gg(d(e(+(t, X1))), +(const(1), X2)) 64.55/17.47 U112_ga(pcA_out_gg(d(e(const(1))), const(0))) -> qcC_out_ga(e(t), const(1)) 64.55/17.47 qcC_in_ga(e(const(X1)), const(0)) -> U113_ga(X1, pcA_in_gg(d(e(const(0))), const(0))) 64.55/17.47 U113_ga(X1, pcA_out_gg(d(e(const(0))), const(0))) -> qcC_out_ga(e(const(X1)), const(0)) 64.55/17.47 qcC_in_ga(e(+(X1, X2)), +(X3, X4)) -> U114_ga(X1, X2, X3, X4, pcH_in_ga(X1, X3)) 64.55/17.47 U114_ga(X1, X2, X3, X4, pcH_out_ga(X1, X3)) -> U115_ga(X1, X2, X3, X4, pcH_in_ga(X2, X4)) 64.55/17.47 U115_ga(X1, X2, X3, X4, pcH_out_ga(X2, X4)) -> U116_ga(X1, X2, X3, X4, pcA_in_gg(d(e(+(X3, X4))), const(0))) 64.55/17.47 U116_ga(X1, X2, X3, X4, pcA_out_gg(d(e(+(X3, X4))), const(0))) -> qcC_out_ga(e(+(X1, X2)), +(X3, X4)) 64.55/17.47 qcC_in_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U117_ga(X1, X2, X3, X4, pcH_in_ga(X1, X4)) 64.55/17.47 U117_ga(X1, X2, X3, X4, pcH_out_ga(X1, X4)) -> U118_ga(X1, X2, X3, X4, pcH_in_ga(X2, X3)) 64.55/17.47 U118_ga(X1, X2, X3, X4, pcH_out_ga(X2, X3)) -> U119_ga(X1, X2, X3, X4, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(0))) 64.55/17.47 U119_ga(X1, X2, X3, X4, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(0))) -> qcC_out_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.55/17.47 qcC_in_ga(d(X1), X2) -> U120_ga(X1, X2, pcJ_in_ga(X1, X3)) 64.55/17.47 U120_ga(X1, X2, pcJ_out_ga(X1, X3)) -> U121_ga(X1, X2, qcC_in_ga(e(X3), X2)) 64.55/17.47 U121_ga(X1, X2, qcC_out_ga(e(X3), X2)) -> qcC_out_ga(d(X1), X2) 64.55/17.47 U81_gg(X1, qcC_out_ga(X1, X2)) -> pcA_out_gg(d(d(X1)), const(0)) 64.55/17.47 U98_ga(pcA_out_gg(d(e(const(1))), const(1))) -> qcB_out_ga(e(t), const(1)) 64.55/17.47 qcB_in_ga(e(const(X1)), const(0)) -> U99_ga(X1, pcA_in_gg(d(e(const(0))), const(1))) 64.55/17.47 U99_ga(X1, pcA_out_gg(d(e(const(0))), const(1))) -> qcB_out_ga(e(const(X1)), const(0)) 64.55/17.47 qcB_in_ga(e(+(X1, X2)), +(X3, X4)) -> U100_ga(X1, X2, X3, X4, pcH_in_ga(X1, X3)) 64.55/17.47 U100_ga(X1, X2, X3, X4, pcH_out_ga(X1, X3)) -> U101_ga(X1, X2, X3, X4, pcH_in_ga(X2, X4)) 64.55/17.47 U101_ga(X1, X2, X3, X4, pcH_out_ga(X2, X4)) -> U102_ga(X1, X2, X3, X4, pcA_in_gg(d(e(+(X3, X4))), const(1))) 64.55/17.47 U102_ga(X1, X2, X3, X4, pcA_out_gg(d(e(+(X3, X4))), const(1))) -> qcB_out_ga(e(+(X1, X2)), +(X3, X4)) 64.55/17.47 qcB_in_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U103_ga(X1, X2, X3, X4, pcH_in_ga(X1, X4)) 64.55/17.47 U103_ga(X1, X2, X3, X4, pcH_out_ga(X1, X4)) -> U104_ga(X1, X2, X3, X4, pcH_in_ga(X2, X3)) 64.55/17.47 U104_ga(X1, X2, X3, X4, pcH_out_ga(X2, X3)) -> U105_ga(X1, X2, X3, X4, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(1))) 64.55/17.47 U105_ga(X1, X2, X3, X4, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(1))) -> qcB_out_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.55/17.47 qcB_in_ga(d(X1), X2) -> U106_ga(X1, X2, pcJ_in_ga(X1, X3)) 64.55/17.47 U106_ga(X1, X2, pcJ_out_ga(X1, X3)) -> U107_ga(X1, X2, qcB_in_ga(e(X3), X2)) 64.55/17.47 U107_ga(X1, X2, qcB_out_ga(e(X3), X2)) -> qcB_out_ga(d(X1), X2) 64.55/17.47 U80_gg(X1, qcB_out_ga(X1, X2)) -> pcA_out_gg(d(d(X1)), const(1)) 64.55/17.47 pcH_in_aa(t, const(1)) -> pcH_out_aa(t, const(1)) 64.55/17.47 pcH_in_aa(const(X1), const(0)) -> pcH_out_aa(const(X1), const(0)) 64.55/17.47 pcH_in_aa(+(X1, X2), +(X3, X4)) -> U94_aa(X1, X2, X3, X4, qcI_in_aaaa(X1, X3, X2, X4)) 64.55/17.47 qcI_in_aaaa(X1, X2, X3, X4) -> U96_aaaa(X1, X2, X3, X4, pcH_in_aa(X1, X2)) 64.55/17.47 pcH_in_aa(*(X1, X2), +(*(X1, X3), *(X2, X4))) -> U95_aa(X1, X2, X3, X4, qcI_in_aaaa(X1, X4, X2, X3)) 64.55/17.47 U95_aa(X1, X2, X3, X4, qcI_out_aaaa(X1, X4, X2, X3)) -> pcH_out_aa(*(X1, X2), +(*(X1, X3), *(X2, X4))) 64.55/17.47 U96_aaaa(X1, X2, X3, X4, pcH_out_aa(X1, X2)) -> U97_aaaa(X1, X2, X3, X4, pcH_in_aa(X3, X4)) 64.55/17.47 U97_aaaa(X1, X2, X3, X4, pcH_out_aa(X3, X4)) -> qcI_out_aaaa(X1, X2, X3, X4) 64.55/17.47 U94_aa(X1, X2, X3, X4, qcI_out_aaaa(X1, X3, X2, X4)) -> pcH_out_aa(+(X1, X2), +(X3, X4)) 64.55/17.47 pcJ_in_aa(e(t), const(1)) -> pcJ_out_aa(e(t), const(1)) 64.55/17.47 pcJ_in_aa(e(const(X1)), const(0)) -> pcJ_out_aa(e(const(X1)), const(0)) 64.55/17.47 pcJ_in_aa(e(+(X1, X2)), +(X3, X4)) -> U108_aa(X1, X2, X3, X4, qcI_in_aaaa(X1, X3, X2, X4)) 64.55/17.47 U108_aa(X1, X2, X3, X4, qcI_out_aaaa(X1, X3, X2, X4)) -> pcJ_out_aa(e(+(X1, X2)), +(X3, X4)) 64.55/17.47 pcJ_in_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U109_aa(X1, X2, X3, X4, qcI_in_aaaa(X1, X4, X2, X3)) 64.55/17.47 U109_aa(X1, X2, X3, X4, qcI_out_aaaa(X1, X4, X2, X3)) -> pcJ_out_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.55/17.47 pcJ_in_aa(d(X1), X2) -> U110_aa(X1, X2, pcJ_in_aa(X1, X3)) 64.55/17.47 U110_aa(X1, X2, pcJ_out_aa(X1, X3)) -> U111_aa(X1, X2, pcH_in_ga(X3, X2)) 64.55/17.47 U111_aa(X1, X2, pcH_out_ga(X3, X2)) -> pcJ_out_aa(d(X1), X2) 64.55/17.47 pcA_in_ag(d(e(t)), const(1)) -> pcA_out_ag(d(e(t)), const(1)) 64.55/17.47 pcA_in_ag(d(d(X1)), const(1)) -> U80_ag(X1, qcB_in_aa(X1, X2)) 64.55/17.47 qcB_in_aa(e(t), const(1)) -> U98_aa(pcA_in_gg(d(e(const(1))), const(1))) 64.55/17.47 U98_aa(pcA_out_gg(d(e(const(1))), const(1))) -> qcB_out_aa(e(t), const(1)) 64.55/17.47 qcB_in_aa(e(const(X1)), const(0)) -> U99_aa(X1, pcA_in_gg(d(e(const(0))), const(1))) 64.55/17.47 U99_aa(X1, pcA_out_gg(d(e(const(0))), const(1))) -> qcB_out_aa(e(const(X1)), const(0)) 64.55/17.47 qcB_in_aa(e(+(X1, X2)), +(X3, X4)) -> U100_aa(X1, X2, X3, X4, pcH_in_aa(X1, X3)) 64.55/17.47 U100_aa(X1, X2, X3, X4, pcH_out_aa(X1, X3)) -> U101_aa(X1, X2, X3, X4, pcH_in_aa(X2, X4)) 64.55/17.47 U101_aa(X1, X2, X3, X4, pcH_out_aa(X2, X4)) -> U102_aa(X1, X2, X3, X4, pcA_in_gg(d(e(+(X3, X4))), const(1))) 64.55/17.47 U102_aa(X1, X2, X3, X4, pcA_out_gg(d(e(+(X3, X4))), const(1))) -> qcB_out_aa(e(+(X1, X2)), +(X3, X4)) 64.55/17.47 qcB_in_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U103_aa(X1, X2, X3, X4, pcH_in_aa(X1, X4)) 64.55/17.47 U103_aa(X1, X2, X3, X4, pcH_out_aa(X1, X4)) -> U104_aa(X1, X2, X3, X4, pcH_in_aa(X2, X3)) 64.55/17.47 U104_aa(X1, X2, X3, X4, pcH_out_aa(X2, X3)) -> U105_aa(X1, X2, X3, X4, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(1))) 64.55/17.47 U105_aa(X1, X2, X3, X4, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(1))) -> qcB_out_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.55/17.47 qcB_in_aa(d(X1), X2) -> U106_aa(X1, X2, pcJ_in_aa(X1, X3)) 64.55/17.47 U106_aa(X1, X2, pcJ_out_aa(X1, X3)) -> U107_aa(X1, X2, qcB_in_ga(e(X3), X2)) 64.55/17.47 U107_aa(X1, X2, qcB_out_ga(e(X3), X2)) -> qcB_out_aa(d(X1), X2) 64.55/17.47 U80_ag(X1, qcB_out_aa(X1, X2)) -> pcA_out_ag(d(d(X1)), const(1)) 64.55/17.47 pcA_in_ag(d(e(const(X1))), const(0)) -> pcA_out_ag(d(e(const(X1))), const(0)) 64.55/17.47 pcA_in_ag(d(d(X1)), const(0)) -> U81_ag(X1, qcC_in_aa(X1, X2)) 64.55/17.47 qcC_in_aa(e(t), const(1)) -> U112_aa(pcA_in_gg(d(e(const(1))), const(0))) 64.55/17.47 U112_aa(pcA_out_gg(d(e(const(1))), const(0))) -> qcC_out_aa(e(t), const(1)) 64.55/17.47 qcC_in_aa(e(const(X1)), const(0)) -> U113_aa(X1, pcA_in_gg(d(e(const(0))), const(0))) 64.55/17.47 U113_aa(X1, pcA_out_gg(d(e(const(0))), const(0))) -> qcC_out_aa(e(const(X1)), const(0)) 64.55/17.47 qcC_in_aa(e(+(X1, X2)), +(X3, X4)) -> U114_aa(X1, X2, X3, X4, pcH_in_aa(X1, X3)) 64.55/17.47 U114_aa(X1, X2, X3, X4, pcH_out_aa(X1, X3)) -> U115_aa(X1, X2, X3, X4, pcH_in_aa(X2, X4)) 64.55/17.47 U115_aa(X1, X2, X3, X4, pcH_out_aa(X2, X4)) -> U116_aa(X1, X2, X3, X4, pcA_in_gg(d(e(+(X3, X4))), const(0))) 64.55/17.47 U116_aa(X1, X2, X3, X4, pcA_out_gg(d(e(+(X3, X4))), const(0))) -> qcC_out_aa(e(+(X1, X2)), +(X3, X4)) 64.55/17.47 qcC_in_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U117_aa(X1, X2, X3, X4, pcH_in_aa(X1, X4)) 64.55/17.47 U117_aa(X1, X2, X3, X4, pcH_out_aa(X1, X4)) -> U118_aa(X1, X2, X3, X4, pcH_in_aa(X2, X3)) 64.55/17.47 U118_aa(X1, X2, X3, X4, pcH_out_aa(X2, X3)) -> U119_aa(X1, X2, X3, X4, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(0))) 64.55/17.47 U119_aa(X1, X2, X3, X4, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(0))) -> qcC_out_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.55/17.47 qcC_in_aa(d(X1), X2) -> U120_aa(X1, X2, pcJ_in_aa(X1, X3)) 64.55/17.47 U120_aa(X1, X2, pcJ_out_aa(X1, X3)) -> U121_aa(X1, X2, qcC_in_ga(e(X3), X2)) 64.55/17.47 U121_aa(X1, X2, qcC_out_ga(e(X3), X2)) -> qcC_out_aa(d(X1), X2) 64.55/17.47 U81_ag(X1, qcC_out_aa(X1, X2)) -> pcA_out_ag(d(d(X1)), const(0)) 64.55/17.47 pcA_in_ag(d(e(+(t, X1))), +(const(1), X2)) -> U82_ag(X1, X2, pcA_in_ag(d(e(X1)), X2)) 64.55/17.47 pcA_in_ag(d(e(+(const(X1), X2))), +(const(0), X3)) -> U83_ag(X1, X2, X3, pcA_in_ag(d(e(X2)), X3)) 64.55/17.47 pcA_in_ag(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) -> U84_ag(X1, X2, X3, X4, X5, X6, qcD_in_agagag(X1, X4, X2, X5, X3, X6)) 64.55/17.47 qcD_in_agagag(X1, X2, X3, X4, X5, X6) -> U122_agagag(X1, X2, X3, X4, X5, X6, pcA_in_ag(d(e(X1)), X2)) 64.55/17.47 pcA_in_ag(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) -> U85_ag(X1, X2, X3, X4, X5, X6, qcD_in_ggggag(X1, X5, X2, X4, X3, X6)) 64.55/17.47 qcD_in_ggggag(X1, X2, X3, X4, X5, X6) -> U122_ggggag(X1, X2, X3, X4, X5, X6, pcA_in_gg(d(e(X1)), X2)) 64.55/17.47 U122_ggggag(X1, X2, X3, X4, X5, X6, pcA_out_gg(d(e(X1)), X2)) -> U123_ggggag(X1, X2, X3, X4, X5, X6, qcE_in_ggag(X3, X4, X5, X6)) 64.55/17.47 qcE_in_ggag(X1, X2, X3, X4) -> U124_ggag(X1, X2, X3, X4, pcA_in_gg(d(e(X1)), X2)) 64.55/17.47 U124_ggag(X1, X2, X3, X4, pcA_out_gg(d(e(X1)), X2)) -> U125_ggag(X1, X2, X3, X4, pcA_in_ag(d(e(X3)), X4)) 64.55/17.47 pcA_in_ag(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) -> U86_ag(X1, X2, X3, X4, qcE_in_gggg(X1, X4, X2, X3)) 64.55/17.47 U86_ag(X1, X2, X3, X4, qcE_out_gggg(X1, X4, X2, X3)) -> pcA_out_ag(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) 64.55/17.47 pcA_in_ag(d(d(X1)), +(X2, X3)) -> U87_ag(X1, X2, X3, qcF_in_aagg(X1, X4, X2, X3)) 64.55/17.47 qcF_in_aagg(X1, X2, X3, X4) -> U126_aagg(X1, X2, X3, X4, pcJ_in_aa(X1, X2)) 64.55/17.47 U126_aagg(X1, X2, X3, X4, pcJ_out_aa(X1, X2)) -> U127_aagg(X1, X2, X3, X4, pcA_in_gg(d(e(X2)), +(X3, X4))) 64.55/17.47 U127_aagg(X1, X2, X3, X4, pcA_out_gg(d(e(X2)), +(X3, X4))) -> qcF_out_aagg(X1, X2, X3, X4) 64.55/17.47 U87_ag(X1, X2, X3, qcF_out_aagg(X1, X4, X2, X3)) -> pcA_out_ag(d(d(X1)), +(X2, X3)) 64.55/17.47 pcA_in_ag(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) -> U88_ag(X1, X2, pcA_in_gg(d(e(X1)), X2)) 64.55/17.47 U88_ag(X1, X2, pcA_out_gg(d(e(X1)), X2)) -> pcA_out_ag(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) 64.55/17.47 pcA_in_ag(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) -> U89_ag(X1, X2, X3, pcA_in_gg(d(e(X2)), X3)) 64.55/17.47 U89_ag(X1, X2, X3, pcA_out_gg(d(e(X2)), X3)) -> pcA_out_ag(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) 64.55/17.47 pcA_in_ag(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) -> U90_ag(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X5, X2, X6, X3, X4)) 64.55/17.47 U90_ag(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X5, X2, X6, X3, X4)) -> pcA_out_ag(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) 64.55/17.47 pcA_in_ag(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) -> U91_ag(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X6, X2, X5, X3, X4)) 64.55/17.47 U91_ag(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X6, X2, X5, X3, X4)) -> pcA_out_ag(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) 64.55/17.47 pcA_in_ag(d(d(X1)), +(*(X2, X3), *(X4, X5))) -> U92_ag(X1, X2, X3, X4, X5, qcF_in_aagg(X1, X6, *(X2, X3), *(X4, X5))) 64.55/17.47 U92_ag(X1, X2, X3, X4, X5, qcF_out_aagg(X1, X6, *(X2, X3), *(X4, X5))) -> pcA_out_ag(d(d(X1)), +(*(X2, X3), *(X4, X5))) 64.55/17.47 pcA_in_ag(d(d(X1)), X2) -> U93_ag(X1, X2, qcG_in_aag(X1, X3, X2)) 64.55/17.47 qcG_in_aag(e(t), const(1), X1) -> U128_aag(X1, pcA_in_gg(d(e(const(1))), X1)) 64.55/17.47 U128_aag(X1, pcA_out_gg(d(e(const(1))), X1)) -> qcG_out_aag(e(t), const(1), X1) 64.55/17.47 qcG_in_aag(e(const(X1)), const(0), X2) -> U129_aag(X1, X2, pcA_in_gg(d(e(const(0))), X2)) 64.55/17.47 U129_aag(X1, X2, pcA_out_gg(d(e(const(0))), X2)) -> qcG_out_aag(e(const(X1)), const(0), X2) 64.55/17.47 qcG_in_aag(e(+(X1, X2)), +(X3, X4), X5) -> U130_aag(X1, X2, X3, X4, X5, pcH_in_aa(X1, X3)) 64.55/17.47 U130_aag(X1, X2, X3, X4, X5, pcH_out_aa(X1, X3)) -> U131_aag(X1, X2, X3, X4, X5, pcH_in_aa(X2, X4)) 64.55/17.47 U131_aag(X1, X2, X3, X4, X5, pcH_out_aa(X2, X4)) -> U132_aag(X1, X2, X3, X4, X5, pcA_in_gg(d(e(+(X3, X4))), X5)) 64.55/17.47 U132_aag(X1, X2, X3, X4, X5, pcA_out_gg(d(e(+(X3, X4))), X5)) -> qcG_out_aag(e(+(X1, X2)), +(X3, X4), X5) 64.55/17.47 qcG_in_aag(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) -> U133_aag(X1, X2, X3, X4, X5, pcH_in_aa(X1, X4)) 64.55/17.47 U133_aag(X1, X2, X3, X4, X5, pcH_out_aa(X1, X4)) -> U134_aag(X1, X2, X3, X4, X5, pcH_in_aa(X2, X3)) 64.55/17.47 U134_aag(X1, X2, X3, X4, X5, pcH_out_aa(X2, X3)) -> U135_aag(X1, X2, X3, X4, X5, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), X5)) 64.55/17.47 U135_aag(X1, X2, X3, X4, X5, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), X5)) -> qcG_out_aag(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) 64.55/17.47 qcG_in_aag(d(X1), X2, X3) -> U136_aag(X1, X2, X3, pcJ_in_aa(X1, X4)) 64.55/17.47 U136_aag(X1, X2, X3, pcJ_out_aa(X1, X4)) -> U137_aag(X1, X2, X3, qcG_in_gag(e(X4), X2, X3)) 64.55/17.47 U137_aag(X1, X2, X3, qcG_out_gag(e(X4), X2, X3)) -> qcG_out_aag(d(X1), X2, X3) 64.55/17.47 U93_ag(X1, X2, qcG_out_aag(X1, X3, X2)) -> pcA_out_ag(d(d(X1)), X2) 64.55/17.47 U125_ggag(X1, X2, X3, X4, pcA_out_ag(d(e(X3)), X4)) -> qcE_out_ggag(X1, X2, X3, X4) 64.55/17.47 U123_ggggag(X1, X2, X3, X4, X5, X6, qcE_out_ggag(X3, X4, X5, X6)) -> qcD_out_ggggag(X1, X2, X3, X4, X5, X6) 64.55/17.47 U85_ag(X1, X2, X3, X4, X5, X6, qcD_out_ggggag(X1, X5, X2, X4, X3, X6)) -> pcA_out_ag(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) 64.55/17.47 U122_agagag(X1, X2, X3, X4, X5, X6, pcA_out_ag(d(e(X1)), X2)) -> U123_agagag(X1, X2, X3, X4, X5, X6, qcE_in_agag(X3, X4, X5, X6)) 64.55/17.47 qcE_in_agag(X1, X2, X3, X4) -> U124_agag(X1, X2, X3, X4, pcA_in_ag(d(e(X1)), X2)) 64.55/17.47 U124_agag(X1, X2, X3, X4, pcA_out_ag(d(e(X1)), X2)) -> U125_agag(X1, X2, X3, X4, pcA_in_ag(d(e(X3)), X4)) 64.55/17.47 U125_agag(X1, X2, X3, X4, pcA_out_ag(d(e(X3)), X4)) -> qcE_out_agag(X1, X2, X3, X4) 64.55/17.47 U123_agagag(X1, X2, X3, X4, X5, X6, qcE_out_agag(X3, X4, X5, X6)) -> qcD_out_agagag(X1, X2, X3, X4, X5, X6) 64.55/17.47 U84_ag(X1, X2, X3, X4, X5, X6, qcD_out_agagag(X1, X4, X2, X5, X3, X6)) -> pcA_out_ag(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) 64.55/17.47 U83_ag(X1, X2, X3, pcA_out_ag(d(e(X2)), X3)) -> pcA_out_ag(d(e(+(const(X1), X2))), +(const(0), X3)) 64.55/17.47 U82_ag(X1, X2, pcA_out_ag(d(e(X1)), X2)) -> pcA_out_ag(d(e(+(t, X1))), +(const(1), X2)) 64.55/17.47 64.55/17.47 The argument filtering Pi contains the following mapping: 64.55/17.47 const(x1) = const 64.55/17.47 64.55/17.47 1 = 1 64.55/17.47 64.55/17.47 d(x1) = d(x1) 64.55/17.47 64.55/17.47 e(x1) = e(x1) 64.55/17.47 64.55/17.47 t = t 64.55/17.47 64.55/17.47 0 = 0 64.55/17.47 64.55/17.47 +(x1, x2) = +(x1, x2) 64.55/17.47 64.55/17.47 *(x1, x2) = *(x1, x2) 64.55/17.47 64.55/17.47 pcA_in_gg(x1, x2) = pcA_in_gg(x1, x2) 64.55/17.47 64.55/17.47 pcA_out_gg(x1, x2) = pcA_out_gg(x1, x2) 64.55/17.47 64.55/17.47 U80_gg(x1, x2) = U80_gg(x1, x2) 64.55/17.47 64.55/17.47 qcB_in_ga(x1, x2) = qcB_in_ga(x1) 64.55/17.47 64.55/17.47 U98_ga(x1) = U98_ga(x1) 64.55/17.47 64.55/17.47 U81_gg(x1, x2) = U81_gg(x1, x2) 64.55/17.47 64.55/17.47 qcC_in_ga(x1, x2) = qcC_in_ga(x1) 64.55/17.47 64.55/17.47 U112_ga(x1) = U112_ga(x1) 64.55/17.47 64.55/17.47 U82_gg(x1, x2, x3) = U82_gg(x1, x2, x3) 64.55/17.47 64.55/17.47 U83_gg(x1, x2, x3, x4) = U83_gg(x2, x3, x4) 64.55/17.47 64.55/17.47 U84_gg(x1, x2, x3, x4, x5, x6, x7) = U84_gg(x1, x2, x3, x4, x5, x6, x7) 64.55/17.47 64.55/17.47 qcD_in_gggggg(x1, x2, x3, x4, x5, x6) = qcD_in_gggggg(x1, x2, x3, x4, x5, x6) 64.55/17.47 64.55/17.47 U122_gggggg(x1, x2, x3, x4, x5, x6, x7) = U122_gggggg(x1, x2, x3, x4, x5, x6, x7) 64.55/17.47 64.55/17.47 U85_gg(x1, x2, x3, x4, x5, x6, x7) = U85_gg(x1, x2, x3, x4, x5, x6, x7) 64.55/17.47 64.55/17.47 qcD_out_gggggg(x1, x2, x3, x4, x5, x6) = qcD_out_gggggg(x1, x2, x3, x4, x5, x6) 64.55/17.47 64.55/17.47 U86_gg(x1, x2, x3, x4, x5) = U86_gg(x1, x2, x3, x4, x5) 64.55/17.47 64.55/17.47 qcE_in_gggg(x1, x2, x3, x4) = qcE_in_gggg(x1, x2, x3, x4) 64.55/17.47 64.55/17.47 U124_gggg(x1, x2, x3, x4, x5) = U124_gggg(x1, x2, x3, x4, x5) 64.55/17.47 64.55/17.47 U87_gg(x1, x2, x3, x4) = U87_gg(x1, x2, x3, x4) 64.55/17.47 64.55/17.47 qcF_in_gagg(x1, x2, x3, x4) = qcF_in_gagg(x1, x3, x4) 64.55/17.47 64.55/17.47 U126_gagg(x1, x2, x3, x4, x5) = U126_gagg(x1, x3, x4, x5) 64.55/17.47 64.55/17.47 pcJ_in_ga(x1, x2) = pcJ_in_ga(x1) 64.55/17.47 64.55/17.47 pcJ_out_ga(x1, x2) = pcJ_out_ga(x1, x2) 64.55/17.47 64.55/17.47 U108_ga(x1, x2, x3, x4, x5) = U108_ga(x1, x2, x5) 64.55/17.47 64.55/17.47 qcI_in_gaga(x1, x2, x3, x4) = qcI_in_gaga(x1, x3) 64.55/17.47 64.55/17.47 U96_gaga(x1, x2, x3, x4, x5) = U96_gaga(x1, x3, x5) 64.55/17.47 64.55/17.47 pcH_in_ga(x1, x2) = pcH_in_ga(x1) 64.55/17.47 64.55/17.47 pcH_out_ga(x1, x2) = pcH_out_ga(x1, x2) 64.55/17.47 64.55/17.47 U94_ga(x1, x2, x3, x4, x5) = U94_ga(x1, x2, x5) 64.55/17.47 64.55/17.47 qcI_out_gaga(x1, x2, x3, x4) = qcI_out_gaga(x1, x2, x3, x4) 64.55/17.47 64.55/17.47 U95_ga(x1, x2, x3, x4, x5) = U95_ga(x1, x2, x5) 64.55/17.47 64.55/17.47 U97_gaga(x1, x2, x3, x4, x5) = U97_gaga(x1, x2, x3, x5) 64.55/17.47 64.55/17.47 U109_ga(x1, x2, x3, x4, x5) = U109_ga(x1, x2, x5) 64.55/17.47 64.55/17.47 U110_ga(x1, x2, x3) = U110_ga(x1, x3) 64.55/17.47 64.55/17.47 U111_ga(x1, x2, x3) = U111_ga(x1, x3) 64.55/17.47 64.55/17.47 U127_gagg(x1, x2, x3, x4, x5) = U127_gagg(x1, x2, x3, x4, x5) 64.55/17.47 64.55/17.47 U88_gg(x1, x2, x3) = U88_gg(x1, x2, x3) 64.55/17.47 64.55/17.47 U89_gg(x1, x2, x3, x4) = U89_gg(x2, x3, x4) 64.55/17.47 64.55/17.47 U90_gg(x1, x2, x3, x4, x5, x6, x7) = U90_gg(x1, x2, x3, x4, x5, x6, x7) 64.55/17.47 64.55/17.47 U91_gg(x1, x2, x3, x4, x5, x6, x7) = U91_gg(x1, x2, x3, x4, x5, x6, x7) 64.55/17.47 64.55/17.47 U92_gg(x1, x2, x3, x4, x5, x6) = U92_gg(x1, x2, x3, x4, x5, x6) 64.55/17.47 64.55/17.47 qcF_out_gagg(x1, x2, x3, x4) = qcF_out_gagg(x1, x2, x3, x4) 64.55/17.47 64.55/17.47 U93_gg(x1, x2, x3) = U93_gg(x1, x2, x3) 64.55/17.47 64.55/17.47 qcG_in_gag(x1, x2, x3) = qcG_in_gag(x1, x3) 64.55/17.47 64.55/17.47 U128_gag(x1, x2) = U128_gag(x1, x2) 64.55/17.47 64.55/17.47 qcG_out_gag(x1, x2, x3) = qcG_out_gag(x1, x2, x3) 64.55/17.47 64.55/17.47 U129_gag(x1, x2, x3) = U129_gag(x2, x3) 64.55/17.47 64.55/17.47 U130_gag(x1, x2, x3, x4, x5, x6) = U130_gag(x1, x2, x5, x6) 64.55/17.47 64.55/17.47 U131_gag(x1, x2, x3, x4, x5, x6) = U131_gag(x1, x2, x3, x5, x6) 64.55/17.47 64.55/17.47 U132_gag(x1, x2, x3, x4, x5, x6) = U132_gag(x1, x2, x3, x4, x5, x6) 64.55/17.47 64.55/17.47 U133_gag(x1, x2, x3, x4, x5, x6) = U133_gag(x1, x2, x5, x6) 64.55/17.47 64.55/17.47 U134_gag(x1, x2, x3, x4, x5, x6) = U134_gag(x1, x2, x4, x5, x6) 64.55/17.47 64.55/17.47 U135_gag(x1, x2, x3, x4, x5, x6) = U135_gag(x1, x2, x3, x4, x5, x6) 64.55/17.47 64.55/17.47 U136_gag(x1, x2, x3, x4) = U136_gag(x1, x3, x4) 64.55/17.47 64.55/17.47 U137_gag(x1, x2, x3, x4) = U137_gag(x1, x3, x4) 64.55/17.47 64.55/17.47 U125_gggg(x1, x2, x3, x4, x5) = U125_gggg(x1, x2, x3, x4, x5) 64.55/17.47 64.55/17.47 qcE_out_gggg(x1, x2, x3, x4) = qcE_out_gggg(x1, x2, x3, x4) 64.55/17.47 64.55/17.47 U123_gggggg(x1, x2, x3, x4, x5, x6, x7) = U123_gggggg(x1, x2, x3, x4, x5, x6, x7) 64.55/17.47 64.55/17.47 qcC_out_ga(x1, x2) = qcC_out_ga(x1, x2) 64.55/17.47 64.55/17.47 U113_ga(x1, x2) = U113_ga(x2) 64.55/17.47 64.55/17.47 U114_ga(x1, x2, x3, x4, x5) = U114_ga(x1, x2, x5) 64.55/17.47 64.55/17.47 U115_ga(x1, x2, x3, x4, x5) = U115_ga(x1, x2, x3, x5) 64.55/17.47 64.55/17.47 U116_ga(x1, x2, x3, x4, x5) = U116_ga(x1, x2, x3, x4, x5) 64.55/17.47 64.55/17.47 U117_ga(x1, x2, x3, x4, x5) = U117_ga(x1, x2, x5) 64.55/17.47 64.55/17.47 U118_ga(x1, x2, x3, x4, x5) = U118_ga(x1, x2, x4, x5) 64.55/17.47 64.55/17.47 U119_ga(x1, x2, x3, x4, x5) = U119_ga(x1, x2, x3, x4, x5) 64.55/17.47 64.55/17.47 U120_ga(x1, x2, x3) = U120_ga(x1, x3) 64.55/17.47 64.55/17.47 U121_ga(x1, x2, x3) = U121_ga(x1, x3) 64.55/17.47 64.55/17.47 qcB_out_ga(x1, x2) = qcB_out_ga(x1, x2) 64.55/17.47 64.55/17.47 U99_ga(x1, x2) = U99_ga(x2) 64.55/17.47 64.55/17.47 U100_ga(x1, x2, x3, x4, x5) = U100_ga(x1, x2, x5) 64.55/17.47 64.55/17.47 U101_ga(x1, x2, x3, x4, x5) = U101_ga(x1, x2, x3, x5) 64.55/17.47 64.55/17.47 U102_ga(x1, x2, x3, x4, x5) = U102_ga(x1, x2, x3, x4, x5) 64.55/17.47 64.55/17.47 U103_ga(x1, x2, x3, x4, x5) = U103_ga(x1, x2, x5) 64.55/17.47 64.55/17.47 U104_ga(x1, x2, x3, x4, x5) = U104_ga(x1, x2, x4, x5) 64.55/17.47 64.55/17.47 U105_ga(x1, x2, x3, x4, x5) = U105_ga(x1, x2, x3, x4, x5) 64.55/17.47 64.55/17.47 U106_ga(x1, x2, x3) = U106_ga(x1, x3) 64.55/17.47 64.55/17.47 U107_ga(x1, x2, x3) = U107_ga(x1, x3) 64.55/17.47 64.55/17.47 pcH_in_aa(x1, x2) = pcH_in_aa 64.55/17.47 64.55/17.47 pcH_out_aa(x1, x2) = pcH_out_aa(x1, x2) 64.55/17.47 64.55/17.47 U94_aa(x1, x2, x3, x4, x5) = U94_aa(x5) 64.55/17.47 64.55/17.47 qcI_in_aaaa(x1, x2, x3, x4) = qcI_in_aaaa 64.55/17.47 64.55/17.47 U96_aaaa(x1, x2, x3, x4, x5) = U96_aaaa(x5) 64.55/17.47 64.55/17.47 U95_aa(x1, x2, x3, x4, x5) = U95_aa(x5) 64.55/17.47 64.55/17.47 qcI_out_aaaa(x1, x2, x3, x4) = qcI_out_aaaa(x1, x2, x3, x4) 64.55/17.47 64.55/17.47 U97_aaaa(x1, x2, x3, x4, x5) = U97_aaaa(x1, x2, x5) 64.55/17.47 64.55/17.47 pcJ_in_aa(x1, x2) = pcJ_in_aa 64.55/17.47 64.55/17.47 pcJ_out_aa(x1, x2) = pcJ_out_aa(x1, x2) 64.55/17.47 64.55/17.47 U108_aa(x1, x2, x3, x4, x5) = U108_aa(x5) 64.55/17.47 64.55/17.47 U109_aa(x1, x2, x3, x4, x5) = U109_aa(x5) 64.55/17.47 64.55/17.47 U110_aa(x1, x2, x3) = U110_aa(x3) 64.55/17.47 64.55/17.47 U111_aa(x1, x2, x3) = U111_aa(x1, x3) 64.55/17.47 64.55/17.47 pcA_in_ag(x1, x2) = pcA_in_ag(x2) 64.55/17.47 64.55/17.47 pcA_out_ag(x1, x2) = pcA_out_ag(x1, x2) 64.55/17.47 64.55/17.47 U80_ag(x1, x2) = U80_ag(x2) 64.55/17.47 64.55/17.47 qcB_in_aa(x1, x2) = qcB_in_aa 64.55/17.47 64.55/17.47 U98_aa(x1) = U98_aa(x1) 64.55/17.47 64.55/17.47 qcB_out_aa(x1, x2) = qcB_out_aa(x1, x2) 64.55/17.47 64.55/17.47 U99_aa(x1, x2) = U99_aa(x2) 64.55/17.47 64.55/17.47 U100_aa(x1, x2, x3, x4, x5) = U100_aa(x5) 64.55/17.47 64.55/17.47 U101_aa(x1, x2, x3, x4, x5) = U101_aa(x1, x3, x5) 64.55/17.47 64.55/17.47 U102_aa(x1, x2, x3, x4, x5) = U102_aa(x1, x2, x3, x4, x5) 64.55/17.47 64.55/17.47 U103_aa(x1, x2, x3, x4, x5) = U103_aa(x5) 64.55/17.47 64.55/17.47 U104_aa(x1, x2, x3, x4, x5) = U104_aa(x1, x4, x5) 64.55/17.47 64.55/17.47 U105_aa(x1, x2, x3, x4, x5) = U105_aa(x1, x2, x3, x4, x5) 64.55/17.47 64.55/17.47 U106_aa(x1, x2, x3) = U106_aa(x3) 64.55/17.47 64.55/17.47 U107_aa(x1, x2, x3) = U107_aa(x1, x3) 64.55/17.47 64.55/17.47 U81_ag(x1, x2) = U81_ag(x2) 64.55/17.47 64.55/17.47 qcC_in_aa(x1, x2) = qcC_in_aa 64.55/17.47 64.55/17.47 U112_aa(x1) = U112_aa(x1) 64.55/17.47 64.55/17.47 qcC_out_aa(x1, x2) = qcC_out_aa(x1, x2) 64.55/17.47 64.55/17.47 U113_aa(x1, x2) = U113_aa(x2) 64.55/17.47 64.55/17.47 U114_aa(x1, x2, x3, x4, x5) = U114_aa(x5) 64.55/17.47 64.55/17.47 U115_aa(x1, x2, x3, x4, x5) = U115_aa(x1, x3, x5) 64.55/17.47 64.55/17.47 U116_aa(x1, x2, x3, x4, x5) = U116_aa(x1, x2, x3, x4, x5) 64.55/17.47 64.55/17.47 U117_aa(x1, x2, x3, x4, x5) = U117_aa(x5) 64.55/17.47 64.55/17.47 U118_aa(x1, x2, x3, x4, x5) = U118_aa(x1, x4, x5) 64.55/17.47 64.55/17.47 U119_aa(x1, x2, x3, x4, x5) = U119_aa(x1, x2, x3, x4, x5) 64.55/17.47 64.55/17.47 U120_aa(x1, x2, x3) = U120_aa(x3) 64.55/17.47 64.55/17.47 U121_aa(x1, x2, x3) = U121_aa(x1, x3) 64.55/17.47 64.55/17.47 U82_ag(x1, x2, x3) = U82_ag(x2, x3) 64.55/17.47 64.55/17.47 U83_ag(x1, x2, x3, x4) = U83_ag(x3, x4) 64.55/17.47 64.55/17.47 U84_ag(x1, x2, x3, x4, x5, x6, x7) = U84_ag(x4, x5, x6, x7) 64.55/17.47 64.55/17.47 qcD_in_agagag(x1, x2, x3, x4, x5, x6) = qcD_in_agagag(x2, x4, x6) 64.55/17.47 64.55/17.47 U122_agagag(x1, x2, x3, x4, x5, x6, x7) = U122_agagag(x2, x4, x6, x7) 64.55/17.47 64.55/17.47 U85_ag(x1, x2, x3, x4, x5, x6, x7) = U85_ag(x1, x2, x4, x5, x6, x7) 64.55/17.47 64.55/17.47 qcD_in_ggggag(x1, x2, x3, x4, x5, x6) = qcD_in_ggggag(x1, x2, x3, x4, x6) 64.55/17.47 64.55/17.47 U122_ggggag(x1, x2, x3, x4, x5, x6, x7) = U122_ggggag(x1, x2, x3, x4, x6, x7) 64.55/17.47 64.55/17.47 U123_ggggag(x1, x2, x3, x4, x5, x6, x7) = U123_ggggag(x1, x2, x3, x4, x6, x7) 64.55/17.47 64.55/17.47 qcE_in_ggag(x1, x2, x3, x4) = qcE_in_ggag(x1, x2, x4) 64.55/17.47 64.55/17.47 U124_ggag(x1, x2, x3, x4, x5) = U124_ggag(x1, x2, x4, x5) 64.55/17.47 64.55/17.47 U125_ggag(x1, x2, x3, x4, x5) = U125_ggag(x1, x2, x4, x5) 64.55/17.47 64.55/17.47 U86_ag(x1, x2, x3, x4, x5) = U86_ag(x1, x2, x3, x4, x5) 64.55/17.47 64.55/17.47 U87_ag(x1, x2, x3, x4) = U87_ag(x2, x3, x4) 64.55/17.47 64.55/17.47 qcF_in_aagg(x1, x2, x3, x4) = qcF_in_aagg(x3, x4) 64.55/17.47 64.55/17.47 U126_aagg(x1, x2, x3, x4, x5) = U126_aagg(x3, x4, x5) 64.55/17.47 64.55/17.47 U127_aagg(x1, x2, x3, x4, x5) = U127_aagg(x1, x2, x3, x4, x5) 64.55/17.47 64.55/17.47 qcF_out_aagg(x1, x2, x3, x4) = qcF_out_aagg(x1, x2, x3, x4) 64.55/17.47 64.55/17.47 U88_ag(x1, x2, x3) = U88_ag(x1, x2, x3) 64.55/17.47 64.55/17.47 U89_ag(x1, x2, x3, x4) = U89_ag(x2, x3, x4) 64.55/17.47 64.55/17.47 U90_ag(x1, x2, x3, x4, x5, x6, x7) = U90_ag(x1, x2, x3, x4, x5, x6, x7) 64.55/17.47 64.55/17.47 U91_ag(x1, x2, x3, x4, x5, x6, x7) = U91_ag(x1, x2, x3, x4, x5, x6, x7) 64.55/17.47 64.55/17.47 U92_ag(x1, x2, x3, x4, x5, x6) = U92_ag(x2, x3, x4, x5, x6) 64.55/17.47 64.55/17.47 U93_ag(x1, x2, x3) = U93_ag(x2, x3) 64.55/17.47 64.55/17.47 qcG_in_aag(x1, x2, x3) = qcG_in_aag(x3) 64.55/17.47 64.55/17.47 U128_aag(x1, x2) = U128_aag(x1, x2) 64.55/17.47 64.55/17.47 qcG_out_aag(x1, x2, x3) = qcG_out_aag(x1, x2, x3) 64.55/17.47 64.55/17.47 U129_aag(x1, x2, x3) = U129_aag(x2, x3) 64.55/17.47 64.55/17.47 U130_aag(x1, x2, x3, x4, x5, x6) = U130_aag(x5, x6) 64.55/17.47 64.55/17.47 U131_aag(x1, x2, x3, x4, x5, x6) = U131_aag(x1, x3, x5, x6) 64.55/17.47 64.55/17.47 U132_aag(x1, x2, x3, x4, x5, x6) = U132_aag(x1, x2, x3, x4, x5, x6) 64.55/17.47 64.55/17.47 U133_aag(x1, x2, x3, x4, x5, x6) = U133_aag(x5, x6) 64.55/17.47 64.55/17.47 U134_aag(x1, x2, x3, x4, x5, x6) = U134_aag(x1, x4, x5, x6) 64.55/17.47 64.55/17.47 U135_aag(x1, x2, x3, x4, x5, x6) = U135_aag(x1, x2, x3, x4, x5, x6) 64.55/17.47 64.55/17.47 U136_aag(x1, x2, x3, x4) = U136_aag(x3, x4) 64.55/17.47 64.55/17.47 U137_aag(x1, x2, x3, x4) = U137_aag(x1, x3, x4) 64.55/17.47 64.55/17.47 qcE_out_ggag(x1, x2, x3, x4) = qcE_out_ggag(x1, x2, x3, x4) 64.55/17.47 64.55/17.47 qcD_out_ggggag(x1, x2, x3, x4, x5, x6) = qcD_out_ggggag(x1, x2, x3, x4, x5, x6) 64.55/17.47 64.55/17.47 U123_agagag(x1, x2, x3, x4, x5, x6, x7) = U123_agagag(x1, x2, x4, x6, x7) 64.55/17.47 64.55/17.47 qcE_in_agag(x1, x2, x3, x4) = qcE_in_agag(x2, x4) 64.55/17.47 64.55/17.47 U124_agag(x1, x2, x3, x4, x5) = U124_agag(x2, x4, x5) 64.55/17.47 64.55/17.47 U125_agag(x1, x2, x3, x4, x5) = U125_agag(x1, x2, x4, x5) 64.55/17.47 64.55/17.47 qcE_out_agag(x1, x2, x3, x4) = qcE_out_agag(x1, x2, x3, x4) 64.55/17.47 64.55/17.47 qcD_out_agagag(x1, x2, x3, x4, x5, x6) = qcD_out_agagag(x1, x2, x3, x4, x5, x6) 64.55/17.47 64.55/17.47 PH_IN_AA(x1, x2) = PH_IN_AA 64.55/17.47 64.55/17.47 PI_IN_AAAA(x1, x2, x3, x4) = PI_IN_AAAA 64.55/17.47 64.55/17.47 U4_AAAA(x1, x2, x3, x4, x5) = U4_AAAA(x5) 64.55/17.47 64.55/17.47 64.55/17.47 We have to consider all (P,R,Pi)-chains 64.55/17.47 ---------------------------------------- 64.55/17.47 64.55/17.47 (122) UsableRulesProof (EQUIVALENT) 64.55/17.47 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 64.55/17.47 ---------------------------------------- 64.55/17.47 64.55/17.47 (123) 64.55/17.47 Obligation: 64.55/17.47 Pi DP problem: 64.55/17.47 The TRS P consists of the following rules: 64.55/17.47 64.55/17.47 PH_IN_AA(+(X1, X2), +(X3, X4)) -> PI_IN_AAAA(X1, X3, X2, X4) 64.55/17.47 PI_IN_AAAA(X1, X2, X3, X4) -> PH_IN_AA(X1, X2) 64.55/17.47 PH_IN_AA(*(X1, X2), +(*(X1, X3), *(X2, X4))) -> PI_IN_AAAA(X1, X4, X2, X3) 64.55/17.47 PI_IN_AAAA(X1, X2, X3, X4) -> U4_AAAA(X1, X2, X3, X4, pcH_in_aa(X1, X2)) 64.55/17.47 U4_AAAA(X1, X2, X3, X4, pcH_out_aa(X1, X2)) -> PH_IN_AA(X3, X4) 64.55/17.47 64.55/17.47 The TRS R consists of the following rules: 64.55/17.47 64.55/17.47 pcH_in_aa(t, const(1)) -> pcH_out_aa(t, const(1)) 64.55/17.47 pcH_in_aa(const(X1), const(0)) -> pcH_out_aa(const(X1), const(0)) 64.55/17.47 pcH_in_aa(+(X1, X2), +(X3, X4)) -> U94_aa(X1, X2, X3, X4, qcI_in_aaaa(X1, X3, X2, X4)) 64.55/17.47 pcH_in_aa(*(X1, X2), +(*(X1, X3), *(X2, X4))) -> U95_aa(X1, X2, X3, X4, qcI_in_aaaa(X1, X4, X2, X3)) 64.55/17.47 U94_aa(X1, X2, X3, X4, qcI_out_aaaa(X1, X3, X2, X4)) -> pcH_out_aa(+(X1, X2), +(X3, X4)) 64.55/17.47 U95_aa(X1, X2, X3, X4, qcI_out_aaaa(X1, X4, X2, X3)) -> pcH_out_aa(*(X1, X2), +(*(X1, X3), *(X2, X4))) 64.55/17.47 qcI_in_aaaa(X1, X2, X3, X4) -> U96_aaaa(X1, X2, X3, X4, pcH_in_aa(X1, X2)) 64.55/17.47 U96_aaaa(X1, X2, X3, X4, pcH_out_aa(X1, X2)) -> U97_aaaa(X1, X2, X3, X4, pcH_in_aa(X3, X4)) 64.55/17.47 U97_aaaa(X1, X2, X3, X4, pcH_out_aa(X3, X4)) -> qcI_out_aaaa(X1, X2, X3, X4) 64.55/17.47 64.55/17.47 The argument filtering Pi contains the following mapping: 64.55/17.47 const(x1) = const 64.55/17.47 64.55/17.47 1 = 1 64.55/17.47 64.55/17.47 t = t 64.55/17.47 64.55/17.47 0 = 0 64.55/17.47 64.55/17.47 +(x1, x2) = +(x1, x2) 64.55/17.47 64.55/17.47 *(x1, x2) = *(x1, x2) 64.55/17.47 64.55/17.47 pcH_in_aa(x1, x2) = pcH_in_aa 64.55/17.47 64.55/17.47 pcH_out_aa(x1, x2) = pcH_out_aa(x1, x2) 64.55/17.47 64.55/17.47 U94_aa(x1, x2, x3, x4, x5) = U94_aa(x5) 64.55/17.47 64.55/17.47 qcI_in_aaaa(x1, x2, x3, x4) = qcI_in_aaaa 64.55/17.47 64.55/17.47 U96_aaaa(x1, x2, x3, x4, x5) = U96_aaaa(x5) 64.55/17.47 64.55/17.47 U95_aa(x1, x2, x3, x4, x5) = U95_aa(x5) 64.55/17.47 64.55/17.47 qcI_out_aaaa(x1, x2, x3, x4) = qcI_out_aaaa(x1, x2, x3, x4) 64.55/17.47 64.55/17.47 U97_aaaa(x1, x2, x3, x4, x5) = U97_aaaa(x1, x2, x5) 64.55/17.47 64.55/17.47 PH_IN_AA(x1, x2) = PH_IN_AA 64.55/17.47 64.55/17.47 PI_IN_AAAA(x1, x2, x3, x4) = PI_IN_AAAA 64.55/17.47 64.55/17.47 U4_AAAA(x1, x2, x3, x4, x5) = U4_AAAA(x5) 64.55/17.47 64.55/17.47 64.55/17.47 We have to consider all (P,R,Pi)-chains 64.55/17.47 ---------------------------------------- 64.55/17.47 64.55/17.47 (124) PiDPToQDPProof (SOUND) 64.55/17.47 Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. 64.55/17.47 ---------------------------------------- 64.55/17.47 64.55/17.47 (125) 64.55/17.47 Obligation: 64.55/17.47 Q DP problem: 64.55/17.47 The TRS P consists of the following rules: 64.55/17.47 64.55/17.47 PH_IN_AA -> PI_IN_AAAA 64.55/17.47 PI_IN_AAAA -> PH_IN_AA 64.55/17.47 PI_IN_AAAA -> U4_AAAA(pcH_in_aa) 64.55/17.47 U4_AAAA(pcH_out_aa(X1, X2)) -> PH_IN_AA 64.55/17.47 64.55/17.47 The TRS R consists of the following rules: 64.55/17.47 64.55/17.47 pcH_in_aa -> pcH_out_aa(t, const) 64.55/17.47 pcH_in_aa -> pcH_out_aa(const, const) 64.55/17.47 pcH_in_aa -> U94_aa(qcI_in_aaaa) 64.55/17.47 pcH_in_aa -> U95_aa(qcI_in_aaaa) 64.55/17.47 U94_aa(qcI_out_aaaa(X1, X3, X2, X4)) -> pcH_out_aa(+(X1, X2), +(X3, X4)) 64.55/17.47 U95_aa(qcI_out_aaaa(X1, X4, X2, X3)) -> pcH_out_aa(*(X1, X2), +(*(X1, X3), *(X2, X4))) 64.55/17.47 qcI_in_aaaa -> U96_aaaa(pcH_in_aa) 64.55/17.47 U96_aaaa(pcH_out_aa(X1, X2)) -> U97_aaaa(X1, X2, pcH_in_aa) 64.55/17.47 U97_aaaa(X1, X2, pcH_out_aa(X3, X4)) -> qcI_out_aaaa(X1, X2, X3, X4) 64.55/17.47 64.55/17.47 The set Q consists of the following terms: 64.55/17.47 64.55/17.47 pcH_in_aa 64.55/17.47 U94_aa(x0) 64.55/17.47 U95_aa(x0) 64.55/17.47 qcI_in_aaaa 64.55/17.47 U96_aaaa(x0) 64.55/17.47 U97_aaaa(x0, x1, x2) 64.55/17.47 64.55/17.47 We have to consider all (P,Q,R)-chains. 64.55/17.47 ---------------------------------------- 64.55/17.47 64.55/17.47 (126) TransformationProof (SOUND) 64.55/17.47 By narrowing [LPAR04] the rule PI_IN_AAAA -> U4_AAAA(pcH_in_aa) at position [0] we obtained the following new rules [LPAR04]: 64.55/17.47 64.55/17.47 (PI_IN_AAAA -> U4_AAAA(pcH_out_aa(t, const)),PI_IN_AAAA -> U4_AAAA(pcH_out_aa(t, const))) 64.55/17.47 (PI_IN_AAAA -> U4_AAAA(pcH_out_aa(const, const)),PI_IN_AAAA -> U4_AAAA(pcH_out_aa(const, const))) 64.55/17.47 (PI_IN_AAAA -> U4_AAAA(U94_aa(qcI_in_aaaa)),PI_IN_AAAA -> U4_AAAA(U94_aa(qcI_in_aaaa))) 64.55/17.47 (PI_IN_AAAA -> U4_AAAA(U95_aa(qcI_in_aaaa)),PI_IN_AAAA -> U4_AAAA(U95_aa(qcI_in_aaaa))) 64.55/17.47 64.55/17.47 64.55/17.47 ---------------------------------------- 64.55/17.47 64.55/17.47 (127) 64.55/17.47 Obligation: 64.55/17.47 Q DP problem: 64.55/17.47 The TRS P consists of the following rules: 64.55/17.47 64.55/17.47 PH_IN_AA -> PI_IN_AAAA 64.55/17.47 PI_IN_AAAA -> PH_IN_AA 64.55/17.47 U4_AAAA(pcH_out_aa(X1, X2)) -> PH_IN_AA 64.55/17.47 PI_IN_AAAA -> U4_AAAA(pcH_out_aa(t, const)) 64.55/17.47 PI_IN_AAAA -> U4_AAAA(pcH_out_aa(const, const)) 64.55/17.47 PI_IN_AAAA -> U4_AAAA(U94_aa(qcI_in_aaaa)) 64.55/17.47 PI_IN_AAAA -> U4_AAAA(U95_aa(qcI_in_aaaa)) 64.55/17.47 64.55/17.47 The TRS R consists of the following rules: 64.55/17.47 64.55/17.47 pcH_in_aa -> pcH_out_aa(t, const) 64.55/17.47 pcH_in_aa -> pcH_out_aa(const, const) 64.55/17.47 pcH_in_aa -> U94_aa(qcI_in_aaaa) 64.55/17.47 pcH_in_aa -> U95_aa(qcI_in_aaaa) 64.55/17.47 U94_aa(qcI_out_aaaa(X1, X3, X2, X4)) -> pcH_out_aa(+(X1, X2), +(X3, X4)) 64.55/17.47 U95_aa(qcI_out_aaaa(X1, X4, X2, X3)) -> pcH_out_aa(*(X1, X2), +(*(X1, X3), *(X2, X4))) 64.55/17.47 qcI_in_aaaa -> U96_aaaa(pcH_in_aa) 64.55/17.47 U96_aaaa(pcH_out_aa(X1, X2)) -> U97_aaaa(X1, X2, pcH_in_aa) 64.55/17.47 U97_aaaa(X1, X2, pcH_out_aa(X3, X4)) -> qcI_out_aaaa(X1, X2, X3, X4) 64.55/17.47 64.55/17.47 The set Q consists of the following terms: 64.55/17.47 64.55/17.47 pcH_in_aa 64.55/17.47 U94_aa(x0) 64.55/17.47 U95_aa(x0) 64.55/17.47 qcI_in_aaaa 64.55/17.47 U96_aaaa(x0) 64.55/17.47 U97_aaaa(x0, x1, x2) 64.55/17.47 64.55/17.47 We have to consider all (P,Q,R)-chains. 64.55/17.47 ---------------------------------------- 64.55/17.47 64.55/17.47 (128) 64.55/17.47 Obligation: 64.55/17.47 Pi DP problem: 64.55/17.47 The TRS P consists of the following rules: 64.55/17.47 64.55/17.47 PI_IN_GAGA(X1, X2, X3, X4) -> PH_IN_GA(X1, X2) 64.55/17.47 PH_IN_GA(+(X1, X2), +(X3, X4)) -> PI_IN_GAGA(X1, X3, X2, X4) 64.55/17.47 PI_IN_GAGA(X1, X2, X3, X4) -> U4_GAGA(X1, X2, X3, X4, pcH_in_ga(X1, X2)) 64.55/17.47 U4_GAGA(X1, X2, X3, X4, pcH_out_ga(X1, X2)) -> PH_IN_GA(X3, X4) 64.55/17.47 PH_IN_GA(*(X1, X2), +(*(X1, X3), *(X2, X4))) -> PI_IN_GAGA(X1, X4, X2, X3) 64.55/17.47 64.55/17.47 The TRS R consists of the following rules: 64.55/17.47 64.55/17.47 pcA_in_gg(d(e(t)), const(1)) -> pcA_out_gg(d(e(t)), const(1)) 64.55/17.47 pcA_in_gg(d(d(X1)), const(1)) -> U80_gg(X1, qcB_in_ga(X1, X2)) 64.55/17.47 qcB_in_ga(e(t), const(1)) -> U98_ga(pcA_in_gg(d(e(const(1))), const(1))) 64.55/17.47 pcA_in_gg(d(e(const(X1))), const(0)) -> pcA_out_gg(d(e(const(X1))), const(0)) 64.55/17.47 pcA_in_gg(d(d(X1)), const(0)) -> U81_gg(X1, qcC_in_ga(X1, X2)) 64.55/17.47 qcC_in_ga(e(t), const(1)) -> U112_ga(pcA_in_gg(d(e(const(1))), const(0))) 64.55/17.47 pcA_in_gg(d(e(+(t, X1))), +(const(1), X2)) -> U82_gg(X1, X2, pcA_in_gg(d(e(X1)), X2)) 64.55/17.47 pcA_in_gg(d(e(+(const(X1), X2))), +(const(0), X3)) -> U83_gg(X1, X2, X3, pcA_in_gg(d(e(X2)), X3)) 64.55/17.47 pcA_in_gg(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) -> U84_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X4, X2, X5, X3, X6)) 64.55/17.47 qcD_in_gggggg(X1, X2, X3, X4, X5, X6) -> U122_gggggg(X1, X2, X3, X4, X5, X6, pcA_in_gg(d(e(X1)), X2)) 64.55/17.47 pcA_in_gg(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) -> U85_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X5, X2, X4, X3, X6)) 64.55/17.47 U85_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X5, X2, X4, X3, X6)) -> pcA_out_gg(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) 64.55/17.47 pcA_in_gg(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) -> U86_gg(X1, X2, X3, X4, qcE_in_gggg(X1, X4, X2, X3)) 64.55/17.47 qcE_in_gggg(X1, X2, X3, X4) -> U124_gggg(X1, X2, X3, X4, pcA_in_gg(d(e(X1)), X2)) 64.55/17.47 pcA_in_gg(d(d(X1)), +(X2, X3)) -> U87_gg(X1, X2, X3, qcF_in_gagg(X1, X4, X2, X3)) 64.55/17.47 qcF_in_gagg(X1, X2, X3, X4) -> U126_gagg(X1, X2, X3, X4, pcJ_in_ga(X1, X2)) 64.55/17.47 pcJ_in_ga(e(t), const(1)) -> pcJ_out_ga(e(t), const(1)) 64.55/17.47 pcJ_in_ga(e(const(X1)), const(0)) -> pcJ_out_ga(e(const(X1)), const(0)) 64.55/17.47 pcJ_in_ga(e(+(X1, X2)), +(X3, X4)) -> U108_ga(X1, X2, X3, X4, qcI_in_gaga(X1, X3, X2, X4)) 64.55/17.47 qcI_in_gaga(X1, X2, X3, X4) -> U96_gaga(X1, X2, X3, X4, pcH_in_ga(X1, X2)) 64.55/17.47 pcH_in_ga(t, const(1)) -> pcH_out_ga(t, const(1)) 64.55/17.47 pcH_in_ga(const(X1), const(0)) -> pcH_out_ga(const(X1), const(0)) 64.55/17.47 pcH_in_ga(+(X1, X2), +(X3, X4)) -> U94_ga(X1, X2, X3, X4, qcI_in_gaga(X1, X3, X2, X4)) 64.55/17.47 U94_ga(X1, X2, X3, X4, qcI_out_gaga(X1, X3, X2, X4)) -> pcH_out_ga(+(X1, X2), +(X3, X4)) 64.55/17.47 pcH_in_ga(*(X1, X2), +(*(X1, X3), *(X2, X4))) -> U95_ga(X1, X2, X3, X4, qcI_in_gaga(X1, X4, X2, X3)) 64.55/17.47 U95_ga(X1, X2, X3, X4, qcI_out_gaga(X1, X4, X2, X3)) -> pcH_out_ga(*(X1, X2), +(*(X1, X3), *(X2, X4))) 64.55/17.47 U96_gaga(X1, X2, X3, X4, pcH_out_ga(X1, X2)) -> U97_gaga(X1, X2, X3, X4, pcH_in_ga(X3, X4)) 64.55/17.47 U97_gaga(X1, X2, X3, X4, pcH_out_ga(X3, X4)) -> qcI_out_gaga(X1, X2, X3, X4) 64.55/17.47 U108_ga(X1, X2, X3, X4, qcI_out_gaga(X1, X3, X2, X4)) -> pcJ_out_ga(e(+(X1, X2)), +(X3, X4)) 64.55/17.47 pcJ_in_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U109_ga(X1, X2, X3, X4, qcI_in_gaga(X1, X4, X2, X3)) 64.55/17.47 U109_ga(X1, X2, X3, X4, qcI_out_gaga(X1, X4, X2, X3)) -> pcJ_out_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.55/17.47 pcJ_in_ga(d(X1), X2) -> U110_ga(X1, X2, pcJ_in_ga(X1, X3)) 64.55/17.47 U110_ga(X1, X2, pcJ_out_ga(X1, X3)) -> U111_ga(X1, X2, pcH_in_ga(X3, X2)) 64.55/17.47 U111_ga(X1, X2, pcH_out_ga(X3, X2)) -> pcJ_out_ga(d(X1), X2) 64.55/17.47 U126_gagg(X1, X2, X3, X4, pcJ_out_ga(X1, X2)) -> U127_gagg(X1, X2, X3, X4, pcA_in_gg(d(e(X2)), +(X3, X4))) 64.55/17.47 pcA_in_gg(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) -> U88_gg(X1, X2, pcA_in_gg(d(e(X1)), X2)) 64.55/17.47 pcA_in_gg(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) -> U89_gg(X1, X2, X3, pcA_in_gg(d(e(X2)), X3)) 64.55/17.47 pcA_in_gg(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) -> U90_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X5, X2, X6, X3, X4)) 64.55/17.47 U90_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X5, X2, X6, X3, X4)) -> pcA_out_gg(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) 64.55/17.47 pcA_in_gg(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) -> U91_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X6, X2, X5, X3, X4)) 64.55/17.47 U91_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X6, X2, X5, X3, X4)) -> pcA_out_gg(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) 64.55/17.47 pcA_in_gg(d(d(X1)), +(*(X2, X3), *(X4, X5))) -> U92_gg(X1, X2, X3, X4, X5, qcF_in_gagg(X1, X6, *(X2, X3), *(X4, X5))) 64.55/17.47 U92_gg(X1, X2, X3, X4, X5, qcF_out_gagg(X1, X6, *(X2, X3), *(X4, X5))) -> pcA_out_gg(d(d(X1)), +(*(X2, X3), *(X4, X5))) 64.55/17.47 pcA_in_gg(d(d(X1)), X2) -> U93_gg(X1, X2, qcG_in_gag(X1, X3, X2)) 64.55/17.47 qcG_in_gag(e(t), const(1), X1) -> U128_gag(X1, pcA_in_gg(d(e(const(1))), X1)) 64.55/17.47 U128_gag(X1, pcA_out_gg(d(e(const(1))), X1)) -> qcG_out_gag(e(t), const(1), X1) 64.55/17.47 qcG_in_gag(e(const(X1)), const(0), X2) -> U129_gag(X1, X2, pcA_in_gg(d(e(const(0))), X2)) 64.55/17.47 U129_gag(X1, X2, pcA_out_gg(d(e(const(0))), X2)) -> qcG_out_gag(e(const(X1)), const(0), X2) 64.55/17.47 qcG_in_gag(e(+(X1, X2)), +(X3, X4), X5) -> U130_gag(X1, X2, X3, X4, X5, pcH_in_ga(X1, X3)) 64.55/17.47 U130_gag(X1, X2, X3, X4, X5, pcH_out_ga(X1, X3)) -> U131_gag(X1, X2, X3, X4, X5, pcH_in_ga(X2, X4)) 64.55/17.47 U131_gag(X1, X2, X3, X4, X5, pcH_out_ga(X2, X4)) -> U132_gag(X1, X2, X3, X4, X5, pcA_in_gg(d(e(+(X3, X4))), X5)) 64.55/17.47 U132_gag(X1, X2, X3, X4, X5, pcA_out_gg(d(e(+(X3, X4))), X5)) -> qcG_out_gag(e(+(X1, X2)), +(X3, X4), X5) 64.55/17.47 qcG_in_gag(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) -> U133_gag(X1, X2, X3, X4, X5, pcH_in_ga(X1, X4)) 64.55/17.47 U133_gag(X1, X2, X3, X4, X5, pcH_out_ga(X1, X4)) -> U134_gag(X1, X2, X3, X4, X5, pcH_in_ga(X2, X3)) 64.55/17.47 U134_gag(X1, X2, X3, X4, X5, pcH_out_ga(X2, X3)) -> U135_gag(X1, X2, X3, X4, X5, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), X5)) 64.55/17.47 U135_gag(X1, X2, X3, X4, X5, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), X5)) -> qcG_out_gag(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) 64.55/17.47 qcG_in_gag(d(X1), X2, X3) -> U136_gag(X1, X2, X3, pcJ_in_ga(X1, X4)) 64.55/17.47 U136_gag(X1, X2, X3, pcJ_out_ga(X1, X4)) -> U137_gag(X1, X2, X3, qcG_in_gag(e(X4), X2, X3)) 64.55/17.47 U137_gag(X1, X2, X3, qcG_out_gag(e(X4), X2, X3)) -> qcG_out_gag(d(X1), X2, X3) 64.55/17.47 U93_gg(X1, X2, qcG_out_gag(X1, X3, X2)) -> pcA_out_gg(d(d(X1)), X2) 64.55/17.47 U89_gg(X1, X2, X3, pcA_out_gg(d(e(X2)), X3)) -> pcA_out_gg(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) 64.55/17.47 U88_gg(X1, X2, pcA_out_gg(d(e(X1)), X2)) -> pcA_out_gg(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) 64.55/17.47 U127_gagg(X1, X2, X3, X4, pcA_out_gg(d(e(X2)), +(X3, X4))) -> qcF_out_gagg(X1, X2, X3, X4) 64.55/17.47 U87_gg(X1, X2, X3, qcF_out_gagg(X1, X4, X2, X3)) -> pcA_out_gg(d(d(X1)), +(X2, X3)) 64.55/17.47 U124_gggg(X1, X2, X3, X4, pcA_out_gg(d(e(X1)), X2)) -> U125_gggg(X1, X2, X3, X4, pcA_in_gg(d(e(X3)), X4)) 64.55/17.47 U125_gggg(X1, X2, X3, X4, pcA_out_gg(d(e(X3)), X4)) -> qcE_out_gggg(X1, X2, X3, X4) 64.55/17.47 U86_gg(X1, X2, X3, X4, qcE_out_gggg(X1, X4, X2, X3)) -> pcA_out_gg(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) 64.55/17.47 U122_gggggg(X1, X2, X3, X4, X5, X6, pcA_out_gg(d(e(X1)), X2)) -> U123_gggggg(X1, X2, X3, X4, X5, X6, qcE_in_gggg(X3, X4, X5, X6)) 64.55/17.47 U123_gggggg(X1, X2, X3, X4, X5, X6, qcE_out_gggg(X3, X4, X5, X6)) -> qcD_out_gggggg(X1, X2, X3, X4, X5, X6) 64.55/17.47 U84_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X4, X2, X5, X3, X6)) -> pcA_out_gg(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) 64.55/17.47 U83_gg(X1, X2, X3, pcA_out_gg(d(e(X2)), X3)) -> pcA_out_gg(d(e(+(const(X1), X2))), +(const(0), X3)) 64.55/17.47 U82_gg(X1, X2, pcA_out_gg(d(e(X1)), X2)) -> pcA_out_gg(d(e(+(t, X1))), +(const(1), X2)) 64.55/17.47 U112_ga(pcA_out_gg(d(e(const(1))), const(0))) -> qcC_out_ga(e(t), const(1)) 64.55/17.47 qcC_in_ga(e(const(X1)), const(0)) -> U113_ga(X1, pcA_in_gg(d(e(const(0))), const(0))) 64.55/17.47 U113_ga(X1, pcA_out_gg(d(e(const(0))), const(0))) -> qcC_out_ga(e(const(X1)), const(0)) 64.55/17.47 qcC_in_ga(e(+(X1, X2)), +(X3, X4)) -> U114_ga(X1, X2, X3, X4, pcH_in_ga(X1, X3)) 64.55/17.47 U114_ga(X1, X2, X3, X4, pcH_out_ga(X1, X3)) -> U115_ga(X1, X2, X3, X4, pcH_in_ga(X2, X4)) 64.55/17.47 U115_ga(X1, X2, X3, X4, pcH_out_ga(X2, X4)) -> U116_ga(X1, X2, X3, X4, pcA_in_gg(d(e(+(X3, X4))), const(0))) 64.55/17.47 U116_ga(X1, X2, X3, X4, pcA_out_gg(d(e(+(X3, X4))), const(0))) -> qcC_out_ga(e(+(X1, X2)), +(X3, X4)) 64.55/17.47 qcC_in_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U117_ga(X1, X2, X3, X4, pcH_in_ga(X1, X4)) 64.55/17.47 U117_ga(X1, X2, X3, X4, pcH_out_ga(X1, X4)) -> U118_ga(X1, X2, X3, X4, pcH_in_ga(X2, X3)) 64.55/17.47 U118_ga(X1, X2, X3, X4, pcH_out_ga(X2, X3)) -> U119_ga(X1, X2, X3, X4, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(0))) 64.55/17.47 U119_ga(X1, X2, X3, X4, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(0))) -> qcC_out_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.55/17.47 qcC_in_ga(d(X1), X2) -> U120_ga(X1, X2, pcJ_in_ga(X1, X3)) 64.55/17.47 U120_ga(X1, X2, pcJ_out_ga(X1, X3)) -> U121_ga(X1, X2, qcC_in_ga(e(X3), X2)) 64.55/17.47 U121_ga(X1, X2, qcC_out_ga(e(X3), X2)) -> qcC_out_ga(d(X1), X2) 64.55/17.47 U81_gg(X1, qcC_out_ga(X1, X2)) -> pcA_out_gg(d(d(X1)), const(0)) 64.55/17.47 U98_ga(pcA_out_gg(d(e(const(1))), const(1))) -> qcB_out_ga(e(t), const(1)) 64.55/17.47 qcB_in_ga(e(const(X1)), const(0)) -> U99_ga(X1, pcA_in_gg(d(e(const(0))), const(1))) 64.55/17.47 U99_ga(X1, pcA_out_gg(d(e(const(0))), const(1))) -> qcB_out_ga(e(const(X1)), const(0)) 64.55/17.47 qcB_in_ga(e(+(X1, X2)), +(X3, X4)) -> U100_ga(X1, X2, X3, X4, pcH_in_ga(X1, X3)) 64.55/17.47 U100_ga(X1, X2, X3, X4, pcH_out_ga(X1, X3)) -> U101_ga(X1, X2, X3, X4, pcH_in_ga(X2, X4)) 64.55/17.47 U101_ga(X1, X2, X3, X4, pcH_out_ga(X2, X4)) -> U102_ga(X1, X2, X3, X4, pcA_in_gg(d(e(+(X3, X4))), const(1))) 64.55/17.47 U102_ga(X1, X2, X3, X4, pcA_out_gg(d(e(+(X3, X4))), const(1))) -> qcB_out_ga(e(+(X1, X2)), +(X3, X4)) 64.55/17.47 qcB_in_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U103_ga(X1, X2, X3, X4, pcH_in_ga(X1, X4)) 64.55/17.47 U103_ga(X1, X2, X3, X4, pcH_out_ga(X1, X4)) -> U104_ga(X1, X2, X3, X4, pcH_in_ga(X2, X3)) 64.55/17.47 U104_ga(X1, X2, X3, X4, pcH_out_ga(X2, X3)) -> U105_ga(X1, X2, X3, X4, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(1))) 64.55/17.47 U105_ga(X1, X2, X3, X4, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(1))) -> qcB_out_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.55/17.47 qcB_in_ga(d(X1), X2) -> U106_ga(X1, X2, pcJ_in_ga(X1, X3)) 64.55/17.47 U106_ga(X1, X2, pcJ_out_ga(X1, X3)) -> U107_ga(X1, X2, qcB_in_ga(e(X3), X2)) 64.55/17.47 U107_ga(X1, X2, qcB_out_ga(e(X3), X2)) -> qcB_out_ga(d(X1), X2) 64.55/17.47 U80_gg(X1, qcB_out_ga(X1, X2)) -> pcA_out_gg(d(d(X1)), const(1)) 64.55/17.47 pcH_in_aa(t, const(1)) -> pcH_out_aa(t, const(1)) 64.55/17.47 pcH_in_aa(const(X1), const(0)) -> pcH_out_aa(const(X1), const(0)) 64.55/17.47 pcH_in_aa(+(X1, X2), +(X3, X4)) -> U94_aa(X1, X2, X3, X4, qcI_in_aaaa(X1, X3, X2, X4)) 64.55/17.47 qcI_in_aaaa(X1, X2, X3, X4) -> U96_aaaa(X1, X2, X3, X4, pcH_in_aa(X1, X2)) 64.55/17.47 pcH_in_aa(*(X1, X2), +(*(X1, X3), *(X2, X4))) -> U95_aa(X1, X2, X3, X4, qcI_in_aaaa(X1, X4, X2, X3)) 64.55/17.47 U95_aa(X1, X2, X3, X4, qcI_out_aaaa(X1, X4, X2, X3)) -> pcH_out_aa(*(X1, X2), +(*(X1, X3), *(X2, X4))) 64.55/17.47 U96_aaaa(X1, X2, X3, X4, pcH_out_aa(X1, X2)) -> U97_aaaa(X1, X2, X3, X4, pcH_in_aa(X3, X4)) 64.55/17.47 U97_aaaa(X1, X2, X3, X4, pcH_out_aa(X3, X4)) -> qcI_out_aaaa(X1, X2, X3, X4) 64.55/17.47 U94_aa(X1, X2, X3, X4, qcI_out_aaaa(X1, X3, X2, X4)) -> pcH_out_aa(+(X1, X2), +(X3, X4)) 64.55/17.47 pcJ_in_aa(e(t), const(1)) -> pcJ_out_aa(e(t), const(1)) 64.55/17.47 pcJ_in_aa(e(const(X1)), const(0)) -> pcJ_out_aa(e(const(X1)), const(0)) 64.55/17.47 pcJ_in_aa(e(+(X1, X2)), +(X3, X4)) -> U108_aa(X1, X2, X3, X4, qcI_in_aaaa(X1, X3, X2, X4)) 64.55/17.47 U108_aa(X1, X2, X3, X4, qcI_out_aaaa(X1, X3, X2, X4)) -> pcJ_out_aa(e(+(X1, X2)), +(X3, X4)) 64.55/17.47 pcJ_in_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U109_aa(X1, X2, X3, X4, qcI_in_aaaa(X1, X4, X2, X3)) 64.55/17.47 U109_aa(X1, X2, X3, X4, qcI_out_aaaa(X1, X4, X2, X3)) -> pcJ_out_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.55/17.47 pcJ_in_aa(d(X1), X2) -> U110_aa(X1, X2, pcJ_in_aa(X1, X3)) 64.55/17.47 U110_aa(X1, X2, pcJ_out_aa(X1, X3)) -> U111_aa(X1, X2, pcH_in_ga(X3, X2)) 64.55/17.47 U111_aa(X1, X2, pcH_out_ga(X3, X2)) -> pcJ_out_aa(d(X1), X2) 64.55/17.47 pcA_in_ag(d(e(t)), const(1)) -> pcA_out_ag(d(e(t)), const(1)) 64.55/17.47 pcA_in_ag(d(d(X1)), const(1)) -> U80_ag(X1, qcB_in_aa(X1, X2)) 64.55/17.47 qcB_in_aa(e(t), const(1)) -> U98_aa(pcA_in_gg(d(e(const(1))), const(1))) 64.55/17.47 U98_aa(pcA_out_gg(d(e(const(1))), const(1))) -> qcB_out_aa(e(t), const(1)) 64.55/17.47 qcB_in_aa(e(const(X1)), const(0)) -> U99_aa(X1, pcA_in_gg(d(e(const(0))), const(1))) 64.55/17.47 U99_aa(X1, pcA_out_gg(d(e(const(0))), const(1))) -> qcB_out_aa(e(const(X1)), const(0)) 64.55/17.47 qcB_in_aa(e(+(X1, X2)), +(X3, X4)) -> U100_aa(X1, X2, X3, X4, pcH_in_aa(X1, X3)) 64.55/17.47 U100_aa(X1, X2, X3, X4, pcH_out_aa(X1, X3)) -> U101_aa(X1, X2, X3, X4, pcH_in_aa(X2, X4)) 64.55/17.47 U101_aa(X1, X2, X3, X4, pcH_out_aa(X2, X4)) -> U102_aa(X1, X2, X3, X4, pcA_in_gg(d(e(+(X3, X4))), const(1))) 64.55/17.47 U102_aa(X1, X2, X3, X4, pcA_out_gg(d(e(+(X3, X4))), const(1))) -> qcB_out_aa(e(+(X1, X2)), +(X3, X4)) 64.55/17.47 qcB_in_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U103_aa(X1, X2, X3, X4, pcH_in_aa(X1, X4)) 64.55/17.47 U103_aa(X1, X2, X3, X4, pcH_out_aa(X1, X4)) -> U104_aa(X1, X2, X3, X4, pcH_in_aa(X2, X3)) 64.55/17.47 U104_aa(X1, X2, X3, X4, pcH_out_aa(X2, X3)) -> U105_aa(X1, X2, X3, X4, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(1))) 64.55/17.47 U105_aa(X1, X2, X3, X4, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(1))) -> qcB_out_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.55/17.47 qcB_in_aa(d(X1), X2) -> U106_aa(X1, X2, pcJ_in_aa(X1, X3)) 64.55/17.47 U106_aa(X1, X2, pcJ_out_aa(X1, X3)) -> U107_aa(X1, X2, qcB_in_ga(e(X3), X2)) 64.55/17.47 U107_aa(X1, X2, qcB_out_ga(e(X3), X2)) -> qcB_out_aa(d(X1), X2) 64.55/17.47 U80_ag(X1, qcB_out_aa(X1, X2)) -> pcA_out_ag(d(d(X1)), const(1)) 64.55/17.47 pcA_in_ag(d(e(const(X1))), const(0)) -> pcA_out_ag(d(e(const(X1))), const(0)) 64.55/17.47 pcA_in_ag(d(d(X1)), const(0)) -> U81_ag(X1, qcC_in_aa(X1, X2)) 64.55/17.47 qcC_in_aa(e(t), const(1)) -> U112_aa(pcA_in_gg(d(e(const(1))), const(0))) 64.55/17.47 U112_aa(pcA_out_gg(d(e(const(1))), const(0))) -> qcC_out_aa(e(t), const(1)) 64.55/17.47 qcC_in_aa(e(const(X1)), const(0)) -> U113_aa(X1, pcA_in_gg(d(e(const(0))), const(0))) 64.55/17.47 U113_aa(X1, pcA_out_gg(d(e(const(0))), const(0))) -> qcC_out_aa(e(const(X1)), const(0)) 64.55/17.47 qcC_in_aa(e(+(X1, X2)), +(X3, X4)) -> U114_aa(X1, X2, X3, X4, pcH_in_aa(X1, X3)) 64.55/17.47 U114_aa(X1, X2, X3, X4, pcH_out_aa(X1, X3)) -> U115_aa(X1, X2, X3, X4, pcH_in_aa(X2, X4)) 64.55/17.47 U115_aa(X1, X2, X3, X4, pcH_out_aa(X2, X4)) -> U116_aa(X1, X2, X3, X4, pcA_in_gg(d(e(+(X3, X4))), const(0))) 64.55/17.47 U116_aa(X1, X2, X3, X4, pcA_out_gg(d(e(+(X3, X4))), const(0))) -> qcC_out_aa(e(+(X1, X2)), +(X3, X4)) 64.55/17.47 qcC_in_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U117_aa(X1, X2, X3, X4, pcH_in_aa(X1, X4)) 64.55/17.47 U117_aa(X1, X2, X3, X4, pcH_out_aa(X1, X4)) -> U118_aa(X1, X2, X3, X4, pcH_in_aa(X2, X3)) 64.55/17.47 U118_aa(X1, X2, X3, X4, pcH_out_aa(X2, X3)) -> U119_aa(X1, X2, X3, X4, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(0))) 64.55/17.47 U119_aa(X1, X2, X3, X4, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(0))) -> qcC_out_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.55/17.47 qcC_in_aa(d(X1), X2) -> U120_aa(X1, X2, pcJ_in_aa(X1, X3)) 64.55/17.47 U120_aa(X1, X2, pcJ_out_aa(X1, X3)) -> U121_aa(X1, X2, qcC_in_ga(e(X3), X2)) 64.55/17.47 U121_aa(X1, X2, qcC_out_ga(e(X3), X2)) -> qcC_out_aa(d(X1), X2) 64.55/17.47 U81_ag(X1, qcC_out_aa(X1, X2)) -> pcA_out_ag(d(d(X1)), const(0)) 64.55/17.47 pcA_in_ag(d(e(+(t, X1))), +(const(1), X2)) -> U82_ag(X1, X2, pcA_in_ag(d(e(X1)), X2)) 64.55/17.47 pcA_in_ag(d(e(+(const(X1), X2))), +(const(0), X3)) -> U83_ag(X1, X2, X3, pcA_in_ag(d(e(X2)), X3)) 64.55/17.47 pcA_in_ag(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) -> U84_ag(X1, X2, X3, X4, X5, X6, qcD_in_agagag(X1, X4, X2, X5, X3, X6)) 64.55/17.47 qcD_in_agagag(X1, X2, X3, X4, X5, X6) -> U122_agagag(X1, X2, X3, X4, X5, X6, pcA_in_ag(d(e(X1)), X2)) 64.55/17.47 pcA_in_ag(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) -> U85_ag(X1, X2, X3, X4, X5, X6, qcD_in_ggggag(X1, X5, X2, X4, X3, X6)) 64.55/17.47 qcD_in_ggggag(X1, X2, X3, X4, X5, X6) -> U122_ggggag(X1, X2, X3, X4, X5, X6, pcA_in_gg(d(e(X1)), X2)) 64.55/17.47 U122_ggggag(X1, X2, X3, X4, X5, X6, pcA_out_gg(d(e(X1)), X2)) -> U123_ggggag(X1, X2, X3, X4, X5, X6, qcE_in_ggag(X3, X4, X5, X6)) 64.55/17.47 qcE_in_ggag(X1, X2, X3, X4) -> U124_ggag(X1, X2, X3, X4, pcA_in_gg(d(e(X1)), X2)) 64.55/17.47 U124_ggag(X1, X2, X3, X4, pcA_out_gg(d(e(X1)), X2)) -> U125_ggag(X1, X2, X3, X4, pcA_in_ag(d(e(X3)), X4)) 64.55/17.47 pcA_in_ag(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) -> U86_ag(X1, X2, X3, X4, qcE_in_gggg(X1, X4, X2, X3)) 64.55/17.47 U86_ag(X1, X2, X3, X4, qcE_out_gggg(X1, X4, X2, X3)) -> pcA_out_ag(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) 64.55/17.47 pcA_in_ag(d(d(X1)), +(X2, X3)) -> U87_ag(X1, X2, X3, qcF_in_aagg(X1, X4, X2, X3)) 64.55/17.47 qcF_in_aagg(X1, X2, X3, X4) -> U126_aagg(X1, X2, X3, X4, pcJ_in_aa(X1, X2)) 64.55/17.47 U126_aagg(X1, X2, X3, X4, pcJ_out_aa(X1, X2)) -> U127_aagg(X1, X2, X3, X4, pcA_in_gg(d(e(X2)), +(X3, X4))) 64.55/17.47 U127_aagg(X1, X2, X3, X4, pcA_out_gg(d(e(X2)), +(X3, X4))) -> qcF_out_aagg(X1, X2, X3, X4) 64.55/17.47 U87_ag(X1, X2, X3, qcF_out_aagg(X1, X4, X2, X3)) -> pcA_out_ag(d(d(X1)), +(X2, X3)) 64.55/17.47 pcA_in_ag(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) -> U88_ag(X1, X2, pcA_in_gg(d(e(X1)), X2)) 64.55/17.47 U88_ag(X1, X2, pcA_out_gg(d(e(X1)), X2)) -> pcA_out_ag(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) 64.55/17.47 pcA_in_ag(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) -> U89_ag(X1, X2, X3, pcA_in_gg(d(e(X2)), X3)) 64.55/17.47 U89_ag(X1, X2, X3, pcA_out_gg(d(e(X2)), X3)) -> pcA_out_ag(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) 64.55/17.47 pcA_in_ag(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) -> U90_ag(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X5, X2, X6, X3, X4)) 64.55/17.47 U90_ag(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X5, X2, X6, X3, X4)) -> pcA_out_ag(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) 64.55/17.47 pcA_in_ag(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) -> U91_ag(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X6, X2, X5, X3, X4)) 64.55/17.47 U91_ag(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X6, X2, X5, X3, X4)) -> pcA_out_ag(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) 64.55/17.47 pcA_in_ag(d(d(X1)), +(*(X2, X3), *(X4, X5))) -> U92_ag(X1, X2, X3, X4, X5, qcF_in_aagg(X1, X6, *(X2, X3), *(X4, X5))) 64.55/17.47 U92_ag(X1, X2, X3, X4, X5, qcF_out_aagg(X1, X6, *(X2, X3), *(X4, X5))) -> pcA_out_ag(d(d(X1)), +(*(X2, X3), *(X4, X5))) 64.55/17.47 pcA_in_ag(d(d(X1)), X2) -> U93_ag(X1, X2, qcG_in_aag(X1, X3, X2)) 64.55/17.47 qcG_in_aag(e(t), const(1), X1) -> U128_aag(X1, pcA_in_gg(d(e(const(1))), X1)) 64.55/17.47 U128_aag(X1, pcA_out_gg(d(e(const(1))), X1)) -> qcG_out_aag(e(t), const(1), X1) 64.55/17.47 qcG_in_aag(e(const(X1)), const(0), X2) -> U129_aag(X1, X2, pcA_in_gg(d(e(const(0))), X2)) 64.55/17.47 U129_aag(X1, X2, pcA_out_gg(d(e(const(0))), X2)) -> qcG_out_aag(e(const(X1)), const(0), X2) 64.55/17.47 qcG_in_aag(e(+(X1, X2)), +(X3, X4), X5) -> U130_aag(X1, X2, X3, X4, X5, pcH_in_aa(X1, X3)) 64.55/17.47 U130_aag(X1, X2, X3, X4, X5, pcH_out_aa(X1, X3)) -> U131_aag(X1, X2, X3, X4, X5, pcH_in_aa(X2, X4)) 64.55/17.47 U131_aag(X1, X2, X3, X4, X5, pcH_out_aa(X2, X4)) -> U132_aag(X1, X2, X3, X4, X5, pcA_in_gg(d(e(+(X3, X4))), X5)) 64.55/17.47 U132_aag(X1, X2, X3, X4, X5, pcA_out_gg(d(e(+(X3, X4))), X5)) -> qcG_out_aag(e(+(X1, X2)), +(X3, X4), X5) 64.55/17.47 qcG_in_aag(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) -> U133_aag(X1, X2, X3, X4, X5, pcH_in_aa(X1, X4)) 64.55/17.47 U133_aag(X1, X2, X3, X4, X5, pcH_out_aa(X1, X4)) -> U134_aag(X1, X2, X3, X4, X5, pcH_in_aa(X2, X3)) 64.55/17.47 U134_aag(X1, X2, X3, X4, X5, pcH_out_aa(X2, X3)) -> U135_aag(X1, X2, X3, X4, X5, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), X5)) 64.55/17.47 U135_aag(X1, X2, X3, X4, X5, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), X5)) -> qcG_out_aag(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) 64.55/17.47 qcG_in_aag(d(X1), X2, X3) -> U136_aag(X1, X2, X3, pcJ_in_aa(X1, X4)) 64.55/17.47 U136_aag(X1, X2, X3, pcJ_out_aa(X1, X4)) -> U137_aag(X1, X2, X3, qcG_in_gag(e(X4), X2, X3)) 64.55/17.47 U137_aag(X1, X2, X3, qcG_out_gag(e(X4), X2, X3)) -> qcG_out_aag(d(X1), X2, X3) 64.55/17.47 U93_ag(X1, X2, qcG_out_aag(X1, X3, X2)) -> pcA_out_ag(d(d(X1)), X2) 64.55/17.47 U125_ggag(X1, X2, X3, X4, pcA_out_ag(d(e(X3)), X4)) -> qcE_out_ggag(X1, X2, X3, X4) 64.55/17.47 U123_ggggag(X1, X2, X3, X4, X5, X6, qcE_out_ggag(X3, X4, X5, X6)) -> qcD_out_ggggag(X1, X2, X3, X4, X5, X6) 64.55/17.47 U85_ag(X1, X2, X3, X4, X5, X6, qcD_out_ggggag(X1, X5, X2, X4, X3, X6)) -> pcA_out_ag(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) 64.55/17.47 U122_agagag(X1, X2, X3, X4, X5, X6, pcA_out_ag(d(e(X1)), X2)) -> U123_agagag(X1, X2, X3, X4, X5, X6, qcE_in_agag(X3, X4, X5, X6)) 64.55/17.47 qcE_in_agag(X1, X2, X3, X4) -> U124_agag(X1, X2, X3, X4, pcA_in_ag(d(e(X1)), X2)) 64.55/17.47 U124_agag(X1, X2, X3, X4, pcA_out_ag(d(e(X1)), X2)) -> U125_agag(X1, X2, X3, X4, pcA_in_ag(d(e(X3)), X4)) 64.55/17.47 U125_agag(X1, X2, X3, X4, pcA_out_ag(d(e(X3)), X4)) -> qcE_out_agag(X1, X2, X3, X4) 64.55/17.47 U123_agagag(X1, X2, X3, X4, X5, X6, qcE_out_agag(X3, X4, X5, X6)) -> qcD_out_agagag(X1, X2, X3, X4, X5, X6) 64.55/17.47 U84_ag(X1, X2, X3, X4, X5, X6, qcD_out_agagag(X1, X4, X2, X5, X3, X6)) -> pcA_out_ag(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) 64.55/17.47 U83_ag(X1, X2, X3, pcA_out_ag(d(e(X2)), X3)) -> pcA_out_ag(d(e(+(const(X1), X2))), +(const(0), X3)) 64.55/17.47 U82_ag(X1, X2, pcA_out_ag(d(e(X1)), X2)) -> pcA_out_ag(d(e(+(t, X1))), +(const(1), X2)) 64.55/17.47 64.55/17.47 The argument filtering Pi contains the following mapping: 64.55/17.47 const(x1) = const 64.55/17.47 64.55/17.47 1 = 1 64.55/17.47 64.55/17.47 d(x1) = d(x1) 64.55/17.47 64.55/17.47 e(x1) = e(x1) 64.55/17.47 64.55/17.47 t = t 64.55/17.47 64.55/17.47 0 = 0 64.55/17.47 64.55/17.47 +(x1, x2) = +(x1, x2) 64.55/17.47 64.55/17.47 *(x1, x2) = *(x1, x2) 64.55/17.47 64.55/17.47 pcA_in_gg(x1, x2) = pcA_in_gg(x1, x2) 64.55/17.47 64.55/17.47 pcA_out_gg(x1, x2) = pcA_out_gg(x1, x2) 64.55/17.47 64.55/17.47 U80_gg(x1, x2) = U80_gg(x1, x2) 64.55/17.47 64.55/17.47 qcB_in_ga(x1, x2) = qcB_in_ga(x1) 64.55/17.47 64.55/17.47 U98_ga(x1) = U98_ga(x1) 64.55/17.47 64.55/17.47 U81_gg(x1, x2) = U81_gg(x1, x2) 64.55/17.47 64.55/17.47 qcC_in_ga(x1, x2) = qcC_in_ga(x1) 64.55/17.47 64.55/17.47 U112_ga(x1) = U112_ga(x1) 64.55/17.47 64.55/17.47 U82_gg(x1, x2, x3) = U82_gg(x1, x2, x3) 64.55/17.47 64.55/17.47 U83_gg(x1, x2, x3, x4) = U83_gg(x2, x3, x4) 64.55/17.47 64.55/17.47 U84_gg(x1, x2, x3, x4, x5, x6, x7) = U84_gg(x1, x2, x3, x4, x5, x6, x7) 64.55/17.47 64.55/17.47 qcD_in_gggggg(x1, x2, x3, x4, x5, x6) = qcD_in_gggggg(x1, x2, x3, x4, x5, x6) 64.55/17.47 64.55/17.47 U122_gggggg(x1, x2, x3, x4, x5, x6, x7) = U122_gggggg(x1, x2, x3, x4, x5, x6, x7) 64.55/17.47 64.55/17.47 U85_gg(x1, x2, x3, x4, x5, x6, x7) = U85_gg(x1, x2, x3, x4, x5, x6, x7) 64.55/17.47 64.55/17.47 qcD_out_gggggg(x1, x2, x3, x4, x5, x6) = qcD_out_gggggg(x1, x2, x3, x4, x5, x6) 64.55/17.47 64.55/17.47 U86_gg(x1, x2, x3, x4, x5) = U86_gg(x1, x2, x3, x4, x5) 64.55/17.47 64.55/17.47 qcE_in_gggg(x1, x2, x3, x4) = qcE_in_gggg(x1, x2, x3, x4) 64.55/17.47 64.55/17.47 U124_gggg(x1, x2, x3, x4, x5) = U124_gggg(x1, x2, x3, x4, x5) 64.55/17.47 64.55/17.47 U87_gg(x1, x2, x3, x4) = U87_gg(x1, x2, x3, x4) 64.55/17.47 64.55/17.47 qcF_in_gagg(x1, x2, x3, x4) = qcF_in_gagg(x1, x3, x4) 64.55/17.47 64.55/17.47 U126_gagg(x1, x2, x3, x4, x5) = U126_gagg(x1, x3, x4, x5) 64.55/17.47 64.55/17.47 pcJ_in_ga(x1, x2) = pcJ_in_ga(x1) 64.55/17.47 64.55/17.47 pcJ_out_ga(x1, x2) = pcJ_out_ga(x1, x2) 64.55/17.47 64.55/17.47 U108_ga(x1, x2, x3, x4, x5) = U108_ga(x1, x2, x5) 64.55/17.47 64.55/17.47 qcI_in_gaga(x1, x2, x3, x4) = qcI_in_gaga(x1, x3) 64.55/17.47 64.55/17.47 U96_gaga(x1, x2, x3, x4, x5) = U96_gaga(x1, x3, x5) 64.55/17.47 64.55/17.47 pcH_in_ga(x1, x2) = pcH_in_ga(x1) 64.55/17.47 64.55/17.47 pcH_out_ga(x1, x2) = pcH_out_ga(x1, x2) 64.55/17.47 64.55/17.47 U94_ga(x1, x2, x3, x4, x5) = U94_ga(x1, x2, x5) 64.55/17.47 64.55/17.47 qcI_out_gaga(x1, x2, x3, x4) = qcI_out_gaga(x1, x2, x3, x4) 64.55/17.47 64.55/17.47 U95_ga(x1, x2, x3, x4, x5) = U95_ga(x1, x2, x5) 64.55/17.47 64.55/17.47 U97_gaga(x1, x2, x3, x4, x5) = U97_gaga(x1, x2, x3, x5) 64.55/17.47 64.55/17.47 U109_ga(x1, x2, x3, x4, x5) = U109_ga(x1, x2, x5) 64.55/17.47 64.55/17.47 U110_ga(x1, x2, x3) = U110_ga(x1, x3) 64.55/17.47 64.55/17.47 U111_ga(x1, x2, x3) = U111_ga(x1, x3) 64.55/17.47 64.55/17.47 U127_gagg(x1, x2, x3, x4, x5) = U127_gagg(x1, x2, x3, x4, x5) 64.55/17.47 64.55/17.47 U88_gg(x1, x2, x3) = U88_gg(x1, x2, x3) 64.55/17.47 64.55/17.47 U89_gg(x1, x2, x3, x4) = U89_gg(x2, x3, x4) 64.55/17.47 64.55/17.47 U90_gg(x1, x2, x3, x4, x5, x6, x7) = U90_gg(x1, x2, x3, x4, x5, x6, x7) 64.55/17.47 64.55/17.47 U91_gg(x1, x2, x3, x4, x5, x6, x7) = U91_gg(x1, x2, x3, x4, x5, x6, x7) 64.55/17.47 64.55/17.47 U92_gg(x1, x2, x3, x4, x5, x6) = U92_gg(x1, x2, x3, x4, x5, x6) 64.55/17.47 64.55/17.47 qcF_out_gagg(x1, x2, x3, x4) = qcF_out_gagg(x1, x2, x3, x4) 64.55/17.47 64.55/17.47 U93_gg(x1, x2, x3) = U93_gg(x1, x2, x3) 64.55/17.47 64.55/17.47 qcG_in_gag(x1, x2, x3) = qcG_in_gag(x1, x3) 64.55/17.47 64.55/17.47 U128_gag(x1, x2) = U128_gag(x1, x2) 64.55/17.47 64.55/17.47 qcG_out_gag(x1, x2, x3) = qcG_out_gag(x1, x2, x3) 64.55/17.47 64.55/17.47 U129_gag(x1, x2, x3) = U129_gag(x2, x3) 64.55/17.47 64.55/17.47 U130_gag(x1, x2, x3, x4, x5, x6) = U130_gag(x1, x2, x5, x6) 64.55/17.47 64.55/17.47 U131_gag(x1, x2, x3, x4, x5, x6) = U131_gag(x1, x2, x3, x5, x6) 64.55/17.47 64.55/17.47 U132_gag(x1, x2, x3, x4, x5, x6) = U132_gag(x1, x2, x3, x4, x5, x6) 64.55/17.47 64.55/17.47 U133_gag(x1, x2, x3, x4, x5, x6) = U133_gag(x1, x2, x5, x6) 64.55/17.47 64.55/17.47 U134_gag(x1, x2, x3, x4, x5, x6) = U134_gag(x1, x2, x4, x5, x6) 64.55/17.47 64.55/17.47 U135_gag(x1, x2, x3, x4, x5, x6) = U135_gag(x1, x2, x3, x4, x5, x6) 64.55/17.47 64.55/17.47 U136_gag(x1, x2, x3, x4) = U136_gag(x1, x3, x4) 64.55/17.47 64.55/17.47 U137_gag(x1, x2, x3, x4) = U137_gag(x1, x3, x4) 64.55/17.47 64.55/17.47 U125_gggg(x1, x2, x3, x4, x5) = U125_gggg(x1, x2, x3, x4, x5) 64.55/17.47 64.55/17.47 qcE_out_gggg(x1, x2, x3, x4) = qcE_out_gggg(x1, x2, x3, x4) 64.55/17.47 64.55/17.47 U123_gggggg(x1, x2, x3, x4, x5, x6, x7) = U123_gggggg(x1, x2, x3, x4, x5, x6, x7) 64.55/17.47 64.55/17.47 qcC_out_ga(x1, x2) = qcC_out_ga(x1, x2) 64.55/17.47 64.55/17.47 U113_ga(x1, x2) = U113_ga(x2) 64.55/17.47 64.55/17.47 U114_ga(x1, x2, x3, x4, x5) = U114_ga(x1, x2, x5) 64.55/17.47 64.55/17.47 U115_ga(x1, x2, x3, x4, x5) = U115_ga(x1, x2, x3, x5) 64.55/17.47 64.55/17.47 U116_ga(x1, x2, x3, x4, x5) = U116_ga(x1, x2, x3, x4, x5) 64.55/17.47 64.55/17.47 U117_ga(x1, x2, x3, x4, x5) = U117_ga(x1, x2, x5) 64.55/17.47 64.55/17.47 U118_ga(x1, x2, x3, x4, x5) = U118_ga(x1, x2, x4, x5) 64.55/17.47 64.55/17.47 U119_ga(x1, x2, x3, x4, x5) = U119_ga(x1, x2, x3, x4, x5) 64.55/17.47 64.55/17.47 U120_ga(x1, x2, x3) = U120_ga(x1, x3) 64.55/17.47 64.55/17.47 U121_ga(x1, x2, x3) = U121_ga(x1, x3) 64.55/17.47 64.55/17.47 qcB_out_ga(x1, x2) = qcB_out_ga(x1, x2) 64.55/17.47 64.55/17.47 U99_ga(x1, x2) = U99_ga(x2) 64.55/17.47 64.55/17.47 U100_ga(x1, x2, x3, x4, x5) = U100_ga(x1, x2, x5) 64.55/17.47 64.55/17.47 U101_ga(x1, x2, x3, x4, x5) = U101_ga(x1, x2, x3, x5) 64.55/17.47 64.55/17.47 U102_ga(x1, x2, x3, x4, x5) = U102_ga(x1, x2, x3, x4, x5) 64.55/17.47 64.55/17.47 U103_ga(x1, x2, x3, x4, x5) = U103_ga(x1, x2, x5) 64.55/17.47 64.55/17.47 U104_ga(x1, x2, x3, x4, x5) = U104_ga(x1, x2, x4, x5) 64.55/17.47 64.55/17.47 U105_ga(x1, x2, x3, x4, x5) = U105_ga(x1, x2, x3, x4, x5) 64.55/17.47 64.55/17.47 U106_ga(x1, x2, x3) = U106_ga(x1, x3) 64.55/17.47 64.55/17.47 U107_ga(x1, x2, x3) = U107_ga(x1, x3) 64.55/17.47 64.55/17.47 pcH_in_aa(x1, x2) = pcH_in_aa 64.55/17.47 64.55/17.47 pcH_out_aa(x1, x2) = pcH_out_aa(x1, x2) 64.55/17.47 64.55/17.47 U94_aa(x1, x2, x3, x4, x5) = U94_aa(x5) 64.55/17.47 64.55/17.47 qcI_in_aaaa(x1, x2, x3, x4) = qcI_in_aaaa 64.55/17.47 64.55/17.47 U96_aaaa(x1, x2, x3, x4, x5) = U96_aaaa(x5) 64.55/17.47 64.55/17.47 U95_aa(x1, x2, x3, x4, x5) = U95_aa(x5) 64.55/17.47 64.55/17.47 qcI_out_aaaa(x1, x2, x3, x4) = qcI_out_aaaa(x1, x2, x3, x4) 64.55/17.47 64.55/17.47 U97_aaaa(x1, x2, x3, x4, x5) = U97_aaaa(x1, x2, x5) 64.55/17.47 64.55/17.47 pcJ_in_aa(x1, x2) = pcJ_in_aa 64.55/17.47 64.55/17.47 pcJ_out_aa(x1, x2) = pcJ_out_aa(x1, x2) 64.55/17.47 64.55/17.47 U108_aa(x1, x2, x3, x4, x5) = U108_aa(x5) 64.55/17.47 64.55/17.47 U109_aa(x1, x2, x3, x4, x5) = U109_aa(x5) 64.55/17.47 64.55/17.47 U110_aa(x1, x2, x3) = U110_aa(x3) 64.55/17.47 64.55/17.47 U111_aa(x1, x2, x3) = U111_aa(x1, x3) 64.55/17.47 64.55/17.47 pcA_in_ag(x1, x2) = pcA_in_ag(x2) 64.55/17.47 64.55/17.47 pcA_out_ag(x1, x2) = pcA_out_ag(x1, x2) 64.55/17.47 64.55/17.47 U80_ag(x1, x2) = U80_ag(x2) 64.55/17.47 64.55/17.47 qcB_in_aa(x1, x2) = qcB_in_aa 64.55/17.47 64.55/17.47 U98_aa(x1) = U98_aa(x1) 64.55/17.47 64.55/17.47 qcB_out_aa(x1, x2) = qcB_out_aa(x1, x2) 64.55/17.47 64.55/17.47 U99_aa(x1, x2) = U99_aa(x2) 64.55/17.47 64.55/17.47 U100_aa(x1, x2, x3, x4, x5) = U100_aa(x5) 64.55/17.47 64.55/17.47 U101_aa(x1, x2, x3, x4, x5) = U101_aa(x1, x3, x5) 64.55/17.47 64.55/17.47 U102_aa(x1, x2, x3, x4, x5) = U102_aa(x1, x2, x3, x4, x5) 64.55/17.47 64.55/17.47 U103_aa(x1, x2, x3, x4, x5) = U103_aa(x5) 64.55/17.47 64.55/17.47 U104_aa(x1, x2, x3, x4, x5) = U104_aa(x1, x4, x5) 64.55/17.47 64.55/17.47 U105_aa(x1, x2, x3, x4, x5) = U105_aa(x1, x2, x3, x4, x5) 64.55/17.47 64.55/17.47 U106_aa(x1, x2, x3) = U106_aa(x3) 64.55/17.47 64.55/17.47 U107_aa(x1, x2, x3) = U107_aa(x1, x3) 64.55/17.47 64.55/17.47 U81_ag(x1, x2) = U81_ag(x2) 64.55/17.47 64.55/17.47 qcC_in_aa(x1, x2) = qcC_in_aa 64.55/17.47 64.55/17.47 U112_aa(x1) = U112_aa(x1) 64.55/17.47 64.55/17.47 qcC_out_aa(x1, x2) = qcC_out_aa(x1, x2) 64.55/17.47 64.55/17.47 U113_aa(x1, x2) = U113_aa(x2) 64.55/17.47 64.55/17.47 U114_aa(x1, x2, x3, x4, x5) = U114_aa(x5) 64.55/17.47 64.55/17.47 U115_aa(x1, x2, x3, x4, x5) = U115_aa(x1, x3, x5) 64.55/17.47 64.55/17.47 U116_aa(x1, x2, x3, x4, x5) = U116_aa(x1, x2, x3, x4, x5) 64.55/17.47 64.55/17.47 U117_aa(x1, x2, x3, x4, x5) = U117_aa(x5) 64.55/17.47 64.55/17.47 U118_aa(x1, x2, x3, x4, x5) = U118_aa(x1, x4, x5) 64.55/17.47 64.55/17.47 U119_aa(x1, x2, x3, x4, x5) = U119_aa(x1, x2, x3, x4, x5) 64.55/17.47 64.55/17.47 U120_aa(x1, x2, x3) = U120_aa(x3) 64.55/17.47 64.55/17.47 U121_aa(x1, x2, x3) = U121_aa(x1, x3) 64.55/17.47 64.55/17.47 U82_ag(x1, x2, x3) = U82_ag(x2, x3) 64.55/17.47 64.55/17.47 U83_ag(x1, x2, x3, x4) = U83_ag(x3, x4) 64.55/17.47 64.55/17.47 U84_ag(x1, x2, x3, x4, x5, x6, x7) = U84_ag(x4, x5, x6, x7) 64.55/17.47 64.55/17.47 qcD_in_agagag(x1, x2, x3, x4, x5, x6) = qcD_in_agagag(x2, x4, x6) 64.55/17.47 64.55/17.47 U122_agagag(x1, x2, x3, x4, x5, x6, x7) = U122_agagag(x2, x4, x6, x7) 64.55/17.47 64.55/17.47 U85_ag(x1, x2, x3, x4, x5, x6, x7) = U85_ag(x1, x2, x4, x5, x6, x7) 64.55/17.47 64.55/17.47 qcD_in_ggggag(x1, x2, x3, x4, x5, x6) = qcD_in_ggggag(x1, x2, x3, x4, x6) 64.55/17.47 64.55/17.47 U122_ggggag(x1, x2, x3, x4, x5, x6, x7) = U122_ggggag(x1, x2, x3, x4, x6, x7) 64.55/17.47 64.55/17.47 U123_ggggag(x1, x2, x3, x4, x5, x6, x7) = U123_ggggag(x1, x2, x3, x4, x6, x7) 64.55/17.47 64.55/17.47 qcE_in_ggag(x1, x2, x3, x4) = qcE_in_ggag(x1, x2, x4) 64.55/17.47 64.55/17.47 U124_ggag(x1, x2, x3, x4, x5) = U124_ggag(x1, x2, x4, x5) 64.55/17.47 64.55/17.47 U125_ggag(x1, x2, x3, x4, x5) = U125_ggag(x1, x2, x4, x5) 64.55/17.47 64.55/17.47 U86_ag(x1, x2, x3, x4, x5) = U86_ag(x1, x2, x3, x4, x5) 64.55/17.47 64.55/17.47 U87_ag(x1, x2, x3, x4) = U87_ag(x2, x3, x4) 64.55/17.47 64.55/17.47 qcF_in_aagg(x1, x2, x3, x4) = qcF_in_aagg(x3, x4) 64.55/17.47 64.55/17.47 U126_aagg(x1, x2, x3, x4, x5) = U126_aagg(x3, x4, x5) 64.55/17.47 64.55/17.47 U127_aagg(x1, x2, x3, x4, x5) = U127_aagg(x1, x2, x3, x4, x5) 64.55/17.47 64.55/17.47 qcF_out_aagg(x1, x2, x3, x4) = qcF_out_aagg(x1, x2, x3, x4) 64.55/17.47 64.55/17.47 U88_ag(x1, x2, x3) = U88_ag(x1, x2, x3) 64.55/17.47 64.55/17.47 U89_ag(x1, x2, x3, x4) = U89_ag(x2, x3, x4) 64.55/17.47 64.55/17.47 U90_ag(x1, x2, x3, x4, x5, x6, x7) = U90_ag(x1, x2, x3, x4, x5, x6, x7) 64.55/17.47 64.55/17.47 U91_ag(x1, x2, x3, x4, x5, x6, x7) = U91_ag(x1, x2, x3, x4, x5, x6, x7) 64.55/17.47 64.55/17.47 U92_ag(x1, x2, x3, x4, x5, x6) = U92_ag(x2, x3, x4, x5, x6) 64.55/17.47 64.55/17.47 U93_ag(x1, x2, x3) = U93_ag(x2, x3) 64.55/17.47 64.55/17.47 qcG_in_aag(x1, x2, x3) = qcG_in_aag(x3) 64.55/17.47 64.55/17.47 U128_aag(x1, x2) = U128_aag(x1, x2) 64.55/17.47 64.55/17.47 qcG_out_aag(x1, x2, x3) = qcG_out_aag(x1, x2, x3) 64.55/17.47 64.55/17.47 U129_aag(x1, x2, x3) = U129_aag(x2, x3) 64.55/17.47 64.55/17.47 U130_aag(x1, x2, x3, x4, x5, x6) = U130_aag(x5, x6) 64.55/17.47 64.55/17.47 U131_aag(x1, x2, x3, x4, x5, x6) = U131_aag(x1, x3, x5, x6) 64.55/17.47 64.55/17.47 U132_aag(x1, x2, x3, x4, x5, x6) = U132_aag(x1, x2, x3, x4, x5, x6) 64.55/17.47 64.55/17.47 U133_aag(x1, x2, x3, x4, x5, x6) = U133_aag(x5, x6) 64.55/17.47 64.55/17.47 U134_aag(x1, x2, x3, x4, x5, x6) = U134_aag(x1, x4, x5, x6) 64.55/17.47 64.55/17.47 U135_aag(x1, x2, x3, x4, x5, x6) = U135_aag(x1, x2, x3, x4, x5, x6) 64.55/17.47 64.55/17.47 U136_aag(x1, x2, x3, x4) = U136_aag(x3, x4) 64.55/17.47 64.55/17.47 U137_aag(x1, x2, x3, x4) = U137_aag(x1, x3, x4) 64.55/17.47 64.55/17.47 qcE_out_ggag(x1, x2, x3, x4) = qcE_out_ggag(x1, x2, x3, x4) 64.55/17.47 64.55/17.47 qcD_out_ggggag(x1, x2, x3, x4, x5, x6) = qcD_out_ggggag(x1, x2, x3, x4, x5, x6) 64.55/17.47 64.55/17.47 U123_agagag(x1, x2, x3, x4, x5, x6, x7) = U123_agagag(x1, x2, x4, x6, x7) 64.55/17.47 64.55/17.47 qcE_in_agag(x1, x2, x3, x4) = qcE_in_agag(x2, x4) 64.55/17.47 64.55/17.47 U124_agag(x1, x2, x3, x4, x5) = U124_agag(x2, x4, x5) 64.55/17.47 64.55/17.47 U125_agag(x1, x2, x3, x4, x5) = U125_agag(x1, x2, x4, x5) 64.55/17.47 64.55/17.47 qcE_out_agag(x1, x2, x3, x4) = qcE_out_agag(x1, x2, x3, x4) 64.55/17.47 64.55/17.47 qcD_out_agagag(x1, x2, x3, x4, x5, x6) = qcD_out_agagag(x1, x2, x3, x4, x5, x6) 64.55/17.47 64.55/17.47 PI_IN_GAGA(x1, x2, x3, x4) = PI_IN_GAGA(x1, x3) 64.55/17.47 64.55/17.47 PH_IN_GA(x1, x2) = PH_IN_GA(x1) 64.55/17.47 64.55/17.47 U4_GAGA(x1, x2, x3, x4, x5) = U4_GAGA(x1, x3, x5) 64.55/17.47 64.55/17.47 64.55/17.47 We have to consider all (P,R,Pi)-chains 64.55/17.47 ---------------------------------------- 64.55/17.47 64.55/17.47 (129) UsableRulesProof (EQUIVALENT) 64.55/17.47 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 64.55/17.47 ---------------------------------------- 64.55/17.47 64.55/17.47 (130) 64.55/17.47 Obligation: 64.55/17.47 Pi DP problem: 64.55/17.47 The TRS P consists of the following rules: 64.55/17.47 64.55/17.47 PI_IN_GAGA(X1, X2, X3, X4) -> PH_IN_GA(X1, X2) 64.55/17.47 PH_IN_GA(+(X1, X2), +(X3, X4)) -> PI_IN_GAGA(X1, X3, X2, X4) 64.55/17.47 PI_IN_GAGA(X1, X2, X3, X4) -> U4_GAGA(X1, X2, X3, X4, pcH_in_ga(X1, X2)) 64.55/17.47 U4_GAGA(X1, X2, X3, X4, pcH_out_ga(X1, X2)) -> PH_IN_GA(X3, X4) 64.55/17.47 PH_IN_GA(*(X1, X2), +(*(X1, X3), *(X2, X4))) -> PI_IN_GAGA(X1, X4, X2, X3) 64.55/17.47 64.55/17.47 The TRS R consists of the following rules: 64.55/17.47 64.55/17.47 pcH_in_ga(t, const(1)) -> pcH_out_ga(t, const(1)) 64.55/17.47 pcH_in_ga(const(X1), const(0)) -> pcH_out_ga(const(X1), const(0)) 64.55/17.47 pcH_in_ga(+(X1, X2), +(X3, X4)) -> U94_ga(X1, X2, X3, X4, qcI_in_gaga(X1, X3, X2, X4)) 64.55/17.47 pcH_in_ga(*(X1, X2), +(*(X1, X3), *(X2, X4))) -> U95_ga(X1, X2, X3, X4, qcI_in_gaga(X1, X4, X2, X3)) 64.55/17.47 U94_ga(X1, X2, X3, X4, qcI_out_gaga(X1, X3, X2, X4)) -> pcH_out_ga(+(X1, X2), +(X3, X4)) 64.55/17.47 U95_ga(X1, X2, X3, X4, qcI_out_gaga(X1, X4, X2, X3)) -> pcH_out_ga(*(X1, X2), +(*(X1, X3), *(X2, X4))) 64.55/17.47 qcI_in_gaga(X1, X2, X3, X4) -> U96_gaga(X1, X2, X3, X4, pcH_in_ga(X1, X2)) 64.55/17.47 U96_gaga(X1, X2, X3, X4, pcH_out_ga(X1, X2)) -> U97_gaga(X1, X2, X3, X4, pcH_in_ga(X3, X4)) 64.55/17.47 U97_gaga(X1, X2, X3, X4, pcH_out_ga(X3, X4)) -> qcI_out_gaga(X1, X2, X3, X4) 64.55/17.47 64.55/17.47 The argument filtering Pi contains the following mapping: 64.55/17.47 const(x1) = const 64.55/17.47 64.55/17.47 1 = 1 64.55/17.47 64.55/17.47 t = t 64.55/17.47 64.55/17.47 0 = 0 64.55/17.47 64.55/17.47 +(x1, x2) = +(x1, x2) 64.55/17.47 64.55/17.47 *(x1, x2) = *(x1, x2) 64.55/17.47 64.55/17.47 qcI_in_gaga(x1, x2, x3, x4) = qcI_in_gaga(x1, x3) 64.55/17.47 64.55/17.47 U96_gaga(x1, x2, x3, x4, x5) = U96_gaga(x1, x3, x5) 64.90/17.49 64.90/17.49 pcH_in_ga(x1, x2) = pcH_in_ga(x1) 64.90/17.49 64.90/17.49 pcH_out_ga(x1, x2) = pcH_out_ga(x1, x2) 64.90/17.49 64.90/17.49 U94_ga(x1, x2, x3, x4, x5) = U94_ga(x1, x2, x5) 64.90/17.49 64.90/17.49 qcI_out_gaga(x1, x2, x3, x4) = qcI_out_gaga(x1, x2, x3, x4) 64.90/17.49 64.90/17.49 U95_ga(x1, x2, x3, x4, x5) = U95_ga(x1, x2, x5) 64.90/17.49 64.90/17.49 U97_gaga(x1, x2, x3, x4, x5) = U97_gaga(x1, x2, x3, x5) 64.90/17.49 64.90/17.49 PI_IN_GAGA(x1, x2, x3, x4) = PI_IN_GAGA(x1, x3) 64.90/17.49 64.90/17.49 PH_IN_GA(x1, x2) = PH_IN_GA(x1) 64.90/17.49 64.90/17.49 U4_GAGA(x1, x2, x3, x4, x5) = U4_GAGA(x1, x3, x5) 64.90/17.49 64.90/17.49 64.90/17.49 We have to consider all (P,R,Pi)-chains 64.90/17.49 ---------------------------------------- 64.90/17.49 64.90/17.49 (131) 64.90/17.49 Obligation: 64.90/17.49 Pi DP problem: 64.90/17.49 The TRS P consists of the following rules: 64.90/17.49 64.90/17.49 PJ_IN_AA(d(X1), X2) -> PJ_IN_AA(X1, X3) 64.90/17.49 64.90/17.49 The TRS R consists of the following rules: 64.90/17.49 64.90/17.49 pcA_in_gg(d(e(t)), const(1)) -> pcA_out_gg(d(e(t)), const(1)) 64.90/17.49 pcA_in_gg(d(d(X1)), const(1)) -> U80_gg(X1, qcB_in_ga(X1, X2)) 64.90/17.49 qcB_in_ga(e(t), const(1)) -> U98_ga(pcA_in_gg(d(e(const(1))), const(1))) 64.90/17.49 pcA_in_gg(d(e(const(X1))), const(0)) -> pcA_out_gg(d(e(const(X1))), const(0)) 64.90/17.49 pcA_in_gg(d(d(X1)), const(0)) -> U81_gg(X1, qcC_in_ga(X1, X2)) 64.90/17.49 qcC_in_ga(e(t), const(1)) -> U112_ga(pcA_in_gg(d(e(const(1))), const(0))) 64.90/17.49 pcA_in_gg(d(e(+(t, X1))), +(const(1), X2)) -> U82_gg(X1, X2, pcA_in_gg(d(e(X1)), X2)) 64.90/17.49 pcA_in_gg(d(e(+(const(X1), X2))), +(const(0), X3)) -> U83_gg(X1, X2, X3, pcA_in_gg(d(e(X2)), X3)) 64.90/17.49 pcA_in_gg(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) -> U84_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X4, X2, X5, X3, X6)) 64.90/17.49 qcD_in_gggggg(X1, X2, X3, X4, X5, X6) -> U122_gggggg(X1, X2, X3, X4, X5, X6, pcA_in_gg(d(e(X1)), X2)) 64.90/17.49 pcA_in_gg(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) -> U85_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X5, X2, X4, X3, X6)) 64.90/17.49 U85_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X5, X2, X4, X3, X6)) -> pcA_out_gg(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) 64.90/17.49 pcA_in_gg(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) -> U86_gg(X1, X2, X3, X4, qcE_in_gggg(X1, X4, X2, X3)) 64.90/17.49 qcE_in_gggg(X1, X2, X3, X4) -> U124_gggg(X1, X2, X3, X4, pcA_in_gg(d(e(X1)), X2)) 64.90/17.49 pcA_in_gg(d(d(X1)), +(X2, X3)) -> U87_gg(X1, X2, X3, qcF_in_gagg(X1, X4, X2, X3)) 64.90/17.49 qcF_in_gagg(X1, X2, X3, X4) -> U126_gagg(X1, X2, X3, X4, pcJ_in_ga(X1, X2)) 64.90/17.49 pcJ_in_ga(e(t), const(1)) -> pcJ_out_ga(e(t), const(1)) 64.90/17.49 pcJ_in_ga(e(const(X1)), const(0)) -> pcJ_out_ga(e(const(X1)), const(0)) 64.90/17.49 pcJ_in_ga(e(+(X1, X2)), +(X3, X4)) -> U108_ga(X1, X2, X3, X4, qcI_in_gaga(X1, X3, X2, X4)) 64.90/17.49 qcI_in_gaga(X1, X2, X3, X4) -> U96_gaga(X1, X2, X3, X4, pcH_in_ga(X1, X2)) 64.90/17.49 pcH_in_ga(t, const(1)) -> pcH_out_ga(t, const(1)) 64.90/17.49 pcH_in_ga(const(X1), const(0)) -> pcH_out_ga(const(X1), const(0)) 64.90/17.49 pcH_in_ga(+(X1, X2), +(X3, X4)) -> U94_ga(X1, X2, X3, X4, qcI_in_gaga(X1, X3, X2, X4)) 64.90/17.49 U94_ga(X1, X2, X3, X4, qcI_out_gaga(X1, X3, X2, X4)) -> pcH_out_ga(+(X1, X2), +(X3, X4)) 64.90/17.49 pcH_in_ga(*(X1, X2), +(*(X1, X3), *(X2, X4))) -> U95_ga(X1, X2, X3, X4, qcI_in_gaga(X1, X4, X2, X3)) 64.90/17.49 U95_ga(X1, X2, X3, X4, qcI_out_gaga(X1, X4, X2, X3)) -> pcH_out_ga(*(X1, X2), +(*(X1, X3), *(X2, X4))) 64.90/17.49 U96_gaga(X1, X2, X3, X4, pcH_out_ga(X1, X2)) -> U97_gaga(X1, X2, X3, X4, pcH_in_ga(X3, X4)) 64.90/17.49 U97_gaga(X1, X2, X3, X4, pcH_out_ga(X3, X4)) -> qcI_out_gaga(X1, X2, X3, X4) 64.90/17.49 U108_ga(X1, X2, X3, X4, qcI_out_gaga(X1, X3, X2, X4)) -> pcJ_out_ga(e(+(X1, X2)), +(X3, X4)) 64.90/17.49 pcJ_in_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U109_ga(X1, X2, X3, X4, qcI_in_gaga(X1, X4, X2, X3)) 64.90/17.49 U109_ga(X1, X2, X3, X4, qcI_out_gaga(X1, X4, X2, X3)) -> pcJ_out_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.90/17.49 pcJ_in_ga(d(X1), X2) -> U110_ga(X1, X2, pcJ_in_ga(X1, X3)) 64.90/17.49 U110_ga(X1, X2, pcJ_out_ga(X1, X3)) -> U111_ga(X1, X2, pcH_in_ga(X3, X2)) 64.90/17.49 U111_ga(X1, X2, pcH_out_ga(X3, X2)) -> pcJ_out_ga(d(X1), X2) 64.90/17.49 U126_gagg(X1, X2, X3, X4, pcJ_out_ga(X1, X2)) -> U127_gagg(X1, X2, X3, X4, pcA_in_gg(d(e(X2)), +(X3, X4))) 64.90/17.49 pcA_in_gg(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) -> U88_gg(X1, X2, pcA_in_gg(d(e(X1)), X2)) 64.90/17.49 pcA_in_gg(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) -> U89_gg(X1, X2, X3, pcA_in_gg(d(e(X2)), X3)) 64.90/17.49 pcA_in_gg(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) -> U90_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X5, X2, X6, X3, X4)) 64.90/17.49 U90_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X5, X2, X6, X3, X4)) -> pcA_out_gg(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) 64.90/17.49 pcA_in_gg(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) -> U91_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X6, X2, X5, X3, X4)) 64.90/17.49 U91_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X6, X2, X5, X3, X4)) -> pcA_out_gg(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) 64.90/17.49 pcA_in_gg(d(d(X1)), +(*(X2, X3), *(X4, X5))) -> U92_gg(X1, X2, X3, X4, X5, qcF_in_gagg(X1, X6, *(X2, X3), *(X4, X5))) 64.90/17.49 U92_gg(X1, X2, X3, X4, X5, qcF_out_gagg(X1, X6, *(X2, X3), *(X4, X5))) -> pcA_out_gg(d(d(X1)), +(*(X2, X3), *(X4, X5))) 64.90/17.49 pcA_in_gg(d(d(X1)), X2) -> U93_gg(X1, X2, qcG_in_gag(X1, X3, X2)) 64.90/17.49 qcG_in_gag(e(t), const(1), X1) -> U128_gag(X1, pcA_in_gg(d(e(const(1))), X1)) 64.90/17.49 U128_gag(X1, pcA_out_gg(d(e(const(1))), X1)) -> qcG_out_gag(e(t), const(1), X1) 64.90/17.49 qcG_in_gag(e(const(X1)), const(0), X2) -> U129_gag(X1, X2, pcA_in_gg(d(e(const(0))), X2)) 64.90/17.49 U129_gag(X1, X2, pcA_out_gg(d(e(const(0))), X2)) -> qcG_out_gag(e(const(X1)), const(0), X2) 64.90/17.49 qcG_in_gag(e(+(X1, X2)), +(X3, X4), X5) -> U130_gag(X1, X2, X3, X4, X5, pcH_in_ga(X1, X3)) 64.90/17.49 U130_gag(X1, X2, X3, X4, X5, pcH_out_ga(X1, X3)) -> U131_gag(X1, X2, X3, X4, X5, pcH_in_ga(X2, X4)) 64.90/17.49 U131_gag(X1, X2, X3, X4, X5, pcH_out_ga(X2, X4)) -> U132_gag(X1, X2, X3, X4, X5, pcA_in_gg(d(e(+(X3, X4))), X5)) 64.90/17.49 U132_gag(X1, X2, X3, X4, X5, pcA_out_gg(d(e(+(X3, X4))), X5)) -> qcG_out_gag(e(+(X1, X2)), +(X3, X4), X5) 64.90/17.49 qcG_in_gag(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) -> U133_gag(X1, X2, X3, X4, X5, pcH_in_ga(X1, X4)) 64.90/17.49 U133_gag(X1, X2, X3, X4, X5, pcH_out_ga(X1, X4)) -> U134_gag(X1, X2, X3, X4, X5, pcH_in_ga(X2, X3)) 64.90/17.49 U134_gag(X1, X2, X3, X4, X5, pcH_out_ga(X2, X3)) -> U135_gag(X1, X2, X3, X4, X5, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), X5)) 64.90/17.49 U135_gag(X1, X2, X3, X4, X5, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), X5)) -> qcG_out_gag(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) 64.90/17.49 qcG_in_gag(d(X1), X2, X3) -> U136_gag(X1, X2, X3, pcJ_in_ga(X1, X4)) 64.90/17.49 U136_gag(X1, X2, X3, pcJ_out_ga(X1, X4)) -> U137_gag(X1, X2, X3, qcG_in_gag(e(X4), X2, X3)) 64.90/17.49 U137_gag(X1, X2, X3, qcG_out_gag(e(X4), X2, X3)) -> qcG_out_gag(d(X1), X2, X3) 64.90/17.49 U93_gg(X1, X2, qcG_out_gag(X1, X3, X2)) -> pcA_out_gg(d(d(X1)), X2) 64.90/17.49 U89_gg(X1, X2, X3, pcA_out_gg(d(e(X2)), X3)) -> pcA_out_gg(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) 64.90/17.49 U88_gg(X1, X2, pcA_out_gg(d(e(X1)), X2)) -> pcA_out_gg(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) 64.90/17.49 U127_gagg(X1, X2, X3, X4, pcA_out_gg(d(e(X2)), +(X3, X4))) -> qcF_out_gagg(X1, X2, X3, X4) 64.90/17.49 U87_gg(X1, X2, X3, qcF_out_gagg(X1, X4, X2, X3)) -> pcA_out_gg(d(d(X1)), +(X2, X3)) 64.90/17.49 U124_gggg(X1, X2, X3, X4, pcA_out_gg(d(e(X1)), X2)) -> U125_gggg(X1, X2, X3, X4, pcA_in_gg(d(e(X3)), X4)) 64.90/17.49 U125_gggg(X1, X2, X3, X4, pcA_out_gg(d(e(X3)), X4)) -> qcE_out_gggg(X1, X2, X3, X4) 64.90/17.49 U86_gg(X1, X2, X3, X4, qcE_out_gggg(X1, X4, X2, X3)) -> pcA_out_gg(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) 64.90/17.49 U122_gggggg(X1, X2, X3, X4, X5, X6, pcA_out_gg(d(e(X1)), X2)) -> U123_gggggg(X1, X2, X3, X4, X5, X6, qcE_in_gggg(X3, X4, X5, X6)) 64.90/17.49 U123_gggggg(X1, X2, X3, X4, X5, X6, qcE_out_gggg(X3, X4, X5, X6)) -> qcD_out_gggggg(X1, X2, X3, X4, X5, X6) 64.90/17.49 U84_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X4, X2, X5, X3, X6)) -> pcA_out_gg(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) 64.90/17.49 U83_gg(X1, X2, X3, pcA_out_gg(d(e(X2)), X3)) -> pcA_out_gg(d(e(+(const(X1), X2))), +(const(0), X3)) 64.90/17.49 U82_gg(X1, X2, pcA_out_gg(d(e(X1)), X2)) -> pcA_out_gg(d(e(+(t, X1))), +(const(1), X2)) 64.90/17.49 U112_ga(pcA_out_gg(d(e(const(1))), const(0))) -> qcC_out_ga(e(t), const(1)) 64.90/17.49 qcC_in_ga(e(const(X1)), const(0)) -> U113_ga(X1, pcA_in_gg(d(e(const(0))), const(0))) 64.90/17.49 U113_ga(X1, pcA_out_gg(d(e(const(0))), const(0))) -> qcC_out_ga(e(const(X1)), const(0)) 64.90/17.49 qcC_in_ga(e(+(X1, X2)), +(X3, X4)) -> U114_ga(X1, X2, X3, X4, pcH_in_ga(X1, X3)) 64.90/17.49 U114_ga(X1, X2, X3, X4, pcH_out_ga(X1, X3)) -> U115_ga(X1, X2, X3, X4, pcH_in_ga(X2, X4)) 64.90/17.49 U115_ga(X1, X2, X3, X4, pcH_out_ga(X2, X4)) -> U116_ga(X1, X2, X3, X4, pcA_in_gg(d(e(+(X3, X4))), const(0))) 64.90/17.49 U116_ga(X1, X2, X3, X4, pcA_out_gg(d(e(+(X3, X4))), const(0))) -> qcC_out_ga(e(+(X1, X2)), +(X3, X4)) 64.90/17.49 qcC_in_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U117_ga(X1, X2, X3, X4, pcH_in_ga(X1, X4)) 64.90/17.49 U117_ga(X1, X2, X3, X4, pcH_out_ga(X1, X4)) -> U118_ga(X1, X2, X3, X4, pcH_in_ga(X2, X3)) 64.90/17.49 U118_ga(X1, X2, X3, X4, pcH_out_ga(X2, X3)) -> U119_ga(X1, X2, X3, X4, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(0))) 64.90/17.49 U119_ga(X1, X2, X3, X4, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(0))) -> qcC_out_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.90/17.49 qcC_in_ga(d(X1), X2) -> U120_ga(X1, X2, pcJ_in_ga(X1, X3)) 64.90/17.49 U120_ga(X1, X2, pcJ_out_ga(X1, X3)) -> U121_ga(X1, X2, qcC_in_ga(e(X3), X2)) 64.90/17.49 U121_ga(X1, X2, qcC_out_ga(e(X3), X2)) -> qcC_out_ga(d(X1), X2) 64.90/17.49 U81_gg(X1, qcC_out_ga(X1, X2)) -> pcA_out_gg(d(d(X1)), const(0)) 64.90/17.49 U98_ga(pcA_out_gg(d(e(const(1))), const(1))) -> qcB_out_ga(e(t), const(1)) 64.90/17.49 qcB_in_ga(e(const(X1)), const(0)) -> U99_ga(X1, pcA_in_gg(d(e(const(0))), const(1))) 64.90/17.49 U99_ga(X1, pcA_out_gg(d(e(const(0))), const(1))) -> qcB_out_ga(e(const(X1)), const(0)) 64.90/17.49 qcB_in_ga(e(+(X1, X2)), +(X3, X4)) -> U100_ga(X1, X2, X3, X4, pcH_in_ga(X1, X3)) 64.90/17.49 U100_ga(X1, X2, X3, X4, pcH_out_ga(X1, X3)) -> U101_ga(X1, X2, X3, X4, pcH_in_ga(X2, X4)) 64.90/17.49 U101_ga(X1, X2, X3, X4, pcH_out_ga(X2, X4)) -> U102_ga(X1, X2, X3, X4, pcA_in_gg(d(e(+(X3, X4))), const(1))) 64.90/17.49 U102_ga(X1, X2, X3, X4, pcA_out_gg(d(e(+(X3, X4))), const(1))) -> qcB_out_ga(e(+(X1, X2)), +(X3, X4)) 64.90/17.49 qcB_in_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U103_ga(X1, X2, X3, X4, pcH_in_ga(X1, X4)) 64.90/17.49 U103_ga(X1, X2, X3, X4, pcH_out_ga(X1, X4)) -> U104_ga(X1, X2, X3, X4, pcH_in_ga(X2, X3)) 64.90/17.49 U104_ga(X1, X2, X3, X4, pcH_out_ga(X2, X3)) -> U105_ga(X1, X2, X3, X4, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(1))) 64.90/17.49 U105_ga(X1, X2, X3, X4, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(1))) -> qcB_out_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.90/17.49 qcB_in_ga(d(X1), X2) -> U106_ga(X1, X2, pcJ_in_ga(X1, X3)) 64.90/17.49 U106_ga(X1, X2, pcJ_out_ga(X1, X3)) -> U107_ga(X1, X2, qcB_in_ga(e(X3), X2)) 64.90/17.49 U107_ga(X1, X2, qcB_out_ga(e(X3), X2)) -> qcB_out_ga(d(X1), X2) 64.90/17.49 U80_gg(X1, qcB_out_ga(X1, X2)) -> pcA_out_gg(d(d(X1)), const(1)) 64.90/17.49 pcH_in_aa(t, const(1)) -> pcH_out_aa(t, const(1)) 64.90/17.49 pcH_in_aa(const(X1), const(0)) -> pcH_out_aa(const(X1), const(0)) 64.90/17.49 pcH_in_aa(+(X1, X2), +(X3, X4)) -> U94_aa(X1, X2, X3, X4, qcI_in_aaaa(X1, X3, X2, X4)) 64.90/17.49 qcI_in_aaaa(X1, X2, X3, X4) -> U96_aaaa(X1, X2, X3, X4, pcH_in_aa(X1, X2)) 64.90/17.49 pcH_in_aa(*(X1, X2), +(*(X1, X3), *(X2, X4))) -> U95_aa(X1, X2, X3, X4, qcI_in_aaaa(X1, X4, X2, X3)) 64.90/17.49 U95_aa(X1, X2, X3, X4, qcI_out_aaaa(X1, X4, X2, X3)) -> pcH_out_aa(*(X1, X2), +(*(X1, X3), *(X2, X4))) 64.90/17.49 U96_aaaa(X1, X2, X3, X4, pcH_out_aa(X1, X2)) -> U97_aaaa(X1, X2, X3, X4, pcH_in_aa(X3, X4)) 64.90/17.49 U97_aaaa(X1, X2, X3, X4, pcH_out_aa(X3, X4)) -> qcI_out_aaaa(X1, X2, X3, X4) 64.90/17.49 U94_aa(X1, X2, X3, X4, qcI_out_aaaa(X1, X3, X2, X4)) -> pcH_out_aa(+(X1, X2), +(X3, X4)) 64.90/17.49 pcJ_in_aa(e(t), const(1)) -> pcJ_out_aa(e(t), const(1)) 64.90/17.49 pcJ_in_aa(e(const(X1)), const(0)) -> pcJ_out_aa(e(const(X1)), const(0)) 64.90/17.49 pcJ_in_aa(e(+(X1, X2)), +(X3, X4)) -> U108_aa(X1, X2, X3, X4, qcI_in_aaaa(X1, X3, X2, X4)) 64.90/17.49 U108_aa(X1, X2, X3, X4, qcI_out_aaaa(X1, X3, X2, X4)) -> pcJ_out_aa(e(+(X1, X2)), +(X3, X4)) 64.90/17.49 pcJ_in_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U109_aa(X1, X2, X3, X4, qcI_in_aaaa(X1, X4, X2, X3)) 64.90/17.49 U109_aa(X1, X2, X3, X4, qcI_out_aaaa(X1, X4, X2, X3)) -> pcJ_out_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.90/17.49 pcJ_in_aa(d(X1), X2) -> U110_aa(X1, X2, pcJ_in_aa(X1, X3)) 64.90/17.49 U110_aa(X1, X2, pcJ_out_aa(X1, X3)) -> U111_aa(X1, X2, pcH_in_ga(X3, X2)) 64.90/17.49 U111_aa(X1, X2, pcH_out_ga(X3, X2)) -> pcJ_out_aa(d(X1), X2) 64.90/17.49 pcA_in_ag(d(e(t)), const(1)) -> pcA_out_ag(d(e(t)), const(1)) 64.90/17.49 pcA_in_ag(d(d(X1)), const(1)) -> U80_ag(X1, qcB_in_aa(X1, X2)) 64.90/17.49 qcB_in_aa(e(t), const(1)) -> U98_aa(pcA_in_gg(d(e(const(1))), const(1))) 64.90/17.49 U98_aa(pcA_out_gg(d(e(const(1))), const(1))) -> qcB_out_aa(e(t), const(1)) 64.90/17.49 qcB_in_aa(e(const(X1)), const(0)) -> U99_aa(X1, pcA_in_gg(d(e(const(0))), const(1))) 64.90/17.49 U99_aa(X1, pcA_out_gg(d(e(const(0))), const(1))) -> qcB_out_aa(e(const(X1)), const(0)) 64.90/17.49 qcB_in_aa(e(+(X1, X2)), +(X3, X4)) -> U100_aa(X1, X2, X3, X4, pcH_in_aa(X1, X3)) 64.90/17.49 U100_aa(X1, X2, X3, X4, pcH_out_aa(X1, X3)) -> U101_aa(X1, X2, X3, X4, pcH_in_aa(X2, X4)) 64.90/17.49 U101_aa(X1, X2, X3, X4, pcH_out_aa(X2, X4)) -> U102_aa(X1, X2, X3, X4, pcA_in_gg(d(e(+(X3, X4))), const(1))) 64.90/17.49 U102_aa(X1, X2, X3, X4, pcA_out_gg(d(e(+(X3, X4))), const(1))) -> qcB_out_aa(e(+(X1, X2)), +(X3, X4)) 64.90/17.49 qcB_in_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U103_aa(X1, X2, X3, X4, pcH_in_aa(X1, X4)) 64.90/17.49 U103_aa(X1, X2, X3, X4, pcH_out_aa(X1, X4)) -> U104_aa(X1, X2, X3, X4, pcH_in_aa(X2, X3)) 64.90/17.49 U104_aa(X1, X2, X3, X4, pcH_out_aa(X2, X3)) -> U105_aa(X1, X2, X3, X4, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(1))) 64.90/17.49 U105_aa(X1, X2, X3, X4, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(1))) -> qcB_out_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.90/17.49 qcB_in_aa(d(X1), X2) -> U106_aa(X1, X2, pcJ_in_aa(X1, X3)) 64.90/17.49 U106_aa(X1, X2, pcJ_out_aa(X1, X3)) -> U107_aa(X1, X2, qcB_in_ga(e(X3), X2)) 64.90/17.49 U107_aa(X1, X2, qcB_out_ga(e(X3), X2)) -> qcB_out_aa(d(X1), X2) 64.90/17.49 U80_ag(X1, qcB_out_aa(X1, X2)) -> pcA_out_ag(d(d(X1)), const(1)) 64.90/17.49 pcA_in_ag(d(e(const(X1))), const(0)) -> pcA_out_ag(d(e(const(X1))), const(0)) 64.90/17.49 pcA_in_ag(d(d(X1)), const(0)) -> U81_ag(X1, qcC_in_aa(X1, X2)) 64.90/17.49 qcC_in_aa(e(t), const(1)) -> U112_aa(pcA_in_gg(d(e(const(1))), const(0))) 64.90/17.49 U112_aa(pcA_out_gg(d(e(const(1))), const(0))) -> qcC_out_aa(e(t), const(1)) 64.90/17.49 qcC_in_aa(e(const(X1)), const(0)) -> U113_aa(X1, pcA_in_gg(d(e(const(0))), const(0))) 64.90/17.49 U113_aa(X1, pcA_out_gg(d(e(const(0))), const(0))) -> qcC_out_aa(e(const(X1)), const(0)) 64.90/17.49 qcC_in_aa(e(+(X1, X2)), +(X3, X4)) -> U114_aa(X1, X2, X3, X4, pcH_in_aa(X1, X3)) 64.90/17.49 U114_aa(X1, X2, X3, X4, pcH_out_aa(X1, X3)) -> U115_aa(X1, X2, X3, X4, pcH_in_aa(X2, X4)) 64.90/17.49 U115_aa(X1, X2, X3, X4, pcH_out_aa(X2, X4)) -> U116_aa(X1, X2, X3, X4, pcA_in_gg(d(e(+(X3, X4))), const(0))) 64.90/17.49 U116_aa(X1, X2, X3, X4, pcA_out_gg(d(e(+(X3, X4))), const(0))) -> qcC_out_aa(e(+(X1, X2)), +(X3, X4)) 64.90/17.49 qcC_in_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U117_aa(X1, X2, X3, X4, pcH_in_aa(X1, X4)) 64.90/17.49 U117_aa(X1, X2, X3, X4, pcH_out_aa(X1, X4)) -> U118_aa(X1, X2, X3, X4, pcH_in_aa(X2, X3)) 64.90/17.49 U118_aa(X1, X2, X3, X4, pcH_out_aa(X2, X3)) -> U119_aa(X1, X2, X3, X4, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(0))) 64.90/17.49 U119_aa(X1, X2, X3, X4, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(0))) -> qcC_out_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.90/17.49 qcC_in_aa(d(X1), X2) -> U120_aa(X1, X2, pcJ_in_aa(X1, X3)) 64.90/17.49 U120_aa(X1, X2, pcJ_out_aa(X1, X3)) -> U121_aa(X1, X2, qcC_in_ga(e(X3), X2)) 64.90/17.49 U121_aa(X1, X2, qcC_out_ga(e(X3), X2)) -> qcC_out_aa(d(X1), X2) 64.90/17.49 U81_ag(X1, qcC_out_aa(X1, X2)) -> pcA_out_ag(d(d(X1)), const(0)) 64.90/17.49 pcA_in_ag(d(e(+(t, X1))), +(const(1), X2)) -> U82_ag(X1, X2, pcA_in_ag(d(e(X1)), X2)) 64.90/17.49 pcA_in_ag(d(e(+(const(X1), X2))), +(const(0), X3)) -> U83_ag(X1, X2, X3, pcA_in_ag(d(e(X2)), X3)) 64.90/17.49 pcA_in_ag(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) -> U84_ag(X1, X2, X3, X4, X5, X6, qcD_in_agagag(X1, X4, X2, X5, X3, X6)) 64.90/17.49 qcD_in_agagag(X1, X2, X3, X4, X5, X6) -> U122_agagag(X1, X2, X3, X4, X5, X6, pcA_in_ag(d(e(X1)), X2)) 64.90/17.49 pcA_in_ag(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) -> U85_ag(X1, X2, X3, X4, X5, X6, qcD_in_ggggag(X1, X5, X2, X4, X3, X6)) 64.90/17.49 qcD_in_ggggag(X1, X2, X3, X4, X5, X6) -> U122_ggggag(X1, X2, X3, X4, X5, X6, pcA_in_gg(d(e(X1)), X2)) 64.90/17.49 U122_ggggag(X1, X2, X3, X4, X5, X6, pcA_out_gg(d(e(X1)), X2)) -> U123_ggggag(X1, X2, X3, X4, X5, X6, qcE_in_ggag(X3, X4, X5, X6)) 64.90/17.49 qcE_in_ggag(X1, X2, X3, X4) -> U124_ggag(X1, X2, X3, X4, pcA_in_gg(d(e(X1)), X2)) 64.90/17.49 U124_ggag(X1, X2, X3, X4, pcA_out_gg(d(e(X1)), X2)) -> U125_ggag(X1, X2, X3, X4, pcA_in_ag(d(e(X3)), X4)) 64.90/17.49 pcA_in_ag(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) -> U86_ag(X1, X2, X3, X4, qcE_in_gggg(X1, X4, X2, X3)) 64.90/17.49 U86_ag(X1, X2, X3, X4, qcE_out_gggg(X1, X4, X2, X3)) -> pcA_out_ag(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) 64.90/17.49 pcA_in_ag(d(d(X1)), +(X2, X3)) -> U87_ag(X1, X2, X3, qcF_in_aagg(X1, X4, X2, X3)) 64.90/17.49 qcF_in_aagg(X1, X2, X3, X4) -> U126_aagg(X1, X2, X3, X4, pcJ_in_aa(X1, X2)) 64.90/17.49 U126_aagg(X1, X2, X3, X4, pcJ_out_aa(X1, X2)) -> U127_aagg(X1, X2, X3, X4, pcA_in_gg(d(e(X2)), +(X3, X4))) 64.90/17.49 U127_aagg(X1, X2, X3, X4, pcA_out_gg(d(e(X2)), +(X3, X4))) -> qcF_out_aagg(X1, X2, X3, X4) 64.90/17.49 U87_ag(X1, X2, X3, qcF_out_aagg(X1, X4, X2, X3)) -> pcA_out_ag(d(d(X1)), +(X2, X3)) 64.90/17.49 pcA_in_ag(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) -> U88_ag(X1, X2, pcA_in_gg(d(e(X1)), X2)) 64.90/17.49 U88_ag(X1, X2, pcA_out_gg(d(e(X1)), X2)) -> pcA_out_ag(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) 64.90/17.49 pcA_in_ag(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) -> U89_ag(X1, X2, X3, pcA_in_gg(d(e(X2)), X3)) 64.90/17.49 U89_ag(X1, X2, X3, pcA_out_gg(d(e(X2)), X3)) -> pcA_out_ag(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) 64.90/17.49 pcA_in_ag(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) -> U90_ag(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X5, X2, X6, X3, X4)) 64.90/17.49 U90_ag(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X5, X2, X6, X3, X4)) -> pcA_out_ag(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) 64.90/17.49 pcA_in_ag(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) -> U91_ag(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X6, X2, X5, X3, X4)) 64.90/17.49 U91_ag(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X6, X2, X5, X3, X4)) -> pcA_out_ag(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) 64.90/17.49 pcA_in_ag(d(d(X1)), +(*(X2, X3), *(X4, X5))) -> U92_ag(X1, X2, X3, X4, X5, qcF_in_aagg(X1, X6, *(X2, X3), *(X4, X5))) 64.90/17.49 U92_ag(X1, X2, X3, X4, X5, qcF_out_aagg(X1, X6, *(X2, X3), *(X4, X5))) -> pcA_out_ag(d(d(X1)), +(*(X2, X3), *(X4, X5))) 64.90/17.49 pcA_in_ag(d(d(X1)), X2) -> U93_ag(X1, X2, qcG_in_aag(X1, X3, X2)) 64.90/17.49 qcG_in_aag(e(t), const(1), X1) -> U128_aag(X1, pcA_in_gg(d(e(const(1))), X1)) 64.90/17.49 U128_aag(X1, pcA_out_gg(d(e(const(1))), X1)) -> qcG_out_aag(e(t), const(1), X1) 64.90/17.49 qcG_in_aag(e(const(X1)), const(0), X2) -> U129_aag(X1, X2, pcA_in_gg(d(e(const(0))), X2)) 64.90/17.49 U129_aag(X1, X2, pcA_out_gg(d(e(const(0))), X2)) -> qcG_out_aag(e(const(X1)), const(0), X2) 64.90/17.49 qcG_in_aag(e(+(X1, X2)), +(X3, X4), X5) -> U130_aag(X1, X2, X3, X4, X5, pcH_in_aa(X1, X3)) 64.90/17.49 U130_aag(X1, X2, X3, X4, X5, pcH_out_aa(X1, X3)) -> U131_aag(X1, X2, X3, X4, X5, pcH_in_aa(X2, X4)) 64.90/17.49 U131_aag(X1, X2, X3, X4, X5, pcH_out_aa(X2, X4)) -> U132_aag(X1, X2, X3, X4, X5, pcA_in_gg(d(e(+(X3, X4))), X5)) 64.90/17.49 U132_aag(X1, X2, X3, X4, X5, pcA_out_gg(d(e(+(X3, X4))), X5)) -> qcG_out_aag(e(+(X1, X2)), +(X3, X4), X5) 64.90/17.49 qcG_in_aag(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) -> U133_aag(X1, X2, X3, X4, X5, pcH_in_aa(X1, X4)) 64.90/17.49 U133_aag(X1, X2, X3, X4, X5, pcH_out_aa(X1, X4)) -> U134_aag(X1, X2, X3, X4, X5, pcH_in_aa(X2, X3)) 64.90/17.49 U134_aag(X1, X2, X3, X4, X5, pcH_out_aa(X2, X3)) -> U135_aag(X1, X2, X3, X4, X5, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), X5)) 64.90/17.49 U135_aag(X1, X2, X3, X4, X5, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), X5)) -> qcG_out_aag(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) 64.90/17.49 qcG_in_aag(d(X1), X2, X3) -> U136_aag(X1, X2, X3, pcJ_in_aa(X1, X4)) 64.90/17.49 U136_aag(X1, X2, X3, pcJ_out_aa(X1, X4)) -> U137_aag(X1, X2, X3, qcG_in_gag(e(X4), X2, X3)) 64.90/17.49 U137_aag(X1, X2, X3, qcG_out_gag(e(X4), X2, X3)) -> qcG_out_aag(d(X1), X2, X3) 64.90/17.49 U93_ag(X1, X2, qcG_out_aag(X1, X3, X2)) -> pcA_out_ag(d(d(X1)), X2) 64.90/17.49 U125_ggag(X1, X2, X3, X4, pcA_out_ag(d(e(X3)), X4)) -> qcE_out_ggag(X1, X2, X3, X4) 64.90/17.49 U123_ggggag(X1, X2, X3, X4, X5, X6, qcE_out_ggag(X3, X4, X5, X6)) -> qcD_out_ggggag(X1, X2, X3, X4, X5, X6) 64.90/17.49 U85_ag(X1, X2, X3, X4, X5, X6, qcD_out_ggggag(X1, X5, X2, X4, X3, X6)) -> pcA_out_ag(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) 64.90/17.49 U122_agagag(X1, X2, X3, X4, X5, X6, pcA_out_ag(d(e(X1)), X2)) -> U123_agagag(X1, X2, X3, X4, X5, X6, qcE_in_agag(X3, X4, X5, X6)) 64.90/17.49 qcE_in_agag(X1, X2, X3, X4) -> U124_agag(X1, X2, X3, X4, pcA_in_ag(d(e(X1)), X2)) 64.90/17.49 U124_agag(X1, X2, X3, X4, pcA_out_ag(d(e(X1)), X2)) -> U125_agag(X1, X2, X3, X4, pcA_in_ag(d(e(X3)), X4)) 64.90/17.49 U125_agag(X1, X2, X3, X4, pcA_out_ag(d(e(X3)), X4)) -> qcE_out_agag(X1, X2, X3, X4) 64.90/17.49 U123_agagag(X1, X2, X3, X4, X5, X6, qcE_out_agag(X3, X4, X5, X6)) -> qcD_out_agagag(X1, X2, X3, X4, X5, X6) 64.90/17.49 U84_ag(X1, X2, X3, X4, X5, X6, qcD_out_agagag(X1, X4, X2, X5, X3, X6)) -> pcA_out_ag(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) 64.90/17.49 U83_ag(X1, X2, X3, pcA_out_ag(d(e(X2)), X3)) -> pcA_out_ag(d(e(+(const(X1), X2))), +(const(0), X3)) 64.90/17.49 U82_ag(X1, X2, pcA_out_ag(d(e(X1)), X2)) -> pcA_out_ag(d(e(+(t, X1))), +(const(1), X2)) 64.90/17.49 64.90/17.49 The argument filtering Pi contains the following mapping: 64.90/17.49 const(x1) = const 64.90/17.49 64.90/17.49 1 = 1 64.90/17.49 64.90/17.49 d(x1) = d(x1) 64.90/17.49 64.90/17.49 e(x1) = e(x1) 64.90/17.49 64.90/17.49 t = t 64.90/17.49 64.90/17.49 0 = 0 64.90/17.49 64.90/17.49 +(x1, x2) = +(x1, x2) 64.90/17.49 64.90/17.49 *(x1, x2) = *(x1, x2) 64.90/17.49 64.90/17.49 pcA_in_gg(x1, x2) = pcA_in_gg(x1, x2) 64.90/17.49 64.90/17.49 pcA_out_gg(x1, x2) = pcA_out_gg(x1, x2) 64.90/17.49 64.90/17.49 U80_gg(x1, x2) = U80_gg(x1, x2) 64.90/17.49 64.90/17.49 qcB_in_ga(x1, x2) = qcB_in_ga(x1) 64.90/17.49 64.90/17.49 U98_ga(x1) = U98_ga(x1) 64.90/17.49 64.90/17.49 U81_gg(x1, x2) = U81_gg(x1, x2) 64.90/17.49 64.90/17.49 qcC_in_ga(x1, x2) = qcC_in_ga(x1) 64.90/17.49 64.90/17.49 U112_ga(x1) = U112_ga(x1) 64.90/17.49 64.90/17.49 U82_gg(x1, x2, x3) = U82_gg(x1, x2, x3) 64.90/17.49 64.90/17.49 U83_gg(x1, x2, x3, x4) = U83_gg(x2, x3, x4) 64.90/17.49 64.90/17.49 U84_gg(x1, x2, x3, x4, x5, x6, x7) = U84_gg(x1, x2, x3, x4, x5, x6, x7) 64.90/17.49 64.90/17.49 qcD_in_gggggg(x1, x2, x3, x4, x5, x6) = qcD_in_gggggg(x1, x2, x3, x4, x5, x6) 64.90/17.49 64.90/17.49 U122_gggggg(x1, x2, x3, x4, x5, x6, x7) = U122_gggggg(x1, x2, x3, x4, x5, x6, x7) 64.90/17.49 64.90/17.49 U85_gg(x1, x2, x3, x4, x5, x6, x7) = U85_gg(x1, x2, x3, x4, x5, x6, x7) 64.90/17.49 64.90/17.49 qcD_out_gggggg(x1, x2, x3, x4, x5, x6) = qcD_out_gggggg(x1, x2, x3, x4, x5, x6) 64.90/17.49 64.90/17.49 U86_gg(x1, x2, x3, x4, x5) = U86_gg(x1, x2, x3, x4, x5) 64.90/17.49 64.90/17.49 qcE_in_gggg(x1, x2, x3, x4) = qcE_in_gggg(x1, x2, x3, x4) 64.90/17.49 64.90/17.49 U124_gggg(x1, x2, x3, x4, x5) = U124_gggg(x1, x2, x3, x4, x5) 64.90/17.49 64.90/17.49 U87_gg(x1, x2, x3, x4) = U87_gg(x1, x2, x3, x4) 64.90/17.49 64.90/17.49 qcF_in_gagg(x1, x2, x3, x4) = qcF_in_gagg(x1, x3, x4) 64.90/17.49 64.90/17.49 U126_gagg(x1, x2, x3, x4, x5) = U126_gagg(x1, x3, x4, x5) 64.90/17.49 64.90/17.49 pcJ_in_ga(x1, x2) = pcJ_in_ga(x1) 64.90/17.49 64.90/17.49 pcJ_out_ga(x1, x2) = pcJ_out_ga(x1, x2) 64.90/17.49 64.90/17.49 U108_ga(x1, x2, x3, x4, x5) = U108_ga(x1, x2, x5) 64.90/17.49 64.90/17.49 qcI_in_gaga(x1, x2, x3, x4) = qcI_in_gaga(x1, x3) 64.90/17.49 64.90/17.49 U96_gaga(x1, x2, x3, x4, x5) = U96_gaga(x1, x3, x5) 64.90/17.49 64.90/17.49 pcH_in_ga(x1, x2) = pcH_in_ga(x1) 64.90/17.49 64.90/17.49 pcH_out_ga(x1, x2) = pcH_out_ga(x1, x2) 64.90/17.49 64.90/17.49 U94_ga(x1, x2, x3, x4, x5) = U94_ga(x1, x2, x5) 64.90/17.49 64.90/17.49 qcI_out_gaga(x1, x2, x3, x4) = qcI_out_gaga(x1, x2, x3, x4) 64.90/17.49 64.90/17.49 U95_ga(x1, x2, x3, x4, x5) = U95_ga(x1, x2, x5) 64.90/17.49 64.90/17.49 U97_gaga(x1, x2, x3, x4, x5) = U97_gaga(x1, x2, x3, x5) 64.90/17.49 64.90/17.49 U109_ga(x1, x2, x3, x4, x5) = U109_ga(x1, x2, x5) 64.90/17.49 64.90/17.49 U110_ga(x1, x2, x3) = U110_ga(x1, x3) 64.90/17.49 64.90/17.49 U111_ga(x1, x2, x3) = U111_ga(x1, x3) 64.90/17.49 64.90/17.49 U127_gagg(x1, x2, x3, x4, x5) = U127_gagg(x1, x2, x3, x4, x5) 64.90/17.49 64.90/17.49 U88_gg(x1, x2, x3) = U88_gg(x1, x2, x3) 64.90/17.49 64.90/17.49 U89_gg(x1, x2, x3, x4) = U89_gg(x2, x3, x4) 64.90/17.49 64.90/17.49 U90_gg(x1, x2, x3, x4, x5, x6, x7) = U90_gg(x1, x2, x3, x4, x5, x6, x7) 64.90/17.49 64.90/17.49 U91_gg(x1, x2, x3, x4, x5, x6, x7) = U91_gg(x1, x2, x3, x4, x5, x6, x7) 64.90/17.49 64.90/17.49 U92_gg(x1, x2, x3, x4, x5, x6) = U92_gg(x1, x2, x3, x4, x5, x6) 64.90/17.49 64.90/17.49 qcF_out_gagg(x1, x2, x3, x4) = qcF_out_gagg(x1, x2, x3, x4) 64.90/17.49 64.90/17.49 U93_gg(x1, x2, x3) = U93_gg(x1, x2, x3) 64.90/17.49 64.90/17.49 qcG_in_gag(x1, x2, x3) = qcG_in_gag(x1, x3) 64.90/17.49 64.90/17.49 U128_gag(x1, x2) = U128_gag(x1, x2) 64.90/17.49 64.90/17.49 qcG_out_gag(x1, x2, x3) = qcG_out_gag(x1, x2, x3) 64.90/17.49 64.90/17.49 U129_gag(x1, x2, x3) = U129_gag(x2, x3) 64.90/17.49 64.90/17.49 U130_gag(x1, x2, x3, x4, x5, x6) = U130_gag(x1, x2, x5, x6) 64.90/17.49 64.90/17.49 U131_gag(x1, x2, x3, x4, x5, x6) = U131_gag(x1, x2, x3, x5, x6) 64.90/17.49 64.90/17.49 U132_gag(x1, x2, x3, x4, x5, x6) = U132_gag(x1, x2, x3, x4, x5, x6) 64.90/17.49 64.90/17.49 U133_gag(x1, x2, x3, x4, x5, x6) = U133_gag(x1, x2, x5, x6) 64.90/17.49 64.90/17.49 U134_gag(x1, x2, x3, x4, x5, x6) = U134_gag(x1, x2, x4, x5, x6) 64.90/17.49 64.90/17.49 U135_gag(x1, x2, x3, x4, x5, x6) = U135_gag(x1, x2, x3, x4, x5, x6) 64.90/17.49 64.90/17.49 U136_gag(x1, x2, x3, x4) = U136_gag(x1, x3, x4) 64.90/17.49 64.90/17.49 U137_gag(x1, x2, x3, x4) = U137_gag(x1, x3, x4) 64.90/17.49 64.90/17.49 U125_gggg(x1, x2, x3, x4, x5) = U125_gggg(x1, x2, x3, x4, x5) 64.90/17.49 64.90/17.49 qcE_out_gggg(x1, x2, x3, x4) = qcE_out_gggg(x1, x2, x3, x4) 64.90/17.49 64.90/17.49 U123_gggggg(x1, x2, x3, x4, x5, x6, x7) = U123_gggggg(x1, x2, x3, x4, x5, x6, x7) 64.90/17.49 64.90/17.49 qcC_out_ga(x1, x2) = qcC_out_ga(x1, x2) 64.90/17.49 64.90/17.49 U113_ga(x1, x2) = U113_ga(x2) 64.90/17.49 64.90/17.49 U114_ga(x1, x2, x3, x4, x5) = U114_ga(x1, x2, x5) 64.90/17.49 64.90/17.49 U115_ga(x1, x2, x3, x4, x5) = U115_ga(x1, x2, x3, x5) 64.90/17.49 64.90/17.49 U116_ga(x1, x2, x3, x4, x5) = U116_ga(x1, x2, x3, x4, x5) 64.90/17.49 64.90/17.49 U117_ga(x1, x2, x3, x4, x5) = U117_ga(x1, x2, x5) 64.90/17.49 64.90/17.49 U118_ga(x1, x2, x3, x4, x5) = U118_ga(x1, x2, x4, x5) 64.90/17.49 64.90/17.49 U119_ga(x1, x2, x3, x4, x5) = U119_ga(x1, x2, x3, x4, x5) 64.90/17.49 64.90/17.49 U120_ga(x1, x2, x3) = U120_ga(x1, x3) 64.90/17.49 64.90/17.49 U121_ga(x1, x2, x3) = U121_ga(x1, x3) 64.90/17.49 64.90/17.49 qcB_out_ga(x1, x2) = qcB_out_ga(x1, x2) 64.90/17.49 64.90/17.49 U99_ga(x1, x2) = U99_ga(x2) 64.90/17.49 64.90/17.49 U100_ga(x1, x2, x3, x4, x5) = U100_ga(x1, x2, x5) 64.90/17.49 64.90/17.49 U101_ga(x1, x2, x3, x4, x5) = U101_ga(x1, x2, x3, x5) 64.90/17.49 64.90/17.49 U102_ga(x1, x2, x3, x4, x5) = U102_ga(x1, x2, x3, x4, x5) 64.90/17.49 64.90/17.49 U103_ga(x1, x2, x3, x4, x5) = U103_ga(x1, x2, x5) 64.90/17.49 64.90/17.49 U104_ga(x1, x2, x3, x4, x5) = U104_ga(x1, x2, x4, x5) 64.90/17.49 64.90/17.49 U105_ga(x1, x2, x3, x4, x5) = U105_ga(x1, x2, x3, x4, x5) 64.90/17.49 64.90/17.49 U106_ga(x1, x2, x3) = U106_ga(x1, x3) 64.90/17.49 64.90/17.49 U107_ga(x1, x2, x3) = U107_ga(x1, x3) 64.90/17.49 64.90/17.49 pcH_in_aa(x1, x2) = pcH_in_aa 64.90/17.49 64.90/17.49 pcH_out_aa(x1, x2) = pcH_out_aa(x1, x2) 64.90/17.49 64.90/17.49 U94_aa(x1, x2, x3, x4, x5) = U94_aa(x5) 64.90/17.49 64.90/17.49 qcI_in_aaaa(x1, x2, x3, x4) = qcI_in_aaaa 64.90/17.49 64.90/17.49 U96_aaaa(x1, x2, x3, x4, x5) = U96_aaaa(x5) 64.90/17.49 64.90/17.49 U95_aa(x1, x2, x3, x4, x5) = U95_aa(x5) 64.90/17.49 64.90/17.49 qcI_out_aaaa(x1, x2, x3, x4) = qcI_out_aaaa(x1, x2, x3, x4) 64.90/17.49 64.90/17.49 U97_aaaa(x1, x2, x3, x4, x5) = U97_aaaa(x1, x2, x5) 64.90/17.49 64.90/17.49 pcJ_in_aa(x1, x2) = pcJ_in_aa 64.90/17.49 64.90/17.49 pcJ_out_aa(x1, x2) = pcJ_out_aa(x1, x2) 64.90/17.49 64.90/17.49 U108_aa(x1, x2, x3, x4, x5) = U108_aa(x5) 64.90/17.49 64.90/17.49 U109_aa(x1, x2, x3, x4, x5) = U109_aa(x5) 64.90/17.49 64.90/17.49 U110_aa(x1, x2, x3) = U110_aa(x3) 64.90/17.49 64.90/17.49 U111_aa(x1, x2, x3) = U111_aa(x1, x3) 64.90/17.49 64.90/17.49 pcA_in_ag(x1, x2) = pcA_in_ag(x2) 64.90/17.49 64.90/17.49 pcA_out_ag(x1, x2) = pcA_out_ag(x1, x2) 64.90/17.49 64.90/17.49 U80_ag(x1, x2) = U80_ag(x2) 64.90/17.49 64.90/17.49 qcB_in_aa(x1, x2) = qcB_in_aa 64.90/17.49 64.90/17.49 U98_aa(x1) = U98_aa(x1) 64.90/17.49 64.90/17.49 qcB_out_aa(x1, x2) = qcB_out_aa(x1, x2) 64.90/17.49 64.90/17.49 U99_aa(x1, x2) = U99_aa(x2) 64.90/17.49 64.90/17.49 U100_aa(x1, x2, x3, x4, x5) = U100_aa(x5) 64.90/17.49 64.90/17.49 U101_aa(x1, x2, x3, x4, x5) = U101_aa(x1, x3, x5) 64.90/17.49 64.90/17.49 U102_aa(x1, x2, x3, x4, x5) = U102_aa(x1, x2, x3, x4, x5) 64.90/17.49 64.90/17.49 U103_aa(x1, x2, x3, x4, x5) = U103_aa(x5) 64.90/17.49 64.90/17.49 U104_aa(x1, x2, x3, x4, x5) = U104_aa(x1, x4, x5) 64.90/17.49 64.90/17.49 U105_aa(x1, x2, x3, x4, x5) = U105_aa(x1, x2, x3, x4, x5) 64.90/17.49 64.90/17.49 U106_aa(x1, x2, x3) = U106_aa(x3) 64.90/17.49 64.90/17.49 U107_aa(x1, x2, x3) = U107_aa(x1, x3) 64.90/17.49 64.90/17.49 U81_ag(x1, x2) = U81_ag(x2) 64.90/17.49 64.90/17.49 qcC_in_aa(x1, x2) = qcC_in_aa 64.90/17.49 64.90/17.49 U112_aa(x1) = U112_aa(x1) 64.90/17.49 64.90/17.49 qcC_out_aa(x1, x2) = qcC_out_aa(x1, x2) 64.90/17.49 64.90/17.49 U113_aa(x1, x2) = U113_aa(x2) 64.90/17.49 64.90/17.49 U114_aa(x1, x2, x3, x4, x5) = U114_aa(x5) 64.90/17.49 64.90/17.49 U115_aa(x1, x2, x3, x4, x5) = U115_aa(x1, x3, x5) 64.90/17.49 64.90/17.49 U116_aa(x1, x2, x3, x4, x5) = U116_aa(x1, x2, x3, x4, x5) 64.90/17.49 64.90/17.49 U117_aa(x1, x2, x3, x4, x5) = U117_aa(x5) 64.90/17.49 64.90/17.49 U118_aa(x1, x2, x3, x4, x5) = U118_aa(x1, x4, x5) 64.90/17.49 64.90/17.49 U119_aa(x1, x2, x3, x4, x5) = U119_aa(x1, x2, x3, x4, x5) 64.90/17.49 64.90/17.49 U120_aa(x1, x2, x3) = U120_aa(x3) 64.90/17.49 64.90/17.49 U121_aa(x1, x2, x3) = U121_aa(x1, x3) 64.90/17.49 64.90/17.49 U82_ag(x1, x2, x3) = U82_ag(x2, x3) 64.90/17.49 64.90/17.49 U83_ag(x1, x2, x3, x4) = U83_ag(x3, x4) 64.90/17.49 64.90/17.49 U84_ag(x1, x2, x3, x4, x5, x6, x7) = U84_ag(x4, x5, x6, x7) 64.90/17.49 64.90/17.49 qcD_in_agagag(x1, x2, x3, x4, x5, x6) = qcD_in_agagag(x2, x4, x6) 64.90/17.49 64.90/17.49 U122_agagag(x1, x2, x3, x4, x5, x6, x7) = U122_agagag(x2, x4, x6, x7) 64.90/17.49 64.90/17.49 U85_ag(x1, x2, x3, x4, x5, x6, x7) = U85_ag(x1, x2, x4, x5, x6, x7) 64.90/17.49 64.90/17.49 qcD_in_ggggag(x1, x2, x3, x4, x5, x6) = qcD_in_ggggag(x1, x2, x3, x4, x6) 64.90/17.49 64.90/17.49 U122_ggggag(x1, x2, x3, x4, x5, x6, x7) = U122_ggggag(x1, x2, x3, x4, x6, x7) 64.90/17.49 64.90/17.49 U123_ggggag(x1, x2, x3, x4, x5, x6, x7) = U123_ggggag(x1, x2, x3, x4, x6, x7) 64.90/17.49 64.90/17.49 qcE_in_ggag(x1, x2, x3, x4) = qcE_in_ggag(x1, x2, x4) 64.90/17.49 64.90/17.49 U124_ggag(x1, x2, x3, x4, x5) = U124_ggag(x1, x2, x4, x5) 64.90/17.49 64.90/17.49 U125_ggag(x1, x2, x3, x4, x5) = U125_ggag(x1, x2, x4, x5) 64.90/17.49 64.90/17.49 U86_ag(x1, x2, x3, x4, x5) = U86_ag(x1, x2, x3, x4, x5) 64.90/17.49 64.90/17.49 U87_ag(x1, x2, x3, x4) = U87_ag(x2, x3, x4) 64.90/17.49 64.90/17.49 qcF_in_aagg(x1, x2, x3, x4) = qcF_in_aagg(x3, x4) 64.90/17.49 64.90/17.49 U126_aagg(x1, x2, x3, x4, x5) = U126_aagg(x3, x4, x5) 64.90/17.49 64.90/17.49 U127_aagg(x1, x2, x3, x4, x5) = U127_aagg(x1, x2, x3, x4, x5) 64.90/17.49 64.90/17.49 qcF_out_aagg(x1, x2, x3, x4) = qcF_out_aagg(x1, x2, x3, x4) 64.90/17.49 64.90/17.49 U88_ag(x1, x2, x3) = U88_ag(x1, x2, x3) 64.90/17.49 64.90/17.49 U89_ag(x1, x2, x3, x4) = U89_ag(x2, x3, x4) 64.90/17.49 64.90/17.49 U90_ag(x1, x2, x3, x4, x5, x6, x7) = U90_ag(x1, x2, x3, x4, x5, x6, x7) 64.90/17.49 64.90/17.49 U91_ag(x1, x2, x3, x4, x5, x6, x7) = U91_ag(x1, x2, x3, x4, x5, x6, x7) 64.90/17.49 64.90/17.49 U92_ag(x1, x2, x3, x4, x5, x6) = U92_ag(x2, x3, x4, x5, x6) 64.90/17.49 64.90/17.49 U93_ag(x1, x2, x3) = U93_ag(x2, x3) 64.90/17.49 64.90/17.49 qcG_in_aag(x1, x2, x3) = qcG_in_aag(x3) 64.90/17.49 64.90/17.49 U128_aag(x1, x2) = U128_aag(x1, x2) 64.90/17.49 64.90/17.49 qcG_out_aag(x1, x2, x3) = qcG_out_aag(x1, x2, x3) 64.90/17.49 64.90/17.49 U129_aag(x1, x2, x3) = U129_aag(x2, x3) 64.90/17.49 64.90/17.49 U130_aag(x1, x2, x3, x4, x5, x6) = U130_aag(x5, x6) 64.90/17.49 64.90/17.49 U131_aag(x1, x2, x3, x4, x5, x6) = U131_aag(x1, x3, x5, x6) 64.90/17.49 64.90/17.49 U132_aag(x1, x2, x3, x4, x5, x6) = U132_aag(x1, x2, x3, x4, x5, x6) 64.90/17.49 64.90/17.49 U133_aag(x1, x2, x3, x4, x5, x6) = U133_aag(x5, x6) 64.90/17.49 64.90/17.49 U134_aag(x1, x2, x3, x4, x5, x6) = U134_aag(x1, x4, x5, x6) 64.90/17.49 64.90/17.49 U135_aag(x1, x2, x3, x4, x5, x6) = U135_aag(x1, x2, x3, x4, x5, x6) 64.90/17.49 64.90/17.49 U136_aag(x1, x2, x3, x4) = U136_aag(x3, x4) 64.90/17.49 64.90/17.49 U137_aag(x1, x2, x3, x4) = U137_aag(x1, x3, x4) 64.90/17.49 64.90/17.49 qcE_out_ggag(x1, x2, x3, x4) = qcE_out_ggag(x1, x2, x3, x4) 64.90/17.49 64.90/17.49 qcD_out_ggggag(x1, x2, x3, x4, x5, x6) = qcD_out_ggggag(x1, x2, x3, x4, x5, x6) 64.90/17.49 64.90/17.49 U123_agagag(x1, x2, x3, x4, x5, x6, x7) = U123_agagag(x1, x2, x4, x6, x7) 64.90/17.49 64.90/17.49 qcE_in_agag(x1, x2, x3, x4) = qcE_in_agag(x2, x4) 64.90/17.49 64.90/17.49 U124_agag(x1, x2, x3, x4, x5) = U124_agag(x2, x4, x5) 64.90/17.49 64.90/17.49 U125_agag(x1, x2, x3, x4, x5) = U125_agag(x1, x2, x4, x5) 64.90/17.49 64.90/17.49 qcE_out_agag(x1, x2, x3, x4) = qcE_out_agag(x1, x2, x3, x4) 64.90/17.49 64.90/17.49 qcD_out_agagag(x1, x2, x3, x4, x5, x6) = qcD_out_agagag(x1, x2, x3, x4, x5, x6) 64.90/17.49 64.90/17.49 PJ_IN_AA(x1, x2) = PJ_IN_AA 64.90/17.49 64.90/17.49 64.90/17.49 We have to consider all (P,R,Pi)-chains 64.90/17.49 ---------------------------------------- 64.90/17.49 64.90/17.49 (132) UsableRulesProof (EQUIVALENT) 64.90/17.49 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 64.90/17.49 ---------------------------------------- 64.90/17.49 64.90/17.49 (133) 64.90/17.49 Obligation: 64.90/17.49 Pi DP problem: 64.90/17.49 The TRS P consists of the following rules: 64.90/17.49 64.90/17.49 PJ_IN_AA(d(X1), X2) -> PJ_IN_AA(X1, X3) 64.90/17.49 64.90/17.49 R is empty. 64.90/17.49 The argument filtering Pi contains the following mapping: 64.90/17.49 d(x1) = d(x1) 64.90/17.49 64.90/17.49 PJ_IN_AA(x1, x2) = PJ_IN_AA 64.90/17.49 64.90/17.49 64.90/17.49 We have to consider all (P,R,Pi)-chains 64.90/17.49 ---------------------------------------- 64.90/17.49 64.90/17.49 (134) 64.90/17.49 Obligation: 64.90/17.49 Pi DP problem: 64.90/17.49 The TRS P consists of the following rules: 64.90/17.49 64.90/17.49 PJ_IN_GA(d(X1), X2) -> PJ_IN_GA(X1, X3) 64.90/17.49 64.90/17.49 The TRS R consists of the following rules: 64.90/17.49 64.90/17.49 pcA_in_gg(d(e(t)), const(1)) -> pcA_out_gg(d(e(t)), const(1)) 64.90/17.49 pcA_in_gg(d(d(X1)), const(1)) -> U80_gg(X1, qcB_in_ga(X1, X2)) 64.90/17.49 qcB_in_ga(e(t), const(1)) -> U98_ga(pcA_in_gg(d(e(const(1))), const(1))) 64.90/17.49 pcA_in_gg(d(e(const(X1))), const(0)) -> pcA_out_gg(d(e(const(X1))), const(0)) 64.90/17.49 pcA_in_gg(d(d(X1)), const(0)) -> U81_gg(X1, qcC_in_ga(X1, X2)) 64.90/17.49 qcC_in_ga(e(t), const(1)) -> U112_ga(pcA_in_gg(d(e(const(1))), const(0))) 64.90/17.49 pcA_in_gg(d(e(+(t, X1))), +(const(1), X2)) -> U82_gg(X1, X2, pcA_in_gg(d(e(X1)), X2)) 64.90/17.49 pcA_in_gg(d(e(+(const(X1), X2))), +(const(0), X3)) -> U83_gg(X1, X2, X3, pcA_in_gg(d(e(X2)), X3)) 64.90/17.49 pcA_in_gg(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) -> U84_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X4, X2, X5, X3, X6)) 64.90/17.49 qcD_in_gggggg(X1, X2, X3, X4, X5, X6) -> U122_gggggg(X1, X2, X3, X4, X5, X6, pcA_in_gg(d(e(X1)), X2)) 64.90/17.49 pcA_in_gg(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) -> U85_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X5, X2, X4, X3, X6)) 64.90/17.49 U85_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X5, X2, X4, X3, X6)) -> pcA_out_gg(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) 64.90/17.49 pcA_in_gg(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) -> U86_gg(X1, X2, X3, X4, qcE_in_gggg(X1, X4, X2, X3)) 64.90/17.49 qcE_in_gggg(X1, X2, X3, X4) -> U124_gggg(X1, X2, X3, X4, pcA_in_gg(d(e(X1)), X2)) 64.90/17.49 pcA_in_gg(d(d(X1)), +(X2, X3)) -> U87_gg(X1, X2, X3, qcF_in_gagg(X1, X4, X2, X3)) 64.90/17.49 qcF_in_gagg(X1, X2, X3, X4) -> U126_gagg(X1, X2, X3, X4, pcJ_in_ga(X1, X2)) 64.90/17.49 pcJ_in_ga(e(t), const(1)) -> pcJ_out_ga(e(t), const(1)) 64.90/17.49 pcJ_in_ga(e(const(X1)), const(0)) -> pcJ_out_ga(e(const(X1)), const(0)) 64.90/17.49 pcJ_in_ga(e(+(X1, X2)), +(X3, X4)) -> U108_ga(X1, X2, X3, X4, qcI_in_gaga(X1, X3, X2, X4)) 64.90/17.49 qcI_in_gaga(X1, X2, X3, X4) -> U96_gaga(X1, X2, X3, X4, pcH_in_ga(X1, X2)) 64.90/17.49 pcH_in_ga(t, const(1)) -> pcH_out_ga(t, const(1)) 64.90/17.49 pcH_in_ga(const(X1), const(0)) -> pcH_out_ga(const(X1), const(0)) 64.90/17.49 pcH_in_ga(+(X1, X2), +(X3, X4)) -> U94_ga(X1, X2, X3, X4, qcI_in_gaga(X1, X3, X2, X4)) 64.90/17.49 U94_ga(X1, X2, X3, X4, qcI_out_gaga(X1, X3, X2, X4)) -> pcH_out_ga(+(X1, X2), +(X3, X4)) 64.90/17.49 pcH_in_ga(*(X1, X2), +(*(X1, X3), *(X2, X4))) -> U95_ga(X1, X2, X3, X4, qcI_in_gaga(X1, X4, X2, X3)) 64.90/17.49 U95_ga(X1, X2, X3, X4, qcI_out_gaga(X1, X4, X2, X3)) -> pcH_out_ga(*(X1, X2), +(*(X1, X3), *(X2, X4))) 64.90/17.49 U96_gaga(X1, X2, X3, X4, pcH_out_ga(X1, X2)) -> U97_gaga(X1, X2, X3, X4, pcH_in_ga(X3, X4)) 64.90/17.49 U97_gaga(X1, X2, X3, X4, pcH_out_ga(X3, X4)) -> qcI_out_gaga(X1, X2, X3, X4) 64.90/17.49 U108_ga(X1, X2, X3, X4, qcI_out_gaga(X1, X3, X2, X4)) -> pcJ_out_ga(e(+(X1, X2)), +(X3, X4)) 64.90/17.49 pcJ_in_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U109_ga(X1, X2, X3, X4, qcI_in_gaga(X1, X4, X2, X3)) 64.90/17.49 U109_ga(X1, X2, X3, X4, qcI_out_gaga(X1, X4, X2, X3)) -> pcJ_out_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.90/17.49 pcJ_in_ga(d(X1), X2) -> U110_ga(X1, X2, pcJ_in_ga(X1, X3)) 64.90/17.49 U110_ga(X1, X2, pcJ_out_ga(X1, X3)) -> U111_ga(X1, X2, pcH_in_ga(X3, X2)) 64.90/17.49 U111_ga(X1, X2, pcH_out_ga(X3, X2)) -> pcJ_out_ga(d(X1), X2) 64.90/17.49 U126_gagg(X1, X2, X3, X4, pcJ_out_ga(X1, X2)) -> U127_gagg(X1, X2, X3, X4, pcA_in_gg(d(e(X2)), +(X3, X4))) 64.90/17.49 pcA_in_gg(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) -> U88_gg(X1, X2, pcA_in_gg(d(e(X1)), X2)) 64.90/17.49 pcA_in_gg(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) -> U89_gg(X1, X2, X3, pcA_in_gg(d(e(X2)), X3)) 64.90/17.49 pcA_in_gg(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) -> U90_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X5, X2, X6, X3, X4)) 64.90/17.49 U90_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X5, X2, X6, X3, X4)) -> pcA_out_gg(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) 64.90/17.49 pcA_in_gg(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) -> U91_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X6, X2, X5, X3, X4)) 64.90/17.49 U91_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X6, X2, X5, X3, X4)) -> pcA_out_gg(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) 64.90/17.49 pcA_in_gg(d(d(X1)), +(*(X2, X3), *(X4, X5))) -> U92_gg(X1, X2, X3, X4, X5, qcF_in_gagg(X1, X6, *(X2, X3), *(X4, X5))) 64.90/17.49 U92_gg(X1, X2, X3, X4, X5, qcF_out_gagg(X1, X6, *(X2, X3), *(X4, X5))) -> pcA_out_gg(d(d(X1)), +(*(X2, X3), *(X4, X5))) 64.90/17.49 pcA_in_gg(d(d(X1)), X2) -> U93_gg(X1, X2, qcG_in_gag(X1, X3, X2)) 64.90/17.49 qcG_in_gag(e(t), const(1), X1) -> U128_gag(X1, pcA_in_gg(d(e(const(1))), X1)) 64.90/17.49 U128_gag(X1, pcA_out_gg(d(e(const(1))), X1)) -> qcG_out_gag(e(t), const(1), X1) 64.90/17.49 qcG_in_gag(e(const(X1)), const(0), X2) -> U129_gag(X1, X2, pcA_in_gg(d(e(const(0))), X2)) 64.90/17.49 U129_gag(X1, X2, pcA_out_gg(d(e(const(0))), X2)) -> qcG_out_gag(e(const(X1)), const(0), X2) 64.90/17.49 qcG_in_gag(e(+(X1, X2)), +(X3, X4), X5) -> U130_gag(X1, X2, X3, X4, X5, pcH_in_ga(X1, X3)) 64.90/17.49 U130_gag(X1, X2, X3, X4, X5, pcH_out_ga(X1, X3)) -> U131_gag(X1, X2, X3, X4, X5, pcH_in_ga(X2, X4)) 64.90/17.49 U131_gag(X1, X2, X3, X4, X5, pcH_out_ga(X2, X4)) -> U132_gag(X1, X2, X3, X4, X5, pcA_in_gg(d(e(+(X3, X4))), X5)) 64.90/17.49 U132_gag(X1, X2, X3, X4, X5, pcA_out_gg(d(e(+(X3, X4))), X5)) -> qcG_out_gag(e(+(X1, X2)), +(X3, X4), X5) 64.90/17.49 qcG_in_gag(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) -> U133_gag(X1, X2, X3, X4, X5, pcH_in_ga(X1, X4)) 64.90/17.49 U133_gag(X1, X2, X3, X4, X5, pcH_out_ga(X1, X4)) -> U134_gag(X1, X2, X3, X4, X5, pcH_in_ga(X2, X3)) 64.90/17.49 U134_gag(X1, X2, X3, X4, X5, pcH_out_ga(X2, X3)) -> U135_gag(X1, X2, X3, X4, X5, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), X5)) 64.90/17.49 U135_gag(X1, X2, X3, X4, X5, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), X5)) -> qcG_out_gag(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) 64.90/17.49 qcG_in_gag(d(X1), X2, X3) -> U136_gag(X1, X2, X3, pcJ_in_ga(X1, X4)) 64.90/17.49 U136_gag(X1, X2, X3, pcJ_out_ga(X1, X4)) -> U137_gag(X1, X2, X3, qcG_in_gag(e(X4), X2, X3)) 64.90/17.49 U137_gag(X1, X2, X3, qcG_out_gag(e(X4), X2, X3)) -> qcG_out_gag(d(X1), X2, X3) 64.90/17.49 U93_gg(X1, X2, qcG_out_gag(X1, X3, X2)) -> pcA_out_gg(d(d(X1)), X2) 64.90/17.49 U89_gg(X1, X2, X3, pcA_out_gg(d(e(X2)), X3)) -> pcA_out_gg(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) 64.90/17.49 U88_gg(X1, X2, pcA_out_gg(d(e(X1)), X2)) -> pcA_out_gg(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) 64.90/17.49 U127_gagg(X1, X2, X3, X4, pcA_out_gg(d(e(X2)), +(X3, X4))) -> qcF_out_gagg(X1, X2, X3, X4) 64.90/17.49 U87_gg(X1, X2, X3, qcF_out_gagg(X1, X4, X2, X3)) -> pcA_out_gg(d(d(X1)), +(X2, X3)) 64.90/17.49 U124_gggg(X1, X2, X3, X4, pcA_out_gg(d(e(X1)), X2)) -> U125_gggg(X1, X2, X3, X4, pcA_in_gg(d(e(X3)), X4)) 64.90/17.49 U125_gggg(X1, X2, X3, X4, pcA_out_gg(d(e(X3)), X4)) -> qcE_out_gggg(X1, X2, X3, X4) 64.90/17.49 U86_gg(X1, X2, X3, X4, qcE_out_gggg(X1, X4, X2, X3)) -> pcA_out_gg(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) 64.90/17.49 U122_gggggg(X1, X2, X3, X4, X5, X6, pcA_out_gg(d(e(X1)), X2)) -> U123_gggggg(X1, X2, X3, X4, X5, X6, qcE_in_gggg(X3, X4, X5, X6)) 64.90/17.49 U123_gggggg(X1, X2, X3, X4, X5, X6, qcE_out_gggg(X3, X4, X5, X6)) -> qcD_out_gggggg(X1, X2, X3, X4, X5, X6) 64.90/17.49 U84_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X4, X2, X5, X3, X6)) -> pcA_out_gg(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) 64.90/17.49 U83_gg(X1, X2, X3, pcA_out_gg(d(e(X2)), X3)) -> pcA_out_gg(d(e(+(const(X1), X2))), +(const(0), X3)) 64.90/17.49 U82_gg(X1, X2, pcA_out_gg(d(e(X1)), X2)) -> pcA_out_gg(d(e(+(t, X1))), +(const(1), X2)) 64.90/17.49 U112_ga(pcA_out_gg(d(e(const(1))), const(0))) -> qcC_out_ga(e(t), const(1)) 64.90/17.49 qcC_in_ga(e(const(X1)), const(0)) -> U113_ga(X1, pcA_in_gg(d(e(const(0))), const(0))) 64.90/17.49 U113_ga(X1, pcA_out_gg(d(e(const(0))), const(0))) -> qcC_out_ga(e(const(X1)), const(0)) 64.90/17.49 qcC_in_ga(e(+(X1, X2)), +(X3, X4)) -> U114_ga(X1, X2, X3, X4, pcH_in_ga(X1, X3)) 64.90/17.49 U114_ga(X1, X2, X3, X4, pcH_out_ga(X1, X3)) -> U115_ga(X1, X2, X3, X4, pcH_in_ga(X2, X4)) 64.90/17.49 U115_ga(X1, X2, X3, X4, pcH_out_ga(X2, X4)) -> U116_ga(X1, X2, X3, X4, pcA_in_gg(d(e(+(X3, X4))), const(0))) 64.90/17.49 U116_ga(X1, X2, X3, X4, pcA_out_gg(d(e(+(X3, X4))), const(0))) -> qcC_out_ga(e(+(X1, X2)), +(X3, X4)) 64.90/17.49 qcC_in_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U117_ga(X1, X2, X3, X4, pcH_in_ga(X1, X4)) 64.90/17.49 U117_ga(X1, X2, X3, X4, pcH_out_ga(X1, X4)) -> U118_ga(X1, X2, X3, X4, pcH_in_ga(X2, X3)) 64.90/17.49 U118_ga(X1, X2, X3, X4, pcH_out_ga(X2, X3)) -> U119_ga(X1, X2, X3, X4, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(0))) 64.90/17.49 U119_ga(X1, X2, X3, X4, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(0))) -> qcC_out_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.90/17.49 qcC_in_ga(d(X1), X2) -> U120_ga(X1, X2, pcJ_in_ga(X1, X3)) 64.90/17.49 U120_ga(X1, X2, pcJ_out_ga(X1, X3)) -> U121_ga(X1, X2, qcC_in_ga(e(X3), X2)) 64.90/17.49 U121_ga(X1, X2, qcC_out_ga(e(X3), X2)) -> qcC_out_ga(d(X1), X2) 64.90/17.49 U81_gg(X1, qcC_out_ga(X1, X2)) -> pcA_out_gg(d(d(X1)), const(0)) 64.90/17.49 U98_ga(pcA_out_gg(d(e(const(1))), const(1))) -> qcB_out_ga(e(t), const(1)) 64.90/17.49 qcB_in_ga(e(const(X1)), const(0)) -> U99_ga(X1, pcA_in_gg(d(e(const(0))), const(1))) 64.90/17.49 U99_ga(X1, pcA_out_gg(d(e(const(0))), const(1))) -> qcB_out_ga(e(const(X1)), const(0)) 64.90/17.49 qcB_in_ga(e(+(X1, X2)), +(X3, X4)) -> U100_ga(X1, X2, X3, X4, pcH_in_ga(X1, X3)) 64.90/17.49 U100_ga(X1, X2, X3, X4, pcH_out_ga(X1, X3)) -> U101_ga(X1, X2, X3, X4, pcH_in_ga(X2, X4)) 64.90/17.49 U101_ga(X1, X2, X3, X4, pcH_out_ga(X2, X4)) -> U102_ga(X1, X2, X3, X4, pcA_in_gg(d(e(+(X3, X4))), const(1))) 64.90/17.49 U102_ga(X1, X2, X3, X4, pcA_out_gg(d(e(+(X3, X4))), const(1))) -> qcB_out_ga(e(+(X1, X2)), +(X3, X4)) 64.90/17.49 qcB_in_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U103_ga(X1, X2, X3, X4, pcH_in_ga(X1, X4)) 64.90/17.49 U103_ga(X1, X2, X3, X4, pcH_out_ga(X1, X4)) -> U104_ga(X1, X2, X3, X4, pcH_in_ga(X2, X3)) 64.90/17.49 U104_ga(X1, X2, X3, X4, pcH_out_ga(X2, X3)) -> U105_ga(X1, X2, X3, X4, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(1))) 64.90/17.49 U105_ga(X1, X2, X3, X4, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(1))) -> qcB_out_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.90/17.49 qcB_in_ga(d(X1), X2) -> U106_ga(X1, X2, pcJ_in_ga(X1, X3)) 64.90/17.49 U106_ga(X1, X2, pcJ_out_ga(X1, X3)) -> U107_ga(X1, X2, qcB_in_ga(e(X3), X2)) 64.90/17.49 U107_ga(X1, X2, qcB_out_ga(e(X3), X2)) -> qcB_out_ga(d(X1), X2) 64.90/17.49 U80_gg(X1, qcB_out_ga(X1, X2)) -> pcA_out_gg(d(d(X1)), const(1)) 64.90/17.49 pcH_in_aa(t, const(1)) -> pcH_out_aa(t, const(1)) 64.90/17.49 pcH_in_aa(const(X1), const(0)) -> pcH_out_aa(const(X1), const(0)) 64.90/17.49 pcH_in_aa(+(X1, X2), +(X3, X4)) -> U94_aa(X1, X2, X3, X4, qcI_in_aaaa(X1, X3, X2, X4)) 64.90/17.49 qcI_in_aaaa(X1, X2, X3, X4) -> U96_aaaa(X1, X2, X3, X4, pcH_in_aa(X1, X2)) 64.90/17.49 pcH_in_aa(*(X1, X2), +(*(X1, X3), *(X2, X4))) -> U95_aa(X1, X2, X3, X4, qcI_in_aaaa(X1, X4, X2, X3)) 64.90/17.49 U95_aa(X1, X2, X3, X4, qcI_out_aaaa(X1, X4, X2, X3)) -> pcH_out_aa(*(X1, X2), +(*(X1, X3), *(X2, X4))) 64.90/17.49 U96_aaaa(X1, X2, X3, X4, pcH_out_aa(X1, X2)) -> U97_aaaa(X1, X2, X3, X4, pcH_in_aa(X3, X4)) 64.90/17.49 U97_aaaa(X1, X2, X3, X4, pcH_out_aa(X3, X4)) -> qcI_out_aaaa(X1, X2, X3, X4) 64.90/17.49 U94_aa(X1, X2, X3, X4, qcI_out_aaaa(X1, X3, X2, X4)) -> pcH_out_aa(+(X1, X2), +(X3, X4)) 64.90/17.49 pcJ_in_aa(e(t), const(1)) -> pcJ_out_aa(e(t), const(1)) 64.90/17.49 pcJ_in_aa(e(const(X1)), const(0)) -> pcJ_out_aa(e(const(X1)), const(0)) 64.90/17.49 pcJ_in_aa(e(+(X1, X2)), +(X3, X4)) -> U108_aa(X1, X2, X3, X4, qcI_in_aaaa(X1, X3, X2, X4)) 64.90/17.49 U108_aa(X1, X2, X3, X4, qcI_out_aaaa(X1, X3, X2, X4)) -> pcJ_out_aa(e(+(X1, X2)), +(X3, X4)) 64.90/17.49 pcJ_in_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U109_aa(X1, X2, X3, X4, qcI_in_aaaa(X1, X4, X2, X3)) 64.90/17.49 U109_aa(X1, X2, X3, X4, qcI_out_aaaa(X1, X4, X2, X3)) -> pcJ_out_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.90/17.49 pcJ_in_aa(d(X1), X2) -> U110_aa(X1, X2, pcJ_in_aa(X1, X3)) 64.90/17.49 U110_aa(X1, X2, pcJ_out_aa(X1, X3)) -> U111_aa(X1, X2, pcH_in_ga(X3, X2)) 64.90/17.49 U111_aa(X1, X2, pcH_out_ga(X3, X2)) -> pcJ_out_aa(d(X1), X2) 64.90/17.49 pcA_in_ag(d(e(t)), const(1)) -> pcA_out_ag(d(e(t)), const(1)) 64.90/17.49 pcA_in_ag(d(d(X1)), const(1)) -> U80_ag(X1, qcB_in_aa(X1, X2)) 64.90/17.49 qcB_in_aa(e(t), const(1)) -> U98_aa(pcA_in_gg(d(e(const(1))), const(1))) 64.90/17.49 U98_aa(pcA_out_gg(d(e(const(1))), const(1))) -> qcB_out_aa(e(t), const(1)) 64.90/17.49 qcB_in_aa(e(const(X1)), const(0)) -> U99_aa(X1, pcA_in_gg(d(e(const(0))), const(1))) 64.90/17.49 U99_aa(X1, pcA_out_gg(d(e(const(0))), const(1))) -> qcB_out_aa(e(const(X1)), const(0)) 64.90/17.49 qcB_in_aa(e(+(X1, X2)), +(X3, X4)) -> U100_aa(X1, X2, X3, X4, pcH_in_aa(X1, X3)) 64.90/17.49 U100_aa(X1, X2, X3, X4, pcH_out_aa(X1, X3)) -> U101_aa(X1, X2, X3, X4, pcH_in_aa(X2, X4)) 64.90/17.49 U101_aa(X1, X2, X3, X4, pcH_out_aa(X2, X4)) -> U102_aa(X1, X2, X3, X4, pcA_in_gg(d(e(+(X3, X4))), const(1))) 64.90/17.49 U102_aa(X1, X2, X3, X4, pcA_out_gg(d(e(+(X3, X4))), const(1))) -> qcB_out_aa(e(+(X1, X2)), +(X3, X4)) 64.90/17.49 qcB_in_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U103_aa(X1, X2, X3, X4, pcH_in_aa(X1, X4)) 64.90/17.49 U103_aa(X1, X2, X3, X4, pcH_out_aa(X1, X4)) -> U104_aa(X1, X2, X3, X4, pcH_in_aa(X2, X3)) 64.90/17.49 U104_aa(X1, X2, X3, X4, pcH_out_aa(X2, X3)) -> U105_aa(X1, X2, X3, X4, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(1))) 64.90/17.49 U105_aa(X1, X2, X3, X4, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(1))) -> qcB_out_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.90/17.49 qcB_in_aa(d(X1), X2) -> U106_aa(X1, X2, pcJ_in_aa(X1, X3)) 64.90/17.49 U106_aa(X1, X2, pcJ_out_aa(X1, X3)) -> U107_aa(X1, X2, qcB_in_ga(e(X3), X2)) 64.90/17.49 U107_aa(X1, X2, qcB_out_ga(e(X3), X2)) -> qcB_out_aa(d(X1), X2) 64.90/17.49 U80_ag(X1, qcB_out_aa(X1, X2)) -> pcA_out_ag(d(d(X1)), const(1)) 64.90/17.49 pcA_in_ag(d(e(const(X1))), const(0)) -> pcA_out_ag(d(e(const(X1))), const(0)) 64.90/17.49 pcA_in_ag(d(d(X1)), const(0)) -> U81_ag(X1, qcC_in_aa(X1, X2)) 64.90/17.49 qcC_in_aa(e(t), const(1)) -> U112_aa(pcA_in_gg(d(e(const(1))), const(0))) 64.90/17.49 U112_aa(pcA_out_gg(d(e(const(1))), const(0))) -> qcC_out_aa(e(t), const(1)) 64.90/17.49 qcC_in_aa(e(const(X1)), const(0)) -> U113_aa(X1, pcA_in_gg(d(e(const(0))), const(0))) 64.90/17.49 U113_aa(X1, pcA_out_gg(d(e(const(0))), const(0))) -> qcC_out_aa(e(const(X1)), const(0)) 64.90/17.49 qcC_in_aa(e(+(X1, X2)), +(X3, X4)) -> U114_aa(X1, X2, X3, X4, pcH_in_aa(X1, X3)) 64.90/17.49 U114_aa(X1, X2, X3, X4, pcH_out_aa(X1, X3)) -> U115_aa(X1, X2, X3, X4, pcH_in_aa(X2, X4)) 64.90/17.49 U115_aa(X1, X2, X3, X4, pcH_out_aa(X2, X4)) -> U116_aa(X1, X2, X3, X4, pcA_in_gg(d(e(+(X3, X4))), const(0))) 64.90/17.49 U116_aa(X1, X2, X3, X4, pcA_out_gg(d(e(+(X3, X4))), const(0))) -> qcC_out_aa(e(+(X1, X2)), +(X3, X4)) 64.90/17.49 qcC_in_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U117_aa(X1, X2, X3, X4, pcH_in_aa(X1, X4)) 64.90/17.49 U117_aa(X1, X2, X3, X4, pcH_out_aa(X1, X4)) -> U118_aa(X1, X2, X3, X4, pcH_in_aa(X2, X3)) 64.90/17.49 U118_aa(X1, X2, X3, X4, pcH_out_aa(X2, X3)) -> U119_aa(X1, X2, X3, X4, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(0))) 64.90/17.49 U119_aa(X1, X2, X3, X4, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(0))) -> qcC_out_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.90/17.49 qcC_in_aa(d(X1), X2) -> U120_aa(X1, X2, pcJ_in_aa(X1, X3)) 64.90/17.49 U120_aa(X1, X2, pcJ_out_aa(X1, X3)) -> U121_aa(X1, X2, qcC_in_ga(e(X3), X2)) 64.90/17.49 U121_aa(X1, X2, qcC_out_ga(e(X3), X2)) -> qcC_out_aa(d(X1), X2) 64.90/17.49 U81_ag(X1, qcC_out_aa(X1, X2)) -> pcA_out_ag(d(d(X1)), const(0)) 64.90/17.49 pcA_in_ag(d(e(+(t, X1))), +(const(1), X2)) -> U82_ag(X1, X2, pcA_in_ag(d(e(X1)), X2)) 64.90/17.49 pcA_in_ag(d(e(+(const(X1), X2))), +(const(0), X3)) -> U83_ag(X1, X2, X3, pcA_in_ag(d(e(X2)), X3)) 64.90/17.49 pcA_in_ag(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) -> U84_ag(X1, X2, X3, X4, X5, X6, qcD_in_agagag(X1, X4, X2, X5, X3, X6)) 64.90/17.49 qcD_in_agagag(X1, X2, X3, X4, X5, X6) -> U122_agagag(X1, X2, X3, X4, X5, X6, pcA_in_ag(d(e(X1)), X2)) 64.90/17.49 pcA_in_ag(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) -> U85_ag(X1, X2, X3, X4, X5, X6, qcD_in_ggggag(X1, X5, X2, X4, X3, X6)) 64.90/17.49 qcD_in_ggggag(X1, X2, X3, X4, X5, X6) -> U122_ggggag(X1, X2, X3, X4, X5, X6, pcA_in_gg(d(e(X1)), X2)) 64.90/17.49 U122_ggggag(X1, X2, X3, X4, X5, X6, pcA_out_gg(d(e(X1)), X2)) -> U123_ggggag(X1, X2, X3, X4, X5, X6, qcE_in_ggag(X3, X4, X5, X6)) 64.90/17.49 qcE_in_ggag(X1, X2, X3, X4) -> U124_ggag(X1, X2, X3, X4, pcA_in_gg(d(e(X1)), X2)) 64.90/17.49 U124_ggag(X1, X2, X3, X4, pcA_out_gg(d(e(X1)), X2)) -> U125_ggag(X1, X2, X3, X4, pcA_in_ag(d(e(X3)), X4)) 64.90/17.49 pcA_in_ag(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) -> U86_ag(X1, X2, X3, X4, qcE_in_gggg(X1, X4, X2, X3)) 64.90/17.49 U86_ag(X1, X2, X3, X4, qcE_out_gggg(X1, X4, X2, X3)) -> pcA_out_ag(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) 64.90/17.49 pcA_in_ag(d(d(X1)), +(X2, X3)) -> U87_ag(X1, X2, X3, qcF_in_aagg(X1, X4, X2, X3)) 64.90/17.49 qcF_in_aagg(X1, X2, X3, X4) -> U126_aagg(X1, X2, X3, X4, pcJ_in_aa(X1, X2)) 64.90/17.49 U126_aagg(X1, X2, X3, X4, pcJ_out_aa(X1, X2)) -> U127_aagg(X1, X2, X3, X4, pcA_in_gg(d(e(X2)), +(X3, X4))) 64.90/17.49 U127_aagg(X1, X2, X3, X4, pcA_out_gg(d(e(X2)), +(X3, X4))) -> qcF_out_aagg(X1, X2, X3, X4) 64.90/17.49 U87_ag(X1, X2, X3, qcF_out_aagg(X1, X4, X2, X3)) -> pcA_out_ag(d(d(X1)), +(X2, X3)) 64.90/17.49 pcA_in_ag(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) -> U88_ag(X1, X2, pcA_in_gg(d(e(X1)), X2)) 64.90/17.49 U88_ag(X1, X2, pcA_out_gg(d(e(X1)), X2)) -> pcA_out_ag(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) 64.90/17.49 pcA_in_ag(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) -> U89_ag(X1, X2, X3, pcA_in_gg(d(e(X2)), X3)) 64.90/17.49 U89_ag(X1, X2, X3, pcA_out_gg(d(e(X2)), X3)) -> pcA_out_ag(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) 64.90/17.49 pcA_in_ag(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) -> U90_ag(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X5, X2, X6, X3, X4)) 64.90/17.49 U90_ag(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X5, X2, X6, X3, X4)) -> pcA_out_ag(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) 64.90/17.49 pcA_in_ag(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) -> U91_ag(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X6, X2, X5, X3, X4)) 64.90/17.49 U91_ag(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X6, X2, X5, X3, X4)) -> pcA_out_ag(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) 64.90/17.49 pcA_in_ag(d(d(X1)), +(*(X2, X3), *(X4, X5))) -> U92_ag(X1, X2, X3, X4, X5, qcF_in_aagg(X1, X6, *(X2, X3), *(X4, X5))) 64.90/17.49 U92_ag(X1, X2, X3, X4, X5, qcF_out_aagg(X1, X6, *(X2, X3), *(X4, X5))) -> pcA_out_ag(d(d(X1)), +(*(X2, X3), *(X4, X5))) 64.90/17.49 pcA_in_ag(d(d(X1)), X2) -> U93_ag(X1, X2, qcG_in_aag(X1, X3, X2)) 64.90/17.49 qcG_in_aag(e(t), const(1), X1) -> U128_aag(X1, pcA_in_gg(d(e(const(1))), X1)) 64.90/17.49 U128_aag(X1, pcA_out_gg(d(e(const(1))), X1)) -> qcG_out_aag(e(t), const(1), X1) 64.90/17.49 qcG_in_aag(e(const(X1)), const(0), X2) -> U129_aag(X1, X2, pcA_in_gg(d(e(const(0))), X2)) 64.90/17.49 U129_aag(X1, X2, pcA_out_gg(d(e(const(0))), X2)) -> qcG_out_aag(e(const(X1)), const(0), X2) 64.90/17.49 qcG_in_aag(e(+(X1, X2)), +(X3, X4), X5) -> U130_aag(X1, X2, X3, X4, X5, pcH_in_aa(X1, X3)) 64.90/17.49 U130_aag(X1, X2, X3, X4, X5, pcH_out_aa(X1, X3)) -> U131_aag(X1, X2, X3, X4, X5, pcH_in_aa(X2, X4)) 64.90/17.49 U131_aag(X1, X2, X3, X4, X5, pcH_out_aa(X2, X4)) -> U132_aag(X1, X2, X3, X4, X5, pcA_in_gg(d(e(+(X3, X4))), X5)) 64.90/17.49 U132_aag(X1, X2, X3, X4, X5, pcA_out_gg(d(e(+(X3, X4))), X5)) -> qcG_out_aag(e(+(X1, X2)), +(X3, X4), X5) 64.90/17.49 qcG_in_aag(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) -> U133_aag(X1, X2, X3, X4, X5, pcH_in_aa(X1, X4)) 64.90/17.49 U133_aag(X1, X2, X3, X4, X5, pcH_out_aa(X1, X4)) -> U134_aag(X1, X2, X3, X4, X5, pcH_in_aa(X2, X3)) 64.90/17.49 U134_aag(X1, X2, X3, X4, X5, pcH_out_aa(X2, X3)) -> U135_aag(X1, X2, X3, X4, X5, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), X5)) 64.90/17.49 U135_aag(X1, X2, X3, X4, X5, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), X5)) -> qcG_out_aag(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) 64.90/17.49 qcG_in_aag(d(X1), X2, X3) -> U136_aag(X1, X2, X3, pcJ_in_aa(X1, X4)) 64.90/17.49 U136_aag(X1, X2, X3, pcJ_out_aa(X1, X4)) -> U137_aag(X1, X2, X3, qcG_in_gag(e(X4), X2, X3)) 64.90/17.49 U137_aag(X1, X2, X3, qcG_out_gag(e(X4), X2, X3)) -> qcG_out_aag(d(X1), X2, X3) 64.90/17.49 U93_ag(X1, X2, qcG_out_aag(X1, X3, X2)) -> pcA_out_ag(d(d(X1)), X2) 64.90/17.49 U125_ggag(X1, X2, X3, X4, pcA_out_ag(d(e(X3)), X4)) -> qcE_out_ggag(X1, X2, X3, X4) 64.90/17.49 U123_ggggag(X1, X2, X3, X4, X5, X6, qcE_out_ggag(X3, X4, X5, X6)) -> qcD_out_ggggag(X1, X2, X3, X4, X5, X6) 64.90/17.49 U85_ag(X1, X2, X3, X4, X5, X6, qcD_out_ggggag(X1, X5, X2, X4, X3, X6)) -> pcA_out_ag(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) 64.90/17.49 U122_agagag(X1, X2, X3, X4, X5, X6, pcA_out_ag(d(e(X1)), X2)) -> U123_agagag(X1, X2, X3, X4, X5, X6, qcE_in_agag(X3, X4, X5, X6)) 64.90/17.49 qcE_in_agag(X1, X2, X3, X4) -> U124_agag(X1, X2, X3, X4, pcA_in_ag(d(e(X1)), X2)) 64.90/17.49 U124_agag(X1, X2, X3, X4, pcA_out_ag(d(e(X1)), X2)) -> U125_agag(X1, X2, X3, X4, pcA_in_ag(d(e(X3)), X4)) 64.90/17.49 U125_agag(X1, X2, X3, X4, pcA_out_ag(d(e(X3)), X4)) -> qcE_out_agag(X1, X2, X3, X4) 64.90/17.49 U123_agagag(X1, X2, X3, X4, X5, X6, qcE_out_agag(X3, X4, X5, X6)) -> qcD_out_agagag(X1, X2, X3, X4, X5, X6) 64.90/17.49 U84_ag(X1, X2, X3, X4, X5, X6, qcD_out_agagag(X1, X4, X2, X5, X3, X6)) -> pcA_out_ag(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) 64.90/17.49 U83_ag(X1, X2, X3, pcA_out_ag(d(e(X2)), X3)) -> pcA_out_ag(d(e(+(const(X1), X2))), +(const(0), X3)) 64.90/17.49 U82_ag(X1, X2, pcA_out_ag(d(e(X1)), X2)) -> pcA_out_ag(d(e(+(t, X1))), +(const(1), X2)) 64.90/17.49 64.90/17.49 The argument filtering Pi contains the following mapping: 64.90/17.49 const(x1) = const 64.90/17.49 64.90/17.49 1 = 1 64.90/17.49 64.90/17.49 d(x1) = d(x1) 64.90/17.49 64.90/17.49 e(x1) = e(x1) 64.90/17.49 64.90/17.49 t = t 64.90/17.49 64.90/17.49 0 = 0 64.90/17.49 64.90/17.49 +(x1, x2) = +(x1, x2) 64.90/17.49 64.90/17.49 *(x1, x2) = *(x1, x2) 64.90/17.49 64.90/17.49 pcA_in_gg(x1, x2) = pcA_in_gg(x1, x2) 64.90/17.49 64.90/17.49 pcA_out_gg(x1, x2) = pcA_out_gg(x1, x2) 64.90/17.49 64.90/17.49 U80_gg(x1, x2) = U80_gg(x1, x2) 64.90/17.49 64.90/17.49 qcB_in_ga(x1, x2) = qcB_in_ga(x1) 64.90/17.49 64.90/17.49 U98_ga(x1) = U98_ga(x1) 64.90/17.49 64.90/17.49 U81_gg(x1, x2) = U81_gg(x1, x2) 64.90/17.49 64.90/17.49 qcC_in_ga(x1, x2) = qcC_in_ga(x1) 64.90/17.49 64.90/17.49 U112_ga(x1) = U112_ga(x1) 64.90/17.49 64.90/17.49 U82_gg(x1, x2, x3) = U82_gg(x1, x2, x3) 64.90/17.49 64.90/17.49 U83_gg(x1, x2, x3, x4) = U83_gg(x2, x3, x4) 64.90/17.49 64.90/17.49 U84_gg(x1, x2, x3, x4, x5, x6, x7) = U84_gg(x1, x2, x3, x4, x5, x6, x7) 64.90/17.49 64.90/17.49 qcD_in_gggggg(x1, x2, x3, x4, x5, x6) = qcD_in_gggggg(x1, x2, x3, x4, x5, x6) 64.90/17.49 64.90/17.49 U122_gggggg(x1, x2, x3, x4, x5, x6, x7) = U122_gggggg(x1, x2, x3, x4, x5, x6, x7) 64.90/17.49 64.90/17.49 U85_gg(x1, x2, x3, x4, x5, x6, x7) = U85_gg(x1, x2, x3, x4, x5, x6, x7) 64.90/17.49 64.90/17.49 qcD_out_gggggg(x1, x2, x3, x4, x5, x6) = qcD_out_gggggg(x1, x2, x3, x4, x5, x6) 64.90/17.49 64.90/17.49 U86_gg(x1, x2, x3, x4, x5) = U86_gg(x1, x2, x3, x4, x5) 64.90/17.49 64.90/17.49 qcE_in_gggg(x1, x2, x3, x4) = qcE_in_gggg(x1, x2, x3, x4) 64.90/17.49 64.90/17.49 U124_gggg(x1, x2, x3, x4, x5) = U124_gggg(x1, x2, x3, x4, x5) 64.90/17.49 64.90/17.49 U87_gg(x1, x2, x3, x4) = U87_gg(x1, x2, x3, x4) 64.90/17.49 64.90/17.49 qcF_in_gagg(x1, x2, x3, x4) = qcF_in_gagg(x1, x3, x4) 64.90/17.49 64.90/17.49 U126_gagg(x1, x2, x3, x4, x5) = U126_gagg(x1, x3, x4, x5) 64.90/17.49 64.90/17.49 pcJ_in_ga(x1, x2) = pcJ_in_ga(x1) 64.90/17.49 64.90/17.49 pcJ_out_ga(x1, x2) = pcJ_out_ga(x1, x2) 64.90/17.49 64.90/17.49 U108_ga(x1, x2, x3, x4, x5) = U108_ga(x1, x2, x5) 64.90/17.49 64.90/17.49 qcI_in_gaga(x1, x2, x3, x4) = qcI_in_gaga(x1, x3) 64.90/17.49 64.90/17.49 U96_gaga(x1, x2, x3, x4, x5) = U96_gaga(x1, x3, x5) 64.90/17.49 64.90/17.49 pcH_in_ga(x1, x2) = pcH_in_ga(x1) 64.90/17.49 64.90/17.49 pcH_out_ga(x1, x2) = pcH_out_ga(x1, x2) 64.90/17.49 64.90/17.49 U94_ga(x1, x2, x3, x4, x5) = U94_ga(x1, x2, x5) 64.90/17.49 64.90/17.49 qcI_out_gaga(x1, x2, x3, x4) = qcI_out_gaga(x1, x2, x3, x4) 64.90/17.49 64.90/17.49 U95_ga(x1, x2, x3, x4, x5) = U95_ga(x1, x2, x5) 64.90/17.49 64.90/17.49 U97_gaga(x1, x2, x3, x4, x5) = U97_gaga(x1, x2, x3, x5) 64.90/17.49 64.90/17.49 U109_ga(x1, x2, x3, x4, x5) = U109_ga(x1, x2, x5) 64.90/17.49 64.90/17.49 U110_ga(x1, x2, x3) = U110_ga(x1, x3) 64.90/17.49 64.90/17.49 U111_ga(x1, x2, x3) = U111_ga(x1, x3) 64.90/17.49 64.90/17.49 U127_gagg(x1, x2, x3, x4, x5) = U127_gagg(x1, x2, x3, x4, x5) 64.90/17.49 64.90/17.49 U88_gg(x1, x2, x3) = U88_gg(x1, x2, x3) 64.90/17.49 64.90/17.49 U89_gg(x1, x2, x3, x4) = U89_gg(x2, x3, x4) 64.90/17.49 64.90/17.49 U90_gg(x1, x2, x3, x4, x5, x6, x7) = U90_gg(x1, x2, x3, x4, x5, x6, x7) 64.90/17.49 64.90/17.49 U91_gg(x1, x2, x3, x4, x5, x6, x7) = U91_gg(x1, x2, x3, x4, x5, x6, x7) 64.90/17.49 64.90/17.49 U92_gg(x1, x2, x3, x4, x5, x6) = U92_gg(x1, x2, x3, x4, x5, x6) 64.90/17.49 64.90/17.49 qcF_out_gagg(x1, x2, x3, x4) = qcF_out_gagg(x1, x2, x3, x4) 64.90/17.49 64.90/17.49 U93_gg(x1, x2, x3) = U93_gg(x1, x2, x3) 64.90/17.49 64.90/17.49 qcG_in_gag(x1, x2, x3) = qcG_in_gag(x1, x3) 64.90/17.49 64.90/17.49 U128_gag(x1, x2) = U128_gag(x1, x2) 64.90/17.49 64.90/17.49 qcG_out_gag(x1, x2, x3) = qcG_out_gag(x1, x2, x3) 64.90/17.49 64.90/17.49 U129_gag(x1, x2, x3) = U129_gag(x2, x3) 64.90/17.49 64.90/17.49 U130_gag(x1, x2, x3, x4, x5, x6) = U130_gag(x1, x2, x5, x6) 64.90/17.49 64.90/17.49 U131_gag(x1, x2, x3, x4, x5, x6) = U131_gag(x1, x2, x3, x5, x6) 64.90/17.49 64.90/17.49 U132_gag(x1, x2, x3, x4, x5, x6) = U132_gag(x1, x2, x3, x4, x5, x6) 64.90/17.49 64.90/17.49 U133_gag(x1, x2, x3, x4, x5, x6) = U133_gag(x1, x2, x5, x6) 64.90/17.49 64.90/17.49 U134_gag(x1, x2, x3, x4, x5, x6) = U134_gag(x1, x2, x4, x5, x6) 64.90/17.49 64.90/17.49 U135_gag(x1, x2, x3, x4, x5, x6) = U135_gag(x1, x2, x3, x4, x5, x6) 64.90/17.49 64.90/17.49 U136_gag(x1, x2, x3, x4) = U136_gag(x1, x3, x4) 64.90/17.49 64.90/17.49 U137_gag(x1, x2, x3, x4) = U137_gag(x1, x3, x4) 64.90/17.49 64.90/17.49 U125_gggg(x1, x2, x3, x4, x5) = U125_gggg(x1, x2, x3, x4, x5) 64.90/17.49 64.90/17.49 qcE_out_gggg(x1, x2, x3, x4) = qcE_out_gggg(x1, x2, x3, x4) 64.90/17.49 64.90/17.49 U123_gggggg(x1, x2, x3, x4, x5, x6, x7) = U123_gggggg(x1, x2, x3, x4, x5, x6, x7) 64.90/17.49 64.90/17.49 qcC_out_ga(x1, x2) = qcC_out_ga(x1, x2) 64.90/17.49 64.90/17.49 U113_ga(x1, x2) = U113_ga(x2) 64.90/17.49 64.90/17.49 U114_ga(x1, x2, x3, x4, x5) = U114_ga(x1, x2, x5) 64.90/17.49 64.90/17.49 U115_ga(x1, x2, x3, x4, x5) = U115_ga(x1, x2, x3, x5) 64.90/17.49 64.90/17.49 U116_ga(x1, x2, x3, x4, x5) = U116_ga(x1, x2, x3, x4, x5) 64.90/17.49 64.90/17.49 U117_ga(x1, x2, x3, x4, x5) = U117_ga(x1, x2, x5) 64.90/17.49 64.90/17.49 U118_ga(x1, x2, x3, x4, x5) = U118_ga(x1, x2, x4, x5) 64.90/17.49 64.90/17.49 U119_ga(x1, x2, x3, x4, x5) = U119_ga(x1, x2, x3, x4, x5) 64.90/17.49 64.90/17.49 U120_ga(x1, x2, x3) = U120_ga(x1, x3) 64.90/17.49 64.90/17.49 U121_ga(x1, x2, x3) = U121_ga(x1, x3) 64.90/17.49 64.90/17.49 qcB_out_ga(x1, x2) = qcB_out_ga(x1, x2) 64.90/17.49 64.90/17.49 U99_ga(x1, x2) = U99_ga(x2) 64.90/17.49 64.90/17.49 U100_ga(x1, x2, x3, x4, x5) = U100_ga(x1, x2, x5) 64.90/17.49 64.90/17.49 U101_ga(x1, x2, x3, x4, x5) = U101_ga(x1, x2, x3, x5) 64.90/17.49 64.90/17.49 U102_ga(x1, x2, x3, x4, x5) = U102_ga(x1, x2, x3, x4, x5) 64.90/17.49 64.90/17.49 U103_ga(x1, x2, x3, x4, x5) = U103_ga(x1, x2, x5) 64.90/17.49 64.90/17.49 U104_ga(x1, x2, x3, x4, x5) = U104_ga(x1, x2, x4, x5) 64.90/17.49 64.90/17.49 U105_ga(x1, x2, x3, x4, x5) = U105_ga(x1, x2, x3, x4, x5) 64.90/17.49 64.90/17.49 U106_ga(x1, x2, x3) = U106_ga(x1, x3) 64.90/17.49 64.90/17.49 U107_ga(x1, x2, x3) = U107_ga(x1, x3) 64.90/17.49 64.90/17.49 pcH_in_aa(x1, x2) = pcH_in_aa 64.90/17.49 64.90/17.49 pcH_out_aa(x1, x2) = pcH_out_aa(x1, x2) 64.90/17.49 64.90/17.49 U94_aa(x1, x2, x3, x4, x5) = U94_aa(x5) 64.90/17.49 64.90/17.49 qcI_in_aaaa(x1, x2, x3, x4) = qcI_in_aaaa 64.90/17.49 64.90/17.49 U96_aaaa(x1, x2, x3, x4, x5) = U96_aaaa(x5) 64.90/17.49 64.90/17.49 U95_aa(x1, x2, x3, x4, x5) = U95_aa(x5) 64.90/17.49 64.90/17.49 qcI_out_aaaa(x1, x2, x3, x4) = qcI_out_aaaa(x1, x2, x3, x4) 64.90/17.49 64.90/17.49 U97_aaaa(x1, x2, x3, x4, x5) = U97_aaaa(x1, x2, x5) 64.90/17.49 64.90/17.49 pcJ_in_aa(x1, x2) = pcJ_in_aa 64.90/17.49 64.90/17.49 pcJ_out_aa(x1, x2) = pcJ_out_aa(x1, x2) 64.90/17.49 64.90/17.49 U108_aa(x1, x2, x3, x4, x5) = U108_aa(x5) 64.90/17.49 64.90/17.49 U109_aa(x1, x2, x3, x4, x5) = U109_aa(x5) 64.90/17.49 64.90/17.49 U110_aa(x1, x2, x3) = U110_aa(x3) 64.90/17.49 64.90/17.49 U111_aa(x1, x2, x3) = U111_aa(x1, x3) 64.90/17.49 64.90/17.49 pcA_in_ag(x1, x2) = pcA_in_ag(x2) 64.90/17.49 64.90/17.49 pcA_out_ag(x1, x2) = pcA_out_ag(x1, x2) 64.90/17.49 64.90/17.49 U80_ag(x1, x2) = U80_ag(x2) 64.90/17.49 64.90/17.49 qcB_in_aa(x1, x2) = qcB_in_aa 64.90/17.49 64.90/17.49 U98_aa(x1) = U98_aa(x1) 64.90/17.49 64.90/17.49 qcB_out_aa(x1, x2) = qcB_out_aa(x1, x2) 64.90/17.49 64.90/17.49 U99_aa(x1, x2) = U99_aa(x2) 64.90/17.49 64.90/17.49 U100_aa(x1, x2, x3, x4, x5) = U100_aa(x5) 64.90/17.49 64.90/17.49 U101_aa(x1, x2, x3, x4, x5) = U101_aa(x1, x3, x5) 64.90/17.49 64.90/17.49 U102_aa(x1, x2, x3, x4, x5) = U102_aa(x1, x2, x3, x4, x5) 64.90/17.49 64.90/17.49 U103_aa(x1, x2, x3, x4, x5) = U103_aa(x5) 64.90/17.49 64.90/17.49 U104_aa(x1, x2, x3, x4, x5) = U104_aa(x1, x4, x5) 64.90/17.49 64.90/17.49 U105_aa(x1, x2, x3, x4, x5) = U105_aa(x1, x2, x3, x4, x5) 64.90/17.49 64.90/17.49 U106_aa(x1, x2, x3) = U106_aa(x3) 64.90/17.49 64.90/17.49 U107_aa(x1, x2, x3) = U107_aa(x1, x3) 64.90/17.49 64.90/17.49 U81_ag(x1, x2) = U81_ag(x2) 64.90/17.49 64.90/17.49 qcC_in_aa(x1, x2) = qcC_in_aa 64.90/17.49 64.90/17.49 U112_aa(x1) = U112_aa(x1) 64.90/17.49 64.90/17.49 qcC_out_aa(x1, x2) = qcC_out_aa(x1, x2) 64.90/17.49 64.90/17.49 U113_aa(x1, x2) = U113_aa(x2) 64.90/17.49 64.90/17.49 U114_aa(x1, x2, x3, x4, x5) = U114_aa(x5) 64.90/17.49 64.90/17.49 U115_aa(x1, x2, x3, x4, x5) = U115_aa(x1, x3, x5) 64.90/17.49 64.90/17.49 U116_aa(x1, x2, x3, x4, x5) = U116_aa(x1, x2, x3, x4, x5) 64.90/17.49 64.90/17.49 U117_aa(x1, x2, x3, x4, x5) = U117_aa(x5) 64.90/17.49 64.90/17.49 U118_aa(x1, x2, x3, x4, x5) = U118_aa(x1, x4, x5) 64.90/17.49 64.90/17.49 U119_aa(x1, x2, x3, x4, x5) = U119_aa(x1, x2, x3, x4, x5) 64.90/17.49 64.90/17.49 U120_aa(x1, x2, x3) = U120_aa(x3) 64.90/17.49 64.90/17.49 U121_aa(x1, x2, x3) = U121_aa(x1, x3) 64.90/17.49 64.90/17.49 U82_ag(x1, x2, x3) = U82_ag(x2, x3) 64.90/17.49 64.90/17.49 U83_ag(x1, x2, x3, x4) = U83_ag(x3, x4) 64.90/17.49 64.90/17.49 U84_ag(x1, x2, x3, x4, x5, x6, x7) = U84_ag(x4, x5, x6, x7) 64.90/17.49 64.90/17.49 qcD_in_agagag(x1, x2, x3, x4, x5, x6) = qcD_in_agagag(x2, x4, x6) 64.90/17.49 64.90/17.49 U122_agagag(x1, x2, x3, x4, x5, x6, x7) = U122_agagag(x2, x4, x6, x7) 64.90/17.49 64.90/17.49 U85_ag(x1, x2, x3, x4, x5, x6, x7) = U85_ag(x1, x2, x4, x5, x6, x7) 64.90/17.49 64.90/17.49 qcD_in_ggggag(x1, x2, x3, x4, x5, x6) = qcD_in_ggggag(x1, x2, x3, x4, x6) 64.90/17.49 64.90/17.49 U122_ggggag(x1, x2, x3, x4, x5, x6, x7) = U122_ggggag(x1, x2, x3, x4, x6, x7) 64.90/17.49 64.90/17.49 U123_ggggag(x1, x2, x3, x4, x5, x6, x7) = U123_ggggag(x1, x2, x3, x4, x6, x7) 64.90/17.49 64.90/17.49 qcE_in_ggag(x1, x2, x3, x4) = qcE_in_ggag(x1, x2, x4) 64.90/17.49 64.90/17.49 U124_ggag(x1, x2, x3, x4, x5) = U124_ggag(x1, x2, x4, x5) 64.90/17.49 64.90/17.49 U125_ggag(x1, x2, x3, x4, x5) = U125_ggag(x1, x2, x4, x5) 64.90/17.49 64.90/17.49 U86_ag(x1, x2, x3, x4, x5) = U86_ag(x1, x2, x3, x4, x5) 64.90/17.49 64.90/17.49 U87_ag(x1, x2, x3, x4) = U87_ag(x2, x3, x4) 64.90/17.49 64.90/17.49 qcF_in_aagg(x1, x2, x3, x4) = qcF_in_aagg(x3, x4) 64.90/17.49 64.90/17.49 U126_aagg(x1, x2, x3, x4, x5) = U126_aagg(x3, x4, x5) 64.90/17.49 64.90/17.49 U127_aagg(x1, x2, x3, x4, x5) = U127_aagg(x1, x2, x3, x4, x5) 64.90/17.49 64.90/17.49 qcF_out_aagg(x1, x2, x3, x4) = qcF_out_aagg(x1, x2, x3, x4) 64.90/17.49 64.90/17.49 U88_ag(x1, x2, x3) = U88_ag(x1, x2, x3) 64.90/17.49 64.90/17.49 U89_ag(x1, x2, x3, x4) = U89_ag(x2, x3, x4) 64.90/17.49 64.90/17.49 U90_ag(x1, x2, x3, x4, x5, x6, x7) = U90_ag(x1, x2, x3, x4, x5, x6, x7) 64.90/17.49 64.90/17.49 U91_ag(x1, x2, x3, x4, x5, x6, x7) = U91_ag(x1, x2, x3, x4, x5, x6, x7) 64.90/17.49 64.90/17.49 U92_ag(x1, x2, x3, x4, x5, x6) = U92_ag(x2, x3, x4, x5, x6) 64.90/17.49 64.90/17.49 U93_ag(x1, x2, x3) = U93_ag(x2, x3) 64.90/17.49 64.90/17.49 qcG_in_aag(x1, x2, x3) = qcG_in_aag(x3) 64.90/17.49 64.90/17.49 U128_aag(x1, x2) = U128_aag(x1, x2) 64.90/17.49 64.90/17.49 qcG_out_aag(x1, x2, x3) = qcG_out_aag(x1, x2, x3) 64.90/17.49 64.90/17.49 U129_aag(x1, x2, x3) = U129_aag(x2, x3) 64.90/17.49 64.90/17.49 U130_aag(x1, x2, x3, x4, x5, x6) = U130_aag(x5, x6) 64.90/17.49 64.90/17.49 U131_aag(x1, x2, x3, x4, x5, x6) = U131_aag(x1, x3, x5, x6) 64.90/17.49 64.90/17.49 U132_aag(x1, x2, x3, x4, x5, x6) = U132_aag(x1, x2, x3, x4, x5, x6) 64.90/17.49 64.90/17.49 U133_aag(x1, x2, x3, x4, x5, x6) = U133_aag(x5, x6) 64.90/17.49 64.90/17.49 U134_aag(x1, x2, x3, x4, x5, x6) = U134_aag(x1, x4, x5, x6) 64.90/17.49 64.90/17.49 U135_aag(x1, x2, x3, x4, x5, x6) = U135_aag(x1, x2, x3, x4, x5, x6) 64.90/17.49 64.90/17.49 U136_aag(x1, x2, x3, x4) = U136_aag(x3, x4) 64.90/17.49 64.90/17.49 U137_aag(x1, x2, x3, x4) = U137_aag(x1, x3, x4) 64.90/17.49 64.90/17.49 qcE_out_ggag(x1, x2, x3, x4) = qcE_out_ggag(x1, x2, x3, x4) 64.90/17.49 64.90/17.49 qcD_out_ggggag(x1, x2, x3, x4, x5, x6) = qcD_out_ggggag(x1, x2, x3, x4, x5, x6) 64.90/17.49 64.90/17.49 U123_agagag(x1, x2, x3, x4, x5, x6, x7) = U123_agagag(x1, x2, x4, x6, x7) 64.90/17.49 64.90/17.49 qcE_in_agag(x1, x2, x3, x4) = qcE_in_agag(x2, x4) 64.90/17.49 64.90/17.49 U124_agag(x1, x2, x3, x4, x5) = U124_agag(x2, x4, x5) 64.90/17.49 64.90/17.49 U125_agag(x1, x2, x3, x4, x5) = U125_agag(x1, x2, x4, x5) 64.90/17.49 64.90/17.49 qcE_out_agag(x1, x2, x3, x4) = qcE_out_agag(x1, x2, x3, x4) 64.90/17.49 64.90/17.49 qcD_out_agagag(x1, x2, x3, x4, x5, x6) = qcD_out_agagag(x1, x2, x3, x4, x5, x6) 64.90/17.49 64.90/17.49 PJ_IN_GA(x1, x2) = PJ_IN_GA(x1) 64.90/17.49 64.90/17.49 64.90/17.49 We have to consider all (P,R,Pi)-chains 64.90/17.49 ---------------------------------------- 64.90/17.49 64.90/17.49 (135) UsableRulesProof (EQUIVALENT) 64.90/17.49 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 64.90/17.49 ---------------------------------------- 64.90/17.49 64.90/17.49 (136) 64.90/17.49 Obligation: 64.90/17.49 Pi DP problem: 64.90/17.49 The TRS P consists of the following rules: 64.90/17.49 64.90/17.49 PJ_IN_GA(d(X1), X2) -> PJ_IN_GA(X1, X3) 64.90/17.49 64.90/17.49 R is empty. 64.90/17.49 The argument filtering Pi contains the following mapping: 64.90/17.49 d(x1) = d(x1) 64.90/17.49 64.90/17.49 PJ_IN_GA(x1, x2) = PJ_IN_GA(x1) 64.90/17.49 64.90/17.49 64.90/17.49 We have to consider all (P,R,Pi)-chains 64.90/17.49 ---------------------------------------- 64.90/17.49 64.90/17.49 (137) 64.90/17.49 Obligation: 64.90/17.49 Pi DP problem: 64.90/17.49 The TRS P consists of the following rules: 64.90/17.49 64.90/17.49 PA_IN_GG(d(e(+(const(X1), X2))), +(const(0), X3)) -> PA_IN_GG(d(e(X2)), X3) 64.90/17.49 PA_IN_GG(d(e(+(t, X1))), +(const(1), X2)) -> PA_IN_GG(d(e(X1)), X2) 64.90/17.49 PA_IN_GG(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) -> PD_IN_GGGGGG(X1, X4, X2, X5, X3, X6) 64.90/17.49 PD_IN_GGGGGG(X1, X2, X3, X4, X5, X6) -> PA_IN_GG(d(e(X1)), X2) 64.90/17.49 PA_IN_GG(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) -> PD_IN_GGGGGG(X1, X5, X2, X4, X3, X6) 64.90/17.49 PD_IN_GGGGGG(X1, X2, X3, X4, X5, X6) -> U42_GGGGGG(X1, X2, X3, X4, X5, X6, pcA_in_gg(d(e(X1)), X2)) 64.90/17.49 U42_GGGGGG(X1, X2, X3, X4, X5, X6, pcA_out_gg(d(e(X1)), X2)) -> PE_IN_GGGG(X3, X4, X5, X6) 64.90/17.49 PE_IN_GGGG(X1, X2, X3, X4) -> PA_IN_GG(d(e(X1)), X2) 64.90/17.49 PA_IN_GG(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) -> PE_IN_GGGG(X1, X4, X2, X3) 64.90/17.49 PE_IN_GGGG(X1, X2, X3, X4) -> U45_GGGG(X1, X2, X3, X4, pcA_in_gg(d(e(X1)), X2)) 64.90/17.49 U45_GGGG(X1, X2, X3, X4, pcA_out_gg(d(e(X1)), X2)) -> PA_IN_GG(d(e(X3)), X4) 64.90/17.49 PA_IN_GG(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) -> PA_IN_GG(d(e(X1)), X2) 64.90/17.49 PA_IN_GG(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) -> PA_IN_GG(d(e(X2)), X3) 64.90/17.49 PA_IN_GG(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) -> PD_IN_GGGGGG(X1, X5, X2, X6, X3, X4) 64.90/17.49 PA_IN_GG(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) -> PD_IN_GGGGGG(X1, X6, X2, X5, X3, X4) 64.90/17.49 64.90/17.49 The TRS R consists of the following rules: 64.90/17.49 64.90/17.49 pcA_in_gg(d(e(t)), const(1)) -> pcA_out_gg(d(e(t)), const(1)) 64.90/17.49 pcA_in_gg(d(d(X1)), const(1)) -> U80_gg(X1, qcB_in_ga(X1, X2)) 64.90/17.49 qcB_in_ga(e(t), const(1)) -> U98_ga(pcA_in_gg(d(e(const(1))), const(1))) 64.90/17.49 pcA_in_gg(d(e(const(X1))), const(0)) -> pcA_out_gg(d(e(const(X1))), const(0)) 64.90/17.49 pcA_in_gg(d(d(X1)), const(0)) -> U81_gg(X1, qcC_in_ga(X1, X2)) 64.90/17.49 qcC_in_ga(e(t), const(1)) -> U112_ga(pcA_in_gg(d(e(const(1))), const(0))) 64.90/17.49 pcA_in_gg(d(e(+(t, X1))), +(const(1), X2)) -> U82_gg(X1, X2, pcA_in_gg(d(e(X1)), X2)) 64.90/17.49 pcA_in_gg(d(e(+(const(X1), X2))), +(const(0), X3)) -> U83_gg(X1, X2, X3, pcA_in_gg(d(e(X2)), X3)) 64.90/17.49 pcA_in_gg(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) -> U84_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X4, X2, X5, X3, X6)) 64.90/17.49 qcD_in_gggggg(X1, X2, X3, X4, X5, X6) -> U122_gggggg(X1, X2, X3, X4, X5, X6, pcA_in_gg(d(e(X1)), X2)) 64.90/17.49 pcA_in_gg(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) -> U85_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X5, X2, X4, X3, X6)) 64.90/17.49 U85_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X5, X2, X4, X3, X6)) -> pcA_out_gg(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) 64.90/17.49 pcA_in_gg(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) -> U86_gg(X1, X2, X3, X4, qcE_in_gggg(X1, X4, X2, X3)) 64.90/17.49 qcE_in_gggg(X1, X2, X3, X4) -> U124_gggg(X1, X2, X3, X4, pcA_in_gg(d(e(X1)), X2)) 64.90/17.49 pcA_in_gg(d(d(X1)), +(X2, X3)) -> U87_gg(X1, X2, X3, qcF_in_gagg(X1, X4, X2, X3)) 64.90/17.49 qcF_in_gagg(X1, X2, X3, X4) -> U126_gagg(X1, X2, X3, X4, pcJ_in_ga(X1, X2)) 64.90/17.49 pcJ_in_ga(e(t), const(1)) -> pcJ_out_ga(e(t), const(1)) 64.90/17.49 pcJ_in_ga(e(const(X1)), const(0)) -> pcJ_out_ga(e(const(X1)), const(0)) 64.90/17.49 pcJ_in_ga(e(+(X1, X2)), +(X3, X4)) -> U108_ga(X1, X2, X3, X4, qcI_in_gaga(X1, X3, X2, X4)) 64.90/17.49 qcI_in_gaga(X1, X2, X3, X4) -> U96_gaga(X1, X2, X3, X4, pcH_in_ga(X1, X2)) 64.90/17.49 pcH_in_ga(t, const(1)) -> pcH_out_ga(t, const(1)) 64.90/17.49 pcH_in_ga(const(X1), const(0)) -> pcH_out_ga(const(X1), const(0)) 64.90/17.49 pcH_in_ga(+(X1, X2), +(X3, X4)) -> U94_ga(X1, X2, X3, X4, qcI_in_gaga(X1, X3, X2, X4)) 64.90/17.49 U94_ga(X1, X2, X3, X4, qcI_out_gaga(X1, X3, X2, X4)) -> pcH_out_ga(+(X1, X2), +(X3, X4)) 64.90/17.49 pcH_in_ga(*(X1, X2), +(*(X1, X3), *(X2, X4))) -> U95_ga(X1, X2, X3, X4, qcI_in_gaga(X1, X4, X2, X3)) 64.90/17.49 U95_ga(X1, X2, X3, X4, qcI_out_gaga(X1, X4, X2, X3)) -> pcH_out_ga(*(X1, X2), +(*(X1, X3), *(X2, X4))) 64.90/17.49 U96_gaga(X1, X2, X3, X4, pcH_out_ga(X1, X2)) -> U97_gaga(X1, X2, X3, X4, pcH_in_ga(X3, X4)) 64.90/17.49 U97_gaga(X1, X2, X3, X4, pcH_out_ga(X3, X4)) -> qcI_out_gaga(X1, X2, X3, X4) 64.90/17.49 U108_ga(X1, X2, X3, X4, qcI_out_gaga(X1, X3, X2, X4)) -> pcJ_out_ga(e(+(X1, X2)), +(X3, X4)) 64.90/17.49 pcJ_in_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U109_ga(X1, X2, X3, X4, qcI_in_gaga(X1, X4, X2, X3)) 64.90/17.49 U109_ga(X1, X2, X3, X4, qcI_out_gaga(X1, X4, X2, X3)) -> pcJ_out_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.90/17.49 pcJ_in_ga(d(X1), X2) -> U110_ga(X1, X2, pcJ_in_ga(X1, X3)) 64.90/17.49 U110_ga(X1, X2, pcJ_out_ga(X1, X3)) -> U111_ga(X1, X2, pcH_in_ga(X3, X2)) 64.90/17.49 U111_ga(X1, X2, pcH_out_ga(X3, X2)) -> pcJ_out_ga(d(X1), X2) 64.90/17.49 U126_gagg(X1, X2, X3, X4, pcJ_out_ga(X1, X2)) -> U127_gagg(X1, X2, X3, X4, pcA_in_gg(d(e(X2)), +(X3, X4))) 64.90/17.49 pcA_in_gg(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) -> U88_gg(X1, X2, pcA_in_gg(d(e(X1)), X2)) 64.90/17.49 pcA_in_gg(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) -> U89_gg(X1, X2, X3, pcA_in_gg(d(e(X2)), X3)) 64.90/17.49 pcA_in_gg(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) -> U90_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X5, X2, X6, X3, X4)) 64.96/17.50 U90_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X5, X2, X6, X3, X4)) -> pcA_out_gg(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) 64.96/17.50 pcA_in_gg(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) -> U91_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X6, X2, X5, X3, X4)) 64.96/17.50 U91_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X6, X2, X5, X3, X4)) -> pcA_out_gg(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) 64.96/17.50 pcA_in_gg(d(d(X1)), +(*(X2, X3), *(X4, X5))) -> U92_gg(X1, X2, X3, X4, X5, qcF_in_gagg(X1, X6, *(X2, X3), *(X4, X5))) 64.96/17.50 U92_gg(X1, X2, X3, X4, X5, qcF_out_gagg(X1, X6, *(X2, X3), *(X4, X5))) -> pcA_out_gg(d(d(X1)), +(*(X2, X3), *(X4, X5))) 64.96/17.50 pcA_in_gg(d(d(X1)), X2) -> U93_gg(X1, X2, qcG_in_gag(X1, X3, X2)) 64.96/17.50 qcG_in_gag(e(t), const(1), X1) -> U128_gag(X1, pcA_in_gg(d(e(const(1))), X1)) 64.96/17.50 U128_gag(X1, pcA_out_gg(d(e(const(1))), X1)) -> qcG_out_gag(e(t), const(1), X1) 64.96/17.50 qcG_in_gag(e(const(X1)), const(0), X2) -> U129_gag(X1, X2, pcA_in_gg(d(e(const(0))), X2)) 64.96/17.50 U129_gag(X1, X2, pcA_out_gg(d(e(const(0))), X2)) -> qcG_out_gag(e(const(X1)), const(0), X2) 64.96/17.50 qcG_in_gag(e(+(X1, X2)), +(X3, X4), X5) -> U130_gag(X1, X2, X3, X4, X5, pcH_in_ga(X1, X3)) 64.96/17.50 U130_gag(X1, X2, X3, X4, X5, pcH_out_ga(X1, X3)) -> U131_gag(X1, X2, X3, X4, X5, pcH_in_ga(X2, X4)) 64.96/17.50 U131_gag(X1, X2, X3, X4, X5, pcH_out_ga(X2, X4)) -> U132_gag(X1, X2, X3, X4, X5, pcA_in_gg(d(e(+(X3, X4))), X5)) 64.96/17.50 U132_gag(X1, X2, X3, X4, X5, pcA_out_gg(d(e(+(X3, X4))), X5)) -> qcG_out_gag(e(+(X1, X2)), +(X3, X4), X5) 64.96/17.50 qcG_in_gag(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) -> U133_gag(X1, X2, X3, X4, X5, pcH_in_ga(X1, X4)) 64.96/17.50 U133_gag(X1, X2, X3, X4, X5, pcH_out_ga(X1, X4)) -> U134_gag(X1, X2, X3, X4, X5, pcH_in_ga(X2, X3)) 64.96/17.50 U134_gag(X1, X2, X3, X4, X5, pcH_out_ga(X2, X3)) -> U135_gag(X1, X2, X3, X4, X5, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), X5)) 64.96/17.50 U135_gag(X1, X2, X3, X4, X5, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), X5)) -> qcG_out_gag(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) 64.96/17.50 qcG_in_gag(d(X1), X2, X3) -> U136_gag(X1, X2, X3, pcJ_in_ga(X1, X4)) 64.96/17.50 U136_gag(X1, X2, X3, pcJ_out_ga(X1, X4)) -> U137_gag(X1, X2, X3, qcG_in_gag(e(X4), X2, X3)) 64.96/17.50 U137_gag(X1, X2, X3, qcG_out_gag(e(X4), X2, X3)) -> qcG_out_gag(d(X1), X2, X3) 64.96/17.50 U93_gg(X1, X2, qcG_out_gag(X1, X3, X2)) -> pcA_out_gg(d(d(X1)), X2) 64.96/17.50 U89_gg(X1, X2, X3, pcA_out_gg(d(e(X2)), X3)) -> pcA_out_gg(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) 64.96/17.50 U88_gg(X1, X2, pcA_out_gg(d(e(X1)), X2)) -> pcA_out_gg(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) 64.96/17.50 U127_gagg(X1, X2, X3, X4, pcA_out_gg(d(e(X2)), +(X3, X4))) -> qcF_out_gagg(X1, X2, X3, X4) 64.96/17.50 U87_gg(X1, X2, X3, qcF_out_gagg(X1, X4, X2, X3)) -> pcA_out_gg(d(d(X1)), +(X2, X3)) 64.96/17.50 U124_gggg(X1, X2, X3, X4, pcA_out_gg(d(e(X1)), X2)) -> U125_gggg(X1, X2, X3, X4, pcA_in_gg(d(e(X3)), X4)) 64.96/17.50 U125_gggg(X1, X2, X3, X4, pcA_out_gg(d(e(X3)), X4)) -> qcE_out_gggg(X1, X2, X3, X4) 64.96/17.50 U86_gg(X1, X2, X3, X4, qcE_out_gggg(X1, X4, X2, X3)) -> pcA_out_gg(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) 64.96/17.50 U122_gggggg(X1, X2, X3, X4, X5, X6, pcA_out_gg(d(e(X1)), X2)) -> U123_gggggg(X1, X2, X3, X4, X5, X6, qcE_in_gggg(X3, X4, X5, X6)) 64.96/17.50 U123_gggggg(X1, X2, X3, X4, X5, X6, qcE_out_gggg(X3, X4, X5, X6)) -> qcD_out_gggggg(X1, X2, X3, X4, X5, X6) 64.96/17.50 U84_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X4, X2, X5, X3, X6)) -> pcA_out_gg(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) 64.96/17.50 U83_gg(X1, X2, X3, pcA_out_gg(d(e(X2)), X3)) -> pcA_out_gg(d(e(+(const(X1), X2))), +(const(0), X3)) 64.96/17.50 U82_gg(X1, X2, pcA_out_gg(d(e(X1)), X2)) -> pcA_out_gg(d(e(+(t, X1))), +(const(1), X2)) 64.96/17.50 U112_ga(pcA_out_gg(d(e(const(1))), const(0))) -> qcC_out_ga(e(t), const(1)) 64.96/17.50 qcC_in_ga(e(const(X1)), const(0)) -> U113_ga(X1, pcA_in_gg(d(e(const(0))), const(0))) 64.96/17.50 U113_ga(X1, pcA_out_gg(d(e(const(0))), const(0))) -> qcC_out_ga(e(const(X1)), const(0)) 64.96/17.50 qcC_in_ga(e(+(X1, X2)), +(X3, X4)) -> U114_ga(X1, X2, X3, X4, pcH_in_ga(X1, X3)) 64.96/17.50 U114_ga(X1, X2, X3, X4, pcH_out_ga(X1, X3)) -> U115_ga(X1, X2, X3, X4, pcH_in_ga(X2, X4)) 64.96/17.50 U115_ga(X1, X2, X3, X4, pcH_out_ga(X2, X4)) -> U116_ga(X1, X2, X3, X4, pcA_in_gg(d(e(+(X3, X4))), const(0))) 64.96/17.50 U116_ga(X1, X2, X3, X4, pcA_out_gg(d(e(+(X3, X4))), const(0))) -> qcC_out_ga(e(+(X1, X2)), +(X3, X4)) 64.96/17.50 qcC_in_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U117_ga(X1, X2, X3, X4, pcH_in_ga(X1, X4)) 64.96/17.50 U117_ga(X1, X2, X3, X4, pcH_out_ga(X1, X4)) -> U118_ga(X1, X2, X3, X4, pcH_in_ga(X2, X3)) 64.96/17.50 U118_ga(X1, X2, X3, X4, pcH_out_ga(X2, X3)) -> U119_ga(X1, X2, X3, X4, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(0))) 64.96/17.50 U119_ga(X1, X2, X3, X4, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(0))) -> qcC_out_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.96/17.50 qcC_in_ga(d(X1), X2) -> U120_ga(X1, X2, pcJ_in_ga(X1, X3)) 64.96/17.50 U120_ga(X1, X2, pcJ_out_ga(X1, X3)) -> U121_ga(X1, X2, qcC_in_ga(e(X3), X2)) 64.96/17.50 U121_ga(X1, X2, qcC_out_ga(e(X3), X2)) -> qcC_out_ga(d(X1), X2) 64.96/17.50 U81_gg(X1, qcC_out_ga(X1, X2)) -> pcA_out_gg(d(d(X1)), const(0)) 64.96/17.50 U98_ga(pcA_out_gg(d(e(const(1))), const(1))) -> qcB_out_ga(e(t), const(1)) 64.96/17.50 qcB_in_ga(e(const(X1)), const(0)) -> U99_ga(X1, pcA_in_gg(d(e(const(0))), const(1))) 64.96/17.50 U99_ga(X1, pcA_out_gg(d(e(const(0))), const(1))) -> qcB_out_ga(e(const(X1)), const(0)) 64.96/17.50 qcB_in_ga(e(+(X1, X2)), +(X3, X4)) -> U100_ga(X1, X2, X3, X4, pcH_in_ga(X1, X3)) 64.96/17.50 U100_ga(X1, X2, X3, X4, pcH_out_ga(X1, X3)) -> U101_ga(X1, X2, X3, X4, pcH_in_ga(X2, X4)) 64.96/17.50 U101_ga(X1, X2, X3, X4, pcH_out_ga(X2, X4)) -> U102_ga(X1, X2, X3, X4, pcA_in_gg(d(e(+(X3, X4))), const(1))) 64.96/17.50 U102_ga(X1, X2, X3, X4, pcA_out_gg(d(e(+(X3, X4))), const(1))) -> qcB_out_ga(e(+(X1, X2)), +(X3, X4)) 64.96/17.50 qcB_in_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U103_ga(X1, X2, X3, X4, pcH_in_ga(X1, X4)) 64.96/17.50 U103_ga(X1, X2, X3, X4, pcH_out_ga(X1, X4)) -> U104_ga(X1, X2, X3, X4, pcH_in_ga(X2, X3)) 64.96/17.50 U104_ga(X1, X2, X3, X4, pcH_out_ga(X2, X3)) -> U105_ga(X1, X2, X3, X4, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(1))) 64.96/17.50 U105_ga(X1, X2, X3, X4, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(1))) -> qcB_out_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.96/17.50 qcB_in_ga(d(X1), X2) -> U106_ga(X1, X2, pcJ_in_ga(X1, X3)) 64.96/17.50 U106_ga(X1, X2, pcJ_out_ga(X1, X3)) -> U107_ga(X1, X2, qcB_in_ga(e(X3), X2)) 64.96/17.50 U107_ga(X1, X2, qcB_out_ga(e(X3), X2)) -> qcB_out_ga(d(X1), X2) 64.96/17.50 U80_gg(X1, qcB_out_ga(X1, X2)) -> pcA_out_gg(d(d(X1)), const(1)) 64.96/17.50 pcH_in_aa(t, const(1)) -> pcH_out_aa(t, const(1)) 64.96/17.50 pcH_in_aa(const(X1), const(0)) -> pcH_out_aa(const(X1), const(0)) 64.96/17.50 pcH_in_aa(+(X1, X2), +(X3, X4)) -> U94_aa(X1, X2, X3, X4, qcI_in_aaaa(X1, X3, X2, X4)) 64.96/17.50 qcI_in_aaaa(X1, X2, X3, X4) -> U96_aaaa(X1, X2, X3, X4, pcH_in_aa(X1, X2)) 64.96/17.50 pcH_in_aa(*(X1, X2), +(*(X1, X3), *(X2, X4))) -> U95_aa(X1, X2, X3, X4, qcI_in_aaaa(X1, X4, X2, X3)) 64.96/17.50 U95_aa(X1, X2, X3, X4, qcI_out_aaaa(X1, X4, X2, X3)) -> pcH_out_aa(*(X1, X2), +(*(X1, X3), *(X2, X4))) 64.96/17.50 U96_aaaa(X1, X2, X3, X4, pcH_out_aa(X1, X2)) -> U97_aaaa(X1, X2, X3, X4, pcH_in_aa(X3, X4)) 64.96/17.50 U97_aaaa(X1, X2, X3, X4, pcH_out_aa(X3, X4)) -> qcI_out_aaaa(X1, X2, X3, X4) 64.96/17.50 U94_aa(X1, X2, X3, X4, qcI_out_aaaa(X1, X3, X2, X4)) -> pcH_out_aa(+(X1, X2), +(X3, X4)) 64.96/17.50 pcJ_in_aa(e(t), const(1)) -> pcJ_out_aa(e(t), const(1)) 64.96/17.50 pcJ_in_aa(e(const(X1)), const(0)) -> pcJ_out_aa(e(const(X1)), const(0)) 64.96/17.50 pcJ_in_aa(e(+(X1, X2)), +(X3, X4)) -> U108_aa(X1, X2, X3, X4, qcI_in_aaaa(X1, X3, X2, X4)) 64.96/17.50 U108_aa(X1, X2, X3, X4, qcI_out_aaaa(X1, X3, X2, X4)) -> pcJ_out_aa(e(+(X1, X2)), +(X3, X4)) 64.96/17.50 pcJ_in_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U109_aa(X1, X2, X3, X4, qcI_in_aaaa(X1, X4, X2, X3)) 64.96/17.50 U109_aa(X1, X2, X3, X4, qcI_out_aaaa(X1, X4, X2, X3)) -> pcJ_out_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.96/17.50 pcJ_in_aa(d(X1), X2) -> U110_aa(X1, X2, pcJ_in_aa(X1, X3)) 64.96/17.50 U110_aa(X1, X2, pcJ_out_aa(X1, X3)) -> U111_aa(X1, X2, pcH_in_ga(X3, X2)) 64.96/17.50 U111_aa(X1, X2, pcH_out_ga(X3, X2)) -> pcJ_out_aa(d(X1), X2) 64.96/17.50 pcA_in_ag(d(e(t)), const(1)) -> pcA_out_ag(d(e(t)), const(1)) 64.96/17.50 pcA_in_ag(d(d(X1)), const(1)) -> U80_ag(X1, qcB_in_aa(X1, X2)) 64.96/17.50 qcB_in_aa(e(t), const(1)) -> U98_aa(pcA_in_gg(d(e(const(1))), const(1))) 64.96/17.50 U98_aa(pcA_out_gg(d(e(const(1))), const(1))) -> qcB_out_aa(e(t), const(1)) 64.96/17.50 qcB_in_aa(e(const(X1)), const(0)) -> U99_aa(X1, pcA_in_gg(d(e(const(0))), const(1))) 64.96/17.50 U99_aa(X1, pcA_out_gg(d(e(const(0))), const(1))) -> qcB_out_aa(e(const(X1)), const(0)) 64.96/17.50 qcB_in_aa(e(+(X1, X2)), +(X3, X4)) -> U100_aa(X1, X2, X3, X4, pcH_in_aa(X1, X3)) 64.96/17.50 U100_aa(X1, X2, X3, X4, pcH_out_aa(X1, X3)) -> U101_aa(X1, X2, X3, X4, pcH_in_aa(X2, X4)) 64.96/17.50 U101_aa(X1, X2, X3, X4, pcH_out_aa(X2, X4)) -> U102_aa(X1, X2, X3, X4, pcA_in_gg(d(e(+(X3, X4))), const(1))) 64.96/17.50 U102_aa(X1, X2, X3, X4, pcA_out_gg(d(e(+(X3, X4))), const(1))) -> qcB_out_aa(e(+(X1, X2)), +(X3, X4)) 64.96/17.50 qcB_in_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U103_aa(X1, X2, X3, X4, pcH_in_aa(X1, X4)) 64.96/17.50 U103_aa(X1, X2, X3, X4, pcH_out_aa(X1, X4)) -> U104_aa(X1, X2, X3, X4, pcH_in_aa(X2, X3)) 64.96/17.50 U104_aa(X1, X2, X3, X4, pcH_out_aa(X2, X3)) -> U105_aa(X1, X2, X3, X4, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(1))) 64.96/17.50 U105_aa(X1, X2, X3, X4, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(1))) -> qcB_out_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.96/17.50 qcB_in_aa(d(X1), X2) -> U106_aa(X1, X2, pcJ_in_aa(X1, X3)) 64.96/17.50 U106_aa(X1, X2, pcJ_out_aa(X1, X3)) -> U107_aa(X1, X2, qcB_in_ga(e(X3), X2)) 64.96/17.50 U107_aa(X1, X2, qcB_out_ga(e(X3), X2)) -> qcB_out_aa(d(X1), X2) 64.96/17.50 U80_ag(X1, qcB_out_aa(X1, X2)) -> pcA_out_ag(d(d(X1)), const(1)) 64.96/17.50 pcA_in_ag(d(e(const(X1))), const(0)) -> pcA_out_ag(d(e(const(X1))), const(0)) 64.96/17.50 pcA_in_ag(d(d(X1)), const(0)) -> U81_ag(X1, qcC_in_aa(X1, X2)) 64.96/17.50 qcC_in_aa(e(t), const(1)) -> U112_aa(pcA_in_gg(d(e(const(1))), const(0))) 64.96/17.50 U112_aa(pcA_out_gg(d(e(const(1))), const(0))) -> qcC_out_aa(e(t), const(1)) 64.96/17.50 qcC_in_aa(e(const(X1)), const(0)) -> U113_aa(X1, pcA_in_gg(d(e(const(0))), const(0))) 64.96/17.50 U113_aa(X1, pcA_out_gg(d(e(const(0))), const(0))) -> qcC_out_aa(e(const(X1)), const(0)) 64.96/17.50 qcC_in_aa(e(+(X1, X2)), +(X3, X4)) -> U114_aa(X1, X2, X3, X4, pcH_in_aa(X1, X3)) 64.96/17.50 U114_aa(X1, X2, X3, X4, pcH_out_aa(X1, X3)) -> U115_aa(X1, X2, X3, X4, pcH_in_aa(X2, X4)) 64.96/17.50 U115_aa(X1, X2, X3, X4, pcH_out_aa(X2, X4)) -> U116_aa(X1, X2, X3, X4, pcA_in_gg(d(e(+(X3, X4))), const(0))) 64.96/17.50 U116_aa(X1, X2, X3, X4, pcA_out_gg(d(e(+(X3, X4))), const(0))) -> qcC_out_aa(e(+(X1, X2)), +(X3, X4)) 64.96/17.50 qcC_in_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U117_aa(X1, X2, X3, X4, pcH_in_aa(X1, X4)) 64.96/17.50 U117_aa(X1, X2, X3, X4, pcH_out_aa(X1, X4)) -> U118_aa(X1, X2, X3, X4, pcH_in_aa(X2, X3)) 64.96/17.50 U118_aa(X1, X2, X3, X4, pcH_out_aa(X2, X3)) -> U119_aa(X1, X2, X3, X4, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(0))) 64.96/17.50 U119_aa(X1, X2, X3, X4, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(0))) -> qcC_out_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.96/17.50 qcC_in_aa(d(X1), X2) -> U120_aa(X1, X2, pcJ_in_aa(X1, X3)) 64.96/17.50 U120_aa(X1, X2, pcJ_out_aa(X1, X3)) -> U121_aa(X1, X2, qcC_in_ga(e(X3), X2)) 64.96/17.50 U121_aa(X1, X2, qcC_out_ga(e(X3), X2)) -> qcC_out_aa(d(X1), X2) 64.96/17.50 U81_ag(X1, qcC_out_aa(X1, X2)) -> pcA_out_ag(d(d(X1)), const(0)) 64.96/17.50 pcA_in_ag(d(e(+(t, X1))), +(const(1), X2)) -> U82_ag(X1, X2, pcA_in_ag(d(e(X1)), X2)) 64.96/17.50 pcA_in_ag(d(e(+(const(X1), X2))), +(const(0), X3)) -> U83_ag(X1, X2, X3, pcA_in_ag(d(e(X2)), X3)) 64.96/17.50 pcA_in_ag(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) -> U84_ag(X1, X2, X3, X4, X5, X6, qcD_in_agagag(X1, X4, X2, X5, X3, X6)) 64.96/17.50 qcD_in_agagag(X1, X2, X3, X4, X5, X6) -> U122_agagag(X1, X2, X3, X4, X5, X6, pcA_in_ag(d(e(X1)), X2)) 64.96/17.50 pcA_in_ag(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) -> U85_ag(X1, X2, X3, X4, X5, X6, qcD_in_ggggag(X1, X5, X2, X4, X3, X6)) 64.96/17.50 qcD_in_ggggag(X1, X2, X3, X4, X5, X6) -> U122_ggggag(X1, X2, X3, X4, X5, X6, pcA_in_gg(d(e(X1)), X2)) 64.96/17.50 U122_ggggag(X1, X2, X3, X4, X5, X6, pcA_out_gg(d(e(X1)), X2)) -> U123_ggggag(X1, X2, X3, X4, X5, X6, qcE_in_ggag(X3, X4, X5, X6)) 64.96/17.50 qcE_in_ggag(X1, X2, X3, X4) -> U124_ggag(X1, X2, X3, X4, pcA_in_gg(d(e(X1)), X2)) 64.96/17.50 U124_ggag(X1, X2, X3, X4, pcA_out_gg(d(e(X1)), X2)) -> U125_ggag(X1, X2, X3, X4, pcA_in_ag(d(e(X3)), X4)) 64.96/17.50 pcA_in_ag(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) -> U86_ag(X1, X2, X3, X4, qcE_in_gggg(X1, X4, X2, X3)) 64.96/17.50 U86_ag(X1, X2, X3, X4, qcE_out_gggg(X1, X4, X2, X3)) -> pcA_out_ag(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) 64.96/17.50 pcA_in_ag(d(d(X1)), +(X2, X3)) -> U87_ag(X1, X2, X3, qcF_in_aagg(X1, X4, X2, X3)) 64.96/17.50 qcF_in_aagg(X1, X2, X3, X4) -> U126_aagg(X1, X2, X3, X4, pcJ_in_aa(X1, X2)) 64.96/17.50 U126_aagg(X1, X2, X3, X4, pcJ_out_aa(X1, X2)) -> U127_aagg(X1, X2, X3, X4, pcA_in_gg(d(e(X2)), +(X3, X4))) 64.96/17.50 U127_aagg(X1, X2, X3, X4, pcA_out_gg(d(e(X2)), +(X3, X4))) -> qcF_out_aagg(X1, X2, X3, X4) 64.96/17.50 U87_ag(X1, X2, X3, qcF_out_aagg(X1, X4, X2, X3)) -> pcA_out_ag(d(d(X1)), +(X2, X3)) 64.96/17.50 pcA_in_ag(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) -> U88_ag(X1, X2, pcA_in_gg(d(e(X1)), X2)) 64.96/17.50 U88_ag(X1, X2, pcA_out_gg(d(e(X1)), X2)) -> pcA_out_ag(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) 64.96/17.50 pcA_in_ag(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) -> U89_ag(X1, X2, X3, pcA_in_gg(d(e(X2)), X3)) 64.96/17.50 U89_ag(X1, X2, X3, pcA_out_gg(d(e(X2)), X3)) -> pcA_out_ag(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) 64.96/17.50 pcA_in_ag(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) -> U90_ag(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X5, X2, X6, X3, X4)) 64.96/17.50 U90_ag(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X5, X2, X6, X3, X4)) -> pcA_out_ag(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) 64.96/17.50 pcA_in_ag(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) -> U91_ag(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X6, X2, X5, X3, X4)) 64.96/17.50 U91_ag(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X6, X2, X5, X3, X4)) -> pcA_out_ag(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) 64.96/17.50 pcA_in_ag(d(d(X1)), +(*(X2, X3), *(X4, X5))) -> U92_ag(X1, X2, X3, X4, X5, qcF_in_aagg(X1, X6, *(X2, X3), *(X4, X5))) 64.96/17.50 U92_ag(X1, X2, X3, X4, X5, qcF_out_aagg(X1, X6, *(X2, X3), *(X4, X5))) -> pcA_out_ag(d(d(X1)), +(*(X2, X3), *(X4, X5))) 64.96/17.50 pcA_in_ag(d(d(X1)), X2) -> U93_ag(X1, X2, qcG_in_aag(X1, X3, X2)) 64.96/17.50 qcG_in_aag(e(t), const(1), X1) -> U128_aag(X1, pcA_in_gg(d(e(const(1))), X1)) 64.96/17.50 U128_aag(X1, pcA_out_gg(d(e(const(1))), X1)) -> qcG_out_aag(e(t), const(1), X1) 64.96/17.50 qcG_in_aag(e(const(X1)), const(0), X2) -> U129_aag(X1, X2, pcA_in_gg(d(e(const(0))), X2)) 64.96/17.50 U129_aag(X1, X2, pcA_out_gg(d(e(const(0))), X2)) -> qcG_out_aag(e(const(X1)), const(0), X2) 64.96/17.50 qcG_in_aag(e(+(X1, X2)), +(X3, X4), X5) -> U130_aag(X1, X2, X3, X4, X5, pcH_in_aa(X1, X3)) 64.96/17.50 U130_aag(X1, X2, X3, X4, X5, pcH_out_aa(X1, X3)) -> U131_aag(X1, X2, X3, X4, X5, pcH_in_aa(X2, X4)) 64.96/17.50 U131_aag(X1, X2, X3, X4, X5, pcH_out_aa(X2, X4)) -> U132_aag(X1, X2, X3, X4, X5, pcA_in_gg(d(e(+(X3, X4))), X5)) 64.96/17.50 U132_aag(X1, X2, X3, X4, X5, pcA_out_gg(d(e(+(X3, X4))), X5)) -> qcG_out_aag(e(+(X1, X2)), +(X3, X4), X5) 64.96/17.50 qcG_in_aag(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) -> U133_aag(X1, X2, X3, X4, X5, pcH_in_aa(X1, X4)) 64.96/17.50 U133_aag(X1, X2, X3, X4, X5, pcH_out_aa(X1, X4)) -> U134_aag(X1, X2, X3, X4, X5, pcH_in_aa(X2, X3)) 64.96/17.50 U134_aag(X1, X2, X3, X4, X5, pcH_out_aa(X2, X3)) -> U135_aag(X1, X2, X3, X4, X5, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), X5)) 64.96/17.50 U135_aag(X1, X2, X3, X4, X5, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), X5)) -> qcG_out_aag(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) 64.96/17.50 qcG_in_aag(d(X1), X2, X3) -> U136_aag(X1, X2, X3, pcJ_in_aa(X1, X4)) 64.96/17.50 U136_aag(X1, X2, X3, pcJ_out_aa(X1, X4)) -> U137_aag(X1, X2, X3, qcG_in_gag(e(X4), X2, X3)) 64.96/17.50 U137_aag(X1, X2, X3, qcG_out_gag(e(X4), X2, X3)) -> qcG_out_aag(d(X1), X2, X3) 64.96/17.50 U93_ag(X1, X2, qcG_out_aag(X1, X3, X2)) -> pcA_out_ag(d(d(X1)), X2) 64.96/17.50 U125_ggag(X1, X2, X3, X4, pcA_out_ag(d(e(X3)), X4)) -> qcE_out_ggag(X1, X2, X3, X4) 64.96/17.50 U123_ggggag(X1, X2, X3, X4, X5, X6, qcE_out_ggag(X3, X4, X5, X6)) -> qcD_out_ggggag(X1, X2, X3, X4, X5, X6) 64.96/17.50 U85_ag(X1, X2, X3, X4, X5, X6, qcD_out_ggggag(X1, X5, X2, X4, X3, X6)) -> pcA_out_ag(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) 64.96/17.50 U122_agagag(X1, X2, X3, X4, X5, X6, pcA_out_ag(d(e(X1)), X2)) -> U123_agagag(X1, X2, X3, X4, X5, X6, qcE_in_agag(X3, X4, X5, X6)) 64.96/17.50 qcE_in_agag(X1, X2, X3, X4) -> U124_agag(X1, X2, X3, X4, pcA_in_ag(d(e(X1)), X2)) 64.96/17.50 U124_agag(X1, X2, X3, X4, pcA_out_ag(d(e(X1)), X2)) -> U125_agag(X1, X2, X3, X4, pcA_in_ag(d(e(X3)), X4)) 64.96/17.50 U125_agag(X1, X2, X3, X4, pcA_out_ag(d(e(X3)), X4)) -> qcE_out_agag(X1, X2, X3, X4) 64.96/17.50 U123_agagag(X1, X2, X3, X4, X5, X6, qcE_out_agag(X3, X4, X5, X6)) -> qcD_out_agagag(X1, X2, X3, X4, X5, X6) 64.96/17.50 U84_ag(X1, X2, X3, X4, X5, X6, qcD_out_agagag(X1, X4, X2, X5, X3, X6)) -> pcA_out_ag(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) 64.96/17.50 U83_ag(X1, X2, X3, pcA_out_ag(d(e(X2)), X3)) -> pcA_out_ag(d(e(+(const(X1), X2))), +(const(0), X3)) 64.96/17.50 U82_ag(X1, X2, pcA_out_ag(d(e(X1)), X2)) -> pcA_out_ag(d(e(+(t, X1))), +(const(1), X2)) 64.96/17.50 64.96/17.50 The argument filtering Pi contains the following mapping: 64.96/17.50 const(x1) = const 64.96/17.50 64.96/17.50 1 = 1 64.96/17.50 64.96/17.50 d(x1) = d(x1) 64.96/17.50 64.96/17.50 e(x1) = e(x1) 64.96/17.50 64.96/17.50 t = t 64.96/17.50 64.96/17.50 0 = 0 64.96/17.50 64.96/17.50 +(x1, x2) = +(x1, x2) 64.96/17.50 64.96/17.50 *(x1, x2) = *(x1, x2) 64.96/17.50 64.96/17.50 pcA_in_gg(x1, x2) = pcA_in_gg(x1, x2) 64.96/17.50 64.96/17.50 pcA_out_gg(x1, x2) = pcA_out_gg(x1, x2) 64.96/17.50 64.96/17.50 U80_gg(x1, x2) = U80_gg(x1, x2) 64.96/17.50 64.96/17.50 qcB_in_ga(x1, x2) = qcB_in_ga(x1) 64.96/17.50 64.96/17.50 U98_ga(x1) = U98_ga(x1) 64.96/17.50 64.96/17.50 U81_gg(x1, x2) = U81_gg(x1, x2) 64.96/17.50 64.96/17.50 qcC_in_ga(x1, x2) = qcC_in_ga(x1) 64.96/17.50 64.96/17.50 U112_ga(x1) = U112_ga(x1) 64.96/17.50 64.96/17.50 U82_gg(x1, x2, x3) = U82_gg(x1, x2, x3) 64.96/17.50 64.96/17.50 U83_gg(x1, x2, x3, x4) = U83_gg(x2, x3, x4) 64.96/17.50 64.96/17.50 U84_gg(x1, x2, x3, x4, x5, x6, x7) = U84_gg(x1, x2, x3, x4, x5, x6, x7) 64.96/17.50 64.96/17.50 qcD_in_gggggg(x1, x2, x3, x4, x5, x6) = qcD_in_gggggg(x1, x2, x3, x4, x5, x6) 64.96/17.50 64.96/17.50 U122_gggggg(x1, x2, x3, x4, x5, x6, x7) = U122_gggggg(x1, x2, x3, x4, x5, x6, x7) 64.96/17.50 64.96/17.50 U85_gg(x1, x2, x3, x4, x5, x6, x7) = U85_gg(x1, x2, x3, x4, x5, x6, x7) 64.96/17.50 64.96/17.50 qcD_out_gggggg(x1, x2, x3, x4, x5, x6) = qcD_out_gggggg(x1, x2, x3, x4, x5, x6) 64.96/17.50 64.96/17.50 U86_gg(x1, x2, x3, x4, x5) = U86_gg(x1, x2, x3, x4, x5) 64.96/17.50 64.96/17.50 qcE_in_gggg(x1, x2, x3, x4) = qcE_in_gggg(x1, x2, x3, x4) 64.96/17.50 64.96/17.50 U124_gggg(x1, x2, x3, x4, x5) = U124_gggg(x1, x2, x3, x4, x5) 64.96/17.50 64.96/17.50 U87_gg(x1, x2, x3, x4) = U87_gg(x1, x2, x3, x4) 64.96/17.50 64.96/17.50 qcF_in_gagg(x1, x2, x3, x4) = qcF_in_gagg(x1, x3, x4) 64.96/17.50 64.96/17.50 U126_gagg(x1, x2, x3, x4, x5) = U126_gagg(x1, x3, x4, x5) 64.96/17.50 64.96/17.50 pcJ_in_ga(x1, x2) = pcJ_in_ga(x1) 64.96/17.50 64.96/17.50 pcJ_out_ga(x1, x2) = pcJ_out_ga(x1, x2) 64.96/17.50 64.96/17.50 U108_ga(x1, x2, x3, x4, x5) = U108_ga(x1, x2, x5) 64.96/17.50 64.96/17.50 qcI_in_gaga(x1, x2, x3, x4) = qcI_in_gaga(x1, x3) 64.96/17.50 64.96/17.50 U96_gaga(x1, x2, x3, x4, x5) = U96_gaga(x1, x3, x5) 64.96/17.50 64.96/17.50 pcH_in_ga(x1, x2) = pcH_in_ga(x1) 64.96/17.50 64.96/17.50 pcH_out_ga(x1, x2) = pcH_out_ga(x1, x2) 64.96/17.50 64.96/17.50 U94_ga(x1, x2, x3, x4, x5) = U94_ga(x1, x2, x5) 64.96/17.50 64.96/17.50 qcI_out_gaga(x1, x2, x3, x4) = qcI_out_gaga(x1, x2, x3, x4) 64.96/17.50 64.96/17.50 U95_ga(x1, x2, x3, x4, x5) = U95_ga(x1, x2, x5) 64.96/17.50 64.96/17.50 U97_gaga(x1, x2, x3, x4, x5) = U97_gaga(x1, x2, x3, x5) 64.96/17.50 64.96/17.50 U109_ga(x1, x2, x3, x4, x5) = U109_ga(x1, x2, x5) 64.96/17.50 64.96/17.50 U110_ga(x1, x2, x3) = U110_ga(x1, x3) 64.96/17.50 64.96/17.50 U111_ga(x1, x2, x3) = U111_ga(x1, x3) 64.96/17.50 64.96/17.50 U127_gagg(x1, x2, x3, x4, x5) = U127_gagg(x1, x2, x3, x4, x5) 64.96/17.50 64.96/17.50 U88_gg(x1, x2, x3) = U88_gg(x1, x2, x3) 64.96/17.50 64.96/17.50 U89_gg(x1, x2, x3, x4) = U89_gg(x2, x3, x4) 64.96/17.50 64.96/17.50 U90_gg(x1, x2, x3, x4, x5, x6, x7) = U90_gg(x1, x2, x3, x4, x5, x6, x7) 64.96/17.50 64.96/17.50 U91_gg(x1, x2, x3, x4, x5, x6, x7) = U91_gg(x1, x2, x3, x4, x5, x6, x7) 64.96/17.50 64.96/17.50 U92_gg(x1, x2, x3, x4, x5, x6) = U92_gg(x1, x2, x3, x4, x5, x6) 64.96/17.50 64.96/17.50 qcF_out_gagg(x1, x2, x3, x4) = qcF_out_gagg(x1, x2, x3, x4) 64.96/17.50 64.96/17.50 U93_gg(x1, x2, x3) = U93_gg(x1, x2, x3) 64.96/17.50 64.96/17.50 qcG_in_gag(x1, x2, x3) = qcG_in_gag(x1, x3) 64.96/17.50 64.96/17.50 U128_gag(x1, x2) = U128_gag(x1, x2) 64.96/17.50 64.96/17.50 qcG_out_gag(x1, x2, x3) = qcG_out_gag(x1, x2, x3) 64.96/17.50 64.96/17.50 U129_gag(x1, x2, x3) = U129_gag(x2, x3) 64.96/17.50 64.96/17.50 U130_gag(x1, x2, x3, x4, x5, x6) = U130_gag(x1, x2, x5, x6) 64.96/17.50 64.96/17.50 U131_gag(x1, x2, x3, x4, x5, x6) = U131_gag(x1, x2, x3, x5, x6) 64.96/17.50 64.96/17.50 U132_gag(x1, x2, x3, x4, x5, x6) = U132_gag(x1, x2, x3, x4, x5, x6) 64.96/17.50 64.96/17.50 U133_gag(x1, x2, x3, x4, x5, x6) = U133_gag(x1, x2, x5, x6) 64.96/17.50 64.96/17.50 U134_gag(x1, x2, x3, x4, x5, x6) = U134_gag(x1, x2, x4, x5, x6) 64.96/17.50 64.96/17.50 U135_gag(x1, x2, x3, x4, x5, x6) = U135_gag(x1, x2, x3, x4, x5, x6) 64.96/17.50 64.96/17.50 U136_gag(x1, x2, x3, x4) = U136_gag(x1, x3, x4) 64.96/17.50 64.96/17.50 U137_gag(x1, x2, x3, x4) = U137_gag(x1, x3, x4) 64.96/17.50 64.96/17.50 U125_gggg(x1, x2, x3, x4, x5) = U125_gggg(x1, x2, x3, x4, x5) 64.96/17.50 64.96/17.50 qcE_out_gggg(x1, x2, x3, x4) = qcE_out_gggg(x1, x2, x3, x4) 64.96/17.50 64.96/17.50 U123_gggggg(x1, x2, x3, x4, x5, x6, x7) = U123_gggggg(x1, x2, x3, x4, x5, x6, x7) 64.96/17.50 64.96/17.50 qcC_out_ga(x1, x2) = qcC_out_ga(x1, x2) 64.96/17.50 64.96/17.50 U113_ga(x1, x2) = U113_ga(x2) 64.96/17.50 64.96/17.50 U114_ga(x1, x2, x3, x4, x5) = U114_ga(x1, x2, x5) 64.96/17.50 64.96/17.50 U115_ga(x1, x2, x3, x4, x5) = U115_ga(x1, x2, x3, x5) 64.96/17.50 64.96/17.50 U116_ga(x1, x2, x3, x4, x5) = U116_ga(x1, x2, x3, x4, x5) 64.96/17.50 64.96/17.50 U117_ga(x1, x2, x3, x4, x5) = U117_ga(x1, x2, x5) 64.96/17.50 64.96/17.50 U118_ga(x1, x2, x3, x4, x5) = U118_ga(x1, x2, x4, x5) 64.96/17.50 64.96/17.50 U119_ga(x1, x2, x3, x4, x5) = U119_ga(x1, x2, x3, x4, x5) 64.96/17.50 64.96/17.50 U120_ga(x1, x2, x3) = U120_ga(x1, x3) 64.96/17.50 64.96/17.50 U121_ga(x1, x2, x3) = U121_ga(x1, x3) 64.96/17.50 64.96/17.50 qcB_out_ga(x1, x2) = qcB_out_ga(x1, x2) 64.96/17.50 64.96/17.50 U99_ga(x1, x2) = U99_ga(x2) 64.96/17.50 64.96/17.50 U100_ga(x1, x2, x3, x4, x5) = U100_ga(x1, x2, x5) 64.96/17.50 64.96/17.50 U101_ga(x1, x2, x3, x4, x5) = U101_ga(x1, x2, x3, x5) 64.96/17.50 64.96/17.50 U102_ga(x1, x2, x3, x4, x5) = U102_ga(x1, x2, x3, x4, x5) 64.96/17.50 64.96/17.50 U103_ga(x1, x2, x3, x4, x5) = U103_ga(x1, x2, x5) 64.96/17.50 64.96/17.50 U104_ga(x1, x2, x3, x4, x5) = U104_ga(x1, x2, x4, x5) 64.96/17.50 64.96/17.50 U105_ga(x1, x2, x3, x4, x5) = U105_ga(x1, x2, x3, x4, x5) 64.96/17.50 64.96/17.50 U106_ga(x1, x2, x3) = U106_ga(x1, x3) 64.96/17.50 64.96/17.50 U107_ga(x1, x2, x3) = U107_ga(x1, x3) 64.96/17.50 64.96/17.50 pcH_in_aa(x1, x2) = pcH_in_aa 64.96/17.50 64.96/17.50 pcH_out_aa(x1, x2) = pcH_out_aa(x1, x2) 64.96/17.50 64.96/17.50 U94_aa(x1, x2, x3, x4, x5) = U94_aa(x5) 64.96/17.50 64.96/17.50 qcI_in_aaaa(x1, x2, x3, x4) = qcI_in_aaaa 64.96/17.50 64.96/17.50 U96_aaaa(x1, x2, x3, x4, x5) = U96_aaaa(x5) 64.96/17.50 64.96/17.50 U95_aa(x1, x2, x3, x4, x5) = U95_aa(x5) 64.96/17.50 64.96/17.50 qcI_out_aaaa(x1, x2, x3, x4) = qcI_out_aaaa(x1, x2, x3, x4) 64.96/17.50 64.96/17.50 U97_aaaa(x1, x2, x3, x4, x5) = U97_aaaa(x1, x2, x5) 64.96/17.50 64.96/17.50 pcJ_in_aa(x1, x2) = pcJ_in_aa 64.96/17.50 64.96/17.50 pcJ_out_aa(x1, x2) = pcJ_out_aa(x1, x2) 64.96/17.50 64.96/17.50 U108_aa(x1, x2, x3, x4, x5) = U108_aa(x5) 64.96/17.50 64.96/17.50 U109_aa(x1, x2, x3, x4, x5) = U109_aa(x5) 64.96/17.50 64.96/17.50 U110_aa(x1, x2, x3) = U110_aa(x3) 64.96/17.50 64.96/17.50 U111_aa(x1, x2, x3) = U111_aa(x1, x3) 64.96/17.50 64.96/17.50 pcA_in_ag(x1, x2) = pcA_in_ag(x2) 64.96/17.50 64.96/17.50 pcA_out_ag(x1, x2) = pcA_out_ag(x1, x2) 64.96/17.50 64.96/17.50 U80_ag(x1, x2) = U80_ag(x2) 64.96/17.50 64.96/17.50 qcB_in_aa(x1, x2) = qcB_in_aa 64.96/17.50 64.96/17.50 U98_aa(x1) = U98_aa(x1) 64.96/17.50 64.96/17.50 qcB_out_aa(x1, x2) = qcB_out_aa(x1, x2) 64.96/17.50 64.96/17.50 U99_aa(x1, x2) = U99_aa(x2) 64.96/17.50 64.96/17.50 U100_aa(x1, x2, x3, x4, x5) = U100_aa(x5) 64.96/17.50 64.96/17.50 U101_aa(x1, x2, x3, x4, x5) = U101_aa(x1, x3, x5) 64.96/17.50 64.96/17.50 U102_aa(x1, x2, x3, x4, x5) = U102_aa(x1, x2, x3, x4, x5) 64.96/17.50 64.96/17.50 U103_aa(x1, x2, x3, x4, x5) = U103_aa(x5) 64.96/17.50 64.96/17.50 U104_aa(x1, x2, x3, x4, x5) = U104_aa(x1, x4, x5) 64.96/17.50 64.96/17.50 U105_aa(x1, x2, x3, x4, x5) = U105_aa(x1, x2, x3, x4, x5) 64.96/17.50 64.96/17.50 U106_aa(x1, x2, x3) = U106_aa(x3) 64.96/17.50 64.96/17.50 U107_aa(x1, x2, x3) = U107_aa(x1, x3) 64.96/17.50 64.96/17.50 U81_ag(x1, x2) = U81_ag(x2) 64.96/17.50 64.96/17.50 qcC_in_aa(x1, x2) = qcC_in_aa 64.96/17.50 64.96/17.50 U112_aa(x1) = U112_aa(x1) 64.96/17.50 64.96/17.50 qcC_out_aa(x1, x2) = qcC_out_aa(x1, x2) 64.96/17.50 64.96/17.50 U113_aa(x1, x2) = U113_aa(x2) 64.96/17.50 64.96/17.50 U114_aa(x1, x2, x3, x4, x5) = U114_aa(x5) 64.96/17.50 64.96/17.50 U115_aa(x1, x2, x3, x4, x5) = U115_aa(x1, x3, x5) 64.96/17.50 64.96/17.50 U116_aa(x1, x2, x3, x4, x5) = U116_aa(x1, x2, x3, x4, x5) 64.96/17.50 64.96/17.50 U117_aa(x1, x2, x3, x4, x5) = U117_aa(x5) 64.96/17.50 64.96/17.50 U118_aa(x1, x2, x3, x4, x5) = U118_aa(x1, x4, x5) 64.96/17.50 64.96/17.50 U119_aa(x1, x2, x3, x4, x5) = U119_aa(x1, x2, x3, x4, x5) 64.96/17.50 64.96/17.50 U120_aa(x1, x2, x3) = U120_aa(x3) 64.96/17.50 64.96/17.50 U121_aa(x1, x2, x3) = U121_aa(x1, x3) 64.96/17.50 64.96/17.50 U82_ag(x1, x2, x3) = U82_ag(x2, x3) 64.96/17.50 64.96/17.50 U83_ag(x1, x2, x3, x4) = U83_ag(x3, x4) 64.96/17.50 64.96/17.50 U84_ag(x1, x2, x3, x4, x5, x6, x7) = U84_ag(x4, x5, x6, x7) 64.96/17.50 64.96/17.50 qcD_in_agagag(x1, x2, x3, x4, x5, x6) = qcD_in_agagag(x2, x4, x6) 64.96/17.50 64.96/17.50 U122_agagag(x1, x2, x3, x4, x5, x6, x7) = U122_agagag(x2, x4, x6, x7) 64.96/17.50 64.96/17.50 U85_ag(x1, x2, x3, x4, x5, x6, x7) = U85_ag(x1, x2, x4, x5, x6, x7) 64.96/17.50 64.96/17.50 qcD_in_ggggag(x1, x2, x3, x4, x5, x6) = qcD_in_ggggag(x1, x2, x3, x4, x6) 64.96/17.50 64.96/17.50 U122_ggggag(x1, x2, x3, x4, x5, x6, x7) = U122_ggggag(x1, x2, x3, x4, x6, x7) 64.96/17.50 64.96/17.50 U123_ggggag(x1, x2, x3, x4, x5, x6, x7) = U123_ggggag(x1, x2, x3, x4, x6, x7) 64.96/17.50 64.96/17.50 qcE_in_ggag(x1, x2, x3, x4) = qcE_in_ggag(x1, x2, x4) 64.96/17.50 64.96/17.50 U124_ggag(x1, x2, x3, x4, x5) = U124_ggag(x1, x2, x4, x5) 64.96/17.50 64.96/17.50 U125_ggag(x1, x2, x3, x4, x5) = U125_ggag(x1, x2, x4, x5) 64.96/17.50 64.96/17.50 U86_ag(x1, x2, x3, x4, x5) = U86_ag(x1, x2, x3, x4, x5) 64.96/17.50 64.96/17.50 U87_ag(x1, x2, x3, x4) = U87_ag(x2, x3, x4) 64.96/17.50 64.96/17.50 qcF_in_aagg(x1, x2, x3, x4) = qcF_in_aagg(x3, x4) 64.96/17.50 64.96/17.50 U126_aagg(x1, x2, x3, x4, x5) = U126_aagg(x3, x4, x5) 64.96/17.50 64.96/17.50 U127_aagg(x1, x2, x3, x4, x5) = U127_aagg(x1, x2, x3, x4, x5) 64.96/17.50 64.96/17.50 qcF_out_aagg(x1, x2, x3, x4) = qcF_out_aagg(x1, x2, x3, x4) 64.96/17.50 64.96/17.50 U88_ag(x1, x2, x3) = U88_ag(x1, x2, x3) 64.96/17.50 64.96/17.50 U89_ag(x1, x2, x3, x4) = U89_ag(x2, x3, x4) 64.96/17.50 64.96/17.50 U90_ag(x1, x2, x3, x4, x5, x6, x7) = U90_ag(x1, x2, x3, x4, x5, x6, x7) 64.96/17.50 64.96/17.50 U91_ag(x1, x2, x3, x4, x5, x6, x7) = U91_ag(x1, x2, x3, x4, x5, x6, x7) 64.96/17.50 64.96/17.50 U92_ag(x1, x2, x3, x4, x5, x6) = U92_ag(x2, x3, x4, x5, x6) 64.96/17.50 64.96/17.50 U93_ag(x1, x2, x3) = U93_ag(x2, x3) 64.96/17.50 64.96/17.50 qcG_in_aag(x1, x2, x3) = qcG_in_aag(x3) 64.96/17.50 64.96/17.50 U128_aag(x1, x2) = U128_aag(x1, x2) 64.96/17.50 64.96/17.50 qcG_out_aag(x1, x2, x3) = qcG_out_aag(x1, x2, x3) 64.96/17.50 64.96/17.50 U129_aag(x1, x2, x3) = U129_aag(x2, x3) 64.96/17.50 64.96/17.50 U130_aag(x1, x2, x3, x4, x5, x6) = U130_aag(x5, x6) 64.96/17.50 64.96/17.50 U131_aag(x1, x2, x3, x4, x5, x6) = U131_aag(x1, x3, x5, x6) 64.96/17.50 64.96/17.50 U132_aag(x1, x2, x3, x4, x5, x6) = U132_aag(x1, x2, x3, x4, x5, x6) 64.96/17.50 64.96/17.50 U133_aag(x1, x2, x3, x4, x5, x6) = U133_aag(x5, x6) 64.96/17.50 64.96/17.50 U134_aag(x1, x2, x3, x4, x5, x6) = U134_aag(x1, x4, x5, x6) 64.96/17.50 64.96/17.50 U135_aag(x1, x2, x3, x4, x5, x6) = U135_aag(x1, x2, x3, x4, x5, x6) 64.96/17.50 64.96/17.50 U136_aag(x1, x2, x3, x4) = U136_aag(x3, x4) 64.96/17.50 64.96/17.50 U137_aag(x1, x2, x3, x4) = U137_aag(x1, x3, x4) 64.96/17.50 64.96/17.50 qcE_out_ggag(x1, x2, x3, x4) = qcE_out_ggag(x1, x2, x3, x4) 64.96/17.50 64.96/17.50 qcD_out_ggggag(x1, x2, x3, x4, x5, x6) = qcD_out_ggggag(x1, x2, x3, x4, x5, x6) 64.96/17.50 64.96/17.50 U123_agagag(x1, x2, x3, x4, x5, x6, x7) = U123_agagag(x1, x2, x4, x6, x7) 64.96/17.50 64.96/17.50 qcE_in_agag(x1, x2, x3, x4) = qcE_in_agag(x2, x4) 64.96/17.51 64.96/17.51 U124_agag(x1, x2, x3, x4, x5) = U124_agag(x2, x4, x5) 64.96/17.51 64.96/17.51 U125_agag(x1, x2, x3, x4, x5) = U125_agag(x1, x2, x4, x5) 64.96/17.51 64.96/17.51 qcE_out_agag(x1, x2, x3, x4) = qcE_out_agag(x1, x2, x3, x4) 64.96/17.51 64.96/17.51 qcD_out_agagag(x1, x2, x3, x4, x5, x6) = qcD_out_agagag(x1, x2, x3, x4, x5, x6) 64.96/17.51 64.96/17.51 PA_IN_GG(x1, x2) = PA_IN_GG(x1, x2) 64.96/17.51 64.96/17.51 PD_IN_GGGGGG(x1, x2, x3, x4, x5, x6) = PD_IN_GGGGGG(x1, x2, x3, x4, x5, x6) 64.96/17.51 64.96/17.51 U42_GGGGGG(x1, x2, x3, x4, x5, x6, x7) = U42_GGGGGG(x1, x2, x3, x4, x5, x6, x7) 64.96/17.51 64.96/17.51 PE_IN_GGGG(x1, x2, x3, x4) = PE_IN_GGGG(x1, x2, x3, x4) 64.96/17.51 64.96/17.51 U45_GGGG(x1, x2, x3, x4, x5) = U45_GGGG(x1, x2, x3, x4, x5) 64.96/17.51 64.96/17.51 64.96/17.51 We have to consider all (P,R,Pi)-chains 64.96/17.51 ---------------------------------------- 64.96/17.51 64.96/17.51 (138) UsableRulesProof (EQUIVALENT) 64.96/17.51 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 64.96/17.51 ---------------------------------------- 64.96/17.51 64.96/17.51 (139) 64.96/17.51 Obligation: 64.96/17.51 Pi DP problem: 64.96/17.51 The TRS P consists of the following rules: 64.96/17.51 64.96/17.51 PA_IN_GG(d(e(+(const(X1), X2))), +(const(0), X3)) -> PA_IN_GG(d(e(X2)), X3) 64.96/17.51 PA_IN_GG(d(e(+(t, X1))), +(const(1), X2)) -> PA_IN_GG(d(e(X1)), X2) 64.96/17.51 PA_IN_GG(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) -> PD_IN_GGGGGG(X1, X4, X2, X5, X3, X6) 64.96/17.51 PD_IN_GGGGGG(X1, X2, X3, X4, X5, X6) -> PA_IN_GG(d(e(X1)), X2) 64.96/17.51 PA_IN_GG(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) -> PD_IN_GGGGGG(X1, X5, X2, X4, X3, X6) 64.96/17.51 PD_IN_GGGGGG(X1, X2, X3, X4, X5, X6) -> U42_GGGGGG(X1, X2, X3, X4, X5, X6, pcA_in_gg(d(e(X1)), X2)) 64.96/17.51 U42_GGGGGG(X1, X2, X3, X4, X5, X6, pcA_out_gg(d(e(X1)), X2)) -> PE_IN_GGGG(X3, X4, X5, X6) 64.96/17.51 PE_IN_GGGG(X1, X2, X3, X4) -> PA_IN_GG(d(e(X1)), X2) 64.96/17.51 PA_IN_GG(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) -> PE_IN_GGGG(X1, X4, X2, X3) 64.96/17.51 PE_IN_GGGG(X1, X2, X3, X4) -> U45_GGGG(X1, X2, X3, X4, pcA_in_gg(d(e(X1)), X2)) 64.96/17.51 U45_GGGG(X1, X2, X3, X4, pcA_out_gg(d(e(X1)), X2)) -> PA_IN_GG(d(e(X3)), X4) 64.96/17.51 PA_IN_GG(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) -> PA_IN_GG(d(e(X1)), X2) 64.96/17.51 PA_IN_GG(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) -> PA_IN_GG(d(e(X2)), X3) 64.96/17.51 PA_IN_GG(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) -> PD_IN_GGGGGG(X1, X5, X2, X6, X3, X4) 64.96/17.51 PA_IN_GG(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) -> PD_IN_GGGGGG(X1, X6, X2, X5, X3, X4) 64.96/17.51 64.96/17.51 The TRS R consists of the following rules: 64.96/17.51 64.96/17.51 pcA_in_gg(d(e(t)), const(1)) -> pcA_out_gg(d(e(t)), const(1)) 64.96/17.51 pcA_in_gg(d(e(const(X1))), const(0)) -> pcA_out_gg(d(e(const(X1))), const(0)) 64.96/17.51 pcA_in_gg(d(e(+(t, X1))), +(const(1), X2)) -> U82_gg(X1, X2, pcA_in_gg(d(e(X1)), X2)) 64.96/17.51 pcA_in_gg(d(e(+(const(X1), X2))), +(const(0), X3)) -> U83_gg(X1, X2, X3, pcA_in_gg(d(e(X2)), X3)) 64.96/17.51 pcA_in_gg(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) -> U84_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X4, X2, X5, X3, X6)) 64.96/17.51 pcA_in_gg(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) -> U85_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X5, X2, X4, X3, X6)) 64.96/17.51 pcA_in_gg(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) -> U86_gg(X1, X2, X3, X4, qcE_in_gggg(X1, X4, X2, X3)) 64.96/17.51 pcA_in_gg(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) -> U88_gg(X1, X2, pcA_in_gg(d(e(X1)), X2)) 64.96/17.51 pcA_in_gg(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) -> U89_gg(X1, X2, X3, pcA_in_gg(d(e(X2)), X3)) 64.96/17.51 pcA_in_gg(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) -> U90_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X5, X2, X6, X3, X4)) 64.96/17.51 pcA_in_gg(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) -> U91_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X6, X2, X5, X3, X4)) 64.96/17.51 U82_gg(X1, X2, pcA_out_gg(d(e(X1)), X2)) -> pcA_out_gg(d(e(+(t, X1))), +(const(1), X2)) 64.96/17.51 U83_gg(X1, X2, X3, pcA_out_gg(d(e(X2)), X3)) -> pcA_out_gg(d(e(+(const(X1), X2))), +(const(0), X3)) 64.96/17.51 U84_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X4, X2, X5, X3, X6)) -> pcA_out_gg(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) 64.96/17.51 U85_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X5, X2, X4, X3, X6)) -> pcA_out_gg(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) 64.96/17.51 U86_gg(X1, X2, X3, X4, qcE_out_gggg(X1, X4, X2, X3)) -> pcA_out_gg(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) 64.96/17.51 U88_gg(X1, X2, pcA_out_gg(d(e(X1)), X2)) -> pcA_out_gg(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) 64.96/17.51 U89_gg(X1, X2, X3, pcA_out_gg(d(e(X2)), X3)) -> pcA_out_gg(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) 64.96/17.51 U90_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X5, X2, X6, X3, X4)) -> pcA_out_gg(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) 64.96/17.51 U91_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X6, X2, X5, X3, X4)) -> pcA_out_gg(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) 64.96/17.51 qcD_in_gggggg(X1, X2, X3, X4, X5, X6) -> U122_gggggg(X1, X2, X3, X4, X5, X6, pcA_in_gg(d(e(X1)), X2)) 64.96/17.51 qcE_in_gggg(X1, X2, X3, X4) -> U124_gggg(X1, X2, X3, X4, pcA_in_gg(d(e(X1)), X2)) 64.96/17.51 U122_gggggg(X1, X2, X3, X4, X5, X6, pcA_out_gg(d(e(X1)), X2)) -> U123_gggggg(X1, X2, X3, X4, X5, X6, qcE_in_gggg(X3, X4, X5, X6)) 64.96/17.51 U124_gggg(X1, X2, X3, X4, pcA_out_gg(d(e(X1)), X2)) -> U125_gggg(X1, X2, X3, X4, pcA_in_gg(d(e(X3)), X4)) 64.96/17.51 U123_gggggg(X1, X2, X3, X4, X5, X6, qcE_out_gggg(X3, X4, X5, X6)) -> qcD_out_gggggg(X1, X2, X3, X4, X5, X6) 64.96/17.51 U125_gggg(X1, X2, X3, X4, pcA_out_gg(d(e(X3)), X4)) -> qcE_out_gggg(X1, X2, X3, X4) 64.96/17.51 64.96/17.51 The argument filtering Pi contains the following mapping: 64.96/17.51 const(x1) = const 64.96/17.51 64.96/17.51 1 = 1 64.96/17.51 64.96/17.51 d(x1) = d(x1) 64.96/17.51 64.96/17.51 e(x1) = e(x1) 64.96/17.51 64.96/17.51 t = t 64.96/17.51 64.96/17.51 0 = 0 64.96/17.51 64.96/17.51 +(x1, x2) = +(x1, x2) 64.96/17.51 64.96/17.51 *(x1, x2) = *(x1, x2) 64.96/17.51 64.96/17.51 pcA_in_gg(x1, x2) = pcA_in_gg(x1, x2) 64.96/17.51 64.96/17.51 pcA_out_gg(x1, x2) = pcA_out_gg(x1, x2) 64.96/17.51 64.96/17.51 U82_gg(x1, x2, x3) = U82_gg(x1, x2, x3) 64.96/17.51 64.96/17.51 U83_gg(x1, x2, x3, x4) = U83_gg(x2, x3, x4) 64.96/17.51 64.96/17.51 U84_gg(x1, x2, x3, x4, x5, x6, x7) = U84_gg(x1, x2, x3, x4, x5, x6, x7) 64.96/17.51 64.96/17.51 qcD_in_gggggg(x1, x2, x3, x4, x5, x6) = qcD_in_gggggg(x1, x2, x3, x4, x5, x6) 64.96/17.51 64.96/17.51 U122_gggggg(x1, x2, x3, x4, x5, x6, x7) = U122_gggggg(x1, x2, x3, x4, x5, x6, x7) 64.96/17.51 64.96/17.51 U85_gg(x1, x2, x3, x4, x5, x6, x7) = U85_gg(x1, x2, x3, x4, x5, x6, x7) 64.96/17.51 64.96/17.51 qcD_out_gggggg(x1, x2, x3, x4, x5, x6) = qcD_out_gggggg(x1, x2, x3, x4, x5, x6) 64.96/17.51 64.96/17.51 U86_gg(x1, x2, x3, x4, x5) = U86_gg(x1, x2, x3, x4, x5) 64.96/17.51 64.96/17.51 qcE_in_gggg(x1, x2, x3, x4) = qcE_in_gggg(x1, x2, x3, x4) 64.96/17.51 64.96/17.51 U124_gggg(x1, x2, x3, x4, x5) = U124_gggg(x1, x2, x3, x4, x5) 64.96/17.51 64.96/17.51 U88_gg(x1, x2, x3) = U88_gg(x1, x2, x3) 64.96/17.51 64.96/17.51 U89_gg(x1, x2, x3, x4) = U89_gg(x2, x3, x4) 64.96/17.51 64.96/17.51 U90_gg(x1, x2, x3, x4, x5, x6, x7) = U90_gg(x1, x2, x3, x4, x5, x6, x7) 64.96/17.51 64.96/17.51 U91_gg(x1, x2, x3, x4, x5, x6, x7) = U91_gg(x1, x2, x3, x4, x5, x6, x7) 64.96/17.51 64.96/17.51 U125_gggg(x1, x2, x3, x4, x5) = U125_gggg(x1, x2, x3, x4, x5) 64.96/17.51 64.96/17.51 qcE_out_gggg(x1, x2, x3, x4) = qcE_out_gggg(x1, x2, x3, x4) 64.96/17.51 64.96/17.51 U123_gggggg(x1, x2, x3, x4, x5, x6, x7) = U123_gggggg(x1, x2, x3, x4, x5, x6, x7) 64.96/17.51 64.96/17.51 PA_IN_GG(x1, x2) = PA_IN_GG(x1, x2) 64.96/17.51 64.96/17.51 PD_IN_GGGGGG(x1, x2, x3, x4, x5, x6) = PD_IN_GGGGGG(x1, x2, x3, x4, x5, x6) 64.96/17.51 64.96/17.51 U42_GGGGGG(x1, x2, x3, x4, x5, x6, x7) = U42_GGGGGG(x1, x2, x3, x4, x5, x6, x7) 64.96/17.51 64.96/17.51 PE_IN_GGGG(x1, x2, x3, x4) = PE_IN_GGGG(x1, x2, x3, x4) 64.96/17.51 64.96/17.51 U45_GGGG(x1, x2, x3, x4, x5) = U45_GGGG(x1, x2, x3, x4, x5) 64.96/17.51 64.96/17.51 64.96/17.51 We have to consider all (P,R,Pi)-chains 64.96/17.51 ---------------------------------------- 64.96/17.51 64.96/17.51 (140) 64.96/17.51 Obligation: 64.96/17.51 Pi DP problem: 64.96/17.51 The TRS P consists of the following rules: 64.96/17.51 64.96/17.51 PD_IN_GGGGAG(X1, X2, X3, X4, X5, X6) -> U42_GGGGAG(X1, X2, X3, X4, X5, X6, pcA_in_gg(d(e(X1)), X2)) 64.96/17.51 U42_GGGGAG(X1, X2, X3, X4, X5, X6, pcA_out_gg(d(e(X1)), X2)) -> PE_IN_GGAG(X3, X4, X5, X6) 64.96/17.51 PE_IN_GGAG(X1, X2, X3, X4) -> U45_GGAG(X1, X2, X3, X4, pcA_in_gg(d(e(X1)), X2)) 64.96/17.51 U45_GGAG(X1, X2, X3, X4, pcA_out_gg(d(e(X1)), X2)) -> PA_IN_AG(d(e(X3)), X4) 64.96/17.51 PA_IN_AG(d(e(+(t, X1))), +(const(1), X2)) -> PA_IN_AG(d(e(X1)), X2) 64.96/17.51 PA_IN_AG(d(e(+(const(X1), X2))), +(const(0), X3)) -> PA_IN_AG(d(e(X2)), X3) 64.96/17.51 PA_IN_AG(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) -> PD_IN_AGAGAG(X1, X4, X2, X5, X3, X6) 64.96/17.51 PD_IN_AGAGAG(X1, X2, X3, X4, X5, X6) -> PA_IN_AG(d(e(X1)), X2) 64.96/17.51 PA_IN_AG(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) -> PD_IN_GGGGAG(X1, X5, X2, X4, X3, X6) 64.96/17.51 PD_IN_AGAGAG(X1, X2, X3, X4, X5, X6) -> U42_AGAGAG(X1, X2, X3, X4, X5, X6, pcA_in_ag(d(e(X1)), X2)) 64.96/17.51 U42_AGAGAG(X1, X2, X3, X4, X5, X6, pcA_out_ag(d(e(X1)), X2)) -> PE_IN_AGAG(X3, X4, X5, X6) 64.96/17.51 PE_IN_AGAG(X1, X2, X3, X4) -> PA_IN_AG(d(e(X1)), X2) 64.96/17.51 PE_IN_AGAG(X1, X2, X3, X4) -> U45_AGAG(X1, X2, X3, X4, pcA_in_ag(d(e(X1)), X2)) 64.96/17.51 U45_AGAG(X1, X2, X3, X4, pcA_out_ag(d(e(X1)), X2)) -> PA_IN_AG(d(e(X3)), X4) 64.96/17.51 64.96/17.51 The TRS R consists of the following rules: 64.96/17.51 64.96/17.51 pcA_in_gg(d(e(t)), const(1)) -> pcA_out_gg(d(e(t)), const(1)) 64.96/17.51 pcA_in_gg(d(d(X1)), const(1)) -> U80_gg(X1, qcB_in_ga(X1, X2)) 64.96/17.51 qcB_in_ga(e(t), const(1)) -> U98_ga(pcA_in_gg(d(e(const(1))), const(1))) 64.96/17.51 pcA_in_gg(d(e(const(X1))), const(0)) -> pcA_out_gg(d(e(const(X1))), const(0)) 64.96/17.51 pcA_in_gg(d(d(X1)), const(0)) -> U81_gg(X1, qcC_in_ga(X1, X2)) 64.96/17.51 qcC_in_ga(e(t), const(1)) -> U112_ga(pcA_in_gg(d(e(const(1))), const(0))) 64.96/17.51 pcA_in_gg(d(e(+(t, X1))), +(const(1), X2)) -> U82_gg(X1, X2, pcA_in_gg(d(e(X1)), X2)) 64.96/17.51 pcA_in_gg(d(e(+(const(X1), X2))), +(const(0), X3)) -> U83_gg(X1, X2, X3, pcA_in_gg(d(e(X2)), X3)) 64.96/17.51 pcA_in_gg(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) -> U84_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X4, X2, X5, X3, X6)) 64.96/17.51 qcD_in_gggggg(X1, X2, X3, X4, X5, X6) -> U122_gggggg(X1, X2, X3, X4, X5, X6, pcA_in_gg(d(e(X1)), X2)) 64.96/17.51 pcA_in_gg(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) -> U85_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X5, X2, X4, X3, X6)) 64.96/17.51 U85_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X5, X2, X4, X3, X6)) -> pcA_out_gg(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) 64.96/17.51 pcA_in_gg(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) -> U86_gg(X1, X2, X3, X4, qcE_in_gggg(X1, X4, X2, X3)) 64.96/17.51 qcE_in_gggg(X1, X2, X3, X4) -> U124_gggg(X1, X2, X3, X4, pcA_in_gg(d(e(X1)), X2)) 64.96/17.51 pcA_in_gg(d(d(X1)), +(X2, X3)) -> U87_gg(X1, X2, X3, qcF_in_gagg(X1, X4, X2, X3)) 64.96/17.51 qcF_in_gagg(X1, X2, X3, X4) -> U126_gagg(X1, X2, X3, X4, pcJ_in_ga(X1, X2)) 64.96/17.51 pcJ_in_ga(e(t), const(1)) -> pcJ_out_ga(e(t), const(1)) 64.96/17.51 pcJ_in_ga(e(const(X1)), const(0)) -> pcJ_out_ga(e(const(X1)), const(0)) 64.96/17.51 pcJ_in_ga(e(+(X1, X2)), +(X3, X4)) -> U108_ga(X1, X2, X3, X4, qcI_in_gaga(X1, X3, X2, X4)) 64.96/17.51 qcI_in_gaga(X1, X2, X3, X4) -> U96_gaga(X1, X2, X3, X4, pcH_in_ga(X1, X2)) 64.96/17.51 pcH_in_ga(t, const(1)) -> pcH_out_ga(t, const(1)) 64.96/17.51 pcH_in_ga(const(X1), const(0)) -> pcH_out_ga(const(X1), const(0)) 64.96/17.51 pcH_in_ga(+(X1, X2), +(X3, X4)) -> U94_ga(X1, X2, X3, X4, qcI_in_gaga(X1, X3, X2, X4)) 64.96/17.51 U94_ga(X1, X2, X3, X4, qcI_out_gaga(X1, X3, X2, X4)) -> pcH_out_ga(+(X1, X2), +(X3, X4)) 64.96/17.51 pcH_in_ga(*(X1, X2), +(*(X1, X3), *(X2, X4))) -> U95_ga(X1, X2, X3, X4, qcI_in_gaga(X1, X4, X2, X3)) 64.96/17.51 U95_ga(X1, X2, X3, X4, qcI_out_gaga(X1, X4, X2, X3)) -> pcH_out_ga(*(X1, X2), +(*(X1, X3), *(X2, X4))) 64.96/17.51 U96_gaga(X1, X2, X3, X4, pcH_out_ga(X1, X2)) -> U97_gaga(X1, X2, X3, X4, pcH_in_ga(X3, X4)) 64.96/17.51 U97_gaga(X1, X2, X3, X4, pcH_out_ga(X3, X4)) -> qcI_out_gaga(X1, X2, X3, X4) 64.96/17.51 U108_ga(X1, X2, X3, X4, qcI_out_gaga(X1, X3, X2, X4)) -> pcJ_out_ga(e(+(X1, X2)), +(X3, X4)) 64.96/17.51 pcJ_in_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U109_ga(X1, X2, X3, X4, qcI_in_gaga(X1, X4, X2, X3)) 64.96/17.51 U109_ga(X1, X2, X3, X4, qcI_out_gaga(X1, X4, X2, X3)) -> pcJ_out_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.96/17.51 pcJ_in_ga(d(X1), X2) -> U110_ga(X1, X2, pcJ_in_ga(X1, X3)) 64.96/17.51 U110_ga(X1, X2, pcJ_out_ga(X1, X3)) -> U111_ga(X1, X2, pcH_in_ga(X3, X2)) 64.96/17.51 U111_ga(X1, X2, pcH_out_ga(X3, X2)) -> pcJ_out_ga(d(X1), X2) 64.96/17.51 U126_gagg(X1, X2, X3, X4, pcJ_out_ga(X1, X2)) -> U127_gagg(X1, X2, X3, X4, pcA_in_gg(d(e(X2)), +(X3, X4))) 64.96/17.51 pcA_in_gg(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) -> U88_gg(X1, X2, pcA_in_gg(d(e(X1)), X2)) 64.96/17.51 pcA_in_gg(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) -> U89_gg(X1, X2, X3, pcA_in_gg(d(e(X2)), X3)) 64.96/17.51 pcA_in_gg(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) -> U90_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X5, X2, X6, X3, X4)) 64.96/17.51 U90_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X5, X2, X6, X3, X4)) -> pcA_out_gg(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) 64.96/17.51 pcA_in_gg(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) -> U91_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X6, X2, X5, X3, X4)) 64.96/17.51 U91_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X6, X2, X5, X3, X4)) -> pcA_out_gg(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) 64.96/17.51 pcA_in_gg(d(d(X1)), +(*(X2, X3), *(X4, X5))) -> U92_gg(X1, X2, X3, X4, X5, qcF_in_gagg(X1, X6, *(X2, X3), *(X4, X5))) 64.96/17.51 U92_gg(X1, X2, X3, X4, X5, qcF_out_gagg(X1, X6, *(X2, X3), *(X4, X5))) -> pcA_out_gg(d(d(X1)), +(*(X2, X3), *(X4, X5))) 64.96/17.51 pcA_in_gg(d(d(X1)), X2) -> U93_gg(X1, X2, qcG_in_gag(X1, X3, X2)) 64.96/17.51 qcG_in_gag(e(t), const(1), X1) -> U128_gag(X1, pcA_in_gg(d(e(const(1))), X1)) 64.96/17.51 U128_gag(X1, pcA_out_gg(d(e(const(1))), X1)) -> qcG_out_gag(e(t), const(1), X1) 64.96/17.51 qcG_in_gag(e(const(X1)), const(0), X2) -> U129_gag(X1, X2, pcA_in_gg(d(e(const(0))), X2)) 64.96/17.51 U129_gag(X1, X2, pcA_out_gg(d(e(const(0))), X2)) -> qcG_out_gag(e(const(X1)), const(0), X2) 64.96/17.51 qcG_in_gag(e(+(X1, X2)), +(X3, X4), X5) -> U130_gag(X1, X2, X3, X4, X5, pcH_in_ga(X1, X3)) 64.96/17.51 U130_gag(X1, X2, X3, X4, X5, pcH_out_ga(X1, X3)) -> U131_gag(X1, X2, X3, X4, X5, pcH_in_ga(X2, X4)) 64.96/17.51 U131_gag(X1, X2, X3, X4, X5, pcH_out_ga(X2, X4)) -> U132_gag(X1, X2, X3, X4, X5, pcA_in_gg(d(e(+(X3, X4))), X5)) 64.96/17.51 U132_gag(X1, X2, X3, X4, X5, pcA_out_gg(d(e(+(X3, X4))), X5)) -> qcG_out_gag(e(+(X1, X2)), +(X3, X4), X5) 64.96/17.51 qcG_in_gag(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) -> U133_gag(X1, X2, X3, X4, X5, pcH_in_ga(X1, X4)) 64.96/17.51 U133_gag(X1, X2, X3, X4, X5, pcH_out_ga(X1, X4)) -> U134_gag(X1, X2, X3, X4, X5, pcH_in_ga(X2, X3)) 64.96/17.51 U134_gag(X1, X2, X3, X4, X5, pcH_out_ga(X2, X3)) -> U135_gag(X1, X2, X3, X4, X5, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), X5)) 64.96/17.51 U135_gag(X1, X2, X3, X4, X5, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), X5)) -> qcG_out_gag(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) 64.96/17.51 qcG_in_gag(d(X1), X2, X3) -> U136_gag(X1, X2, X3, pcJ_in_ga(X1, X4)) 64.96/17.51 U136_gag(X1, X2, X3, pcJ_out_ga(X1, X4)) -> U137_gag(X1, X2, X3, qcG_in_gag(e(X4), X2, X3)) 64.96/17.51 U137_gag(X1, X2, X3, qcG_out_gag(e(X4), X2, X3)) -> qcG_out_gag(d(X1), X2, X3) 64.96/17.51 U93_gg(X1, X2, qcG_out_gag(X1, X3, X2)) -> pcA_out_gg(d(d(X1)), X2) 64.96/17.51 U89_gg(X1, X2, X3, pcA_out_gg(d(e(X2)), X3)) -> pcA_out_gg(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) 64.96/17.51 U88_gg(X1, X2, pcA_out_gg(d(e(X1)), X2)) -> pcA_out_gg(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) 64.96/17.51 U127_gagg(X1, X2, X3, X4, pcA_out_gg(d(e(X2)), +(X3, X4))) -> qcF_out_gagg(X1, X2, X3, X4) 64.96/17.51 U87_gg(X1, X2, X3, qcF_out_gagg(X1, X4, X2, X3)) -> pcA_out_gg(d(d(X1)), +(X2, X3)) 64.96/17.51 U124_gggg(X1, X2, X3, X4, pcA_out_gg(d(e(X1)), X2)) -> U125_gggg(X1, X2, X3, X4, pcA_in_gg(d(e(X3)), X4)) 64.96/17.51 U125_gggg(X1, X2, X3, X4, pcA_out_gg(d(e(X3)), X4)) -> qcE_out_gggg(X1, X2, X3, X4) 64.96/17.51 U86_gg(X1, X2, X3, X4, qcE_out_gggg(X1, X4, X2, X3)) -> pcA_out_gg(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) 64.96/17.51 U122_gggggg(X1, X2, X3, X4, X5, X6, pcA_out_gg(d(e(X1)), X2)) -> U123_gggggg(X1, X2, X3, X4, X5, X6, qcE_in_gggg(X3, X4, X5, X6)) 64.96/17.51 U123_gggggg(X1, X2, X3, X4, X5, X6, qcE_out_gggg(X3, X4, X5, X6)) -> qcD_out_gggggg(X1, X2, X3, X4, X5, X6) 64.96/17.51 U84_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X4, X2, X5, X3, X6)) -> pcA_out_gg(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) 64.96/17.51 U83_gg(X1, X2, X3, pcA_out_gg(d(e(X2)), X3)) -> pcA_out_gg(d(e(+(const(X1), X2))), +(const(0), X3)) 64.96/17.51 U82_gg(X1, X2, pcA_out_gg(d(e(X1)), X2)) -> pcA_out_gg(d(e(+(t, X1))), +(const(1), X2)) 64.96/17.51 U112_ga(pcA_out_gg(d(e(const(1))), const(0))) -> qcC_out_ga(e(t), const(1)) 64.96/17.51 qcC_in_ga(e(const(X1)), const(0)) -> U113_ga(X1, pcA_in_gg(d(e(const(0))), const(0))) 64.96/17.51 U113_ga(X1, pcA_out_gg(d(e(const(0))), const(0))) -> qcC_out_ga(e(const(X1)), const(0)) 64.96/17.51 qcC_in_ga(e(+(X1, X2)), +(X3, X4)) -> U114_ga(X1, X2, X3, X4, pcH_in_ga(X1, X3)) 64.96/17.51 U114_ga(X1, X2, X3, X4, pcH_out_ga(X1, X3)) -> U115_ga(X1, X2, X3, X4, pcH_in_ga(X2, X4)) 64.96/17.51 U115_ga(X1, X2, X3, X4, pcH_out_ga(X2, X4)) -> U116_ga(X1, X2, X3, X4, pcA_in_gg(d(e(+(X3, X4))), const(0))) 64.96/17.51 U116_ga(X1, X2, X3, X4, pcA_out_gg(d(e(+(X3, X4))), const(0))) -> qcC_out_ga(e(+(X1, X2)), +(X3, X4)) 64.96/17.51 qcC_in_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U117_ga(X1, X2, X3, X4, pcH_in_ga(X1, X4)) 64.96/17.51 U117_ga(X1, X2, X3, X4, pcH_out_ga(X1, X4)) -> U118_ga(X1, X2, X3, X4, pcH_in_ga(X2, X3)) 64.96/17.51 U118_ga(X1, X2, X3, X4, pcH_out_ga(X2, X3)) -> U119_ga(X1, X2, X3, X4, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(0))) 64.96/17.51 U119_ga(X1, X2, X3, X4, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(0))) -> qcC_out_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.96/17.51 qcC_in_ga(d(X1), X2) -> U120_ga(X1, X2, pcJ_in_ga(X1, X3)) 64.96/17.51 U120_ga(X1, X2, pcJ_out_ga(X1, X3)) -> U121_ga(X1, X2, qcC_in_ga(e(X3), X2)) 64.96/17.51 U121_ga(X1, X2, qcC_out_ga(e(X3), X2)) -> qcC_out_ga(d(X1), X2) 64.96/17.51 U81_gg(X1, qcC_out_ga(X1, X2)) -> pcA_out_gg(d(d(X1)), const(0)) 64.96/17.51 U98_ga(pcA_out_gg(d(e(const(1))), const(1))) -> qcB_out_ga(e(t), const(1)) 64.96/17.51 qcB_in_ga(e(const(X1)), const(0)) -> U99_ga(X1, pcA_in_gg(d(e(const(0))), const(1))) 64.96/17.51 U99_ga(X1, pcA_out_gg(d(e(const(0))), const(1))) -> qcB_out_ga(e(const(X1)), const(0)) 64.96/17.51 qcB_in_ga(e(+(X1, X2)), +(X3, X4)) -> U100_ga(X1, X2, X3, X4, pcH_in_ga(X1, X3)) 64.96/17.51 U100_ga(X1, X2, X3, X4, pcH_out_ga(X1, X3)) -> U101_ga(X1, X2, X3, X4, pcH_in_ga(X2, X4)) 64.96/17.51 U101_ga(X1, X2, X3, X4, pcH_out_ga(X2, X4)) -> U102_ga(X1, X2, X3, X4, pcA_in_gg(d(e(+(X3, X4))), const(1))) 64.96/17.51 U102_ga(X1, X2, X3, X4, pcA_out_gg(d(e(+(X3, X4))), const(1))) -> qcB_out_ga(e(+(X1, X2)), +(X3, X4)) 64.96/17.51 qcB_in_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U103_ga(X1, X2, X3, X4, pcH_in_ga(X1, X4)) 64.96/17.51 U103_ga(X1, X2, X3, X4, pcH_out_ga(X1, X4)) -> U104_ga(X1, X2, X3, X4, pcH_in_ga(X2, X3)) 64.96/17.51 U104_ga(X1, X2, X3, X4, pcH_out_ga(X2, X3)) -> U105_ga(X1, X2, X3, X4, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(1))) 64.96/17.51 U105_ga(X1, X2, X3, X4, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(1))) -> qcB_out_ga(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.96/17.51 qcB_in_ga(d(X1), X2) -> U106_ga(X1, X2, pcJ_in_ga(X1, X3)) 64.96/17.51 U106_ga(X1, X2, pcJ_out_ga(X1, X3)) -> U107_ga(X1, X2, qcB_in_ga(e(X3), X2)) 64.96/17.51 U107_ga(X1, X2, qcB_out_ga(e(X3), X2)) -> qcB_out_ga(d(X1), X2) 64.96/17.51 U80_gg(X1, qcB_out_ga(X1, X2)) -> pcA_out_gg(d(d(X1)), const(1)) 64.96/17.51 pcH_in_aa(t, const(1)) -> pcH_out_aa(t, const(1)) 64.96/17.51 pcH_in_aa(const(X1), const(0)) -> pcH_out_aa(const(X1), const(0)) 64.96/17.51 pcH_in_aa(+(X1, X2), +(X3, X4)) -> U94_aa(X1, X2, X3, X4, qcI_in_aaaa(X1, X3, X2, X4)) 64.96/17.51 qcI_in_aaaa(X1, X2, X3, X4) -> U96_aaaa(X1, X2, X3, X4, pcH_in_aa(X1, X2)) 64.96/17.51 pcH_in_aa(*(X1, X2), +(*(X1, X3), *(X2, X4))) -> U95_aa(X1, X2, X3, X4, qcI_in_aaaa(X1, X4, X2, X3)) 64.96/17.51 U95_aa(X1, X2, X3, X4, qcI_out_aaaa(X1, X4, X2, X3)) -> pcH_out_aa(*(X1, X2), +(*(X1, X3), *(X2, X4))) 64.96/17.51 U96_aaaa(X1, X2, X3, X4, pcH_out_aa(X1, X2)) -> U97_aaaa(X1, X2, X3, X4, pcH_in_aa(X3, X4)) 64.96/17.51 U97_aaaa(X1, X2, X3, X4, pcH_out_aa(X3, X4)) -> qcI_out_aaaa(X1, X2, X3, X4) 64.96/17.51 U94_aa(X1, X2, X3, X4, qcI_out_aaaa(X1, X3, X2, X4)) -> pcH_out_aa(+(X1, X2), +(X3, X4)) 64.96/17.51 pcJ_in_aa(e(t), const(1)) -> pcJ_out_aa(e(t), const(1)) 64.96/17.51 pcJ_in_aa(e(const(X1)), const(0)) -> pcJ_out_aa(e(const(X1)), const(0)) 64.96/17.51 pcJ_in_aa(e(+(X1, X2)), +(X3, X4)) -> U108_aa(X1, X2, X3, X4, qcI_in_aaaa(X1, X3, X2, X4)) 64.96/17.51 U108_aa(X1, X2, X3, X4, qcI_out_aaaa(X1, X3, X2, X4)) -> pcJ_out_aa(e(+(X1, X2)), +(X3, X4)) 64.96/17.51 pcJ_in_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U109_aa(X1, X2, X3, X4, qcI_in_aaaa(X1, X4, X2, X3)) 64.96/17.51 U109_aa(X1, X2, X3, X4, qcI_out_aaaa(X1, X4, X2, X3)) -> pcJ_out_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.96/17.51 pcJ_in_aa(d(X1), X2) -> U110_aa(X1, X2, pcJ_in_aa(X1, X3)) 64.96/17.51 U110_aa(X1, X2, pcJ_out_aa(X1, X3)) -> U111_aa(X1, X2, pcH_in_ga(X3, X2)) 64.96/17.51 U111_aa(X1, X2, pcH_out_ga(X3, X2)) -> pcJ_out_aa(d(X1), X2) 64.96/17.51 pcA_in_ag(d(e(t)), const(1)) -> pcA_out_ag(d(e(t)), const(1)) 64.96/17.51 pcA_in_ag(d(d(X1)), const(1)) -> U80_ag(X1, qcB_in_aa(X1, X2)) 64.96/17.51 qcB_in_aa(e(t), const(1)) -> U98_aa(pcA_in_gg(d(e(const(1))), const(1))) 64.96/17.51 U98_aa(pcA_out_gg(d(e(const(1))), const(1))) -> qcB_out_aa(e(t), const(1)) 64.96/17.51 qcB_in_aa(e(const(X1)), const(0)) -> U99_aa(X1, pcA_in_gg(d(e(const(0))), const(1))) 64.96/17.51 U99_aa(X1, pcA_out_gg(d(e(const(0))), const(1))) -> qcB_out_aa(e(const(X1)), const(0)) 64.96/17.51 qcB_in_aa(e(+(X1, X2)), +(X3, X4)) -> U100_aa(X1, X2, X3, X4, pcH_in_aa(X1, X3)) 64.96/17.51 U100_aa(X1, X2, X3, X4, pcH_out_aa(X1, X3)) -> U101_aa(X1, X2, X3, X4, pcH_in_aa(X2, X4)) 64.96/17.51 U101_aa(X1, X2, X3, X4, pcH_out_aa(X2, X4)) -> U102_aa(X1, X2, X3, X4, pcA_in_gg(d(e(+(X3, X4))), const(1))) 64.96/17.51 U102_aa(X1, X2, X3, X4, pcA_out_gg(d(e(+(X3, X4))), const(1))) -> qcB_out_aa(e(+(X1, X2)), +(X3, X4)) 64.96/17.51 qcB_in_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U103_aa(X1, X2, X3, X4, pcH_in_aa(X1, X4)) 64.96/17.51 U103_aa(X1, X2, X3, X4, pcH_out_aa(X1, X4)) -> U104_aa(X1, X2, X3, X4, pcH_in_aa(X2, X3)) 64.96/17.51 U104_aa(X1, X2, X3, X4, pcH_out_aa(X2, X3)) -> U105_aa(X1, X2, X3, X4, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(1))) 64.96/17.51 U105_aa(X1, X2, X3, X4, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(1))) -> qcB_out_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.96/17.51 qcB_in_aa(d(X1), X2) -> U106_aa(X1, X2, pcJ_in_aa(X1, X3)) 64.96/17.51 U106_aa(X1, X2, pcJ_out_aa(X1, X3)) -> U107_aa(X1, X2, qcB_in_ga(e(X3), X2)) 64.96/17.51 U107_aa(X1, X2, qcB_out_ga(e(X3), X2)) -> qcB_out_aa(d(X1), X2) 64.96/17.51 U80_ag(X1, qcB_out_aa(X1, X2)) -> pcA_out_ag(d(d(X1)), const(1)) 64.96/17.51 pcA_in_ag(d(e(const(X1))), const(0)) -> pcA_out_ag(d(e(const(X1))), const(0)) 64.96/17.51 pcA_in_ag(d(d(X1)), const(0)) -> U81_ag(X1, qcC_in_aa(X1, X2)) 64.96/17.51 qcC_in_aa(e(t), const(1)) -> U112_aa(pcA_in_gg(d(e(const(1))), const(0))) 64.96/17.51 U112_aa(pcA_out_gg(d(e(const(1))), const(0))) -> qcC_out_aa(e(t), const(1)) 64.96/17.51 qcC_in_aa(e(const(X1)), const(0)) -> U113_aa(X1, pcA_in_gg(d(e(const(0))), const(0))) 64.96/17.51 U113_aa(X1, pcA_out_gg(d(e(const(0))), const(0))) -> qcC_out_aa(e(const(X1)), const(0)) 64.96/17.51 qcC_in_aa(e(+(X1, X2)), +(X3, X4)) -> U114_aa(X1, X2, X3, X4, pcH_in_aa(X1, X3)) 64.96/17.51 U114_aa(X1, X2, X3, X4, pcH_out_aa(X1, X3)) -> U115_aa(X1, X2, X3, X4, pcH_in_aa(X2, X4)) 64.96/17.51 U115_aa(X1, X2, X3, X4, pcH_out_aa(X2, X4)) -> U116_aa(X1, X2, X3, X4, pcA_in_gg(d(e(+(X3, X4))), const(0))) 64.96/17.51 U116_aa(X1, X2, X3, X4, pcA_out_gg(d(e(+(X3, X4))), const(0))) -> qcC_out_aa(e(+(X1, X2)), +(X3, X4)) 64.96/17.51 qcC_in_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) -> U117_aa(X1, X2, X3, X4, pcH_in_aa(X1, X4)) 64.96/17.51 U117_aa(X1, X2, X3, X4, pcH_out_aa(X1, X4)) -> U118_aa(X1, X2, X3, X4, pcH_in_aa(X2, X3)) 64.96/17.51 U118_aa(X1, X2, X3, X4, pcH_out_aa(X2, X3)) -> U119_aa(X1, X2, X3, X4, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(0))) 64.96/17.51 U119_aa(X1, X2, X3, X4, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), const(0))) -> qcC_out_aa(e(*(X1, X2)), +(*(X1, X3), *(X2, X4))) 64.96/17.51 qcC_in_aa(d(X1), X2) -> U120_aa(X1, X2, pcJ_in_aa(X1, X3)) 64.96/17.51 U120_aa(X1, X2, pcJ_out_aa(X1, X3)) -> U121_aa(X1, X2, qcC_in_ga(e(X3), X2)) 64.96/17.51 U121_aa(X1, X2, qcC_out_ga(e(X3), X2)) -> qcC_out_aa(d(X1), X2) 64.96/17.51 U81_ag(X1, qcC_out_aa(X1, X2)) -> pcA_out_ag(d(d(X1)), const(0)) 64.96/17.51 pcA_in_ag(d(e(+(t, X1))), +(const(1), X2)) -> U82_ag(X1, X2, pcA_in_ag(d(e(X1)), X2)) 64.96/17.51 pcA_in_ag(d(e(+(const(X1), X2))), +(const(0), X3)) -> U83_ag(X1, X2, X3, pcA_in_ag(d(e(X2)), X3)) 64.96/17.51 pcA_in_ag(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) -> U84_ag(X1, X2, X3, X4, X5, X6, qcD_in_agagag(X1, X4, X2, X5, X3, X6)) 64.96/17.51 qcD_in_agagag(X1, X2, X3, X4, X5, X6) -> U122_agagag(X1, X2, X3, X4, X5, X6, pcA_in_ag(d(e(X1)), X2)) 64.96/17.51 pcA_in_ag(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) -> U85_ag(X1, X2, X3, X4, X5, X6, qcD_in_ggggag(X1, X5, X2, X4, X3, X6)) 64.96/17.51 qcD_in_ggggag(X1, X2, X3, X4, X5, X6) -> U122_ggggag(X1, X2, X3, X4, X5, X6, pcA_in_gg(d(e(X1)), X2)) 64.96/17.51 U122_ggggag(X1, X2, X3, X4, X5, X6, pcA_out_gg(d(e(X1)), X2)) -> U123_ggggag(X1, X2, X3, X4, X5, X6, qcE_in_ggag(X3, X4, X5, X6)) 64.96/17.51 qcE_in_ggag(X1, X2, X3, X4) -> U124_ggag(X1, X2, X3, X4, pcA_in_gg(d(e(X1)), X2)) 64.96/17.51 U124_ggag(X1, X2, X3, X4, pcA_out_gg(d(e(X1)), X2)) -> U125_ggag(X1, X2, X3, X4, pcA_in_ag(d(e(X3)), X4)) 64.96/17.51 pcA_in_ag(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) -> U86_ag(X1, X2, X3, X4, qcE_in_gggg(X1, X4, X2, X3)) 64.96/17.51 U86_ag(X1, X2, X3, X4, qcE_out_gggg(X1, X4, X2, X3)) -> pcA_out_ag(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) 64.96/17.51 pcA_in_ag(d(d(X1)), +(X2, X3)) -> U87_ag(X1, X2, X3, qcF_in_aagg(X1, X4, X2, X3)) 64.96/17.51 qcF_in_aagg(X1, X2, X3, X4) -> U126_aagg(X1, X2, X3, X4, pcJ_in_aa(X1, X2)) 64.96/17.51 U126_aagg(X1, X2, X3, X4, pcJ_out_aa(X1, X2)) -> U127_aagg(X1, X2, X3, X4, pcA_in_gg(d(e(X2)), +(X3, X4))) 64.96/17.51 U127_aagg(X1, X2, X3, X4, pcA_out_gg(d(e(X2)), +(X3, X4))) -> qcF_out_aagg(X1, X2, X3, X4) 64.96/17.51 U87_ag(X1, X2, X3, qcF_out_aagg(X1, X4, X2, X3)) -> pcA_out_ag(d(d(X1)), +(X2, X3)) 64.96/17.51 pcA_in_ag(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) -> U88_ag(X1, X2, pcA_in_gg(d(e(X1)), X2)) 64.96/17.51 U88_ag(X1, X2, pcA_out_gg(d(e(X1)), X2)) -> pcA_out_ag(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) 64.96/17.51 pcA_in_ag(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) -> U89_ag(X1, X2, X3, pcA_in_gg(d(e(X2)), X3)) 64.96/17.51 U89_ag(X1, X2, X3, pcA_out_gg(d(e(X2)), X3)) -> pcA_out_ag(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) 64.96/17.51 pcA_in_ag(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) -> U90_ag(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X5, X2, X6, X3, X4)) 64.96/17.51 U90_ag(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X5, X2, X6, X3, X4)) -> pcA_out_ag(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) 64.96/17.51 pcA_in_ag(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) -> U91_ag(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X6, X2, X5, X3, X4)) 64.96/17.51 U91_ag(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X6, X2, X5, X3, X4)) -> pcA_out_ag(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) 64.96/17.51 pcA_in_ag(d(d(X1)), +(*(X2, X3), *(X4, X5))) -> U92_ag(X1, X2, X3, X4, X5, qcF_in_aagg(X1, X6, *(X2, X3), *(X4, X5))) 64.96/17.51 U92_ag(X1, X2, X3, X4, X5, qcF_out_aagg(X1, X6, *(X2, X3), *(X4, X5))) -> pcA_out_ag(d(d(X1)), +(*(X2, X3), *(X4, X5))) 64.96/17.51 pcA_in_ag(d(d(X1)), X2) -> U93_ag(X1, X2, qcG_in_aag(X1, X3, X2)) 64.96/17.51 qcG_in_aag(e(t), const(1), X1) -> U128_aag(X1, pcA_in_gg(d(e(const(1))), X1)) 64.96/17.51 U128_aag(X1, pcA_out_gg(d(e(const(1))), X1)) -> qcG_out_aag(e(t), const(1), X1) 64.96/17.51 qcG_in_aag(e(const(X1)), const(0), X2) -> U129_aag(X1, X2, pcA_in_gg(d(e(const(0))), X2)) 64.96/17.51 U129_aag(X1, X2, pcA_out_gg(d(e(const(0))), X2)) -> qcG_out_aag(e(const(X1)), const(0), X2) 64.96/17.51 qcG_in_aag(e(+(X1, X2)), +(X3, X4), X5) -> U130_aag(X1, X2, X3, X4, X5, pcH_in_aa(X1, X3)) 64.96/17.51 U130_aag(X1, X2, X3, X4, X5, pcH_out_aa(X1, X3)) -> U131_aag(X1, X2, X3, X4, X5, pcH_in_aa(X2, X4)) 64.96/17.51 U131_aag(X1, X2, X3, X4, X5, pcH_out_aa(X2, X4)) -> U132_aag(X1, X2, X3, X4, X5, pcA_in_gg(d(e(+(X3, X4))), X5)) 64.96/17.51 U132_aag(X1, X2, X3, X4, X5, pcA_out_gg(d(e(+(X3, X4))), X5)) -> qcG_out_aag(e(+(X1, X2)), +(X3, X4), X5) 64.96/17.51 qcG_in_aag(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) -> U133_aag(X1, X2, X3, X4, X5, pcH_in_aa(X1, X4)) 64.96/17.51 U133_aag(X1, X2, X3, X4, X5, pcH_out_aa(X1, X4)) -> U134_aag(X1, X2, X3, X4, X5, pcH_in_aa(X2, X3)) 64.96/17.51 U134_aag(X1, X2, X3, X4, X5, pcH_out_aa(X2, X3)) -> U135_aag(X1, X2, X3, X4, X5, pcA_in_gg(d(e(+(*(X1, X3), *(X2, X4)))), X5)) 64.96/17.51 U135_aag(X1, X2, X3, X4, X5, pcA_out_gg(d(e(+(*(X1, X3), *(X2, X4)))), X5)) -> qcG_out_aag(e(*(X1, X2)), +(*(X1, X3), *(X2, X4)), X5) 64.96/17.51 qcG_in_aag(d(X1), X2, X3) -> U136_aag(X1, X2, X3, pcJ_in_aa(X1, X4)) 64.96/17.51 U136_aag(X1, X2, X3, pcJ_out_aa(X1, X4)) -> U137_aag(X1, X2, X3, qcG_in_gag(e(X4), X2, X3)) 64.96/17.51 U137_aag(X1, X2, X3, qcG_out_gag(e(X4), X2, X3)) -> qcG_out_aag(d(X1), X2, X3) 64.96/17.51 U93_ag(X1, X2, qcG_out_aag(X1, X3, X2)) -> pcA_out_ag(d(d(X1)), X2) 64.96/17.51 U125_ggag(X1, X2, X3, X4, pcA_out_ag(d(e(X3)), X4)) -> qcE_out_ggag(X1, X2, X3, X4) 64.96/17.51 U123_ggggag(X1, X2, X3, X4, X5, X6, qcE_out_ggag(X3, X4, X5, X6)) -> qcD_out_ggggag(X1, X2, X3, X4, X5, X6) 64.96/17.51 U85_ag(X1, X2, X3, X4, X5, X6, qcD_out_ggggag(X1, X5, X2, X4, X3, X6)) -> pcA_out_ag(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) 64.96/17.51 U122_agagag(X1, X2, X3, X4, X5, X6, pcA_out_ag(d(e(X1)), X2)) -> U123_agagag(X1, X2, X3, X4, X5, X6, qcE_in_agag(X3, X4, X5, X6)) 64.96/17.51 qcE_in_agag(X1, X2, X3, X4) -> U124_agag(X1, X2, X3, X4, pcA_in_ag(d(e(X1)), X2)) 64.96/17.51 U124_agag(X1, X2, X3, X4, pcA_out_ag(d(e(X1)), X2)) -> U125_agag(X1, X2, X3, X4, pcA_in_ag(d(e(X3)), X4)) 64.96/17.51 U125_agag(X1, X2, X3, X4, pcA_out_ag(d(e(X3)), X4)) -> qcE_out_agag(X1, X2, X3, X4) 64.96/17.51 U123_agagag(X1, X2, X3, X4, X5, X6, qcE_out_agag(X3, X4, X5, X6)) -> qcD_out_agagag(X1, X2, X3, X4, X5, X6) 64.96/17.51 U84_ag(X1, X2, X3, X4, X5, X6, qcD_out_agagag(X1, X4, X2, X5, X3, X6)) -> pcA_out_ag(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) 64.96/17.51 U83_ag(X1, X2, X3, pcA_out_ag(d(e(X2)), X3)) -> pcA_out_ag(d(e(+(const(X1), X2))), +(const(0), X3)) 64.96/17.51 U82_ag(X1, X2, pcA_out_ag(d(e(X1)), X2)) -> pcA_out_ag(d(e(+(t, X1))), +(const(1), X2)) 64.96/17.51 64.96/17.51 The argument filtering Pi contains the following mapping: 64.96/17.51 const(x1) = const 64.96/17.51 64.96/17.51 1 = 1 64.96/17.51 64.96/17.51 d(x1) = d(x1) 64.96/17.51 64.96/17.51 e(x1) = e(x1) 64.96/17.51 64.96/17.51 t = t 64.96/17.51 64.96/17.51 0 = 0 64.96/17.51 64.96/17.51 +(x1, x2) = +(x1, x2) 64.96/17.51 64.96/17.51 *(x1, x2) = *(x1, x2) 64.96/17.51 64.96/17.51 pcA_in_gg(x1, x2) = pcA_in_gg(x1, x2) 64.96/17.51 64.96/17.51 pcA_out_gg(x1, x2) = pcA_out_gg(x1, x2) 64.96/17.51 64.96/17.51 U80_gg(x1, x2) = U80_gg(x1, x2) 64.96/17.51 64.96/17.51 qcB_in_ga(x1, x2) = qcB_in_ga(x1) 64.96/17.51 64.96/17.51 U98_ga(x1) = U98_ga(x1) 64.96/17.51 64.96/17.51 U81_gg(x1, x2) = U81_gg(x1, x2) 64.96/17.51 64.96/17.51 qcC_in_ga(x1, x2) = qcC_in_ga(x1) 64.96/17.51 64.96/17.51 U112_ga(x1) = U112_ga(x1) 64.96/17.51 64.96/17.51 U82_gg(x1, x2, x3) = U82_gg(x1, x2, x3) 64.96/17.51 64.96/17.51 U83_gg(x1, x2, x3, x4) = U83_gg(x2, x3, x4) 64.96/17.51 64.96/17.51 U84_gg(x1, x2, x3, x4, x5, x6, x7) = U84_gg(x1, x2, x3, x4, x5, x6, x7) 64.96/17.51 64.96/17.51 qcD_in_gggggg(x1, x2, x3, x4, x5, x6) = qcD_in_gggggg(x1, x2, x3, x4, x5, x6) 64.96/17.51 64.96/17.51 U122_gggggg(x1, x2, x3, x4, x5, x6, x7) = U122_gggggg(x1, x2, x3, x4, x5, x6, x7) 64.96/17.51 64.96/17.51 U85_gg(x1, x2, x3, x4, x5, x6, x7) = U85_gg(x1, x2, x3, x4, x5, x6, x7) 64.96/17.51 64.96/17.51 qcD_out_gggggg(x1, x2, x3, x4, x5, x6) = qcD_out_gggggg(x1, x2, x3, x4, x5, x6) 64.96/17.51 64.96/17.51 U86_gg(x1, x2, x3, x4, x5) = U86_gg(x1, x2, x3, x4, x5) 64.96/17.51 64.96/17.51 qcE_in_gggg(x1, x2, x3, x4) = qcE_in_gggg(x1, x2, x3, x4) 64.96/17.51 64.96/17.51 U124_gggg(x1, x2, x3, x4, x5) = U124_gggg(x1, x2, x3, x4, x5) 64.96/17.51 64.96/17.51 U87_gg(x1, x2, x3, x4) = U87_gg(x1, x2, x3, x4) 64.96/17.51 64.96/17.51 qcF_in_gagg(x1, x2, x3, x4) = qcF_in_gagg(x1, x3, x4) 64.96/17.51 64.96/17.51 U126_gagg(x1, x2, x3, x4, x5) = U126_gagg(x1, x3, x4, x5) 64.96/17.51 64.96/17.51 pcJ_in_ga(x1, x2) = pcJ_in_ga(x1) 64.96/17.51 64.96/17.51 pcJ_out_ga(x1, x2) = pcJ_out_ga(x1, x2) 64.96/17.51 64.96/17.51 U108_ga(x1, x2, x3, x4, x5) = U108_ga(x1, x2, x5) 64.96/17.51 64.96/17.51 qcI_in_gaga(x1, x2, x3, x4) = qcI_in_gaga(x1, x3) 64.96/17.51 64.96/17.51 U96_gaga(x1, x2, x3, x4, x5) = U96_gaga(x1, x3, x5) 64.96/17.51 64.96/17.51 pcH_in_ga(x1, x2) = pcH_in_ga(x1) 64.96/17.51 64.96/17.51 pcH_out_ga(x1, x2) = pcH_out_ga(x1, x2) 64.96/17.51 64.96/17.51 U94_ga(x1, x2, x3, x4, x5) = U94_ga(x1, x2, x5) 64.96/17.51 64.96/17.51 qcI_out_gaga(x1, x2, x3, x4) = qcI_out_gaga(x1, x2, x3, x4) 64.96/17.51 64.96/17.51 U95_ga(x1, x2, x3, x4, x5) = U95_ga(x1, x2, x5) 64.96/17.51 64.96/17.51 U97_gaga(x1, x2, x3, x4, x5) = U97_gaga(x1, x2, x3, x5) 64.96/17.51 64.96/17.51 U109_ga(x1, x2, x3, x4, x5) = U109_ga(x1, x2, x5) 64.96/17.51 64.96/17.51 U110_ga(x1, x2, x3) = U110_ga(x1, x3) 64.96/17.51 64.96/17.51 U111_ga(x1, x2, x3) = U111_ga(x1, x3) 64.96/17.51 64.96/17.51 U127_gagg(x1, x2, x3, x4, x5) = U127_gagg(x1, x2, x3, x4, x5) 64.96/17.51 64.96/17.51 U88_gg(x1, x2, x3) = U88_gg(x1, x2, x3) 64.96/17.51 64.96/17.51 U89_gg(x1, x2, x3, x4) = U89_gg(x2, x3, x4) 64.96/17.51 64.96/17.51 U90_gg(x1, x2, x3, x4, x5, x6, x7) = U90_gg(x1, x2, x3, x4, x5, x6, x7) 64.96/17.51 64.96/17.51 U91_gg(x1, x2, x3, x4, x5, x6, x7) = U91_gg(x1, x2, x3, x4, x5, x6, x7) 64.96/17.51 64.96/17.51 U92_gg(x1, x2, x3, x4, x5, x6) = U92_gg(x1, x2, x3, x4, x5, x6) 64.96/17.51 64.96/17.51 qcF_out_gagg(x1, x2, x3, x4) = qcF_out_gagg(x1, x2, x3, x4) 64.96/17.51 64.96/17.51 U93_gg(x1, x2, x3) = U93_gg(x1, x2, x3) 64.96/17.51 64.96/17.51 qcG_in_gag(x1, x2, x3) = qcG_in_gag(x1, x3) 64.96/17.51 64.96/17.51 U128_gag(x1, x2) = U128_gag(x1, x2) 64.96/17.51 64.96/17.51 qcG_out_gag(x1, x2, x3) = qcG_out_gag(x1, x2, x3) 64.96/17.51 64.96/17.51 U129_gag(x1, x2, x3) = U129_gag(x2, x3) 64.96/17.51 64.96/17.51 U130_gag(x1, x2, x3, x4, x5, x6) = U130_gag(x1, x2, x5, x6) 64.96/17.51 64.96/17.51 U131_gag(x1, x2, x3, x4, x5, x6) = U131_gag(x1, x2, x3, x5, x6) 64.96/17.51 64.96/17.51 U132_gag(x1, x2, x3, x4, x5, x6) = U132_gag(x1, x2, x3, x4, x5, x6) 64.96/17.51 64.96/17.51 U133_gag(x1, x2, x3, x4, x5, x6) = U133_gag(x1, x2, x5, x6) 64.96/17.51 64.96/17.51 U134_gag(x1, x2, x3, x4, x5, x6) = U134_gag(x1, x2, x4, x5, x6) 64.96/17.51 64.96/17.51 U135_gag(x1, x2, x3, x4, x5, x6) = U135_gag(x1, x2, x3, x4, x5, x6) 64.96/17.51 64.96/17.51 U136_gag(x1, x2, x3, x4) = U136_gag(x1, x3, x4) 64.96/17.51 64.96/17.51 U137_gag(x1, x2, x3, x4) = U137_gag(x1, x3, x4) 64.96/17.51 64.96/17.51 U125_gggg(x1, x2, x3, x4, x5) = U125_gggg(x1, x2, x3, x4, x5) 64.96/17.51 64.96/17.51 qcE_out_gggg(x1, x2, x3, x4) = qcE_out_gggg(x1, x2, x3, x4) 64.96/17.51 64.96/17.51 U123_gggggg(x1, x2, x3, x4, x5, x6, x7) = U123_gggggg(x1, x2, x3, x4, x5, x6, x7) 64.96/17.51 64.96/17.51 qcC_out_ga(x1, x2) = qcC_out_ga(x1, x2) 64.96/17.51 64.96/17.51 U113_ga(x1, x2) = U113_ga(x2) 64.96/17.51 64.96/17.51 U114_ga(x1, x2, x3, x4, x5) = U114_ga(x1, x2, x5) 64.96/17.51 64.96/17.51 U115_ga(x1, x2, x3, x4, x5) = U115_ga(x1, x2, x3, x5) 64.96/17.51 64.96/17.51 U116_ga(x1, x2, x3, x4, x5) = U116_ga(x1, x2, x3, x4, x5) 64.96/17.51 64.96/17.51 U117_ga(x1, x2, x3, x4, x5) = U117_ga(x1, x2, x5) 64.96/17.51 64.96/17.51 U118_ga(x1, x2, x3, x4, x5) = U118_ga(x1, x2, x4, x5) 64.96/17.51 64.96/17.51 U119_ga(x1, x2, x3, x4, x5) = U119_ga(x1, x2, x3, x4, x5) 64.96/17.51 64.96/17.51 U120_ga(x1, x2, x3) = U120_ga(x1, x3) 64.96/17.51 64.96/17.51 U121_ga(x1, x2, x3) = U121_ga(x1, x3) 64.96/17.51 64.96/17.51 qcB_out_ga(x1, x2) = qcB_out_ga(x1, x2) 64.96/17.51 64.96/17.51 U99_ga(x1, x2) = U99_ga(x2) 64.96/17.51 64.96/17.51 U100_ga(x1, x2, x3, x4, x5) = U100_ga(x1, x2, x5) 64.96/17.51 64.96/17.51 U101_ga(x1, x2, x3, x4, x5) = U101_ga(x1, x2, x3, x5) 64.96/17.51 64.96/17.51 U102_ga(x1, x2, x3, x4, x5) = U102_ga(x1, x2, x3, x4, x5) 64.96/17.51 64.96/17.51 U103_ga(x1, x2, x3, x4, x5) = U103_ga(x1, x2, x5) 64.96/17.51 64.96/17.51 U104_ga(x1, x2, x3, x4, x5) = U104_ga(x1, x2, x4, x5) 64.96/17.51 64.96/17.51 U105_ga(x1, x2, x3, x4, x5) = U105_ga(x1, x2, x3, x4, x5) 64.96/17.51 64.96/17.51 U106_ga(x1, x2, x3) = U106_ga(x1, x3) 64.96/17.51 64.96/17.51 U107_ga(x1, x2, x3) = U107_ga(x1, x3) 64.96/17.51 64.96/17.51 pcH_in_aa(x1, x2) = pcH_in_aa 64.96/17.51 64.96/17.51 pcH_out_aa(x1, x2) = pcH_out_aa(x1, x2) 64.96/17.51 64.96/17.51 U94_aa(x1, x2, x3, x4, x5) = U94_aa(x5) 64.96/17.51 64.96/17.51 qcI_in_aaaa(x1, x2, x3, x4) = qcI_in_aaaa 64.96/17.51 64.96/17.51 U96_aaaa(x1, x2, x3, x4, x5) = U96_aaaa(x5) 64.96/17.51 64.96/17.51 U95_aa(x1, x2, x3, x4, x5) = U95_aa(x5) 64.96/17.51 64.96/17.51 qcI_out_aaaa(x1, x2, x3, x4) = qcI_out_aaaa(x1, x2, x3, x4) 64.96/17.51 64.96/17.51 U97_aaaa(x1, x2, x3, x4, x5) = U97_aaaa(x1, x2, x5) 64.96/17.51 64.96/17.51 pcJ_in_aa(x1, x2) = pcJ_in_aa 64.96/17.51 64.96/17.51 pcJ_out_aa(x1, x2) = pcJ_out_aa(x1, x2) 64.96/17.51 64.96/17.51 U108_aa(x1, x2, x3, x4, x5) = U108_aa(x5) 64.96/17.51 64.96/17.51 U109_aa(x1, x2, x3, x4, x5) = U109_aa(x5) 64.96/17.51 64.96/17.51 U110_aa(x1, x2, x3) = U110_aa(x3) 64.96/17.51 64.96/17.51 U111_aa(x1, x2, x3) = U111_aa(x1, x3) 64.96/17.51 64.96/17.51 pcA_in_ag(x1, x2) = pcA_in_ag(x2) 64.96/17.51 64.96/17.51 pcA_out_ag(x1, x2) = pcA_out_ag(x1, x2) 64.96/17.51 64.96/17.51 U80_ag(x1, x2) = U80_ag(x2) 64.96/17.51 64.96/17.51 qcB_in_aa(x1, x2) = qcB_in_aa 64.96/17.51 64.96/17.51 U98_aa(x1) = U98_aa(x1) 64.96/17.51 64.96/17.51 qcB_out_aa(x1, x2) = qcB_out_aa(x1, x2) 64.96/17.51 64.96/17.51 U99_aa(x1, x2) = U99_aa(x2) 64.96/17.51 64.96/17.51 U100_aa(x1, x2, x3, x4, x5) = U100_aa(x5) 64.96/17.51 64.96/17.51 U101_aa(x1, x2, x3, x4, x5) = U101_aa(x1, x3, x5) 64.96/17.51 64.96/17.51 U102_aa(x1, x2, x3, x4, x5) = U102_aa(x1, x2, x3, x4, x5) 64.96/17.51 64.96/17.51 U103_aa(x1, x2, x3, x4, x5) = U103_aa(x5) 64.96/17.51 64.96/17.51 U104_aa(x1, x2, x3, x4, x5) = U104_aa(x1, x4, x5) 64.96/17.51 64.96/17.51 U105_aa(x1, x2, x3, x4, x5) = U105_aa(x1, x2, x3, x4, x5) 64.96/17.51 64.96/17.51 U106_aa(x1, x2, x3) = U106_aa(x3) 64.96/17.51 64.96/17.51 U107_aa(x1, x2, x3) = U107_aa(x1, x3) 64.96/17.51 64.96/17.51 U81_ag(x1, x2) = U81_ag(x2) 64.96/17.51 64.96/17.51 qcC_in_aa(x1, x2) = qcC_in_aa 64.96/17.51 64.96/17.51 U112_aa(x1) = U112_aa(x1) 64.96/17.51 64.96/17.51 qcC_out_aa(x1, x2) = qcC_out_aa(x1, x2) 64.96/17.51 64.96/17.51 U113_aa(x1, x2) = U113_aa(x2) 64.96/17.51 64.96/17.51 U114_aa(x1, x2, x3, x4, x5) = U114_aa(x5) 64.96/17.51 64.96/17.51 U115_aa(x1, x2, x3, x4, x5) = U115_aa(x1, x3, x5) 64.96/17.51 64.96/17.51 U116_aa(x1, x2, x3, x4, x5) = U116_aa(x1, x2, x3, x4, x5) 64.96/17.51 64.96/17.51 U117_aa(x1, x2, x3, x4, x5) = U117_aa(x5) 64.96/17.51 64.96/17.51 U118_aa(x1, x2, x3, x4, x5) = U118_aa(x1, x4, x5) 64.96/17.51 64.96/17.51 U119_aa(x1, x2, x3, x4, x5) = U119_aa(x1, x2, x3, x4, x5) 64.96/17.51 64.96/17.51 U120_aa(x1, x2, x3) = U120_aa(x3) 64.96/17.51 64.96/17.51 U121_aa(x1, x2, x3) = U121_aa(x1, x3) 64.96/17.51 64.96/17.51 U82_ag(x1, x2, x3) = U82_ag(x2, x3) 64.96/17.51 64.96/17.51 U83_ag(x1, x2, x3, x4) = U83_ag(x3, x4) 64.96/17.51 64.96/17.51 U84_ag(x1, x2, x3, x4, x5, x6, x7) = U84_ag(x4, x5, x6, x7) 64.96/17.51 64.96/17.51 qcD_in_agagag(x1, x2, x3, x4, x5, x6) = qcD_in_agagag(x2, x4, x6) 64.96/17.51 64.96/17.51 U122_agagag(x1, x2, x3, x4, x5, x6, x7) = U122_agagag(x2, x4, x6, x7) 64.96/17.51 64.96/17.51 U85_ag(x1, x2, x3, x4, x5, x6, x7) = U85_ag(x1, x2, x4, x5, x6, x7) 64.96/17.51 64.96/17.51 qcD_in_ggggag(x1, x2, x3, x4, x5, x6) = qcD_in_ggggag(x1, x2, x3, x4, x6) 64.96/17.51 64.96/17.51 U122_ggggag(x1, x2, x3, x4, x5, x6, x7) = U122_ggggag(x1, x2, x3, x4, x6, x7) 64.96/17.51 64.96/17.51 U123_ggggag(x1, x2, x3, x4, x5, x6, x7) = U123_ggggag(x1, x2, x3, x4, x6, x7) 64.96/17.51 64.96/17.51 qcE_in_ggag(x1, x2, x3, x4) = qcE_in_ggag(x1, x2, x4) 64.96/17.51 64.96/17.51 U124_ggag(x1, x2, x3, x4, x5) = U124_ggag(x1, x2, x4, x5) 64.96/17.51 64.96/17.51 U125_ggag(x1, x2, x3, x4, x5) = U125_ggag(x1, x2, x4, x5) 64.96/17.51 64.96/17.51 U86_ag(x1, x2, x3, x4, x5) = U86_ag(x1, x2, x3, x4, x5) 64.96/17.51 64.96/17.51 U87_ag(x1, x2, x3, x4) = U87_ag(x2, x3, x4) 64.96/17.51 64.96/17.51 qcF_in_aagg(x1, x2, x3, x4) = qcF_in_aagg(x3, x4) 64.96/17.51 64.96/17.51 U126_aagg(x1, x2, x3, x4, x5) = U126_aagg(x3, x4, x5) 64.96/17.51 64.96/17.51 U127_aagg(x1, x2, x3, x4, x5) = U127_aagg(x1, x2, x3, x4, x5) 64.96/17.51 64.96/17.51 qcF_out_aagg(x1, x2, x3, x4) = qcF_out_aagg(x1, x2, x3, x4) 64.96/17.51 64.96/17.51 U88_ag(x1, x2, x3) = U88_ag(x1, x2, x3) 64.96/17.51 64.96/17.51 U89_ag(x1, x2, x3, x4) = U89_ag(x2, x3, x4) 64.96/17.51 64.96/17.51 U90_ag(x1, x2, x3, x4, x5, x6, x7) = U90_ag(x1, x2, x3, x4, x5, x6, x7) 64.96/17.51 64.96/17.51 U91_ag(x1, x2, x3, x4, x5, x6, x7) = U91_ag(x1, x2, x3, x4, x5, x6, x7) 64.96/17.51 64.96/17.51 U92_ag(x1, x2, x3, x4, x5, x6) = U92_ag(x2, x3, x4, x5, x6) 64.96/17.51 64.96/17.51 U93_ag(x1, x2, x3) = U93_ag(x2, x3) 64.96/17.51 64.96/17.51 qcG_in_aag(x1, x2, x3) = qcG_in_aag(x3) 64.96/17.51 64.96/17.51 U128_aag(x1, x2) = U128_aag(x1, x2) 64.96/17.51 64.96/17.51 qcG_out_aag(x1, x2, x3) = qcG_out_aag(x1, x2, x3) 64.96/17.51 64.96/17.51 U129_aag(x1, x2, x3) = U129_aag(x2, x3) 64.96/17.51 64.96/17.51 U130_aag(x1, x2, x3, x4, x5, x6) = U130_aag(x5, x6) 64.96/17.51 64.96/17.51 U131_aag(x1, x2, x3, x4, x5, x6) = U131_aag(x1, x3, x5, x6) 64.96/17.51 64.96/17.51 U132_aag(x1, x2, x3, x4, x5, x6) = U132_aag(x1, x2, x3, x4, x5, x6) 64.96/17.51 64.96/17.51 U133_aag(x1, x2, x3, x4, x5, x6) = U133_aag(x5, x6) 64.96/17.51 64.96/17.51 U134_aag(x1, x2, x3, x4, x5, x6) = U134_aag(x1, x4, x5, x6) 64.96/17.51 64.96/17.51 U135_aag(x1, x2, x3, x4, x5, x6) = U135_aag(x1, x2, x3, x4, x5, x6) 64.96/17.51 64.96/17.51 U136_aag(x1, x2, x3, x4) = U136_aag(x3, x4) 64.96/17.51 64.96/17.51 U137_aag(x1, x2, x3, x4) = U137_aag(x1, x3, x4) 64.96/17.51 64.96/17.51 qcE_out_ggag(x1, x2, x3, x4) = qcE_out_ggag(x1, x2, x3, x4) 64.96/17.51 64.96/17.51 qcD_out_ggggag(x1, x2, x3, x4, x5, x6) = qcD_out_ggggag(x1, x2, x3, x4, x5, x6) 64.96/17.51 64.96/17.51 U123_agagag(x1, x2, x3, x4, x5, x6, x7) = U123_agagag(x1, x2, x4, x6, x7) 64.96/17.51 64.96/17.51 qcE_in_agag(x1, x2, x3, x4) = qcE_in_agag(x2, x4) 64.96/17.51 64.96/17.51 U124_agag(x1, x2, x3, x4, x5) = U124_agag(x2, x4, x5) 64.96/17.51 64.96/17.51 U125_agag(x1, x2, x3, x4, x5) = U125_agag(x1, x2, x4, x5) 64.96/17.51 64.96/17.51 qcE_out_agag(x1, x2, x3, x4) = qcE_out_agag(x1, x2, x3, x4) 64.96/17.51 64.96/17.51 qcD_out_agagag(x1, x2, x3, x4, x5, x6) = qcD_out_agagag(x1, x2, x3, x4, x5, x6) 64.96/17.51 64.96/17.51 PA_IN_AG(x1, x2) = PA_IN_AG(x2) 64.96/17.51 64.96/17.51 PD_IN_AGAGAG(x1, x2, x3, x4, x5, x6) = PD_IN_AGAGAG(x2, x4, x6) 64.96/17.51 64.96/17.51 PD_IN_GGGGAG(x1, x2, x3, x4, x5, x6) = PD_IN_GGGGAG(x1, x2, x3, x4, x6) 64.96/17.51 64.96/17.51 U42_GGGGAG(x1, x2, x3, x4, x5, x6, x7) = U42_GGGGAG(x1, x2, x3, x4, x6, x7) 64.96/17.51 64.96/17.51 PE_IN_GGAG(x1, x2, x3, x4) = PE_IN_GGAG(x1, x2, x4) 64.96/17.51 64.96/17.51 U45_GGAG(x1, x2, x3, x4, x5) = U45_GGAG(x1, x2, x4, x5) 64.96/17.51 64.96/17.51 U42_AGAGAG(x1, x2, x3, x4, x5, x6, x7) = U42_AGAGAG(x2, x4, x6, x7) 64.96/17.51 64.96/17.51 PE_IN_AGAG(x1, x2, x3, x4) = PE_IN_AGAG(x2, x4) 64.96/17.51 64.96/17.51 U45_AGAG(x1, x2, x3, x4, x5) = U45_AGAG(x2, x4, x5) 64.96/17.51 64.96/17.51 64.96/17.51 We have to consider all (P,R,Pi)-chains 64.96/17.51 ---------------------------------------- 64.96/17.51 64.96/17.51 (141) UsableRulesProof (EQUIVALENT) 64.96/17.51 For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. 64.96/17.51 ---------------------------------------- 64.96/17.51 64.96/17.51 (142) 64.96/17.51 Obligation: 64.96/17.51 Pi DP problem: 64.96/17.51 The TRS P consists of the following rules: 64.96/17.51 64.96/17.51 PD_IN_GGGGAG(X1, X2, X3, X4, X5, X6) -> U42_GGGGAG(X1, X2, X3, X4, X5, X6, pcA_in_gg(d(e(X1)), X2)) 64.96/17.51 U42_GGGGAG(X1, X2, X3, X4, X5, X6, pcA_out_gg(d(e(X1)), X2)) -> PE_IN_GGAG(X3, X4, X5, X6) 64.96/17.51 PE_IN_GGAG(X1, X2, X3, X4) -> U45_GGAG(X1, X2, X3, X4, pcA_in_gg(d(e(X1)), X2)) 64.96/17.51 U45_GGAG(X1, X2, X3, X4, pcA_out_gg(d(e(X1)), X2)) -> PA_IN_AG(d(e(X3)), X4) 64.96/17.51 PA_IN_AG(d(e(+(t, X1))), +(const(1), X2)) -> PA_IN_AG(d(e(X1)), X2) 64.96/17.51 PA_IN_AG(d(e(+(const(X1), X2))), +(const(0), X3)) -> PA_IN_AG(d(e(X2)), X3) 64.96/17.51 PA_IN_AG(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) -> PD_IN_AGAGAG(X1, X4, X2, X5, X3, X6) 64.96/17.51 PD_IN_AGAGAG(X1, X2, X3, X4, X5, X6) -> PA_IN_AG(d(e(X1)), X2) 64.96/17.51 PA_IN_AG(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) -> PD_IN_GGGGAG(X1, X5, X2, X4, X3, X6) 64.96/17.51 PD_IN_AGAGAG(X1, X2, X3, X4, X5, X6) -> U42_AGAGAG(X1, X2, X3, X4, X5, X6, pcA_in_ag(d(e(X1)), X2)) 64.96/17.51 U42_AGAGAG(X1, X2, X3, X4, X5, X6, pcA_out_ag(d(e(X1)), X2)) -> PE_IN_AGAG(X3, X4, X5, X6) 64.96/17.51 PE_IN_AGAG(X1, X2, X3, X4) -> PA_IN_AG(d(e(X1)), X2) 64.96/17.51 PE_IN_AGAG(X1, X2, X3, X4) -> U45_AGAG(X1, X2, X3, X4, pcA_in_ag(d(e(X1)), X2)) 64.96/17.51 U45_AGAG(X1, X2, X3, X4, pcA_out_ag(d(e(X1)), X2)) -> PA_IN_AG(d(e(X3)), X4) 64.96/17.51 64.96/17.51 The TRS R consists of the following rules: 64.96/17.51 64.96/17.51 pcA_in_gg(d(e(t)), const(1)) -> pcA_out_gg(d(e(t)), const(1)) 64.96/17.51 pcA_in_gg(d(e(const(X1))), const(0)) -> pcA_out_gg(d(e(const(X1))), const(0)) 64.96/17.51 pcA_in_gg(d(e(+(t, X1))), +(const(1), X2)) -> U82_gg(X1, X2, pcA_in_gg(d(e(X1)), X2)) 64.96/17.51 pcA_in_gg(d(e(+(const(X1), X2))), +(const(0), X3)) -> U83_gg(X1, X2, X3, pcA_in_gg(d(e(X2)), X3)) 64.96/17.51 pcA_in_gg(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) -> U84_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X4, X2, X5, X3, X6)) 64.96/17.51 pcA_in_gg(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) -> U85_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X5, X2, X4, X3, X6)) 64.96/17.51 pcA_in_gg(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) -> U86_gg(X1, X2, X3, X4, qcE_in_gggg(X1, X4, X2, X3)) 64.96/17.51 pcA_in_gg(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) -> U88_gg(X1, X2, pcA_in_gg(d(e(X1)), X2)) 64.96/17.51 pcA_in_gg(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) -> U89_gg(X1, X2, X3, pcA_in_gg(d(e(X2)), X3)) 64.96/17.51 pcA_in_gg(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) -> U90_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X5, X2, X6, X3, X4)) 64.96/17.51 pcA_in_gg(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) -> U91_gg(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X6, X2, X5, X3, X4)) 64.96/17.51 pcA_in_ag(d(e(t)), const(1)) -> pcA_out_ag(d(e(t)), const(1)) 64.96/17.51 pcA_in_ag(d(e(const(X1))), const(0)) -> pcA_out_ag(d(e(const(X1))), const(0)) 64.96/17.51 pcA_in_ag(d(e(+(t, X1))), +(const(1), X2)) -> U82_ag(X1, X2, pcA_in_ag(d(e(X1)), X2)) 64.96/17.51 pcA_in_ag(d(e(+(const(X1), X2))), +(const(0), X3)) -> U83_ag(X1, X2, X3, pcA_in_ag(d(e(X2)), X3)) 64.96/17.51 pcA_in_ag(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) -> U84_ag(X1, X2, X3, X4, X5, X6, qcD_in_agagag(X1, X4, X2, X5, X3, X6)) 64.96/17.51 pcA_in_ag(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) -> U85_ag(X1, X2, X3, X4, X5, X6, qcD_in_ggggag(X1, X5, X2, X4, X3, X6)) 64.96/17.51 pcA_in_ag(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) -> U86_ag(X1, X2, X3, X4, qcE_in_gggg(X1, X4, X2, X3)) 64.96/17.51 pcA_in_ag(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) -> U88_ag(X1, X2, pcA_in_gg(d(e(X1)), X2)) 64.96/17.51 pcA_in_ag(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) -> U89_ag(X1, X2, X3, pcA_in_gg(d(e(X2)), X3)) 64.96/17.51 pcA_in_ag(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) -> U90_ag(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X5, X2, X6, X3, X4)) 64.96/17.51 pcA_in_ag(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) -> U91_ag(X1, X2, X3, X4, X5, X6, qcD_in_gggggg(X1, X6, X2, X5, X3, X4)) 64.96/17.51 U82_gg(X1, X2, pcA_out_gg(d(e(X1)), X2)) -> pcA_out_gg(d(e(+(t, X1))), +(const(1), X2)) 64.96/17.51 U83_gg(X1, X2, X3, pcA_out_gg(d(e(X2)), X3)) -> pcA_out_gg(d(e(+(const(X1), X2))), +(const(0), X3)) 64.96/17.51 U84_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X4, X2, X5, X3, X6)) -> pcA_out_gg(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) 64.96/17.51 U85_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X5, X2, X4, X3, X6)) -> pcA_out_gg(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) 64.96/17.51 U86_gg(X1, X2, X3, X4, qcE_out_gggg(X1, X4, X2, X3)) -> pcA_out_gg(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) 64.96/17.51 U88_gg(X1, X2, pcA_out_gg(d(e(X1)), X2)) -> pcA_out_gg(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) 64.96/17.51 U89_gg(X1, X2, X3, pcA_out_gg(d(e(X2)), X3)) -> pcA_out_gg(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) 64.96/17.51 U90_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X5, X2, X6, X3, X4)) -> pcA_out_gg(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) 64.96/17.51 U91_gg(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X6, X2, X5, X3, X4)) -> pcA_out_gg(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) 64.96/17.51 U82_ag(X1, X2, pcA_out_ag(d(e(X1)), X2)) -> pcA_out_ag(d(e(+(t, X1))), +(const(1), X2)) 64.96/17.51 U83_ag(X1, X2, X3, pcA_out_ag(d(e(X2)), X3)) -> pcA_out_ag(d(e(+(const(X1), X2))), +(const(0), X3)) 64.96/17.51 U84_ag(X1, X2, X3, X4, X5, X6, qcD_out_agagag(X1, X4, X2, X5, X3, X6)) -> pcA_out_ag(d(e(+(+(X1, X2), X3))), +(+(X4, X5), X6)) 64.96/17.51 U85_ag(X1, X2, X3, X4, X5, X6, qcD_out_ggggag(X1, X5, X2, X4, X3, X6)) -> pcA_out_ag(d(e(+(*(X1, X2), X3))), +(+(*(X1, X4), *(X2, X5)), X6)) 64.96/17.51 U86_ag(X1, X2, X3, X4, qcE_out_gggg(X1, X4, X2, X3)) -> pcA_out_ag(d(e(*(X1, X2))), +(*(X1, X3), *(X2, X4))) 64.96/17.51 U88_ag(X1, X2, pcA_out_gg(d(e(X1)), X2)) -> pcA_out_ag(d(e(*(t, X1))), +(*(t, X2), *(X1, const(1)))) 64.96/17.51 U89_ag(X1, X2, X3, pcA_out_gg(d(e(X2)), X3)) -> pcA_out_ag(d(e(*(const(X1), X2))), +(*(const(X1), X3), *(X2, const(0)))) 64.96/17.51 U90_ag(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X5, X2, X6, X3, X4)) -> pcA_out_ag(d(e(*(+(X1, X2), X3))), +(*(+(X1, X2), X4), *(X3, +(X5, X6)))) 64.96/17.51 U91_ag(X1, X2, X3, X4, X5, X6, qcD_out_gggggg(X1, X6, X2, X5, X3, X4)) -> pcA_out_ag(d(e(*(*(X1, X2), X3))), +(*(*(X1, X2), X4), *(X3, +(*(X1, X5), *(X2, X6))))) 64.96/17.51 qcD_in_gggggg(X1, X2, X3, X4, X5, X6) -> U122_gggggg(X1, X2, X3, X4, X5, X6, pcA_in_gg(d(e(X1)), X2)) 64.96/17.51 qcE_in_gggg(X1, X2, X3, X4) -> U124_gggg(X1, X2, X3, X4, pcA_in_gg(d(e(X1)), X2)) 64.96/17.51 qcD_in_agagag(X1, X2, X3, X4, X5, X6) -> U122_agagag(X1, X2, X3, X4, X5, X6, pcA_in_ag(d(e(X1)), X2)) 64.96/17.51 qcD_in_ggggag(X1, X2, X3, X4, X5, X6) -> U122_ggggag(X1, X2, X3, X4, X5, X6, pcA_in_gg(d(e(X1)), X2)) 64.96/17.51 U122_gggggg(X1, X2, X3, X4, X5, X6, pcA_out_gg(d(e(X1)), X2)) -> U123_gggggg(X1, X2, X3, X4, X5, X6, qcE_in_gggg(X3, X4, X5, X6)) 64.96/17.51 U124_gggg(X1, X2, X3, X4, pcA_out_gg(d(e(X1)), X2)) -> U125_gggg(X1, X2, X3, X4, pcA_in_gg(d(e(X3)), X4)) 64.96/17.51 U122_agagag(X1, X2, X3, X4, X5, X6, pcA_out_ag(d(e(X1)), X2)) -> U123_agagag(X1, X2, X3, X4, X5, X6, qcE_in_agag(X3, X4, X5, X6)) 64.96/17.51 U122_ggggag(X1, X2, X3, X4, X5, X6, pcA_out_gg(d(e(X1)), X2)) -> U123_ggggag(X1, X2, X3, X4, X5, X6, qcE_in_ggag(X3, X4, X5, X6)) 64.96/17.51 U123_gggggg(X1, X2, X3, X4, X5, X6, qcE_out_gggg(X3, X4, X5, X6)) -> qcD_out_gggggg(X1, X2, X3, X4, X5, X6) 64.96/17.51 U125_gggg(X1, X2, X3, X4, pcA_out_gg(d(e(X3)), X4)) -> qcE_out_gggg(X1, X2, X3, X4) 64.96/17.51 U123_agagag(X1, X2, X3, X4, X5, X6, qcE_out_agag(X3, X4, X5, X6)) -> qcD_out_agagag(X1, X2, X3, X4, X5, X6) 64.96/17.51 U123_ggggag(X1, X2, X3, X4, X5, X6, qcE_out_ggag(X3, X4, X5, X6)) -> qcD_out_ggggag(X1, X2, X3, X4, X5, X6) 64.96/17.51 qcE_in_agag(X1, X2, X3, X4) -> U124_agag(X1, X2, X3, X4, pcA_in_ag(d(e(X1)), X2)) 64.96/17.51 qcE_in_ggag(X1, X2, X3, X4) -> U124_ggag(X1, X2, X3, X4, pcA_in_gg(d(e(X1)), X2)) 64.96/17.51 U124_agag(X1, X2, X3, X4, pcA_out_ag(d(e(X1)), X2)) -> U125_agag(X1, X2, X3, X4, pcA_in_ag(d(e(X3)), X4)) 64.96/17.51 U124_ggag(X1, X2, X3, X4, pcA_out_gg(d(e(X1)), X2)) -> U125_ggag(X1, X2, X3, X4, pcA_in_ag(d(e(X3)), X4)) 64.96/17.51 U125_agag(X1, X2, X3, X4, pcA_out_ag(d(e(X3)), X4)) -> qcE_out_agag(X1, X2, X3, X4) 64.96/17.51 U125_ggag(X1, X2, X3, X4, pcA_out_ag(d(e(X3)), X4)) -> qcE_out_ggag(X1, X2, X3, X4) 64.96/17.51 64.96/17.51 The argument filtering Pi contains the following mapping: 64.96/17.51 const(x1) = const 64.96/17.51 64.96/17.51 1 = 1 64.96/17.51 64.96/17.51 d(x1) = d(x1) 64.96/17.51 64.96/17.51 e(x1) = e(x1) 64.96/17.51 64.96/17.51 t = t 64.96/17.51 64.96/17.51 0 = 0 64.96/17.51 64.96/17.51 +(x1, x2) = +(x1, x2) 64.96/17.51 64.96/17.51 *(x1, x2) = *(x1, x2) 64.96/17.51 64.96/17.51 pcA_in_gg(x1, x2) = pcA_in_gg(x1, x2) 64.96/17.51 64.96/17.51 pcA_out_gg(x1, x2) = pcA_out_gg(x1, x2) 64.96/17.51 64.96/17.51 U82_gg(x1, x2, x3) = U82_gg(x1, x2, x3) 64.96/17.51 64.96/17.51 U83_gg(x1, x2, x3, x4) = U83_gg(x2, x3, x4) 64.96/17.51 64.96/17.51 U84_gg(x1, x2, x3, x4, x5, x6, x7) = U84_gg(x1, x2, x3, x4, x5, x6, x7) 64.96/17.51 64.96/17.51 qcD_in_gggggg(x1, x2, x3, x4, x5, x6) = qcD_in_gggggg(x1, x2, x3, x4, x5, x6) 64.96/17.51 64.96/17.51 U122_gggggg(x1, x2, x3, x4, x5, x6, x7) = U122_gggggg(x1, x2, x3, x4, x5, x6, x7) 64.96/17.51 64.96/17.51 U85_gg(x1, x2, x3, x4, x5, x6, x7) = U85_gg(x1, x2, x3, x4, x5, x6, x7) 64.96/17.51 64.96/17.51 qcD_out_gggggg(x1, x2, x3, x4, x5, x6) = qcD_out_gggggg(x1, x2, x3, x4, x5, x6) 64.96/17.51 64.96/17.51 U86_gg(x1, x2, x3, x4, x5) = U86_gg(x1, x2, x3, x4, x5) 64.96/17.51 64.96/17.51 qcE_in_gggg(x1, x2, x3, x4) = qcE_in_gggg(x1, x2, x3, x4) 64.96/17.51 64.96/17.51 U124_gggg(x1, x2, x3, x4, x5) = U124_gggg(x1, x2, x3, x4, x5) 64.96/17.51 64.96/17.51 U88_gg(x1, x2, x3) = U88_gg(x1, x2, x3) 64.96/17.51 64.96/17.51 U89_gg(x1, x2, x3, x4) = U89_gg(x2, x3, x4) 64.96/17.51 64.96/17.51 U90_gg(x1, x2, x3, x4, x5, x6, x7) = U90_gg(x1, x2, x3, x4, x5, x6, x7) 64.96/17.51 64.96/17.51 U91_gg(x1, x2, x3, x4, x5, x6, x7) = U91_gg(x1, x2, x3, x4, x5, x6, x7) 64.96/17.51 64.96/17.51 U125_gggg(x1, x2, x3, x4, x5) = U125_gggg(x1, x2, x3, x4, x5) 64.96/17.51 64.96/17.51 qcE_out_gggg(x1, x2, x3, x4) = qcE_out_gggg(x1, x2, x3, x4) 64.96/17.51 64.96/17.51 U123_gggggg(x1, x2, x3, x4, x5, x6, x7) = U123_gggggg(x1, x2, x3, x4, x5, x6, x7) 64.96/17.51 64.96/17.51 pcA_in_ag(x1, x2) = pcA_in_ag(x2) 64.96/17.51 64.96/17.51 pcA_out_ag(x1, x2) = pcA_out_ag(x1, x2) 64.96/17.51 64.96/17.51 U82_ag(x1, x2, x3) = U82_ag(x2, x3) 64.96/17.51 64.96/17.51 U83_ag(x1, x2, x3, x4) = U83_ag(x3, x4) 64.96/17.51 64.96/17.51 U84_ag(x1, x2, x3, x4, x5, x6, x7) = U84_ag(x4, x5, x6, x7) 64.96/17.51 64.96/17.51 qcD_in_agagag(x1, x2, x3, x4, x5, x6) = qcD_in_agagag(x2, x4, x6) 65.00/17.53 65.00/17.53 U122_agagag(x1, x2, x3, x4, x5, x6, x7) = U122_agagag(x2, x4, x6, x7) 65.00/17.53 65.00/17.53 U85_ag(x1, x2, x3, x4, x5, x6, x7) = U85_ag(x1, x2, x4, x5, x6, x7) 65.00/17.53 65.00/17.53 qcD_in_ggggag(x1, x2, x3, x4, x5, x6) = qcD_in_ggggag(x1, x2, x3, x4, x6) 65.00/17.53 65.00/17.53 U122_ggggag(x1, x2, x3, x4, x5, x6, x7) = U122_ggggag(x1, x2, x3, x4, x6, x7) 65.00/17.53 65.00/17.53 U123_ggggag(x1, x2, x3, x4, x5, x6, x7) = U123_ggggag(x1, x2, x3, x4, x6, x7) 65.00/17.53 65.00/17.53 qcE_in_ggag(x1, x2, x3, x4) = qcE_in_ggag(x1, x2, x4) 65.00/17.53 65.00/17.53 U124_ggag(x1, x2, x3, x4, x5) = U124_ggag(x1, x2, x4, x5) 65.00/17.53 65.00/17.53 U125_ggag(x1, x2, x3, x4, x5) = U125_ggag(x1, x2, x4, x5) 65.00/17.53 65.00/17.53 U86_ag(x1, x2, x3, x4, x5) = U86_ag(x1, x2, x3, x4, x5) 65.00/17.53 65.00/17.53 U88_ag(x1, x2, x3) = U88_ag(x1, x2, x3) 65.00/17.53 65.00/17.53 U89_ag(x1, x2, x3, x4) = U89_ag(x2, x3, x4) 65.00/17.53 65.00/17.53 U90_ag(x1, x2, x3, x4, x5, x6, x7) = U90_ag(x1, x2, x3, x4, x5, x6, x7) 65.00/17.53 65.00/17.53 U91_ag(x1, x2, x3, x4, x5, x6, x7) = U91_ag(x1, x2, x3, x4, x5, x6, x7) 65.00/17.53 65.00/17.53 qcE_out_ggag(x1, x2, x3, x4) = qcE_out_ggag(x1, x2, x3, x4) 65.00/17.53 65.00/17.53 qcD_out_ggggag(x1, x2, x3, x4, x5, x6) = qcD_out_ggggag(x1, x2, x3, x4, x5, x6) 65.00/17.53 65.00/17.53 U123_agagag(x1, x2, x3, x4, x5, x6, x7) = U123_agagag(x1, x2, x4, x6, x7) 65.00/17.53 65.00/17.53 qcE_in_agag(x1, x2, x3, x4) = qcE_in_agag(x2, x4) 65.00/17.53 65.00/17.53 U124_agag(x1, x2, x3, x4, x5) = U124_agag(x2, x4, x5) 65.00/17.53 65.00/17.53 U125_agag(x1, x2, x3, x4, x5) = U125_agag(x1, x2, x4, x5) 65.00/17.53 65.00/17.53 qcE_out_agag(x1, x2, x3, x4) = qcE_out_agag(x1, x2, x3, x4) 65.00/17.53 65.00/17.53 qcD_out_agagag(x1, x2, x3, x4, x5, x6) = qcD_out_agagag(x1, x2, x3, x4, x5, x6) 65.00/17.53 65.00/17.53 PA_IN_AG(x1, x2) = PA_IN_AG(x2) 65.00/17.53 65.00/17.53 PD_IN_AGAGAG(x1, x2, x3, x4, x5, x6) = PD_IN_AGAGAG(x2, x4, x6) 65.00/17.53 65.00/17.53 PD_IN_GGGGAG(x1, x2, x3, x4, x5, x6) = PD_IN_GGGGAG(x1, x2, x3, x4, x6) 65.00/17.53 65.00/17.53 U42_GGGGAG(x1, x2, x3, x4, x5, x6, x7) = U42_GGGGAG(x1, x2, x3, x4, x6, x7) 65.00/17.53 65.00/17.53 PE_IN_GGAG(x1, x2, x3, x4) = PE_IN_GGAG(x1, x2, x4) 65.00/17.53 65.00/17.53 U45_GGAG(x1, x2, x3, x4, x5) = U45_GGAG(x1, x2, x4, x5) 65.00/17.53 65.00/17.53 U42_AGAGAG(x1, x2, x3, x4, x5, x6, x7) = U42_AGAGAG(x2, x4, x6, x7) 65.00/17.53 65.00/17.53 PE_IN_AGAG(x1, x2, x3, x4) = PE_IN_AGAG(x2, x4) 65.00/17.53 65.00/17.53 U45_AGAG(x1, x2, x3, x4, x5) = U45_AGAG(x2, x4, x5) 65.00/17.53 65.00/17.53 65.00/17.53 We have to consider all (P,R,Pi)-chains 65.00/17.60 EOF