570.35/147.41 YES 590.55/152.57 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 590.55/152.57 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 590.55/152.57 590.55/152.57 590.55/152.57 Termination w.r.t. Q of the given QTRS could be proven: 590.55/152.57 590.55/152.57 (0) QTRS 590.55/152.57 (1) QTRS Reverse [EQUIVALENT, 0 ms] 590.55/152.57 (2) QTRS 590.55/152.57 (3) DependencyPairsProof [EQUIVALENT, 777 ms] 590.55/152.57 (4) QDP 590.55/152.57 (5) DependencyGraphProof [EQUIVALENT, 0 ms] 590.55/152.57 (6) QDP 590.55/152.57 (7) TransformationProof [EQUIVALENT, 0 ms] 590.55/152.57 (8) QDP 590.55/152.57 (9) DependencyGraphProof [EQUIVALENT, 0 ms] 590.55/152.57 (10) QDP 590.55/152.57 (11) TransformationProof [EQUIVALENT, 0 ms] 590.55/152.57 (12) QDP 590.55/152.57 (13) DependencyGraphProof [EQUIVALENT, 0 ms] 590.55/152.57 (14) QDP 590.55/152.57 (15) TransformationProof [EQUIVALENT, 0 ms] 590.55/152.57 (16) QDP 590.55/152.57 (17) DependencyGraphProof [EQUIVALENT, 0 ms] 590.55/152.57 (18) QDP 590.55/152.57 (19) TransformationProof [EQUIVALENT, 0 ms] 590.55/152.57 (20) QDP 590.55/152.57 (21) DependencyGraphProof [EQUIVALENT, 0 ms] 590.55/152.57 (22) QDP 590.55/152.57 (23) TransformationProof [EQUIVALENT, 0 ms] 590.55/152.57 (24) QDP 590.55/152.57 (25) DependencyGraphProof [EQUIVALENT, 0 ms] 590.55/152.57 (26) QDP 590.55/152.57 (27) TransformationProof [EQUIVALENT, 0 ms] 590.55/152.57 (28) QDP 590.55/152.57 (29) DependencyGraphProof [EQUIVALENT, 0 ms] 590.55/152.57 (30) QDP 590.55/152.57 (31) TransformationProof [EQUIVALENT, 0 ms] 590.55/152.57 (32) QDP 590.55/152.57 (33) DependencyGraphProof [EQUIVALENT, 0 ms] 590.55/152.57 (34) QDP 590.55/152.57 (35) TransformationProof [EQUIVALENT, 0 ms] 590.55/152.57 (36) QDP 590.55/152.57 (37) DependencyGraphProof [EQUIVALENT, 0 ms] 590.55/152.57 (38) QDP 590.55/152.57 (39) TransformationProof [EQUIVALENT, 0 ms] 590.55/152.57 (40) QDP 590.55/152.57 (41) DependencyGraphProof [EQUIVALENT, 0 ms] 590.55/152.57 (42) QDP 590.55/152.57 (43) TransformationProof [EQUIVALENT, 0 ms] 590.55/152.57 (44) QDP 590.55/152.57 (45) DependencyGraphProof [EQUIVALENT, 0 ms] 590.55/152.57 (46) QDP 590.55/152.57 (47) TransformationProof [EQUIVALENT, 0 ms] 590.55/152.57 (48) QDP 590.55/152.57 (49) DependencyGraphProof [EQUIVALENT, 0 ms] 590.55/152.57 (50) QDP 590.55/152.57 (51) TransformationProof [EQUIVALENT, 0 ms] 590.55/152.57 (52) QDP 590.55/152.57 (53) DependencyGraphProof [EQUIVALENT, 0 ms] 590.55/152.57 (54) QDP 590.55/152.57 (55) TransformationProof [EQUIVALENT, 0 ms] 590.55/152.57 (56) QDP 590.55/152.57 (57) DependencyGraphProof [EQUIVALENT, 0 ms] 590.55/152.57 (58) QDP 590.55/152.57 (59) TransformationProof [EQUIVALENT, 0 ms] 590.55/152.57 (60) QDP 590.55/152.57 (61) DependencyGraphProof [EQUIVALENT, 0 ms] 590.55/152.57 (62) QDP 590.55/152.57 (63) TransformationProof [EQUIVALENT, 0 ms] 590.55/152.57 (64) QDP 590.55/152.57 (65) DependencyGraphProof [EQUIVALENT, 0 ms] 590.55/152.57 (66) QDP 590.55/152.57 (67) TransformationProof [EQUIVALENT, 0 ms] 590.55/152.57 (68) QDP 590.55/152.57 (69) DependencyGraphProof [EQUIVALENT, 0 ms] 590.55/152.57 (70) QDP 590.55/152.57 (71) TransformationProof [EQUIVALENT, 0 ms] 590.55/152.57 (72) QDP 590.55/152.57 (73) DependencyGraphProof [EQUIVALENT, 0 ms] 590.55/152.57 (74) QDP 590.55/152.57 (75) TransformationProof [EQUIVALENT, 106 ms] 590.55/152.57 (76) QDP 590.55/152.57 (77) DependencyGraphProof [EQUIVALENT, 0 ms] 590.55/152.57 (78) QDP 590.55/152.57 (79) TransformationProof [EQUIVALENT, 38 ms] 590.55/152.57 (80) QDP 590.55/152.57 (81) DependencyGraphProof [EQUIVALENT, 0 ms] 590.55/152.57 (82) QDP 590.55/152.57 (83) TransformationProof [EQUIVALENT, 63 ms] 590.55/152.57 (84) QDP 590.55/152.57 (85) DependencyGraphProof [EQUIVALENT, 0 ms] 590.55/152.57 (86) QDP 590.55/152.57 (87) TransformationProof [EQUIVALENT, 52 ms] 590.55/152.57 (88) QDP 590.55/152.57 (89) DependencyGraphProof [EQUIVALENT, 0 ms] 590.55/152.57 (90) QDP 590.55/152.57 (91) TransformationProof [EQUIVALENT, 54 ms] 590.55/152.57 (92) QDP 590.55/152.57 (93) DependencyGraphProof [EQUIVALENT, 0 ms] 590.55/152.57 (94) QDP 590.55/152.57 (95) TransformationProof [EQUIVALENT, 43 ms] 590.55/152.57 (96) QDP 590.55/152.57 (97) DependencyGraphProof [EQUIVALENT, 0 ms] 590.55/152.57 (98) QDP 590.55/152.57 (99) TransformationProof [EQUIVALENT, 33 ms] 590.55/152.57 (100) QDP 590.55/152.57 (101) DependencyGraphProof [EQUIVALENT, 0 ms] 590.55/152.57 (102) QDP 590.55/152.57 (103) TransformationProof [EQUIVALENT, 6 ms] 590.55/152.57 (104) QDP 590.55/152.57 (105) DependencyGraphProof [EQUIVALENT, 0 ms] 590.55/152.57 (106) QDP 590.55/152.57 (107) TransformationProof [EQUIVALENT, 0 ms] 590.55/152.57 (108) QDP 590.55/152.57 (109) DependencyGraphProof [EQUIVALENT, 0 ms] 590.55/152.57 (110) QDP 590.55/152.57 (111) TransformationProof [EQUIVALENT, 37 ms] 590.55/152.57 (112) QDP 590.55/152.57 (113) DependencyGraphProof [EQUIVALENT, 0 ms] 590.55/152.57 (114) QDP 590.55/152.57 (115) TransformationProof [EQUIVALENT, 64 ms] 590.55/152.57 (116) QDP 590.55/152.57 (117) DependencyGraphProof [EQUIVALENT, 0 ms] 590.55/152.57 (118) QDP 590.55/152.57 (119) TransformationProof [EQUIVALENT, 0 ms] 590.55/152.57 (120) QDP 590.55/152.57 (121) DependencyGraphProof [EQUIVALENT, 0 ms] 590.55/152.57 (122) QDP 590.55/152.57 (123) TransformationProof [EQUIVALENT, 13 ms] 590.55/152.57 (124) QDP 590.55/152.57 (125) DependencyGraphProof [EQUIVALENT, 0 ms] 590.55/152.57 (126) QDP 590.55/152.57 (127) TransformationProof [EQUIVALENT, 21 ms] 590.55/152.57 (128) QDP 590.55/152.57 (129) DependencyGraphProof [EQUIVALENT, 0 ms] 590.55/152.57 (130) QDP 590.55/152.57 (131) TransformationProof [EQUIVALENT, 46 ms] 590.55/152.57 (132) QDP 590.55/152.57 (133) DependencyGraphProof [EQUIVALENT, 0 ms] 590.55/152.57 (134) QDP 590.55/152.57 (135) TransformationProof [EQUIVALENT, 5 ms] 590.55/152.57 (136) QDP 590.55/152.57 (137) DependencyGraphProof [EQUIVALENT, 0 ms] 590.55/152.57 (138) QDP 590.55/152.57 (139) TransformationProof [EQUIVALENT, 40 ms] 590.55/152.57 (140) QDP 590.55/152.57 (141) DependencyGraphProof [EQUIVALENT, 0 ms] 590.55/152.57 (142) QDP 590.55/152.57 (143) QDPOrderProof [EQUIVALENT, 135 ms] 590.55/152.57 (144) QDP 590.55/152.57 (145) DependencyGraphProof [EQUIVALENT, 0 ms] 590.55/152.57 (146) QDP 590.55/152.57 (147) QDPOrderProof [EQUIVALENT, 1578 ms] 590.55/152.57 (148) QDP 590.55/152.57 (149) QDPOrderProof [EQUIVALENT, 817 ms] 590.55/152.57 (150) QDP 590.55/152.57 (151) PisEmptyProof [EQUIVALENT, 0 ms] 590.55/152.57 (152) YES 590.55/152.57 590.55/152.57 590.55/152.57 ---------------------------------------- 590.55/152.57 590.55/152.57 (0) 590.55/152.57 Obligation: 590.55/152.57 Q restricted rewrite system: 590.55/152.57 The TRS R consists of the following rules: 590.55/152.57 590.55/152.57 0(0(1(0(x1)))) -> 0(1(2(0(2(0(x1)))))) 590.55/152.57 0(1(0(0(x1)))) -> 1(2(0(0(0(x1))))) 590.55/152.57 0(1(0(1(x1)))) -> 1(1(0(3(0(2(x1)))))) 590.55/152.57 0(4(1(0(x1)))) -> 0(3(1(4(0(x1))))) 590.55/152.57 0(4(1(0(x1)))) -> 1(4(0(0(5(x1))))) 590.55/152.57 0(4(1(0(x1)))) -> 1(5(0(4(0(x1))))) 590.55/152.57 0(4(1(0(x1)))) -> 0(5(1(4(5(0(x1)))))) 590.55/152.57 0(4(1(0(x1)))) -> 0(5(1(5(4(0(x1)))))) 590.55/152.57 0(4(1(0(x1)))) -> 1(5(0(4(0(5(x1)))))) 590.55/152.57 4(2(1(0(x1)))) -> 1(2(5(0(4(x1))))) 590.55/152.57 4(2(1(0(x1)))) -> 1(4(2(5(0(x1))))) 590.55/152.57 4(2(1(0(x1)))) -> 1(4(5(2(0(x1))))) 590.55/152.57 4(2(1(0(x1)))) -> 2(0(3(1(4(x1))))) 590.55/152.57 4(2(1(0(x1)))) -> 2(0(5(1(4(x1))))) 590.55/152.57 4(2(1(0(x1)))) -> 2(1(2(0(4(x1))))) 590.55/152.57 4(2(1(0(x1)))) -> 2(1(4(0(5(x1))))) 590.55/152.57 4(2(1(0(x1)))) -> 3(0(2(1(4(x1))))) 590.55/152.57 4(2(1(0(x1)))) -> 4(1(2(2(0(x1))))) 590.55/152.57 4(2(1(0(x1)))) -> 4(3(2(1(0(x1))))) 590.55/152.57 4(2(1(0(x1)))) -> 4(5(1(2(0(x1))))) 590.55/152.57 4(2(1(0(x1)))) -> 5(0(2(1(4(x1))))) 590.55/152.57 4(2(1(0(x1)))) -> 5(4(1(2(0(x1))))) 590.55/152.57 4(2(1(0(x1)))) -> 2(1(5(2(0(4(x1)))))) 590.55/152.57 4(2(1(0(x1)))) -> 4(1(2(5(2(0(x1)))))) 590.55/152.57 4(2(1(0(x1)))) -> 4(3(0(2(1(4(x1)))))) 590.55/152.57 4(3(0(0(x1)))) -> 3(0(2(0(4(x1))))) 590.55/152.57 4(3(0(0(x1)))) -> 3(2(0(4(0(x1))))) 590.55/152.57 4(4(1(0(x1)))) -> 4(0(5(1(4(x1))))) 590.55/152.57 4(4(1(0(x1)))) -> 4(1(2(0(4(x1))))) 590.55/152.57 4(4(1(0(x1)))) -> 4(1(4(0(5(x1))))) 590.55/152.57 4(4(1(0(x1)))) -> 4(1(5(0(4(x1))))) 590.55/152.57 4(4(1(0(x1)))) -> 4(1(5(4(0(x1))))) 590.55/152.57 0(0(2(1(0(x1))))) -> 0(1(2(0(2(0(x1)))))) 590.55/152.57 0(4(2(1(0(x1))))) -> 0(4(1(2(1(0(x1)))))) 590.55/152.57 0(4(2(1(0(x1))))) -> 1(2(0(3(4(0(x1)))))) 590.55/152.57 0(4(2(1(0(x1))))) -> 4(0(3(1(0(2(x1)))))) 590.55/152.57 0(4(4(1(0(x1))))) -> 1(4(4(0(5(0(x1)))))) 590.55/152.57 0(4(4(1(0(x1))))) -> 4(0(1(2(0(4(x1)))))) 590.55/152.57 0(4(4(1(0(x1))))) -> 5(0(4(1(4(0(x1)))))) 590.55/152.57 1(0(1(1(4(x1))))) -> 1(1(1(4(0(5(x1)))))) 590.55/152.57 1(0(4(1(0(x1))))) -> 4(0(5(1(1(0(x1)))))) 590.55/152.57 1(1(3(0(0(x1))))) -> 1(3(1(0(2(0(x1)))))) 590.55/152.57 1(3(0(0(1(x1))))) -> 0(1(5(1(0(3(x1)))))) 590.55/152.57 1(4(1(0(0(x1))))) -> 5(1(1(4(0(0(x1)))))) 590.55/152.57 1(4(2(1(0(x1))))) -> 4(1(2(1(2(0(x1)))))) 590.55/152.57 1(4(2(1(0(x1))))) -> 4(1(2(1(5(0(x1)))))) 590.55/152.57 1(4(3(0(0(x1))))) -> 3(2(1(0(4(0(x1)))))) 590.55/152.57 4(0(2(1(0(x1))))) -> 2(0(2(1(4(0(x1)))))) 590.55/152.57 4(1(0(1(0(x1))))) -> 1(0(4(3(1(0(x1)))))) 590.55/152.57 4(1(3(0(0(x1))))) -> 3(1(0(4(5(0(x1)))))) 590.55/152.57 4(1(3(0(0(x1))))) -> 4(3(1(0(2(0(x1)))))) 590.55/152.57 4(2(0(1(0(x1))))) -> 1(4(3(0(2(0(x1)))))) 590.55/152.57 4(2(0(1(0(x1))))) -> 1(5(0(2(0(4(x1)))))) 590.55/152.57 4(2(0(1(0(x1))))) -> 3(0(2(1(4(0(x1)))))) 590.55/152.57 4(2(1(0(0(x1))))) -> 2(1(4(2(0(0(x1)))))) 590.55/152.57 4(2(1(0(1(x1))))) -> 1(2(0(4(1(5(x1)))))) 590.55/152.57 4(2(1(0(4(x1))))) -> 4(1(2(2(0(4(x1)))))) 590.55/152.57 4(2(1(0(4(x1))))) -> 4(1(5(2(4(0(x1)))))) 590.55/152.57 4(2(1(1(0(x1))))) -> 4(1(2(1(5(0(x1)))))) 590.55/152.57 4(2(2(1(0(x1))))) -> 1(2(5(0(2(4(x1)))))) 590.55/152.57 4(2(2(1(0(x1))))) -> 1(4(2(2(0(5(x1)))))) 590.55/152.57 4(2(2(1(0(x1))))) -> 2(1(3(2(4(0(x1)))))) 590.55/152.57 4(2(2(1(0(x1))))) -> 2(1(4(1(2(0(x1)))))) 590.55/152.57 4(2(3(0(0(x1))))) -> 3(2(5(4(0(0(x1)))))) 590.55/152.57 4(2(4(1(0(x1))))) -> 1(4(4(2(0(5(x1)))))) 590.55/152.57 4(2(4(1(0(x1))))) -> 4(0(1(2(4(4(x1)))))) 590.55/152.57 4(2(4(1(0(x1))))) -> 4(1(2(0(4(5(x1)))))) 590.55/152.57 4(2(4(1(0(x1))))) -> 4(1(3(4(0(2(x1)))))) 590.55/152.57 4(2(4(1(0(x1))))) -> 4(1(4(2(0(5(x1)))))) 590.55/152.57 4(2(4(1(0(x1))))) -> 4(1(4(5(2(0(x1)))))) 590.55/152.57 4(3(1(2(1(x1))))) -> 3(2(2(1(4(1(x1)))))) 590.55/152.57 4(3(5(0(0(x1))))) -> 3(0(5(4(0(0(x1)))))) 590.55/152.57 4(3(5(0(0(x1))))) -> 5(0(3(1(4(0(x1)))))) 590.55/152.57 4(4(0(1(0(x1))))) -> 4(0(3(1(4(0(x1)))))) 590.55/152.57 4(4(1(0(1(x1))))) -> 4(0(3(1(4(1(x1)))))) 590.55/152.57 4(4(2(1(0(x1))))) -> 1(0(3(4(2(4(x1)))))) 590.55/152.57 4(4(2(1(0(x1))))) -> 4(0(3(1(4(2(x1)))))) 590.55/152.57 4(4(3(0(0(x1))))) -> 2(0(3(0(4(4(x1)))))) 590.55/152.57 4(4(3(0(0(x1))))) -> 4(3(0(4(5(0(x1)))))) 590.55/152.57 4(4(4(1(0(x1))))) -> 4(4(3(1(0(4(x1)))))) 590.55/152.57 4(5(2(1(0(x1))))) -> 3(2(1(4(5(0(x1)))))) 590.55/152.57 4(5(4(1(0(x1))))) -> 4(1(4(0(5(0(x1)))))) 590.55/152.57 590.55/152.57 Q is empty. 590.55/152.57 590.55/152.57 ---------------------------------------- 590.55/152.57 590.55/152.57 (1) QTRS Reverse (EQUIVALENT) 590.55/152.57 We applied the QTRS Reverse Processor [REVERSE]. 590.55/152.57 ---------------------------------------- 590.55/152.57 590.55/152.57 (2) 590.55/152.57 Obligation: 590.55/152.57 Q restricted rewrite system: 590.55/152.57 The TRS R consists of the following rules: 590.55/152.57 590.55/152.57 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.55/152.57 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.55/152.57 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.55/152.57 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.55/152.57 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.55/152.57 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.55/152.57 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.55/152.57 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.55/152.57 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.55/152.57 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.55/152.57 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.55/152.57 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.55/152.57 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.55/152.57 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.55/152.57 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.55/152.57 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.55/152.57 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.55/152.57 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.55/152.57 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.55/152.57 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.55/152.57 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.55/152.57 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.55/152.57 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.55/152.57 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.55/152.57 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.55/152.57 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.55/152.57 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.55/152.57 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.55/152.57 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.55/152.57 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.55/152.57 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.55/152.57 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.55/152.57 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.55/152.57 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.55/152.57 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.55/152.57 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.55/152.57 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.55/152.57 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.55/152.57 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.55/152.57 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.55/152.57 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.55/152.57 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.55/152.57 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.55/152.57 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.55/152.57 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.55/152.57 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.55/152.57 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.55/152.57 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.55/152.57 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.55/152.57 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.55/152.57 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.55/152.57 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.55/152.57 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.55/152.57 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.55/152.57 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.55/152.57 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.55/152.57 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.55/152.57 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.55/152.57 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.55/152.57 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.55/152.57 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.55/152.57 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.55/152.57 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.55/152.57 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.55/152.57 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.55/152.57 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.55/152.57 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.55/152.57 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.55/152.57 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.55/152.57 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.55/152.57 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.55/152.57 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.55/152.57 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.55/152.57 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.55/152.57 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.55/152.57 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.55/152.57 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.55/152.57 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.55/152.57 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.55/152.57 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.55/152.57 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.55/152.57 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.55/152.57 590.55/152.57 Q is empty. 590.55/152.57 590.55/152.57 ---------------------------------------- 590.55/152.57 590.55/152.57 (3) DependencyPairsProof (EQUIVALENT) 590.55/152.57 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 590.55/152.57 ---------------------------------------- 590.55/152.57 590.55/152.57 (4) 590.55/152.57 Obligation: 590.55/152.57 Q DP problem: 590.55/152.57 The TRS P consists of the following rules: 590.55/152.57 590.55/152.57 0^1(1(0(0(x1)))) -> 0^1(2(0(2(1(0(x1)))))) 590.55/152.57 0^1(1(0(0(x1)))) -> 0^1(2(1(0(x1)))) 590.55/152.57 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.55/152.57 0^1(0(1(0(x1)))) -> 0^1(0(0(2(1(x1))))) 590.55/152.57 0^1(0(1(0(x1)))) -> 0^1(0(2(1(x1)))) 590.55/152.57 0^1(0(1(0(x1)))) -> 0^1(2(1(x1))) 590.55/152.57 0^1(0(1(0(x1)))) -> 1^1(x1) 590.55/152.57 1^1(0(1(0(x1)))) -> 0^1(3(0(1(1(x1))))) 590.55/152.57 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.55/152.57 1^1(0(1(0(x1)))) -> 1^1(1(x1)) 590.55/152.57 1^1(0(1(0(x1)))) -> 1^1(x1) 590.55/152.57 0^1(1(4(0(x1)))) -> 0^1(4(1(3(0(x1))))) 590.55/152.57 0^1(1(4(0(x1)))) -> 4^1(1(3(0(x1)))) 590.55/152.57 0^1(1(4(0(x1)))) -> 1^1(3(0(x1))) 590.55/152.57 0^1(1(4(0(x1)))) -> 0^1(0(4(1(x1)))) 590.55/152.57 0^1(1(4(0(x1)))) -> 0^1(4(1(x1))) 590.55/152.57 0^1(1(4(0(x1)))) -> 4^1(1(x1)) 590.55/152.57 0^1(1(4(0(x1)))) -> 1^1(x1) 590.55/152.57 0^1(1(4(0(x1)))) -> 0^1(4(0(5(1(x1))))) 590.55/152.57 0^1(1(4(0(x1)))) -> 4^1(0(5(1(x1)))) 590.55/152.57 0^1(1(4(0(x1)))) -> 0^1(5(1(x1))) 590.55/152.57 0^1(1(4(0(x1)))) -> 0^1(5(4(1(5(0(x1)))))) 590.55/152.57 0^1(1(4(0(x1)))) -> 4^1(1(5(0(x1)))) 590.55/152.57 0^1(1(4(0(x1)))) -> 1^1(5(0(x1))) 590.55/152.57 0^1(1(4(0(x1)))) -> 0^1(4(5(1(5(0(x1)))))) 590.55/152.57 0^1(1(4(0(x1)))) -> 4^1(5(1(5(0(x1))))) 590.55/152.57 0^1(1(2(4(x1)))) -> 4^1(0(5(2(1(x1))))) 590.55/152.57 0^1(1(2(4(x1)))) -> 0^1(5(2(1(x1)))) 590.55/152.57 0^1(1(2(4(x1)))) -> 1^1(x1) 590.55/152.57 0^1(1(2(4(x1)))) -> 0^1(5(2(4(1(x1))))) 590.55/152.57 0^1(1(2(4(x1)))) -> 4^1(1(x1)) 590.55/152.57 0^1(1(2(4(x1)))) -> 0^1(2(5(4(1(x1))))) 590.55/152.57 0^1(1(2(4(x1)))) -> 4^1(1(3(0(2(x1))))) 590.55/152.57 0^1(1(2(4(x1)))) -> 1^1(3(0(2(x1)))) 590.55/152.57 0^1(1(2(4(x1)))) -> 0^1(2(x1)) 590.55/152.57 0^1(1(2(4(x1)))) -> 4^1(1(5(0(2(x1))))) 590.55/152.57 0^1(1(2(4(x1)))) -> 1^1(5(0(2(x1)))) 590.55/152.57 0^1(1(2(4(x1)))) -> 4^1(0(2(1(2(x1))))) 590.55/152.57 0^1(1(2(4(x1)))) -> 0^1(2(1(2(x1)))) 590.55/152.57 0^1(1(2(4(x1)))) -> 1^1(2(x1)) 590.55/152.57 0^1(1(2(4(x1)))) -> 0^1(4(1(2(x1)))) 590.55/152.57 0^1(1(2(4(x1)))) -> 4^1(1(2(x1))) 590.55/152.57 0^1(1(2(4(x1)))) -> 4^1(1(2(0(3(x1))))) 590.55/152.57 0^1(1(2(4(x1)))) -> 1^1(2(0(3(x1)))) 590.55/152.57 0^1(1(2(4(x1)))) -> 0^1(3(x1)) 590.55/152.57 0^1(1(2(4(x1)))) -> 0^1(2(2(1(4(x1))))) 590.55/152.57 0^1(1(2(4(x1)))) -> 1^1(4(x1)) 590.55/152.57 0^1(1(2(4(x1)))) -> 0^1(1(2(3(4(x1))))) 590.55/152.57 0^1(1(2(4(x1)))) -> 1^1(2(3(4(x1)))) 590.55/152.57 0^1(1(2(4(x1)))) -> 0^1(2(1(5(4(x1))))) 590.55/152.57 0^1(1(2(4(x1)))) -> 1^1(5(4(x1))) 590.55/152.57 0^1(1(2(4(x1)))) -> 4^1(1(2(0(5(x1))))) 590.55/152.57 0^1(1(2(4(x1)))) -> 1^1(2(0(5(x1)))) 590.55/152.57 0^1(1(2(4(x1)))) -> 0^1(5(x1)) 590.55/152.57 0^1(1(2(4(x1)))) -> 0^1(2(1(4(5(x1))))) 590.55/152.57 0^1(1(2(4(x1)))) -> 1^1(4(5(x1))) 590.55/152.57 0^1(1(2(4(x1)))) -> 4^1(5(x1)) 590.55/152.57 0^1(1(2(4(x1)))) -> 4^1(0(2(5(1(2(x1)))))) 590.55/152.57 0^1(1(2(4(x1)))) -> 0^1(2(5(1(2(x1))))) 590.55/152.57 0^1(1(2(4(x1)))) -> 0^1(2(5(2(1(4(x1)))))) 590.55/152.57 0^1(1(2(4(x1)))) -> 4^1(1(2(0(3(4(x1)))))) 590.55/152.57 0^1(1(2(4(x1)))) -> 1^1(2(0(3(4(x1))))) 590.55/152.57 0^1(1(2(4(x1)))) -> 0^1(3(4(x1))) 590.55/152.57 0^1(0(3(4(x1)))) -> 4^1(0(2(0(3(x1))))) 590.55/152.57 0^1(0(3(4(x1)))) -> 0^1(2(0(3(x1)))) 590.55/152.57 0^1(0(3(4(x1)))) -> 0^1(3(x1)) 590.55/152.57 0^1(0(3(4(x1)))) -> 0^1(4(0(2(3(x1))))) 590.55/152.57 0^1(0(3(4(x1)))) -> 4^1(0(2(3(x1)))) 590.55/152.57 0^1(0(3(4(x1)))) -> 0^1(2(3(x1))) 590.55/152.57 0^1(1(4(4(x1)))) -> 4^1(1(5(0(4(x1))))) 590.55/152.57 0^1(1(4(4(x1)))) -> 1^1(5(0(4(x1)))) 590.55/152.57 0^1(1(4(4(x1)))) -> 0^1(4(x1)) 590.55/152.57 0^1(1(4(4(x1)))) -> 4^1(0(2(1(4(x1))))) 590.55/152.57 0^1(1(4(4(x1)))) -> 0^1(2(1(4(x1)))) 590.55/152.57 0^1(1(4(4(x1)))) -> 1^1(4(x1)) 590.55/152.57 0^1(1(4(4(x1)))) -> 0^1(4(1(4(x1)))) 590.55/152.57 0^1(1(4(4(x1)))) -> 4^1(1(4(x1))) 590.55/152.57 0^1(1(4(4(x1)))) -> 4^1(0(5(1(4(x1))))) 590.55/152.57 0^1(1(4(4(x1)))) -> 0^1(5(1(4(x1)))) 590.55/152.57 0^1(1(4(4(x1)))) -> 0^1(4(5(1(4(x1))))) 590.55/152.57 0^1(1(4(4(x1)))) -> 4^1(5(1(4(x1)))) 590.55/152.57 0^1(1(2(0(0(x1))))) -> 0^1(2(0(2(1(0(x1)))))) 590.55/152.57 0^1(1(2(0(0(x1))))) -> 0^1(2(1(0(x1)))) 590.55/152.57 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.55/152.57 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.55/152.57 0^1(1(2(4(0(x1))))) -> 1^1(2(1(4(0(x1))))) 590.55/152.57 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.55/152.57 0^1(1(2(4(0(x1))))) -> 0^1(4(3(0(2(1(x1)))))) 590.55/152.57 0^1(1(2(4(0(x1))))) -> 4^1(3(0(2(1(x1))))) 590.55/152.57 0^1(1(2(4(0(x1))))) -> 0^1(2(1(x1))) 590.55/152.57 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.55/152.57 0^1(1(2(4(0(x1))))) -> 0^1(1(3(0(4(x1))))) 590.55/152.57 0^1(1(2(4(0(x1))))) -> 1^1(3(0(4(x1)))) 590.55/152.57 0^1(1(2(4(0(x1))))) -> 0^1(4(x1)) 590.55/152.57 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.55/152.57 0^1(1(4(4(0(x1))))) -> 0^1(5(0(4(4(1(x1)))))) 590.55/152.57 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.55/152.57 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.55/152.57 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.55/152.57 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.55/152.57 0^1(1(4(4(0(x1))))) -> 4^1(0(2(1(0(4(x1)))))) 590.55/152.57 0^1(1(4(4(0(x1))))) -> 0^1(2(1(0(4(x1))))) 590.55/152.57 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.55/152.57 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.55/152.57 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.55/152.57 0^1(1(4(4(0(x1))))) -> 0^1(4(1(4(0(5(x1)))))) 590.55/152.57 0^1(1(4(4(0(x1))))) -> 4^1(1(4(0(5(x1))))) 590.55/152.57 0^1(1(4(4(0(x1))))) -> 1^1(4(0(5(x1)))) 590.55/152.57 0^1(1(4(4(0(x1))))) -> 4^1(0(5(x1))) 590.55/152.57 0^1(1(4(4(0(x1))))) -> 0^1(5(x1)) 590.55/152.57 4^1(1(1(0(1(x1))))) -> 0^1(4(1(1(1(x1))))) 590.55/152.57 4^1(1(1(0(1(x1))))) -> 4^1(1(1(1(x1)))) 590.55/152.57 4^1(1(1(0(1(x1))))) -> 1^1(1(1(x1))) 590.55/152.57 4^1(1(1(0(1(x1))))) -> 1^1(1(x1)) 590.55/152.57 0^1(1(4(0(1(x1))))) -> 0^1(1(1(5(0(4(x1)))))) 590.55/152.57 0^1(1(4(0(1(x1))))) -> 1^1(1(5(0(4(x1))))) 590.55/152.57 0^1(1(4(0(1(x1))))) -> 1^1(5(0(4(x1)))) 590.55/152.57 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.55/152.57 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.55/152.57 0^1(0(3(1(1(x1))))) -> 0^1(2(0(1(3(1(x1)))))) 590.55/152.57 0^1(0(3(1(1(x1))))) -> 0^1(1(3(1(x1)))) 590.55/152.57 0^1(0(3(1(1(x1))))) -> 1^1(3(1(x1))) 590.55/152.57 1^1(0(0(3(1(x1))))) -> 0^1(1(5(1(0(x1))))) 590.55/152.57 1^1(0(0(3(1(x1))))) -> 1^1(5(1(0(x1)))) 590.55/152.57 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.55/152.57 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.55/152.57 0^1(0(1(4(1(x1))))) -> 0^1(0(4(1(1(5(x1)))))) 590.55/152.57 0^1(0(1(4(1(x1))))) -> 0^1(4(1(1(5(x1))))) 590.55/152.57 0^1(0(1(4(1(x1))))) -> 4^1(1(1(5(x1)))) 590.55/152.57 0^1(0(1(4(1(x1))))) -> 1^1(1(5(x1))) 590.55/152.57 0^1(0(1(4(1(x1))))) -> 1^1(5(x1)) 590.55/152.57 0^1(1(2(4(1(x1))))) -> 0^1(2(1(2(1(4(x1)))))) 590.55/152.57 0^1(1(2(4(1(x1))))) -> 1^1(2(1(4(x1)))) 590.55/152.57 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.55/152.57 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.55/152.57 0^1(1(2(4(1(x1))))) -> 0^1(5(1(2(1(4(x1)))))) 590.55/152.57 0^1(0(3(4(1(x1))))) -> 0^1(4(0(1(2(3(x1)))))) 590.55/152.57 0^1(0(3(4(1(x1))))) -> 4^1(0(1(2(3(x1))))) 590.55/152.57 0^1(0(3(4(1(x1))))) -> 0^1(1(2(3(x1)))) 590.55/152.57 0^1(0(3(4(1(x1))))) -> 1^1(2(3(x1))) 590.55/152.57 0^1(1(2(0(4(x1))))) -> 0^1(4(1(2(0(2(x1)))))) 590.55/152.57 0^1(1(2(0(4(x1))))) -> 4^1(1(2(0(2(x1))))) 590.55/152.57 0^1(1(2(0(4(x1))))) -> 1^1(2(0(2(x1)))) 590.55/152.57 0^1(1(2(0(4(x1))))) -> 0^1(2(x1)) 590.55/152.57 0^1(1(0(1(4(x1))))) -> 0^1(1(3(4(0(1(x1)))))) 590.55/152.57 0^1(1(0(1(4(x1))))) -> 1^1(3(4(0(1(x1))))) 590.55/152.57 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.55/152.57 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.55/152.57 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.55/152.57 0^1(0(3(1(4(x1))))) -> 0^1(5(4(0(1(3(x1)))))) 590.55/152.57 0^1(0(3(1(4(x1))))) -> 4^1(0(1(3(x1)))) 590.55/152.57 0^1(0(3(1(4(x1))))) -> 0^1(1(3(x1))) 590.55/152.57 0^1(0(3(1(4(x1))))) -> 1^1(3(x1)) 590.55/152.57 0^1(0(3(1(4(x1))))) -> 0^1(2(0(1(3(4(x1)))))) 590.55/152.57 0^1(0(3(1(4(x1))))) -> 0^1(1(3(4(x1)))) 590.55/152.57 0^1(0(3(1(4(x1))))) -> 1^1(3(4(x1))) 590.55/152.57 0^1(1(0(2(4(x1))))) -> 0^1(2(0(3(4(1(x1)))))) 590.55/152.57 0^1(1(0(2(4(x1))))) -> 0^1(3(4(1(x1)))) 590.55/152.57 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.55/152.57 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.55/152.57 0^1(1(0(2(4(x1))))) -> 4^1(0(2(0(5(1(x1)))))) 590.55/152.57 0^1(1(0(2(4(x1))))) -> 0^1(2(0(5(1(x1))))) 590.55/152.57 0^1(1(0(2(4(x1))))) -> 0^1(5(1(x1))) 590.55/152.57 0^1(1(0(2(4(x1))))) -> 0^1(4(1(2(0(3(x1)))))) 590.55/152.57 0^1(1(0(2(4(x1))))) -> 4^1(1(2(0(3(x1))))) 590.55/152.57 0^1(1(0(2(4(x1))))) -> 1^1(2(0(3(x1)))) 590.55/152.57 0^1(1(0(2(4(x1))))) -> 0^1(3(x1)) 590.55/152.57 0^1(0(1(2(4(x1))))) -> 0^1(0(2(4(1(2(x1)))))) 590.55/152.57 0^1(0(1(2(4(x1))))) -> 0^1(2(4(1(2(x1))))) 590.55/152.57 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.55/152.57 0^1(0(1(2(4(x1))))) -> 1^1(2(x1)) 590.55/152.57 1^1(0(1(2(4(x1))))) -> 1^1(4(0(2(1(x1))))) 590.55/152.57 1^1(0(1(2(4(x1))))) -> 4^1(0(2(1(x1)))) 590.55/152.57 1^1(0(1(2(4(x1))))) -> 0^1(2(1(x1))) 590.55/152.57 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.55/152.57 4^1(0(1(2(4(x1))))) -> 4^1(0(2(2(1(4(x1)))))) 590.55/152.57 4^1(0(1(2(4(x1))))) -> 0^1(2(2(1(4(x1))))) 590.55/152.57 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.55/152.57 4^1(0(1(2(4(x1))))) -> 0^1(4(2(5(1(4(x1)))))) 590.55/152.57 4^1(0(1(2(4(x1))))) -> 4^1(2(5(1(4(x1))))) 590.55/152.57 0^1(1(1(2(4(x1))))) -> 0^1(5(1(2(1(4(x1)))))) 590.55/152.57 0^1(1(1(2(4(x1))))) -> 1^1(2(1(4(x1)))) 590.55/152.57 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.55/152.57 0^1(1(2(2(4(x1))))) -> 4^1(2(0(5(2(1(x1)))))) 590.55/152.57 0^1(1(2(2(4(x1))))) -> 0^1(5(2(1(x1)))) 590.55/152.57 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.55/152.57 0^1(1(2(2(4(x1))))) -> 0^1(2(2(4(1(x1))))) 590.55/152.57 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.55/152.57 0^1(1(2(2(4(x1))))) -> 0^1(4(2(3(1(2(x1)))))) 590.55/152.57 0^1(1(2(2(4(x1))))) -> 4^1(2(3(1(2(x1))))) 590.55/152.57 0^1(1(2(2(4(x1))))) -> 1^1(2(x1)) 590.55/152.57 0^1(1(2(2(4(x1))))) -> 0^1(2(1(4(1(2(x1)))))) 590.55/152.57 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.55/152.57 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.55/152.57 0^1(0(3(2(4(x1))))) -> 0^1(0(4(5(2(3(x1)))))) 590.55/152.57 0^1(0(3(2(4(x1))))) -> 0^1(4(5(2(3(x1))))) 590.55/152.57 0^1(0(3(2(4(x1))))) -> 4^1(5(2(3(x1)))) 590.55/152.57 0^1(1(4(2(4(x1))))) -> 0^1(2(4(4(1(x1))))) 590.55/152.57 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.55/152.57 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.55/152.57 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.55/152.57 0^1(1(4(2(4(x1))))) -> 4^1(4(2(1(0(4(x1)))))) 590.55/152.57 0^1(1(4(2(4(x1))))) -> 4^1(2(1(0(4(x1))))) 590.55/152.57 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.55/152.57 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.55/152.57 0^1(1(4(2(4(x1))))) -> 4^1(0(2(1(4(x1))))) 590.55/152.57 0^1(1(4(2(4(x1))))) -> 0^1(2(1(4(x1)))) 590.55/152.57 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.55/152.57 0^1(1(4(2(4(x1))))) -> 0^1(4(3(1(4(x1))))) 590.55/152.57 0^1(1(4(2(4(x1))))) -> 4^1(3(1(4(x1)))) 590.55/152.57 0^1(1(4(2(4(x1))))) -> 0^1(2(4(1(4(x1))))) 590.55/152.57 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.55/152.57 0^1(1(4(2(4(x1))))) -> 0^1(2(5(4(1(4(x1)))))) 590.55/152.57 1^1(2(1(3(4(x1))))) -> 1^1(4(1(2(2(3(x1)))))) 590.55/152.57 1^1(2(1(3(4(x1))))) -> 4^1(1(2(2(3(x1))))) 590.55/152.57 1^1(2(1(3(4(x1))))) -> 1^1(2(2(3(x1)))) 590.55/152.57 0^1(0(5(3(4(x1))))) -> 0^1(0(4(5(0(3(x1)))))) 590.55/152.57 0^1(0(5(3(4(x1))))) -> 0^1(4(5(0(3(x1))))) 590.55/152.57 0^1(0(5(3(4(x1))))) -> 4^1(5(0(3(x1)))) 590.55/152.57 0^1(0(5(3(4(x1))))) -> 0^1(3(x1)) 590.55/152.57 0^1(0(5(3(4(x1))))) -> 0^1(4(1(3(0(5(x1)))))) 590.55/152.57 0^1(0(5(3(4(x1))))) -> 4^1(1(3(0(5(x1))))) 590.55/152.57 0^1(0(5(3(4(x1))))) -> 1^1(3(0(5(x1)))) 590.55/152.57 0^1(0(5(3(4(x1))))) -> 0^1(5(x1)) 590.55/152.57 0^1(1(0(4(4(x1))))) -> 0^1(4(1(3(0(4(x1)))))) 590.55/152.57 0^1(1(0(4(4(x1))))) -> 4^1(1(3(0(4(x1))))) 590.55/152.57 0^1(1(0(4(4(x1))))) -> 1^1(3(0(4(x1)))) 590.55/152.57 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.55/152.57 1^1(0(1(4(4(x1))))) -> 1^1(4(1(3(0(4(x1)))))) 590.55/152.57 1^1(0(1(4(4(x1))))) -> 4^1(1(3(0(4(x1))))) 590.55/152.57 1^1(0(1(4(4(x1))))) -> 1^1(3(0(4(x1)))) 590.55/152.57 1^1(0(1(4(4(x1))))) -> 0^1(4(x1)) 590.55/152.57 0^1(1(2(4(4(x1))))) -> 4^1(2(4(3(0(1(x1)))))) 590.55/152.57 0^1(1(2(4(4(x1))))) -> 4^1(3(0(1(x1)))) 590.55/152.57 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.55/152.57 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.55/152.57 0^1(1(2(4(4(x1))))) -> 4^1(1(3(0(4(x1))))) 590.55/152.57 0^1(1(2(4(4(x1))))) -> 1^1(3(0(4(x1)))) 590.55/152.57 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.55/152.57 0^1(0(3(4(4(x1))))) -> 4^1(4(0(3(0(2(x1)))))) 590.55/152.57 0^1(0(3(4(4(x1))))) -> 4^1(0(3(0(2(x1))))) 590.55/152.57 0^1(0(3(4(4(x1))))) -> 0^1(3(0(2(x1)))) 590.55/152.57 0^1(0(3(4(4(x1))))) -> 0^1(2(x1)) 590.55/152.57 0^1(0(3(4(4(x1))))) -> 0^1(5(4(0(3(4(x1)))))) 590.55/152.57 0^1(0(3(4(4(x1))))) -> 4^1(0(3(4(x1)))) 590.55/152.57 0^1(0(3(4(4(x1))))) -> 0^1(3(4(x1))) 590.55/152.57 0^1(1(4(4(4(x1))))) -> 4^1(0(1(3(4(4(x1)))))) 590.55/152.57 0^1(1(4(4(4(x1))))) -> 0^1(1(3(4(4(x1))))) 590.55/152.57 0^1(1(4(4(4(x1))))) -> 1^1(3(4(4(x1)))) 590.55/152.57 0^1(1(2(5(4(x1))))) -> 0^1(5(4(1(2(3(x1)))))) 590.55/152.57 0^1(1(2(5(4(x1))))) -> 4^1(1(2(3(x1)))) 590.55/152.57 0^1(1(2(5(4(x1))))) -> 1^1(2(3(x1))) 590.55/152.57 0^1(1(4(5(4(x1))))) -> 0^1(5(0(4(1(4(x1)))))) 590.55/152.57 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.55/152.57 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.55/152.57 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.55/152.57 590.55/152.57 The TRS R consists of the following rules: 590.55/152.57 590.55/152.57 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.55/152.57 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.55/152.57 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.55/152.57 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.55/152.57 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.55/152.57 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.55/152.57 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.55/152.57 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.55/152.57 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.55/152.57 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.55/152.57 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.55/152.57 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.55/152.57 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.55/152.57 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.55/152.57 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.55/152.57 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.55/152.57 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.55/152.57 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.55/152.57 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.55/152.57 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.55/152.57 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.55/152.57 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.55/152.57 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.55/152.57 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.55/152.57 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.55/152.57 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.55/152.57 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.55/152.57 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.55/152.57 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.55/152.57 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.55/152.57 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.55/152.57 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.55/152.57 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.55/152.57 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.55/152.57 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.55/152.57 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.55/152.57 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.55/152.57 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.55/152.57 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.55/152.57 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.55/152.57 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.55/152.57 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.55/152.57 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.55/152.57 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.60 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.60 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.60 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.60 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.60 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.60 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.60 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.60 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.60 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.60 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.60 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.60 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.60 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.60 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.60 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.60 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.60 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.60 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.60 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.60 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.60 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.60 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.60 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.60 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.60 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.60 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.60 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.60 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.60 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.60 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.60 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.60 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.60 590.70/152.60 Q is empty. 590.70/152.60 We have to consider all minimal (P,Q,R)-chains. 590.70/152.60 ---------------------------------------- 590.70/152.60 590.70/152.60 (5) DependencyGraphProof (EQUIVALENT) 590.70/152.60 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 187 less nodes. 590.70/152.60 ---------------------------------------- 590.70/152.60 590.70/152.60 (6) 590.70/152.60 Obligation: 590.70/152.60 Q DP problem: 590.70/152.60 The TRS P consists of the following rules: 590.70/152.60 590.70/152.60 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.60 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.60 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.60 1^1(0(1(0(x1)))) -> 1^1(1(x1)) 590.70/152.60 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.60 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.60 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.60 0^1(1(4(0(x1)))) -> 0^1(0(4(1(x1)))) 590.70/152.60 0^1(1(4(0(x1)))) -> 0^1(4(1(x1))) 590.70/152.60 0^1(1(4(0(x1)))) -> 4^1(1(x1)) 590.70/152.60 4^1(1(1(0(1(x1))))) -> 0^1(4(1(1(1(x1))))) 590.70/152.60 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.60 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.60 1^1(0(1(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.60 0^1(1(2(4(x1)))) -> 4^1(1(x1)) 590.70/152.60 4^1(1(1(0(1(x1))))) -> 4^1(1(1(1(x1)))) 590.70/152.60 4^1(1(1(0(1(x1))))) -> 1^1(1(1(x1))) 590.70/152.60 4^1(1(1(0(1(x1))))) -> 1^1(1(x1)) 590.70/152.60 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(2(4(x1)))) -> 0^1(4(1(2(x1)))) 590.70/152.60 0^1(1(2(4(x1)))) -> 4^1(1(2(x1))) 590.70/152.60 0^1(1(2(4(x1)))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(4(4(x1)))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(4(x1)))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(4(4(x1)))) -> 0^1(4(1(4(x1)))) 590.70/152.60 0^1(1(4(4(x1)))) -> 4^1(1(4(x1))) 590.70/152.60 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.60 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.60 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.60 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.60 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.60 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.60 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.60 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.60 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.60 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.60 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.60 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.60 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.60 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.60 590.70/152.60 The TRS R consists of the following rules: 590.70/152.60 590.70/152.60 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.60 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.60 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.60 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.60 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.60 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.60 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.60 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.60 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.60 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.60 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.60 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.60 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.60 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.60 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.60 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.60 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.60 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.60 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.60 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.60 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.60 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.60 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.60 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.60 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.60 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.60 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.60 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.60 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.60 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.60 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.60 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.60 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.60 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.60 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.60 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.60 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.60 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.60 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.60 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.60 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.60 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.60 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.60 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.60 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.60 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.60 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.60 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.60 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.60 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.60 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.60 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.60 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.60 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.60 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.60 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.60 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.60 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.60 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.60 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.60 590.70/152.60 Q is empty. 590.70/152.60 We have to consider all minimal (P,Q,R)-chains. 590.70/152.60 ---------------------------------------- 590.70/152.60 590.70/152.60 (7) TransformationProof (EQUIVALENT) 590.70/152.60 By narrowing [LPAR04] the rule 1^1(0(1(0(x1)))) -> 1^1(1(x1)) at position [0] we obtained the following new rules [LPAR04]: 590.70/152.60 590.70/152.60 (1^1(0(1(0(0(1(0(x0))))))) -> 1^1(2(0(3(0(1(1(x0))))))),1^1(0(1(0(0(1(0(x0))))))) -> 1^1(2(0(3(0(1(1(x0)))))))) 590.70/152.60 (1^1(0(1(0(0(0(3(1(x0)))))))) -> 1^1(3(0(1(5(1(0(x0))))))),1^1(0(1(0(0(0(3(1(x0)))))))) -> 1^1(3(0(1(5(1(0(x0)))))))) 590.70/152.60 (1^1(0(1(0(0(1(2(4(x0)))))))) -> 1^1(5(1(4(0(2(1(x0))))))),1^1(0(1(0(0(1(2(4(x0)))))))) -> 1^1(5(1(4(0(2(1(x0)))))))) 590.70/152.60 (1^1(0(1(0(2(1(3(4(x0)))))))) -> 1^1(1(4(1(2(2(3(x0))))))),1^1(0(1(0(2(1(3(4(x0)))))))) -> 1^1(1(4(1(2(2(3(x0)))))))) 590.70/152.60 (1^1(0(1(0(0(1(4(4(x0)))))))) -> 1^1(1(4(1(3(0(4(x0))))))),1^1(0(1(0(0(1(4(4(x0)))))))) -> 1^1(1(4(1(3(0(4(x0)))))))) 590.70/152.60 590.70/152.60 590.70/152.60 ---------------------------------------- 590.70/152.60 590.70/152.60 (8) 590.70/152.60 Obligation: 590.70/152.60 Q DP problem: 590.70/152.60 The TRS P consists of the following rules: 590.70/152.60 590.70/152.60 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.60 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.60 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.60 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.60 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.60 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.60 0^1(1(4(0(x1)))) -> 0^1(0(4(1(x1)))) 590.70/152.60 0^1(1(4(0(x1)))) -> 0^1(4(1(x1))) 590.70/152.60 0^1(1(4(0(x1)))) -> 4^1(1(x1)) 590.70/152.60 4^1(1(1(0(1(x1))))) -> 0^1(4(1(1(1(x1))))) 590.70/152.60 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.60 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.60 1^1(0(1(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.60 0^1(1(2(4(x1)))) -> 4^1(1(x1)) 590.70/152.60 4^1(1(1(0(1(x1))))) -> 4^1(1(1(1(x1)))) 590.70/152.60 4^1(1(1(0(1(x1))))) -> 1^1(1(1(x1))) 590.70/152.60 4^1(1(1(0(1(x1))))) -> 1^1(1(x1)) 590.70/152.60 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(2(4(x1)))) -> 0^1(4(1(2(x1)))) 590.70/152.60 0^1(1(2(4(x1)))) -> 4^1(1(2(x1))) 590.70/152.60 0^1(1(2(4(x1)))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(4(4(x1)))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(4(x1)))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(4(4(x1)))) -> 0^1(4(1(4(x1)))) 590.70/152.60 0^1(1(4(4(x1)))) -> 4^1(1(4(x1))) 590.70/152.60 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.60 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.60 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.60 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.60 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.60 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.60 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.60 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.60 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.60 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.60 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.60 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.60 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.60 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.60 1^1(0(1(0(0(1(0(x0))))))) -> 1^1(2(0(3(0(1(1(x0))))))) 590.70/152.60 1^1(0(1(0(0(0(3(1(x0)))))))) -> 1^1(3(0(1(5(1(0(x0))))))) 590.70/152.60 1^1(0(1(0(0(1(2(4(x0)))))))) -> 1^1(5(1(4(0(2(1(x0))))))) 590.70/152.60 1^1(0(1(0(2(1(3(4(x0)))))))) -> 1^1(1(4(1(2(2(3(x0))))))) 590.70/152.60 1^1(0(1(0(0(1(4(4(x0)))))))) -> 1^1(1(4(1(3(0(4(x0))))))) 590.70/152.60 590.70/152.60 The TRS R consists of the following rules: 590.70/152.60 590.70/152.60 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.60 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.60 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.60 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.60 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.60 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.60 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.60 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.60 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.60 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.60 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.60 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.60 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.60 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.60 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.60 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.60 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.60 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.60 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.60 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.60 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.60 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.60 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.60 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.60 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.60 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.60 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.60 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.60 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.60 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.60 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.60 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.60 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.60 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.60 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.60 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.60 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.60 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.60 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.60 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.60 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.60 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.60 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.60 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.60 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.60 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.60 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.60 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.60 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.60 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.60 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.60 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.60 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.60 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.60 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.60 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.60 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.60 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.60 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.60 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.60 590.70/152.60 Q is empty. 590.70/152.60 We have to consider all minimal (P,Q,R)-chains. 590.70/152.60 ---------------------------------------- 590.70/152.60 590.70/152.60 (9) DependencyGraphProof (EQUIVALENT) 590.70/152.60 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 5 less nodes. 590.70/152.60 ---------------------------------------- 590.70/152.60 590.70/152.60 (10) 590.70/152.60 Obligation: 590.70/152.60 Q DP problem: 590.70/152.60 The TRS P consists of the following rules: 590.70/152.60 590.70/152.60 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.60 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.60 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.60 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.60 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.60 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.60 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.60 1^1(0(1(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(0(x1)))) -> 0^1(0(4(1(x1)))) 590.70/152.60 0^1(1(4(0(x1)))) -> 0^1(4(1(x1))) 590.70/152.60 0^1(1(4(0(x1)))) -> 4^1(1(x1)) 590.70/152.60 4^1(1(1(0(1(x1))))) -> 0^1(4(1(1(1(x1))))) 590.70/152.60 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.60 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.60 0^1(1(2(4(x1)))) -> 4^1(1(x1)) 590.70/152.60 4^1(1(1(0(1(x1))))) -> 4^1(1(1(1(x1)))) 590.70/152.60 4^1(1(1(0(1(x1))))) -> 1^1(1(1(x1))) 590.70/152.60 4^1(1(1(0(1(x1))))) -> 1^1(1(x1)) 590.70/152.60 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(2(4(x1)))) -> 0^1(4(1(2(x1)))) 590.70/152.60 0^1(1(2(4(x1)))) -> 4^1(1(2(x1))) 590.70/152.60 0^1(1(2(4(x1)))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(4(4(x1)))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(4(x1)))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(4(4(x1)))) -> 0^1(4(1(4(x1)))) 590.70/152.60 0^1(1(4(4(x1)))) -> 4^1(1(4(x1))) 590.70/152.60 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.60 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.60 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.60 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.60 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.60 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.60 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.60 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.60 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.60 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.60 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.60 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.60 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.60 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.60 590.70/152.60 The TRS R consists of the following rules: 590.70/152.60 590.70/152.60 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.60 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.60 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.60 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.60 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.60 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.60 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.60 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.60 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.60 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.60 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.60 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.60 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.60 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.60 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.60 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.60 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.60 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.60 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.60 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.60 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.60 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.60 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.60 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.60 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.60 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.60 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.60 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.60 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.60 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.60 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.60 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.60 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.60 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.60 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.60 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.60 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.60 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.60 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.60 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.60 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.60 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.60 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.60 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.60 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.60 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.60 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.60 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.60 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.60 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.60 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.60 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.60 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.60 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.60 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.60 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.60 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.60 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.60 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.60 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.60 590.70/152.60 Q is empty. 590.70/152.60 We have to consider all minimal (P,Q,R)-chains. 590.70/152.60 ---------------------------------------- 590.70/152.60 590.70/152.60 (11) TransformationProof (EQUIVALENT) 590.70/152.60 By narrowing [LPAR04] the rule 1^1(0(1(4(4(x1))))) -> 0^1(4(x1)) at position [0] we obtained the following new rules [LPAR04]: 590.70/152.60 590.70/152.60 (1^1(0(1(4(4(1(1(0(1(x0))))))))) -> 0^1(5(0(4(1(1(1(x0))))))),1^1(0(1(4(4(1(1(0(1(x0))))))))) -> 0^1(5(0(4(1(1(1(x0)))))))) 590.70/152.60 (1^1(0(1(4(4(0(1(2(4(x0))))))))) -> 0^1(4(0(2(2(1(4(x0))))))),1^1(0(1(4(4(0(1(2(4(x0))))))))) -> 0^1(4(0(2(2(1(4(x0)))))))) 590.70/152.60 (1^1(0(1(4(4(0(1(2(4(x0))))))))) -> 0^1(0(4(2(5(1(4(x0))))))),1^1(0(1(4(4(0(1(2(4(x0))))))))) -> 0^1(0(4(2(5(1(4(x0)))))))) 590.70/152.60 590.70/152.60 590.70/152.60 ---------------------------------------- 590.70/152.60 590.70/152.60 (12) 590.70/152.60 Obligation: 590.70/152.60 Q DP problem: 590.70/152.60 The TRS P consists of the following rules: 590.70/152.60 590.70/152.60 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.60 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.60 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.60 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.60 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.60 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.60 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(4(0(x1)))) -> 0^1(0(4(1(x1)))) 590.70/152.60 0^1(1(4(0(x1)))) -> 0^1(4(1(x1))) 590.70/152.60 0^1(1(4(0(x1)))) -> 4^1(1(x1)) 590.70/152.60 4^1(1(1(0(1(x1))))) -> 0^1(4(1(1(1(x1))))) 590.70/152.60 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.60 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.60 0^1(1(2(4(x1)))) -> 4^1(1(x1)) 590.70/152.60 4^1(1(1(0(1(x1))))) -> 4^1(1(1(1(x1)))) 590.70/152.60 4^1(1(1(0(1(x1))))) -> 1^1(1(1(x1))) 590.70/152.60 4^1(1(1(0(1(x1))))) -> 1^1(1(x1)) 590.70/152.60 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(2(4(x1)))) -> 0^1(4(1(2(x1)))) 590.70/152.60 0^1(1(2(4(x1)))) -> 4^1(1(2(x1))) 590.70/152.60 0^1(1(2(4(x1)))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(4(4(x1)))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(4(x1)))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(4(4(x1)))) -> 0^1(4(1(4(x1)))) 590.70/152.60 0^1(1(4(4(x1)))) -> 4^1(1(4(x1))) 590.70/152.60 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.60 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.60 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.60 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.60 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.60 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.60 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.60 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.60 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.60 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.60 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.60 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.60 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.60 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.60 1^1(0(1(4(4(1(1(0(1(x0))))))))) -> 0^1(5(0(4(1(1(1(x0))))))) 590.70/152.60 1^1(0(1(4(4(0(1(2(4(x0))))))))) -> 0^1(4(0(2(2(1(4(x0))))))) 590.70/152.60 1^1(0(1(4(4(0(1(2(4(x0))))))))) -> 0^1(0(4(2(5(1(4(x0))))))) 590.70/152.60 590.70/152.60 The TRS R consists of the following rules: 590.70/152.60 590.70/152.60 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.60 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.60 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.60 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.60 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.60 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.60 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.60 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.60 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.60 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.60 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.60 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.60 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.60 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.60 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.60 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.60 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.60 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.60 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.60 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.60 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.60 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.60 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.60 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.60 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.60 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.60 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.60 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.60 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.60 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.60 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.60 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.60 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.60 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.60 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.60 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.60 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.60 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.60 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.60 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.60 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.60 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.60 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.60 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.60 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.60 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.60 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.60 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.60 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.60 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.60 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.60 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.60 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.60 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.60 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.60 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.60 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.60 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.60 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.60 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.60 590.70/152.60 Q is empty. 590.70/152.60 We have to consider all minimal (P,Q,R)-chains. 590.70/152.60 ---------------------------------------- 590.70/152.60 590.70/152.60 (13) DependencyGraphProof (EQUIVALENT) 590.70/152.60 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes. 590.70/152.60 ---------------------------------------- 590.70/152.60 590.70/152.60 (14) 590.70/152.60 Obligation: 590.70/152.60 Q DP problem: 590.70/152.60 The TRS P consists of the following rules: 590.70/152.60 590.70/152.60 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.60 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.60 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.60 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.60 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.60 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.60 0^1(1(4(0(x1)))) -> 0^1(0(4(1(x1)))) 590.70/152.60 0^1(1(4(0(x1)))) -> 0^1(4(1(x1))) 590.70/152.60 0^1(1(4(0(x1)))) -> 4^1(1(x1)) 590.70/152.60 4^1(1(1(0(1(x1))))) -> 0^1(4(1(1(1(x1))))) 590.70/152.60 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.60 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.60 0^1(1(2(4(x1)))) -> 4^1(1(x1)) 590.70/152.60 4^1(1(1(0(1(x1))))) -> 4^1(1(1(1(x1)))) 590.70/152.60 4^1(1(1(0(1(x1))))) -> 1^1(1(1(x1))) 590.70/152.60 4^1(1(1(0(1(x1))))) -> 1^1(1(x1)) 590.70/152.60 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(2(4(x1)))) -> 0^1(4(1(2(x1)))) 590.70/152.60 0^1(1(2(4(x1)))) -> 4^1(1(2(x1))) 590.70/152.60 0^1(1(2(4(x1)))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(4(4(x1)))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(4(x1)))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(4(4(x1)))) -> 0^1(4(1(4(x1)))) 590.70/152.60 0^1(1(4(4(x1)))) -> 4^1(1(4(x1))) 590.70/152.60 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.60 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.60 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.60 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.60 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.60 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.60 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.60 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.60 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.60 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.60 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.60 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.60 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.60 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.60 590.70/152.60 The TRS R consists of the following rules: 590.70/152.60 590.70/152.60 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.60 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.60 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.60 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.60 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.60 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.60 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.60 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.60 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.60 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.60 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.60 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.60 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.60 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.60 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.60 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.60 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.60 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.60 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.60 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.60 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.60 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.60 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.60 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.60 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.60 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.60 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.60 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.60 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.60 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.60 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.60 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.60 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.60 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.60 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.60 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.60 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.60 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.60 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.60 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.60 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.60 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.60 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.60 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.60 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.60 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.60 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.60 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.60 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.60 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.60 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.60 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.60 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.60 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.60 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.60 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.60 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.60 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.60 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.60 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.60 590.70/152.60 Q is empty. 590.70/152.60 We have to consider all minimal (P,Q,R)-chains. 590.70/152.60 ---------------------------------------- 590.70/152.60 590.70/152.60 (15) TransformationProof (EQUIVALENT) 590.70/152.60 By narrowing [LPAR04] the rule 0^1(1(4(0(x1)))) -> 0^1(0(4(1(x1)))) at position [0] we obtained the following new rules [LPAR04]: 590.70/152.60 590.70/152.60 (0^1(1(4(0(1(0(1(x0))))))) -> 0^1(0(5(0(4(1(1(1(x0)))))))),0^1(1(4(0(1(0(1(x0))))))) -> 0^1(0(5(0(4(1(1(1(x0))))))))) 590.70/152.60 (0^1(1(4(0(0(1(0(x0))))))) -> 0^1(0(4(2(0(3(0(1(1(x0))))))))),0^1(1(4(0(0(1(0(x0))))))) -> 0^1(0(4(2(0(3(0(1(1(x0)))))))))) 590.70/152.60 (0^1(1(4(0(0(0(3(1(x0)))))))) -> 0^1(0(4(3(0(1(5(1(0(x0))))))))),0^1(1(4(0(0(0(3(1(x0)))))))) -> 0^1(0(4(3(0(1(5(1(0(x0)))))))))) 590.70/152.60 (0^1(1(4(0(0(1(2(4(x0)))))))) -> 0^1(0(4(5(1(4(0(2(1(x0))))))))),0^1(1(4(0(0(1(2(4(x0)))))))) -> 0^1(0(4(5(1(4(0(2(1(x0)))))))))) 590.70/152.60 (0^1(1(4(0(2(1(3(4(x0)))))))) -> 0^1(0(4(1(4(1(2(2(3(x0))))))))),0^1(1(4(0(2(1(3(4(x0)))))))) -> 0^1(0(4(1(4(1(2(2(3(x0)))))))))) 590.70/152.60 (0^1(1(4(0(0(1(4(4(x0)))))))) -> 0^1(0(4(1(4(1(3(0(4(x0))))))))),0^1(1(4(0(0(1(4(4(x0)))))))) -> 0^1(0(4(1(4(1(3(0(4(x0)))))))))) 590.70/152.60 590.70/152.60 590.70/152.60 ---------------------------------------- 590.70/152.60 590.70/152.60 (16) 590.70/152.60 Obligation: 590.70/152.60 Q DP problem: 590.70/152.60 The TRS P consists of the following rules: 590.70/152.60 590.70/152.60 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.60 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.60 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.60 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.60 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.60 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.60 0^1(1(4(0(x1)))) -> 0^1(4(1(x1))) 590.70/152.60 0^1(1(4(0(x1)))) -> 4^1(1(x1)) 590.70/152.60 4^1(1(1(0(1(x1))))) -> 0^1(4(1(1(1(x1))))) 590.70/152.60 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.60 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.60 0^1(1(2(4(x1)))) -> 4^1(1(x1)) 590.70/152.60 4^1(1(1(0(1(x1))))) -> 4^1(1(1(1(x1)))) 590.70/152.60 4^1(1(1(0(1(x1))))) -> 1^1(1(1(x1))) 590.70/152.60 4^1(1(1(0(1(x1))))) -> 1^1(1(x1)) 590.70/152.60 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(2(4(x1)))) -> 0^1(4(1(2(x1)))) 590.70/152.60 0^1(1(2(4(x1)))) -> 4^1(1(2(x1))) 590.70/152.60 0^1(1(2(4(x1)))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(4(4(x1)))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(4(x1)))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(4(4(x1)))) -> 0^1(4(1(4(x1)))) 590.70/152.60 0^1(1(4(4(x1)))) -> 4^1(1(4(x1))) 590.70/152.60 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.60 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.60 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.60 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.60 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.60 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.60 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.60 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.60 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.60 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.60 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.60 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.60 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.60 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(4(0(1(0(1(x0))))))) -> 0^1(0(5(0(4(1(1(1(x0)))))))) 590.70/152.60 0^1(1(4(0(0(1(0(x0))))))) -> 0^1(0(4(2(0(3(0(1(1(x0))))))))) 590.70/152.60 0^1(1(4(0(0(0(3(1(x0)))))))) -> 0^1(0(4(3(0(1(5(1(0(x0))))))))) 590.70/152.60 0^1(1(4(0(0(1(2(4(x0)))))))) -> 0^1(0(4(5(1(4(0(2(1(x0))))))))) 590.70/152.60 0^1(1(4(0(2(1(3(4(x0)))))))) -> 0^1(0(4(1(4(1(2(2(3(x0))))))))) 590.70/152.60 0^1(1(4(0(0(1(4(4(x0)))))))) -> 0^1(0(4(1(4(1(3(0(4(x0))))))))) 590.70/152.60 590.70/152.60 The TRS R consists of the following rules: 590.70/152.60 590.70/152.60 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.60 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.60 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.60 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.60 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.60 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.60 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.60 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.60 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.60 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.60 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.60 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.60 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.60 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.60 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.60 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.60 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.60 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.60 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.60 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.60 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.60 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.60 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.60 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.60 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.60 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.60 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.60 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.60 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.60 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.60 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.60 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.60 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.60 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.60 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.60 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.60 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.60 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.60 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.60 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.60 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.60 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.60 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.60 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.60 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.60 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.60 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.60 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.60 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.60 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.60 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.60 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.60 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.60 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.60 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.60 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.60 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.60 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.60 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.60 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.60 590.70/152.60 Q is empty. 590.70/152.60 We have to consider all minimal (P,Q,R)-chains. 590.70/152.60 ---------------------------------------- 590.70/152.60 590.70/152.60 (17) DependencyGraphProof (EQUIVALENT) 590.70/152.60 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 6 less nodes. 590.70/152.60 ---------------------------------------- 590.70/152.60 590.70/152.60 (18) 590.70/152.60 Obligation: 590.70/152.60 Q DP problem: 590.70/152.60 The TRS P consists of the following rules: 590.70/152.60 590.70/152.60 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.60 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.60 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.60 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.60 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.60 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.60 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(4(0(x1)))) -> 0^1(4(1(x1))) 590.70/152.60 0^1(1(4(0(x1)))) -> 4^1(1(x1)) 590.70/152.60 4^1(1(1(0(1(x1))))) -> 0^1(4(1(1(1(x1))))) 590.70/152.60 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.60 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.60 0^1(1(2(4(x1)))) -> 4^1(1(x1)) 590.70/152.60 4^1(1(1(0(1(x1))))) -> 4^1(1(1(1(x1)))) 590.70/152.60 4^1(1(1(0(1(x1))))) -> 1^1(1(1(x1))) 590.70/152.60 4^1(1(1(0(1(x1))))) -> 1^1(1(x1)) 590.70/152.60 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(2(4(x1)))) -> 0^1(4(1(2(x1)))) 590.70/152.60 0^1(1(2(4(x1)))) -> 4^1(1(2(x1))) 590.70/152.60 0^1(1(2(4(x1)))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(4(4(x1)))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(4(x1)))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(4(4(x1)))) -> 0^1(4(1(4(x1)))) 590.70/152.60 0^1(1(4(4(x1)))) -> 4^1(1(4(x1))) 590.70/152.60 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.60 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.60 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.60 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.60 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.60 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.60 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.60 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.60 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.60 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.60 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.60 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.60 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.60 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.60 590.70/152.60 The TRS R consists of the following rules: 590.70/152.60 590.70/152.60 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.60 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.60 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.60 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.60 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.60 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.60 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.60 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.60 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.60 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.60 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.60 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.60 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.60 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.60 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.60 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.60 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.60 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.60 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.60 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.60 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.60 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.60 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.60 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.60 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.60 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.60 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.60 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.60 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.60 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.60 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.60 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.60 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.60 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.60 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.60 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.60 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.60 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.60 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.60 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.60 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.60 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.60 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.60 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.60 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.60 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.60 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.60 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.60 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.60 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.60 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.60 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.60 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.60 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.60 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.60 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.60 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.60 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.60 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.60 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.60 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.60 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.60 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.60 590.70/152.60 Q is empty. 590.70/152.60 We have to consider all minimal (P,Q,R)-chains. 590.70/152.60 ---------------------------------------- 590.70/152.60 590.70/152.60 (19) TransformationProof (EQUIVALENT) 590.70/152.60 By narrowing [LPAR04] the rule 0^1(1(4(0(x1)))) -> 0^1(4(1(x1))) at position [0] we obtained the following new rules [LPAR04]: 590.70/152.60 590.70/152.60 (0^1(1(4(0(1(0(1(x0))))))) -> 0^1(5(0(4(1(1(1(x0))))))),0^1(1(4(0(1(0(1(x0))))))) -> 0^1(5(0(4(1(1(1(x0)))))))) 590.70/152.60 (0^1(1(4(0(0(1(0(x0))))))) -> 0^1(4(2(0(3(0(1(1(x0)))))))),0^1(1(4(0(0(1(0(x0))))))) -> 0^1(4(2(0(3(0(1(1(x0))))))))) 590.70/152.60 (0^1(1(4(0(0(0(3(1(x0)))))))) -> 0^1(4(3(0(1(5(1(0(x0)))))))),0^1(1(4(0(0(0(3(1(x0)))))))) -> 0^1(4(3(0(1(5(1(0(x0))))))))) 590.70/152.60 (0^1(1(4(0(0(1(2(4(x0)))))))) -> 0^1(4(5(1(4(0(2(1(x0)))))))),0^1(1(4(0(0(1(2(4(x0)))))))) -> 0^1(4(5(1(4(0(2(1(x0))))))))) 590.70/152.60 (0^1(1(4(0(2(1(3(4(x0)))))))) -> 0^1(4(1(4(1(2(2(3(x0)))))))),0^1(1(4(0(2(1(3(4(x0)))))))) -> 0^1(4(1(4(1(2(2(3(x0))))))))) 590.70/152.60 (0^1(1(4(0(0(1(4(4(x0)))))))) -> 0^1(4(1(4(1(3(0(4(x0)))))))),0^1(1(4(0(0(1(4(4(x0)))))))) -> 0^1(4(1(4(1(3(0(4(x0))))))))) 590.70/152.60 590.70/152.60 590.70/152.60 ---------------------------------------- 590.70/152.60 590.70/152.60 (20) 590.70/152.60 Obligation: 590.70/152.60 Q DP problem: 590.70/152.60 The TRS P consists of the following rules: 590.70/152.60 590.70/152.60 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.60 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.60 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.60 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.60 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.60 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.60 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(4(0(x1)))) -> 4^1(1(x1)) 590.70/152.60 4^1(1(1(0(1(x1))))) -> 0^1(4(1(1(1(x1))))) 590.70/152.60 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.60 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.60 0^1(1(2(4(x1)))) -> 4^1(1(x1)) 590.70/152.60 4^1(1(1(0(1(x1))))) -> 4^1(1(1(1(x1)))) 590.70/152.60 4^1(1(1(0(1(x1))))) -> 1^1(1(1(x1))) 590.70/152.60 4^1(1(1(0(1(x1))))) -> 1^1(1(x1)) 590.70/152.60 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(2(4(x1)))) -> 0^1(4(1(2(x1)))) 590.70/152.60 0^1(1(2(4(x1)))) -> 4^1(1(2(x1))) 590.70/152.60 0^1(1(2(4(x1)))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(4(4(x1)))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(4(x1)))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(4(4(x1)))) -> 0^1(4(1(4(x1)))) 590.70/152.60 0^1(1(4(4(x1)))) -> 4^1(1(4(x1))) 590.70/152.60 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.60 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.60 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.60 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.60 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.60 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.60 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.60 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.60 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.60 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.60 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.60 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.60 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.60 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.60 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.60 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.60 0^1(1(4(0(1(0(1(x0))))))) -> 0^1(5(0(4(1(1(1(x0))))))) 590.70/152.60 0^1(1(4(0(0(1(0(x0))))))) -> 0^1(4(2(0(3(0(1(1(x0)))))))) 590.70/152.60 0^1(1(4(0(0(0(3(1(x0)))))))) -> 0^1(4(3(0(1(5(1(0(x0)))))))) 590.70/152.60 0^1(1(4(0(0(1(2(4(x0)))))))) -> 0^1(4(5(1(4(0(2(1(x0)))))))) 590.70/152.60 0^1(1(4(0(2(1(3(4(x0)))))))) -> 0^1(4(1(4(1(2(2(3(x0)))))))) 590.70/152.61 0^1(1(4(0(0(1(4(4(x0)))))))) -> 0^1(4(1(4(1(3(0(4(x0)))))))) 590.70/152.61 590.70/152.61 The TRS R consists of the following rules: 590.70/152.61 590.70/152.61 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.61 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.61 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.61 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.61 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.61 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.61 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.61 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.61 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.61 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.61 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.61 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.61 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.61 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.61 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.61 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.61 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.61 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.61 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.61 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.61 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.61 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.61 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.61 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.61 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.61 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.61 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.61 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.61 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.61 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.61 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.61 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.61 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.61 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.61 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.61 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.61 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.61 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.61 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.61 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.61 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.61 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.61 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.61 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.61 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.61 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.61 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.61 590.70/152.61 Q is empty. 590.70/152.61 We have to consider all minimal (P,Q,R)-chains. 590.70/152.61 ---------------------------------------- 590.70/152.61 590.70/152.61 (21) DependencyGraphProof (EQUIVALENT) 590.70/152.61 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 6 less nodes. 590.70/152.61 ---------------------------------------- 590.70/152.61 590.70/152.61 (22) 590.70/152.61 Obligation: 590.70/152.61 Q DP problem: 590.70/152.61 The TRS P consists of the following rules: 590.70/152.61 590.70/152.61 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.61 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.61 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.61 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.61 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.61 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.61 0^1(1(4(0(x1)))) -> 4^1(1(x1)) 590.70/152.61 4^1(1(1(0(1(x1))))) -> 0^1(4(1(1(1(x1))))) 590.70/152.61 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.61 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(x1)))) -> 4^1(1(x1)) 590.70/152.61 4^1(1(1(0(1(x1))))) -> 4^1(1(1(1(x1)))) 590.70/152.61 4^1(1(1(0(1(x1))))) -> 1^1(1(1(x1))) 590.70/152.61 4^1(1(1(0(1(x1))))) -> 1^1(1(x1)) 590.70/152.61 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(2(4(x1)))) -> 0^1(4(1(2(x1)))) 590.70/152.61 0^1(1(2(4(x1)))) -> 4^1(1(2(x1))) 590.70/152.61 0^1(1(2(4(x1)))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(4(4(x1)))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(4(x1)))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(4(4(x1)))) -> 0^1(4(1(4(x1)))) 590.70/152.61 0^1(1(4(4(x1)))) -> 4^1(1(4(x1))) 590.70/152.61 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.61 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.61 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.61 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.61 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.61 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.61 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.61 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.61 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.61 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.61 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.61 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.61 590.70/152.61 The TRS R consists of the following rules: 590.70/152.61 590.70/152.61 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.61 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.61 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.61 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.61 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.61 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.61 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.61 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.61 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.61 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.61 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.61 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.61 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.61 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.61 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.61 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.61 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.61 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.61 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.61 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.61 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.61 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.61 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.61 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.61 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.61 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.61 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.61 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.61 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.61 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.61 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.61 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.61 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.61 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.61 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.61 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.61 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.61 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.61 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.61 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.61 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.61 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.61 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.61 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.61 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.61 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.61 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.61 590.70/152.61 Q is empty. 590.70/152.61 We have to consider all minimal (P,Q,R)-chains. 590.70/152.61 ---------------------------------------- 590.70/152.61 590.70/152.61 (23) TransformationProof (EQUIVALENT) 590.70/152.61 By narrowing [LPAR04] the rule 4^1(1(1(0(1(x1))))) -> 0^1(4(1(1(1(x1))))) at position [0] we obtained the following new rules [LPAR04]: 590.70/152.61 590.70/152.61 (4^1(1(1(0(1(0(1(0(x0)))))))) -> 0^1(4(1(1(2(0(3(0(1(1(x0)))))))))),4^1(1(1(0(1(0(1(0(x0)))))))) -> 0^1(4(1(1(2(0(3(0(1(1(x0))))))))))) 590.70/152.61 (4^1(1(1(0(1(0(0(3(1(x0))))))))) -> 0^1(4(1(1(3(0(1(5(1(0(x0)))))))))),4^1(1(1(0(1(0(0(3(1(x0))))))))) -> 0^1(4(1(1(3(0(1(5(1(0(x0))))))))))) 590.70/152.61 (4^1(1(1(0(1(0(1(2(4(x0))))))))) -> 0^1(4(1(1(5(1(4(0(2(1(x0)))))))))),4^1(1(1(0(1(0(1(2(4(x0))))))))) -> 0^1(4(1(1(5(1(4(0(2(1(x0))))))))))) 590.70/152.61 (4^1(1(1(0(1(2(1(3(4(x0))))))))) -> 0^1(4(1(1(1(4(1(2(2(3(x0)))))))))),4^1(1(1(0(1(2(1(3(4(x0))))))))) -> 0^1(4(1(1(1(4(1(2(2(3(x0))))))))))) 590.70/152.61 (4^1(1(1(0(1(0(1(4(4(x0))))))))) -> 0^1(4(1(1(1(4(1(3(0(4(x0)))))))))),4^1(1(1(0(1(0(1(4(4(x0))))))))) -> 0^1(4(1(1(1(4(1(3(0(4(x0))))))))))) 590.70/152.61 590.70/152.61 590.70/152.61 ---------------------------------------- 590.70/152.61 590.70/152.61 (24) 590.70/152.61 Obligation: 590.70/152.61 Q DP problem: 590.70/152.61 The TRS P consists of the following rules: 590.70/152.61 590.70/152.61 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.61 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.61 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.61 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.61 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.61 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.61 0^1(1(4(0(x1)))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.61 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(x1)))) -> 4^1(1(x1)) 590.70/152.61 4^1(1(1(0(1(x1))))) -> 4^1(1(1(1(x1)))) 590.70/152.61 4^1(1(1(0(1(x1))))) -> 1^1(1(1(x1))) 590.70/152.61 4^1(1(1(0(1(x1))))) -> 1^1(1(x1)) 590.70/152.61 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(2(4(x1)))) -> 0^1(4(1(2(x1)))) 590.70/152.61 0^1(1(2(4(x1)))) -> 4^1(1(2(x1))) 590.70/152.61 0^1(1(2(4(x1)))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(4(4(x1)))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(4(x1)))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(4(4(x1)))) -> 0^1(4(1(4(x1)))) 590.70/152.61 0^1(1(4(4(x1)))) -> 4^1(1(4(x1))) 590.70/152.61 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.61 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.61 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.61 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.61 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.61 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.61 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.61 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.61 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.61 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.61 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.61 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.61 4^1(1(1(0(1(0(1(0(x0)))))))) -> 0^1(4(1(1(2(0(3(0(1(1(x0)))))))))) 590.70/152.61 4^1(1(1(0(1(0(0(3(1(x0))))))))) -> 0^1(4(1(1(3(0(1(5(1(0(x0)))))))))) 590.70/152.61 4^1(1(1(0(1(0(1(2(4(x0))))))))) -> 0^1(4(1(1(5(1(4(0(2(1(x0)))))))))) 590.70/152.61 4^1(1(1(0(1(2(1(3(4(x0))))))))) -> 0^1(4(1(1(1(4(1(2(2(3(x0)))))))))) 590.70/152.61 4^1(1(1(0(1(0(1(4(4(x0))))))))) -> 0^1(4(1(1(1(4(1(3(0(4(x0)))))))))) 590.70/152.61 590.70/152.61 The TRS R consists of the following rules: 590.70/152.61 590.70/152.61 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.61 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.61 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.61 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.61 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.61 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.61 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.61 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.61 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.61 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.61 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.61 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.61 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.61 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.61 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.61 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.61 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.61 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.61 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.61 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.61 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.61 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.61 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.61 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.61 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.61 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.61 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.61 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.61 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.61 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.61 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.61 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.61 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.61 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.61 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.61 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.61 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.61 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.61 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.61 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.61 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.61 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.61 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.61 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.61 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.61 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.61 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.61 590.70/152.61 Q is empty. 590.70/152.61 We have to consider all minimal (P,Q,R)-chains. 590.70/152.61 ---------------------------------------- 590.70/152.61 590.70/152.61 (25) DependencyGraphProof (EQUIVALENT) 590.70/152.61 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 5 less nodes. 590.70/152.61 ---------------------------------------- 590.70/152.61 590.70/152.61 (26) 590.70/152.61 Obligation: 590.70/152.61 Q DP problem: 590.70/152.61 The TRS P consists of the following rules: 590.70/152.61 590.70/152.61 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.61 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.61 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.61 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.61 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.61 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.61 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(4(0(x1)))) -> 4^1(1(x1)) 590.70/152.61 4^1(1(1(0(1(x1))))) -> 4^1(1(1(1(x1)))) 590.70/152.61 4^1(1(1(0(1(x1))))) -> 1^1(1(1(x1))) 590.70/152.61 4^1(1(1(0(1(x1))))) -> 1^1(1(x1)) 590.70/152.61 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(x1)))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(2(4(x1)))) -> 0^1(4(1(2(x1)))) 590.70/152.61 0^1(1(2(4(x1)))) -> 4^1(1(2(x1))) 590.70/152.61 0^1(1(2(4(x1)))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(4(4(x1)))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(4(x1)))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(4(4(x1)))) -> 0^1(4(1(4(x1)))) 590.70/152.61 0^1(1(4(4(x1)))) -> 4^1(1(4(x1))) 590.70/152.61 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.61 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.61 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.61 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.61 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.61 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.61 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.61 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.61 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.61 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.61 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.61 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.61 590.70/152.61 The TRS R consists of the following rules: 590.70/152.61 590.70/152.61 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.61 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.61 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.61 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.61 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.61 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.61 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.61 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.61 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.61 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.61 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.61 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.61 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.61 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.61 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.61 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.61 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.61 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.61 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.61 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.61 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.61 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.61 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.61 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.61 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.61 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.61 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.61 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.61 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.61 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.61 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.61 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.61 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.61 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.61 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.61 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.61 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.61 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.61 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.61 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.61 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.61 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.61 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.61 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.61 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.61 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.61 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.61 590.70/152.61 Q is empty. 590.70/152.61 We have to consider all minimal (P,Q,R)-chains. 590.70/152.61 ---------------------------------------- 590.70/152.61 590.70/152.61 (27) TransformationProof (EQUIVALENT) 590.70/152.61 By narrowing [LPAR04] the rule 4^1(1(1(0(1(x1))))) -> 4^1(1(1(1(x1)))) at position [0] we obtained the following new rules [LPAR04]: 590.70/152.61 590.70/152.61 (4^1(1(1(0(1(0(1(0(x0)))))))) -> 4^1(1(1(2(0(3(0(1(1(x0))))))))),4^1(1(1(0(1(0(1(0(x0)))))))) -> 4^1(1(1(2(0(3(0(1(1(x0)))))))))) 590.70/152.61 (4^1(1(1(0(1(0(0(3(1(x0))))))))) -> 4^1(1(1(3(0(1(5(1(0(x0))))))))),4^1(1(1(0(1(0(0(3(1(x0))))))))) -> 4^1(1(1(3(0(1(5(1(0(x0)))))))))) 590.70/152.61 (4^1(1(1(0(1(0(1(2(4(x0))))))))) -> 4^1(1(1(5(1(4(0(2(1(x0))))))))),4^1(1(1(0(1(0(1(2(4(x0))))))))) -> 4^1(1(1(5(1(4(0(2(1(x0)))))))))) 590.70/152.61 (4^1(1(1(0(1(2(1(3(4(x0))))))))) -> 4^1(1(1(1(4(1(2(2(3(x0))))))))),4^1(1(1(0(1(2(1(3(4(x0))))))))) -> 4^1(1(1(1(4(1(2(2(3(x0)))))))))) 590.70/152.61 (4^1(1(1(0(1(0(1(4(4(x0))))))))) -> 4^1(1(1(1(4(1(3(0(4(x0))))))))),4^1(1(1(0(1(0(1(4(4(x0))))))))) -> 4^1(1(1(1(4(1(3(0(4(x0)))))))))) 590.70/152.61 590.70/152.61 590.70/152.61 ---------------------------------------- 590.70/152.61 590.70/152.61 (28) 590.70/152.61 Obligation: 590.70/152.61 Q DP problem: 590.70/152.61 The TRS P consists of the following rules: 590.70/152.61 590.70/152.61 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.61 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.61 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.61 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.61 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.61 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.61 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(4(0(x1)))) -> 4^1(1(x1)) 590.70/152.61 4^1(1(1(0(1(x1))))) -> 1^1(1(1(x1))) 590.70/152.61 4^1(1(1(0(1(x1))))) -> 1^1(1(x1)) 590.70/152.61 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(x1)))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(2(4(x1)))) -> 0^1(4(1(2(x1)))) 590.70/152.61 0^1(1(2(4(x1)))) -> 4^1(1(2(x1))) 590.70/152.61 0^1(1(2(4(x1)))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(4(4(x1)))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(4(x1)))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(4(4(x1)))) -> 0^1(4(1(4(x1)))) 590.70/152.61 0^1(1(4(4(x1)))) -> 4^1(1(4(x1))) 590.70/152.61 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.61 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.61 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.61 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.61 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.61 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.61 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.61 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.61 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.61 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.61 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.61 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.61 4^1(1(1(0(1(0(1(0(x0)))))))) -> 4^1(1(1(2(0(3(0(1(1(x0))))))))) 590.70/152.61 4^1(1(1(0(1(0(0(3(1(x0))))))))) -> 4^1(1(1(3(0(1(5(1(0(x0))))))))) 590.70/152.61 4^1(1(1(0(1(0(1(2(4(x0))))))))) -> 4^1(1(1(5(1(4(0(2(1(x0))))))))) 590.70/152.61 4^1(1(1(0(1(2(1(3(4(x0))))))))) -> 4^1(1(1(1(4(1(2(2(3(x0))))))))) 590.70/152.61 4^1(1(1(0(1(0(1(4(4(x0))))))))) -> 4^1(1(1(1(4(1(3(0(4(x0))))))))) 590.70/152.61 590.70/152.61 The TRS R consists of the following rules: 590.70/152.61 590.70/152.61 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.61 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.61 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.61 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.61 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.61 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.61 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.61 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.61 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.61 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.61 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.61 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.61 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.61 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.61 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.61 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.61 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.61 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.61 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.61 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.61 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.61 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.61 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.61 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.61 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.61 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.61 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.61 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.61 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.61 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.61 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.61 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.61 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.61 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.61 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.61 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.61 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.61 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.61 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.61 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.61 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.61 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.61 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.61 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.61 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.61 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.61 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.61 590.70/152.61 Q is empty. 590.70/152.61 We have to consider all minimal (P,Q,R)-chains. 590.70/152.61 ---------------------------------------- 590.70/152.61 590.70/152.61 (29) DependencyGraphProof (EQUIVALENT) 590.70/152.61 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 5 less nodes. 590.70/152.61 ---------------------------------------- 590.70/152.61 590.70/152.61 (30) 590.70/152.61 Obligation: 590.70/152.61 Q DP problem: 590.70/152.61 The TRS P consists of the following rules: 590.70/152.61 590.70/152.61 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.61 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.61 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.61 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.61 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.61 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.61 0^1(1(4(0(x1)))) -> 4^1(1(x1)) 590.70/152.61 4^1(1(1(0(1(x1))))) -> 1^1(1(1(x1))) 590.70/152.61 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.61 4^1(1(1(0(1(x1))))) -> 1^1(1(x1)) 590.70/152.61 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(x1)))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(2(4(x1)))) -> 0^1(4(1(2(x1)))) 590.70/152.61 0^1(1(2(4(x1)))) -> 4^1(1(2(x1))) 590.70/152.61 0^1(1(2(4(x1)))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(4(4(x1)))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(4(x1)))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(4(4(x1)))) -> 0^1(4(1(4(x1)))) 590.70/152.61 0^1(1(4(4(x1)))) -> 4^1(1(4(x1))) 590.70/152.61 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.61 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.61 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.61 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.61 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.61 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.61 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.61 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.61 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.61 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.61 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.61 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.61 590.70/152.61 The TRS R consists of the following rules: 590.70/152.61 590.70/152.61 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.61 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.61 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.61 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.61 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.61 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.61 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.61 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.61 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.61 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.61 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.61 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.61 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.61 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.61 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.61 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.61 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.61 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.61 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.61 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.61 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.61 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.61 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.61 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.61 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.61 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.61 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.61 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.61 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.61 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.61 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.61 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.61 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.61 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.61 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.61 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.61 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.61 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.61 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.61 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.61 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.61 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.61 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.61 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.61 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.61 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.61 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.61 590.70/152.61 Q is empty. 590.70/152.61 We have to consider all minimal (P,Q,R)-chains. 590.70/152.61 ---------------------------------------- 590.70/152.61 590.70/152.61 (31) TransformationProof (EQUIVALENT) 590.70/152.61 By narrowing [LPAR04] the rule 4^1(1(1(0(1(x1))))) -> 1^1(1(1(x1))) at position [0] we obtained the following new rules [LPAR04]: 590.70/152.61 590.70/152.61 (4^1(1(1(0(1(0(1(0(x0)))))))) -> 1^1(1(2(0(3(0(1(1(x0)))))))),4^1(1(1(0(1(0(1(0(x0)))))))) -> 1^1(1(2(0(3(0(1(1(x0))))))))) 590.70/152.61 (4^1(1(1(0(1(0(0(3(1(x0))))))))) -> 1^1(1(3(0(1(5(1(0(x0)))))))),4^1(1(1(0(1(0(0(3(1(x0))))))))) -> 1^1(1(3(0(1(5(1(0(x0))))))))) 590.70/152.61 (4^1(1(1(0(1(0(1(2(4(x0))))))))) -> 1^1(1(5(1(4(0(2(1(x0)))))))),4^1(1(1(0(1(0(1(2(4(x0))))))))) -> 1^1(1(5(1(4(0(2(1(x0))))))))) 590.70/152.61 (4^1(1(1(0(1(2(1(3(4(x0))))))))) -> 1^1(1(1(4(1(2(2(3(x0)))))))),4^1(1(1(0(1(2(1(3(4(x0))))))))) -> 1^1(1(1(4(1(2(2(3(x0))))))))) 590.70/152.61 (4^1(1(1(0(1(0(1(4(4(x0))))))))) -> 1^1(1(1(4(1(3(0(4(x0)))))))),4^1(1(1(0(1(0(1(4(4(x0))))))))) -> 1^1(1(1(4(1(3(0(4(x0))))))))) 590.70/152.61 590.70/152.61 590.70/152.61 ---------------------------------------- 590.70/152.61 590.70/152.61 (32) 590.70/152.61 Obligation: 590.70/152.61 Q DP problem: 590.70/152.61 The TRS P consists of the following rules: 590.70/152.61 590.70/152.61 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.61 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.61 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.61 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.61 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.61 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.61 0^1(1(4(0(x1)))) -> 4^1(1(x1)) 590.70/152.61 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.61 4^1(1(1(0(1(x1))))) -> 1^1(1(x1)) 590.70/152.61 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(x1)))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(2(4(x1)))) -> 0^1(4(1(2(x1)))) 590.70/152.61 0^1(1(2(4(x1)))) -> 4^1(1(2(x1))) 590.70/152.61 0^1(1(2(4(x1)))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(4(4(x1)))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(4(x1)))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(4(4(x1)))) -> 0^1(4(1(4(x1)))) 590.70/152.61 0^1(1(4(4(x1)))) -> 4^1(1(4(x1))) 590.70/152.61 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.61 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.61 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.61 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.61 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.61 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.61 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.61 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.61 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.61 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.61 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.61 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.61 4^1(1(1(0(1(0(1(0(x0)))))))) -> 1^1(1(2(0(3(0(1(1(x0)))))))) 590.70/152.61 4^1(1(1(0(1(0(0(3(1(x0))))))))) -> 1^1(1(3(0(1(5(1(0(x0)))))))) 590.70/152.61 4^1(1(1(0(1(0(1(2(4(x0))))))))) -> 1^1(1(5(1(4(0(2(1(x0)))))))) 590.70/152.61 4^1(1(1(0(1(2(1(3(4(x0))))))))) -> 1^1(1(1(4(1(2(2(3(x0)))))))) 590.70/152.61 4^1(1(1(0(1(0(1(4(4(x0))))))))) -> 1^1(1(1(4(1(3(0(4(x0)))))))) 590.70/152.61 590.70/152.61 The TRS R consists of the following rules: 590.70/152.61 590.70/152.61 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.61 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.61 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.61 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.61 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.61 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.61 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.61 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.61 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.61 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.61 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.61 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.61 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.61 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.61 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.61 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.61 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.61 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.61 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.61 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.61 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.61 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.61 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.61 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.61 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.61 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.61 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.61 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.61 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.61 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.61 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.61 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.61 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.61 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.61 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.61 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.61 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.61 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.61 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.61 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.61 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.61 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.61 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.61 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.61 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.61 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.61 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.61 590.70/152.61 Q is empty. 590.70/152.61 We have to consider all minimal (P,Q,R)-chains. 590.70/152.61 ---------------------------------------- 590.70/152.61 590.70/152.61 (33) DependencyGraphProof (EQUIVALENT) 590.70/152.61 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 5 less nodes. 590.70/152.61 ---------------------------------------- 590.70/152.61 590.70/152.61 (34) 590.70/152.61 Obligation: 590.70/152.61 Q DP problem: 590.70/152.61 The TRS P consists of the following rules: 590.70/152.61 590.70/152.61 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.61 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.61 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.61 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.61 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.61 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.61 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(4(0(x1)))) -> 4^1(1(x1)) 590.70/152.61 4^1(1(1(0(1(x1))))) -> 1^1(1(x1)) 590.70/152.61 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(x1)))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(2(4(x1)))) -> 0^1(4(1(2(x1)))) 590.70/152.61 0^1(1(2(4(x1)))) -> 4^1(1(2(x1))) 590.70/152.61 0^1(1(2(4(x1)))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(4(4(x1)))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(4(x1)))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(4(4(x1)))) -> 0^1(4(1(4(x1)))) 590.70/152.61 0^1(1(4(4(x1)))) -> 4^1(1(4(x1))) 590.70/152.61 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.61 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.61 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.61 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.61 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.61 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.61 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.61 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.61 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.61 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.61 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.61 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.61 590.70/152.61 The TRS R consists of the following rules: 590.70/152.61 590.70/152.61 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.61 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.61 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.61 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.61 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.61 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.61 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.61 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.61 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.61 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.61 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.61 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.61 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.61 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.61 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.61 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.61 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.61 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.61 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.61 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.61 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.61 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.61 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.61 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.61 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.61 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.61 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.61 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.61 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.61 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.61 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.61 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.61 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.61 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.61 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.61 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.61 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.61 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.61 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.61 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.61 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.61 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.61 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.61 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.61 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.61 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.61 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.61 590.70/152.61 Q is empty. 590.70/152.61 We have to consider all minimal (P,Q,R)-chains. 590.70/152.61 ---------------------------------------- 590.70/152.61 590.70/152.61 (35) TransformationProof (EQUIVALENT) 590.70/152.61 By narrowing [LPAR04] the rule 4^1(1(1(0(1(x1))))) -> 1^1(1(x1)) at position [0] we obtained the following new rules [LPAR04]: 590.70/152.61 590.70/152.61 (4^1(1(1(0(1(0(1(0(x0)))))))) -> 1^1(2(0(3(0(1(1(x0))))))),4^1(1(1(0(1(0(1(0(x0)))))))) -> 1^1(2(0(3(0(1(1(x0)))))))) 590.70/152.61 (4^1(1(1(0(1(0(0(3(1(x0))))))))) -> 1^1(3(0(1(5(1(0(x0))))))),4^1(1(1(0(1(0(0(3(1(x0))))))))) -> 1^1(3(0(1(5(1(0(x0)))))))) 590.70/152.61 (4^1(1(1(0(1(0(1(2(4(x0))))))))) -> 1^1(5(1(4(0(2(1(x0))))))),4^1(1(1(0(1(0(1(2(4(x0))))))))) -> 1^1(5(1(4(0(2(1(x0)))))))) 590.70/152.61 (4^1(1(1(0(1(2(1(3(4(x0))))))))) -> 1^1(1(4(1(2(2(3(x0))))))),4^1(1(1(0(1(2(1(3(4(x0))))))))) -> 1^1(1(4(1(2(2(3(x0)))))))) 590.70/152.61 (4^1(1(1(0(1(0(1(4(4(x0))))))))) -> 1^1(1(4(1(3(0(4(x0))))))),4^1(1(1(0(1(0(1(4(4(x0))))))))) -> 1^1(1(4(1(3(0(4(x0)))))))) 590.70/152.61 590.70/152.61 590.70/152.61 ---------------------------------------- 590.70/152.61 590.70/152.61 (36) 590.70/152.61 Obligation: 590.70/152.61 Q DP problem: 590.70/152.61 The TRS P consists of the following rules: 590.70/152.61 590.70/152.61 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.61 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.61 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.61 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.61 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.61 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.61 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(4(0(x1)))) -> 4^1(1(x1)) 590.70/152.61 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(x1)))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(2(4(x1)))) -> 0^1(4(1(2(x1)))) 590.70/152.61 0^1(1(2(4(x1)))) -> 4^1(1(2(x1))) 590.70/152.61 0^1(1(2(4(x1)))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(4(4(x1)))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(4(x1)))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(4(4(x1)))) -> 0^1(4(1(4(x1)))) 590.70/152.61 0^1(1(4(4(x1)))) -> 4^1(1(4(x1))) 590.70/152.61 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.61 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.61 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.61 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.61 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.61 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.61 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.61 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.61 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.61 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.61 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.61 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.61 4^1(1(1(0(1(0(1(0(x0)))))))) -> 1^1(2(0(3(0(1(1(x0))))))) 590.70/152.61 4^1(1(1(0(1(0(0(3(1(x0))))))))) -> 1^1(3(0(1(5(1(0(x0))))))) 590.70/152.61 4^1(1(1(0(1(0(1(2(4(x0))))))))) -> 1^1(5(1(4(0(2(1(x0))))))) 590.70/152.61 4^1(1(1(0(1(2(1(3(4(x0))))))))) -> 1^1(1(4(1(2(2(3(x0))))))) 590.70/152.61 4^1(1(1(0(1(0(1(4(4(x0))))))))) -> 1^1(1(4(1(3(0(4(x0))))))) 590.70/152.61 590.70/152.61 The TRS R consists of the following rules: 590.70/152.61 590.70/152.61 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.61 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.61 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.61 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.61 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.61 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.61 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.61 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.61 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.61 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.61 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.61 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.61 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.61 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.61 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.61 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.61 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.61 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.61 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.61 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.61 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.61 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.61 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.61 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.61 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.61 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.61 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.61 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.61 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.61 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.61 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.61 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.61 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.61 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.61 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.61 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.61 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.61 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.61 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.61 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.61 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.61 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.61 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.61 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.61 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.61 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.61 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.61 590.70/152.61 Q is empty. 590.70/152.61 We have to consider all minimal (P,Q,R)-chains. 590.70/152.61 ---------------------------------------- 590.70/152.61 590.70/152.61 (37) DependencyGraphProof (EQUIVALENT) 590.70/152.61 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 5 less nodes. 590.70/152.61 ---------------------------------------- 590.70/152.61 590.70/152.61 (38) 590.70/152.61 Obligation: 590.70/152.61 Q DP problem: 590.70/152.61 The TRS P consists of the following rules: 590.70/152.61 590.70/152.61 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.61 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.61 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.61 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.61 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.61 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.61 0^1(1(4(0(x1)))) -> 4^1(1(x1)) 590.70/152.61 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.61 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(x1)))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(2(4(x1)))) -> 0^1(4(1(2(x1)))) 590.70/152.61 0^1(1(2(4(x1)))) -> 4^1(1(2(x1))) 590.70/152.61 0^1(1(2(4(x1)))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(4(4(x1)))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(4(x1)))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(4(4(x1)))) -> 0^1(4(1(4(x1)))) 590.70/152.61 0^1(1(4(4(x1)))) -> 4^1(1(4(x1))) 590.70/152.61 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.61 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.61 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.61 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.61 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.61 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.61 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.61 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.61 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.61 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.61 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.61 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.61 590.70/152.61 The TRS R consists of the following rules: 590.70/152.61 590.70/152.61 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.61 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.61 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.61 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.61 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.61 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.61 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.61 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.61 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.61 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.61 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.61 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.61 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.61 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.61 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.61 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.61 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.61 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.61 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.61 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.61 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.61 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.61 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.61 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.61 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.61 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.61 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.61 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.61 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.61 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.61 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.61 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.61 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.61 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.61 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.61 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.61 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.61 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.61 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.61 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.61 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.61 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.61 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.61 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.61 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.61 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.61 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.61 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.61 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.61 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.61 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.61 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.61 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.61 590.70/152.61 Q is empty. 590.70/152.61 We have to consider all minimal (P,Q,R)-chains. 590.70/152.61 ---------------------------------------- 590.70/152.61 590.70/152.61 (39) TransformationProof (EQUIVALENT) 590.70/152.61 By narrowing [LPAR04] the rule 0^1(1(4(0(x1)))) -> 4^1(1(x1)) at position [0] we obtained the following new rules [LPAR04]: 590.70/152.61 590.70/152.61 (0^1(1(4(0(0(1(0(x0))))))) -> 4^1(2(0(3(0(1(1(x0))))))),0^1(1(4(0(0(1(0(x0))))))) -> 4^1(2(0(3(0(1(1(x0)))))))) 590.70/152.61 (0^1(1(4(0(0(0(3(1(x0)))))))) -> 4^1(3(0(1(5(1(0(x0))))))),0^1(1(4(0(0(0(3(1(x0)))))))) -> 4^1(3(0(1(5(1(0(x0)))))))) 590.70/152.61 (0^1(1(4(0(0(1(2(4(x0)))))))) -> 4^1(5(1(4(0(2(1(x0))))))),0^1(1(4(0(0(1(2(4(x0)))))))) -> 4^1(5(1(4(0(2(1(x0)))))))) 590.70/152.61 (0^1(1(4(0(2(1(3(4(x0)))))))) -> 4^1(1(4(1(2(2(3(x0))))))),0^1(1(4(0(2(1(3(4(x0)))))))) -> 4^1(1(4(1(2(2(3(x0)))))))) 590.70/152.61 (0^1(1(4(0(0(1(4(4(x0)))))))) -> 4^1(1(4(1(3(0(4(x0))))))),0^1(1(4(0(0(1(4(4(x0)))))))) -> 4^1(1(4(1(3(0(4(x0)))))))) 590.70/152.61 590.70/152.61 590.70/152.61 ---------------------------------------- 590.70/152.61 590.70/152.61 (40) 590.70/152.61 Obligation: 590.70/152.61 Q DP problem: 590.70/152.61 The TRS P consists of the following rules: 590.70/152.61 590.70/152.61 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.61 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.61 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.61 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.61 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.61 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.61 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.61 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.61 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.61 0^1(1(2(4(x1)))) -> 4^1(1(x1)) 590.70/152.61 0^1(1(2(4(x1)))) -> 0^1(4(1(2(x1)))) 590.70/152.61 0^1(1(2(4(x1)))) -> 4^1(1(2(x1))) 590.70/152.61 0^1(1(2(4(x1)))) -> 1^1(4(x1)) 590.70/152.61 0^1(1(4(4(x1)))) -> 0^1(4(x1)) 590.70/152.61 0^1(1(4(4(x1)))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(4(4(x1)))) -> 0^1(4(1(4(x1)))) 590.70/152.62 0^1(1(4(4(x1)))) -> 4^1(1(4(x1))) 590.70/152.62 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.62 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.62 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.62 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.62 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.62 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(4(0(0(1(0(x0))))))) -> 4^1(2(0(3(0(1(1(x0))))))) 590.70/152.62 0^1(1(4(0(0(0(3(1(x0)))))))) -> 4^1(3(0(1(5(1(0(x0))))))) 590.70/152.62 0^1(1(4(0(0(1(2(4(x0)))))))) -> 4^1(5(1(4(0(2(1(x0))))))) 590.70/152.62 0^1(1(4(0(2(1(3(4(x0)))))))) -> 4^1(1(4(1(2(2(3(x0))))))) 590.70/152.62 0^1(1(4(0(0(1(4(4(x0)))))))) -> 4^1(1(4(1(3(0(4(x0))))))) 590.70/152.62 590.70/152.62 The TRS R consists of the following rules: 590.70/152.62 590.70/152.62 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.62 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.62 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.62 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.62 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.62 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.62 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.62 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.62 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.62 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.62 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.62 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.62 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.62 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.62 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.62 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.62 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.62 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.62 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.62 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.62 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.62 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.62 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.62 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.62 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.62 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.62 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.62 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.62 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.62 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.62 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.62 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.62 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.62 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.62 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.62 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.62 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.62 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.62 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.62 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.62 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.62 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.62 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.62 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.62 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.62 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.62 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.62 590.70/152.62 Q is empty. 590.70/152.62 We have to consider all minimal (P,Q,R)-chains. 590.70/152.62 ---------------------------------------- 590.70/152.62 590.70/152.62 (41) DependencyGraphProof (EQUIVALENT) 590.70/152.62 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 5 less nodes. 590.70/152.62 ---------------------------------------- 590.70/152.62 590.70/152.62 (42) 590.70/152.62 Obligation: 590.70/152.62 Q DP problem: 590.70/152.62 The TRS P consists of the following rules: 590.70/152.62 590.70/152.62 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.62 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.62 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.62 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.62 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.62 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.62 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(x1)))) -> 4^1(1(x1)) 590.70/152.62 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(4(x1)))) -> 0^1(4(1(2(x1)))) 590.70/152.62 0^1(1(2(4(x1)))) -> 4^1(1(2(x1))) 590.70/152.62 0^1(1(2(4(x1)))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(4(4(x1)))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(4(x1)))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(4(4(x1)))) -> 0^1(4(1(4(x1)))) 590.70/152.62 0^1(1(4(4(x1)))) -> 4^1(1(4(x1))) 590.70/152.62 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.62 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.62 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.62 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.62 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.62 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 590.70/152.62 The TRS R consists of the following rules: 590.70/152.62 590.70/152.62 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.62 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.62 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.62 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.62 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.62 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.62 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.62 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.62 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.62 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.62 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.62 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.62 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.62 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.62 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.62 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.62 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.62 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.62 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.62 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.62 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.62 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.62 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.62 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.62 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.62 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.62 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.62 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.62 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.62 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.62 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.62 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.62 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.62 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.62 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.62 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.62 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.62 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.62 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.62 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.62 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.62 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.62 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.62 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.62 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.62 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.62 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.62 590.70/152.62 Q is empty. 590.70/152.62 We have to consider all minimal (P,Q,R)-chains. 590.70/152.62 ---------------------------------------- 590.70/152.62 590.70/152.62 (43) TransformationProof (EQUIVALENT) 590.70/152.62 By narrowing [LPAR04] the rule 0^1(1(2(4(x1)))) -> 4^1(1(x1)) at position [0] we obtained the following new rules [LPAR04]: 590.70/152.62 590.70/152.62 (0^1(1(2(4(0(1(0(x0))))))) -> 4^1(2(0(3(0(1(1(x0))))))),0^1(1(2(4(0(1(0(x0))))))) -> 4^1(2(0(3(0(1(1(x0)))))))) 590.70/152.62 (0^1(1(2(4(0(0(3(1(x0)))))))) -> 4^1(3(0(1(5(1(0(x0))))))),0^1(1(2(4(0(0(3(1(x0)))))))) -> 4^1(3(0(1(5(1(0(x0)))))))) 590.70/152.62 (0^1(1(2(4(0(1(2(4(x0)))))))) -> 4^1(5(1(4(0(2(1(x0))))))),0^1(1(2(4(0(1(2(4(x0)))))))) -> 4^1(5(1(4(0(2(1(x0)))))))) 590.70/152.62 (0^1(1(2(4(2(1(3(4(x0)))))))) -> 4^1(1(4(1(2(2(3(x0))))))),0^1(1(2(4(2(1(3(4(x0)))))))) -> 4^1(1(4(1(2(2(3(x0)))))))) 590.70/152.62 (0^1(1(2(4(0(1(4(4(x0)))))))) -> 4^1(1(4(1(3(0(4(x0))))))),0^1(1(2(4(0(1(4(4(x0)))))))) -> 4^1(1(4(1(3(0(4(x0)))))))) 590.70/152.62 590.70/152.62 590.70/152.62 ---------------------------------------- 590.70/152.62 590.70/152.62 (44) 590.70/152.62 Obligation: 590.70/152.62 Q DP problem: 590.70/152.62 The TRS P consists of the following rules: 590.70/152.62 590.70/152.62 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.62 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.62 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.62 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.62 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.62 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.62 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.62 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(4(x1)))) -> 0^1(4(1(2(x1)))) 590.70/152.62 0^1(1(2(4(x1)))) -> 4^1(1(2(x1))) 590.70/152.62 0^1(1(2(4(x1)))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(4(4(x1)))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(4(x1)))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(4(4(x1)))) -> 0^1(4(1(4(x1)))) 590.70/152.62 0^1(1(4(4(x1)))) -> 4^1(1(4(x1))) 590.70/152.62 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.62 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.62 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.62 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.62 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.62 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(4(0(1(0(x0))))))) -> 4^1(2(0(3(0(1(1(x0))))))) 590.70/152.62 0^1(1(2(4(0(0(3(1(x0)))))))) -> 4^1(3(0(1(5(1(0(x0))))))) 590.70/152.62 0^1(1(2(4(0(1(2(4(x0)))))))) -> 4^1(5(1(4(0(2(1(x0))))))) 590.70/152.62 0^1(1(2(4(2(1(3(4(x0)))))))) -> 4^1(1(4(1(2(2(3(x0))))))) 590.70/152.62 0^1(1(2(4(0(1(4(4(x0)))))))) -> 4^1(1(4(1(3(0(4(x0))))))) 590.70/152.62 590.70/152.62 The TRS R consists of the following rules: 590.70/152.62 590.70/152.62 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.62 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.62 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.62 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.62 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.62 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.62 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.62 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.62 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.62 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.62 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.62 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.62 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.62 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.62 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.62 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.62 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.62 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.62 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.62 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.62 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.62 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.62 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.62 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.62 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.62 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.62 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.62 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.62 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.62 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.62 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.62 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.62 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.62 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.62 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.62 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.62 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.62 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.62 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.62 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.62 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.62 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.62 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.62 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.62 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.62 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.62 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.62 590.70/152.62 Q is empty. 590.70/152.62 We have to consider all minimal (P,Q,R)-chains. 590.70/152.62 ---------------------------------------- 590.70/152.62 590.70/152.62 (45) DependencyGraphProof (EQUIVALENT) 590.70/152.62 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 5 less nodes. 590.70/152.62 ---------------------------------------- 590.70/152.62 590.70/152.62 (46) 590.70/152.62 Obligation: 590.70/152.62 Q DP problem: 590.70/152.62 The TRS P consists of the following rules: 590.70/152.62 590.70/152.62 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.62 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.62 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.62 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.62 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.62 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.62 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.62 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(x1)))) -> 0^1(4(1(2(x1)))) 590.70/152.62 0^1(1(2(4(x1)))) -> 4^1(1(2(x1))) 590.70/152.62 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(4(x1)))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(4(4(x1)))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(4(x1)))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(4(4(x1)))) -> 0^1(4(1(4(x1)))) 590.70/152.62 0^1(1(4(4(x1)))) -> 4^1(1(4(x1))) 590.70/152.62 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.62 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.62 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.62 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.62 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.62 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 590.70/152.62 The TRS R consists of the following rules: 590.70/152.62 590.70/152.62 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.62 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.62 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.62 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.62 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.62 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.62 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.62 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.62 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.62 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.62 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.62 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.62 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.62 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.62 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.62 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.62 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.62 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.62 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.62 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.62 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.62 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.62 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.62 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.62 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.62 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.62 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.62 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.62 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.62 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.62 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.62 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.62 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.62 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.62 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.62 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.62 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.62 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.62 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.62 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.62 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.62 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.62 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.62 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.62 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.62 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.62 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.62 590.70/152.62 Q is empty. 590.70/152.62 We have to consider all minimal (P,Q,R)-chains. 590.70/152.62 ---------------------------------------- 590.70/152.62 590.70/152.62 (47) TransformationProof (EQUIVALENT) 590.70/152.62 By narrowing [LPAR04] the rule 0^1(1(2(4(x1)))) -> 0^1(4(1(2(x1)))) at position [0] we obtained the following new rules [LPAR04]: 590.70/152.62 590.70/152.62 (0^1(1(2(4(1(3(4(x0))))))) -> 0^1(4(1(4(1(2(2(3(x0)))))))),0^1(1(2(4(1(3(4(x0))))))) -> 0^1(4(1(4(1(2(2(3(x0))))))))) 590.70/152.62 590.70/152.62 590.70/152.62 ---------------------------------------- 590.70/152.62 590.70/152.62 (48) 590.70/152.62 Obligation: 590.70/152.62 Q DP problem: 590.70/152.62 The TRS P consists of the following rules: 590.70/152.62 590.70/152.62 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.62 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.62 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.62 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.62 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.62 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.62 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.62 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(x1)))) -> 4^1(1(2(x1))) 590.70/152.62 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(4(x1)))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(4(4(x1)))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(4(x1)))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(4(4(x1)))) -> 0^1(4(1(4(x1)))) 590.70/152.62 0^1(1(4(4(x1)))) -> 4^1(1(4(x1))) 590.70/152.62 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.62 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.62 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.62 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.62 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.62 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(4(1(3(4(x0))))))) -> 0^1(4(1(4(1(2(2(3(x0)))))))) 590.70/152.62 590.70/152.62 The TRS R consists of the following rules: 590.70/152.62 590.70/152.62 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.62 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.62 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.62 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.62 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.62 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.62 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.62 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.62 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.62 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.62 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.62 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.62 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.62 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.62 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.62 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.62 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.62 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.62 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.62 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.62 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.62 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.62 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.62 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.62 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.62 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.62 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.62 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.62 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.62 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.62 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.62 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.62 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.62 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.62 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.62 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.62 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.62 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.62 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.62 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.62 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.62 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.62 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.62 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.62 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.62 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.62 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.62 590.70/152.62 Q is empty. 590.70/152.62 We have to consider all minimal (P,Q,R)-chains. 590.70/152.62 ---------------------------------------- 590.70/152.62 590.70/152.62 (49) DependencyGraphProof (EQUIVALENT) 590.70/152.62 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 590.70/152.62 ---------------------------------------- 590.70/152.62 590.70/152.62 (50) 590.70/152.62 Obligation: 590.70/152.62 Q DP problem: 590.70/152.62 The TRS P consists of the following rules: 590.70/152.62 590.70/152.62 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.62 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.62 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.62 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.62 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.62 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.62 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(x1)))) -> 4^1(1(2(x1))) 590.70/152.62 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(4(x1)))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(4(4(x1)))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(4(x1)))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(4(4(x1)))) -> 0^1(4(1(4(x1)))) 590.70/152.62 0^1(1(4(4(x1)))) -> 4^1(1(4(x1))) 590.70/152.62 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.62 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.62 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.62 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.62 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.62 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 590.70/152.62 The TRS R consists of the following rules: 590.70/152.62 590.70/152.62 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.62 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.62 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.62 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.62 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.62 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.62 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.62 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.62 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.62 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.62 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.62 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.62 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.62 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.62 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.62 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.62 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.62 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.62 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.62 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.62 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.62 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.62 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.62 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.62 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.62 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.62 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.62 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.62 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.62 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.62 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.62 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.62 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.62 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.62 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.62 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.62 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.62 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.62 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.62 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.62 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.62 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.62 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.62 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.62 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.62 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.62 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.62 590.70/152.62 Q is empty. 590.70/152.62 We have to consider all minimal (P,Q,R)-chains. 590.70/152.62 ---------------------------------------- 590.70/152.62 590.70/152.62 (51) TransformationProof (EQUIVALENT) 590.70/152.62 By narrowing [LPAR04] the rule 0^1(1(2(4(x1)))) -> 4^1(1(2(x1))) at position [0] we obtained the following new rules [LPAR04]: 590.70/152.62 590.70/152.62 (0^1(1(2(4(1(3(4(x0))))))) -> 4^1(1(4(1(2(2(3(x0))))))),0^1(1(2(4(1(3(4(x0))))))) -> 4^1(1(4(1(2(2(3(x0)))))))) 590.70/152.62 590.70/152.62 590.70/152.62 ---------------------------------------- 590.70/152.62 590.70/152.62 (52) 590.70/152.62 Obligation: 590.70/152.62 Q DP problem: 590.70/152.62 The TRS P consists of the following rules: 590.70/152.62 590.70/152.62 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.62 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.62 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.62 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.62 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.62 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.62 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.62 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(4(x1)))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(4(4(x1)))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(4(x1)))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(4(4(x1)))) -> 0^1(4(1(4(x1)))) 590.70/152.62 0^1(1(4(4(x1)))) -> 4^1(1(4(x1))) 590.70/152.62 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.62 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.62 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.62 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.62 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.62 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(4(1(3(4(x0))))))) -> 4^1(1(4(1(2(2(3(x0))))))) 590.70/152.62 590.70/152.62 The TRS R consists of the following rules: 590.70/152.62 590.70/152.62 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.62 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.62 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.62 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.62 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.62 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.62 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.62 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.62 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.62 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.62 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.62 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.62 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.62 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.62 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.62 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.62 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.62 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.62 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.62 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.62 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.62 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.62 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.62 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.62 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.62 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.62 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.62 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.62 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.62 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.62 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.62 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.62 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.62 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.62 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.62 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.62 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.62 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.62 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.62 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.62 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.62 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.62 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.62 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.62 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.62 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.62 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.62 590.70/152.62 Q is empty. 590.70/152.62 We have to consider all minimal (P,Q,R)-chains. 590.70/152.62 ---------------------------------------- 590.70/152.62 590.70/152.62 (53) DependencyGraphProof (EQUIVALENT) 590.70/152.62 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 590.70/152.62 ---------------------------------------- 590.70/152.62 590.70/152.62 (54) 590.70/152.62 Obligation: 590.70/152.62 Q DP problem: 590.70/152.62 The TRS P consists of the following rules: 590.70/152.62 590.70/152.62 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.62 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.62 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.62 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.62 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.62 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.62 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.62 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(x1)))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(4(4(x1)))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(4(x1)))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(4(4(x1)))) -> 0^1(4(1(4(x1)))) 590.70/152.62 0^1(1(4(4(x1)))) -> 4^1(1(4(x1))) 590.70/152.62 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.62 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.62 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.62 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.62 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.62 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 590.70/152.62 The TRS R consists of the following rules: 590.70/152.62 590.70/152.62 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.62 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.62 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.62 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.62 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.62 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.62 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.62 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.62 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.62 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.62 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.62 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.62 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.62 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.62 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.62 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.62 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.62 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.62 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.62 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.62 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.62 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.62 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.62 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.62 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.62 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.62 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.62 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.62 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.62 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.62 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.62 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.62 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.62 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.62 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.62 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.62 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.62 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.62 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.62 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.62 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.62 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.62 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.62 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.62 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.62 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.62 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.62 590.70/152.62 Q is empty. 590.70/152.62 We have to consider all minimal (P,Q,R)-chains. 590.70/152.62 ---------------------------------------- 590.70/152.62 590.70/152.62 (55) TransformationProof (EQUIVALENT) 590.70/152.62 By narrowing [LPAR04] the rule 0^1(1(2(4(x1)))) -> 1^1(4(x1)) at position [0] we obtained the following new rules [LPAR04]: 590.70/152.62 590.70/152.62 (0^1(1(2(4(1(1(0(1(x0)))))))) -> 1^1(5(0(4(1(1(1(x0))))))),0^1(1(2(4(1(1(0(1(x0)))))))) -> 1^1(5(0(4(1(1(1(x0)))))))) 590.70/152.62 (0^1(1(2(4(0(1(2(4(x0)))))))) -> 1^1(4(0(2(2(1(4(x0))))))),0^1(1(2(4(0(1(2(4(x0)))))))) -> 1^1(4(0(2(2(1(4(x0)))))))) 590.70/152.62 (0^1(1(2(4(0(1(2(4(x0)))))))) -> 1^1(0(4(2(5(1(4(x0))))))),0^1(1(2(4(0(1(2(4(x0)))))))) -> 1^1(0(4(2(5(1(4(x0)))))))) 590.70/152.62 590.70/152.62 590.70/152.62 ---------------------------------------- 590.70/152.62 590.70/152.62 (56) 590.70/152.62 Obligation: 590.70/152.62 Q DP problem: 590.70/152.62 The TRS P consists of the following rules: 590.70/152.62 590.70/152.62 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.62 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.62 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.62 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.62 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.62 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.62 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.62 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.62 0^1(1(4(4(x1)))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(4(x1)))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(4(4(x1)))) -> 0^1(4(1(4(x1)))) 590.70/152.62 0^1(1(4(4(x1)))) -> 4^1(1(4(x1))) 590.70/152.62 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.62 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.62 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.62 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.62 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.62 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(4(1(1(0(1(x0)))))))) -> 1^1(5(0(4(1(1(1(x0))))))) 590.70/152.62 0^1(1(2(4(0(1(2(4(x0)))))))) -> 1^1(4(0(2(2(1(4(x0))))))) 590.70/152.62 0^1(1(2(4(0(1(2(4(x0)))))))) -> 1^1(0(4(2(5(1(4(x0))))))) 590.70/152.62 590.70/152.62 The TRS R consists of the following rules: 590.70/152.62 590.70/152.62 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.62 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.62 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.62 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.62 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.62 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.62 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.62 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.62 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.62 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.62 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.62 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.62 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.62 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.62 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.62 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.62 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.62 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.62 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.62 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.62 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.62 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.62 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.62 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.62 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.62 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.62 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.62 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.62 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.62 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.62 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.62 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.62 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.62 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.62 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.62 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.62 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.62 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.62 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.62 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.62 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.62 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.62 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.62 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.62 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.62 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.62 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.62 590.70/152.62 Q is empty. 590.70/152.62 We have to consider all minimal (P,Q,R)-chains. 590.70/152.62 ---------------------------------------- 590.70/152.62 590.70/152.62 (57) DependencyGraphProof (EQUIVALENT) 590.70/152.62 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes. 590.70/152.62 ---------------------------------------- 590.70/152.62 590.70/152.62 (58) 590.70/152.62 Obligation: 590.70/152.62 Q DP problem: 590.70/152.62 The TRS P consists of the following rules: 590.70/152.62 590.70/152.62 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.62 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.62 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.62 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.62 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.62 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.62 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.62 0^1(1(4(4(x1)))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(4(x1)))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(4(4(x1)))) -> 0^1(4(1(4(x1)))) 590.70/152.62 0^1(1(4(4(x1)))) -> 4^1(1(4(x1))) 590.70/152.62 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.62 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.62 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.62 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.62 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.62 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 590.70/152.62 The TRS R consists of the following rules: 590.70/152.62 590.70/152.62 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.62 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.62 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.62 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.62 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.62 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.62 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.62 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.62 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.62 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.62 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.62 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.62 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.62 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.62 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.62 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.62 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.62 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.62 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.62 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.62 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.62 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.62 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.62 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.62 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.62 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.62 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.62 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.62 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.62 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.62 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.62 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.62 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.62 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.62 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.62 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.62 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.62 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.62 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.62 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.62 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.62 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.62 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.62 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.62 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.62 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.62 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.62 590.70/152.62 Q is empty. 590.70/152.62 We have to consider all minimal (P,Q,R)-chains. 590.70/152.62 ---------------------------------------- 590.70/152.62 590.70/152.62 (59) TransformationProof (EQUIVALENT) 590.70/152.62 By narrowing [LPAR04] the rule 0^1(1(4(4(x1)))) -> 0^1(4(x1)) at position [0] we obtained the following new rules [LPAR04]: 590.70/152.62 590.70/152.62 (0^1(1(4(4(1(1(0(1(x0)))))))) -> 0^1(5(0(4(1(1(1(x0))))))),0^1(1(4(4(1(1(0(1(x0)))))))) -> 0^1(5(0(4(1(1(1(x0)))))))) 590.70/152.62 (0^1(1(4(4(0(1(2(4(x0)))))))) -> 0^1(4(0(2(2(1(4(x0))))))),0^1(1(4(4(0(1(2(4(x0)))))))) -> 0^1(4(0(2(2(1(4(x0)))))))) 590.70/152.62 (0^1(1(4(4(0(1(2(4(x0)))))))) -> 0^1(0(4(2(5(1(4(x0))))))),0^1(1(4(4(0(1(2(4(x0)))))))) -> 0^1(0(4(2(5(1(4(x0)))))))) 590.70/152.62 590.70/152.62 590.70/152.62 ---------------------------------------- 590.70/152.62 590.70/152.62 (60) 590.70/152.62 Obligation: 590.70/152.62 Q DP problem: 590.70/152.62 The TRS P consists of the following rules: 590.70/152.62 590.70/152.62 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.62 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.62 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.62 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.62 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.62 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.62 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.62 0^1(1(4(4(x1)))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(4(4(x1)))) -> 0^1(4(1(4(x1)))) 590.70/152.62 0^1(1(4(4(x1)))) -> 4^1(1(4(x1))) 590.70/152.62 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.62 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.62 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.62 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.62 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.62 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(4(4(1(1(0(1(x0)))))))) -> 0^1(5(0(4(1(1(1(x0))))))) 590.70/152.62 0^1(1(4(4(0(1(2(4(x0)))))))) -> 0^1(4(0(2(2(1(4(x0))))))) 590.70/152.62 0^1(1(4(4(0(1(2(4(x0)))))))) -> 0^1(0(4(2(5(1(4(x0))))))) 590.70/152.62 590.70/152.62 The TRS R consists of the following rules: 590.70/152.62 590.70/152.62 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.62 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.62 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.62 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.62 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.62 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.62 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.62 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.62 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.62 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.62 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.62 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.62 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.62 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.62 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.62 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.62 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.62 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.62 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.62 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.62 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.62 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.62 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.62 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.62 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.62 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.62 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.62 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.62 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.62 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.62 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.62 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.62 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.62 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.62 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.62 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.62 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.62 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.62 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.62 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.62 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.62 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.62 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.62 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.62 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.62 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.62 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.62 590.70/152.62 Q is empty. 590.70/152.62 We have to consider all minimal (P,Q,R)-chains. 590.70/152.62 ---------------------------------------- 590.70/152.62 590.70/152.62 (61) DependencyGraphProof (EQUIVALENT) 590.70/152.62 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes. 590.70/152.62 ---------------------------------------- 590.70/152.62 590.70/152.62 (62) 590.70/152.62 Obligation: 590.70/152.62 Q DP problem: 590.70/152.62 The TRS P consists of the following rules: 590.70/152.62 590.70/152.62 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.62 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.62 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.62 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.62 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.62 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.62 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.62 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.62 0^1(1(4(4(x1)))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(4(4(x1)))) -> 0^1(4(1(4(x1)))) 590.70/152.62 0^1(1(4(4(x1)))) -> 4^1(1(4(x1))) 590.70/152.62 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.62 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.62 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.62 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.62 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.62 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 590.70/152.62 The TRS R consists of the following rules: 590.70/152.62 590.70/152.62 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.62 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.62 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.62 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.62 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.62 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.62 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.62 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.62 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.62 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.62 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.62 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.62 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.62 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.62 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.62 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.62 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.62 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.62 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.62 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.62 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.62 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.62 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.62 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.62 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.62 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.62 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.62 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.62 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.62 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.62 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.62 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.62 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.62 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.62 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.62 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.62 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.62 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.62 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.62 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.62 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.62 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.62 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.62 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.62 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.62 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.62 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.62 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.62 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.62 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.62 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.62 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.62 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.62 590.70/152.62 Q is empty. 590.70/152.62 We have to consider all minimal (P,Q,R)-chains. 590.70/152.62 ---------------------------------------- 590.70/152.62 590.70/152.62 (63) TransformationProof (EQUIVALENT) 590.70/152.62 By narrowing [LPAR04] the rule 0^1(1(4(4(x1)))) -> 1^1(4(x1)) at position [0] we obtained the following new rules [LPAR04]: 590.70/152.62 590.70/152.62 (0^1(1(4(4(1(1(0(1(x0)))))))) -> 1^1(5(0(4(1(1(1(x0))))))),0^1(1(4(4(1(1(0(1(x0)))))))) -> 1^1(5(0(4(1(1(1(x0)))))))) 590.70/152.62 (0^1(1(4(4(0(1(2(4(x0)))))))) -> 1^1(4(0(2(2(1(4(x0))))))),0^1(1(4(4(0(1(2(4(x0)))))))) -> 1^1(4(0(2(2(1(4(x0)))))))) 590.70/152.62 (0^1(1(4(4(0(1(2(4(x0)))))))) -> 1^1(0(4(2(5(1(4(x0))))))),0^1(1(4(4(0(1(2(4(x0)))))))) -> 1^1(0(4(2(5(1(4(x0)))))))) 590.70/152.62 590.70/152.62 590.70/152.62 ---------------------------------------- 590.70/152.62 590.70/152.62 (64) 590.70/152.62 Obligation: 590.70/152.62 Q DP problem: 590.70/152.62 The TRS P consists of the following rules: 590.70/152.62 590.70/152.62 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.62 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.62 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.62 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.62 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.62 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.62 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.62 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.62 0^1(1(4(4(x1)))) -> 0^1(4(1(4(x1)))) 590.70/152.62 0^1(1(4(4(x1)))) -> 4^1(1(4(x1))) 590.70/152.62 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.62 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.62 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.62 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.62 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.62 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.63 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.63 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.63 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.63 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.63 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.63 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.63 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.63 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.63 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.63 0^1(1(4(4(1(1(0(1(x0)))))))) -> 1^1(5(0(4(1(1(1(x0))))))) 590.70/152.63 0^1(1(4(4(0(1(2(4(x0)))))))) -> 1^1(4(0(2(2(1(4(x0))))))) 590.70/152.63 0^1(1(4(4(0(1(2(4(x0)))))))) -> 1^1(0(4(2(5(1(4(x0))))))) 590.70/152.63 590.70/152.63 The TRS R consists of the following rules: 590.70/152.63 590.70/152.63 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.63 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.63 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.63 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.63 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.63 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.63 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.63 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.63 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.63 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.63 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.64 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.64 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.64 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.64 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.64 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.64 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.64 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.64 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.64 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.64 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.64 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.64 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.64 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.64 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.64 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.64 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.64 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.64 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.64 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.64 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.64 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.64 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.64 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.64 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.64 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.64 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.64 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.64 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.64 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.64 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.64 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.64 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.64 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.64 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.64 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.64 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.64 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.64 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.64 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.64 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.64 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.64 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.64 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.64 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.64 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.64 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.64 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.64 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.64 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.64 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.64 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.64 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.64 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.64 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.64 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.64 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.64 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.64 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.64 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.64 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.64 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.64 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.64 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.64 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.64 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.64 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.64 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.64 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.64 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.64 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.64 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.65 590.70/152.65 Q is empty. 590.70/152.65 We have to consider all minimal (P,Q,R)-chains. 590.70/152.65 ---------------------------------------- 590.70/152.65 590.70/152.65 (65) DependencyGraphProof (EQUIVALENT) 590.70/152.65 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes. 590.70/152.65 ---------------------------------------- 590.70/152.65 590.70/152.65 (66) 590.70/152.65 Obligation: 590.70/152.65 Q DP problem: 590.70/152.65 The TRS P consists of the following rules: 590.70/152.65 590.70/152.65 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.65 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.65 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.65 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.65 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.65 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.65 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.65 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.65 0^1(1(4(4(x1)))) -> 0^1(4(1(4(x1)))) 590.70/152.65 0^1(1(4(4(x1)))) -> 4^1(1(4(x1))) 590.70/152.65 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.65 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.65 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.65 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.65 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.65 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.65 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.65 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.65 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.65 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.65 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.65 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 590.70/152.65 The TRS R consists of the following rules: 590.70/152.65 590.70/152.65 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.65 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.65 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.65 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.65 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.65 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.65 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.65 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.65 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.65 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.65 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.65 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.65 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.65 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.65 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.65 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.65 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.65 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.65 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.65 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.65 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.65 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.65 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.65 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.65 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.65 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.65 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.65 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.65 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.65 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.65 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.65 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.65 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.65 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.65 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.65 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.65 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.65 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.65 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.65 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.65 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.65 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.65 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.65 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.65 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.65 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.65 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.65 590.70/152.65 Q is empty. 590.70/152.65 We have to consider all minimal (P,Q,R)-chains. 590.70/152.65 ---------------------------------------- 590.70/152.65 590.70/152.65 (67) TransformationProof (EQUIVALENT) 590.70/152.65 By narrowing [LPAR04] the rule 0^1(1(4(4(x1)))) -> 0^1(4(1(4(x1)))) at position [0] we obtained the following new rules [LPAR04]: 590.70/152.65 590.70/152.65 (0^1(1(4(4(1(1(0(1(x0)))))))) -> 0^1(4(1(5(0(4(1(1(1(x0))))))))),0^1(1(4(4(1(1(0(1(x0)))))))) -> 0^1(4(1(5(0(4(1(1(1(x0)))))))))) 590.70/152.65 (0^1(1(4(4(0(1(2(4(x0)))))))) -> 0^1(4(1(4(0(2(2(1(4(x0))))))))),0^1(1(4(4(0(1(2(4(x0)))))))) -> 0^1(4(1(4(0(2(2(1(4(x0)))))))))) 590.70/152.65 (0^1(1(4(4(0(1(2(4(x0)))))))) -> 0^1(4(1(0(4(2(5(1(4(x0))))))))),0^1(1(4(4(0(1(2(4(x0)))))))) -> 0^1(4(1(0(4(2(5(1(4(x0)))))))))) 590.70/152.65 590.70/152.65 590.70/152.65 ---------------------------------------- 590.70/152.65 590.70/152.65 (68) 590.70/152.65 Obligation: 590.70/152.65 Q DP problem: 590.70/152.65 The TRS P consists of the following rules: 590.70/152.65 590.70/152.65 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.65 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.65 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.65 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.65 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.65 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.65 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.65 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.65 0^1(1(4(4(x1)))) -> 4^1(1(4(x1))) 590.70/152.65 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.65 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.65 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.65 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.65 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.65 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.65 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.65 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.65 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.65 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.65 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.65 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(4(4(1(1(0(1(x0)))))))) -> 0^1(4(1(5(0(4(1(1(1(x0))))))))) 590.70/152.65 0^1(1(4(4(0(1(2(4(x0)))))))) -> 0^1(4(1(4(0(2(2(1(4(x0))))))))) 590.70/152.65 0^1(1(4(4(0(1(2(4(x0)))))))) -> 0^1(4(1(0(4(2(5(1(4(x0))))))))) 590.70/152.65 590.70/152.65 The TRS R consists of the following rules: 590.70/152.65 590.70/152.65 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.65 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.65 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.65 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.65 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.65 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.65 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.65 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.65 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.65 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.65 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.65 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.65 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.65 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.65 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.65 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.65 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.65 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.65 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.65 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.65 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.65 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.65 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.65 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.65 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.65 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.65 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.65 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.65 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.65 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.65 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.65 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.65 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.65 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.65 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.65 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.65 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.65 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.65 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.65 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.65 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.65 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.65 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.65 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.65 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.65 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.65 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.65 590.70/152.65 Q is empty. 590.70/152.65 We have to consider all minimal (P,Q,R)-chains. 590.70/152.65 ---------------------------------------- 590.70/152.65 590.70/152.65 (69) DependencyGraphProof (EQUIVALENT) 590.70/152.65 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes. 590.70/152.65 ---------------------------------------- 590.70/152.65 590.70/152.65 (70) 590.70/152.65 Obligation: 590.70/152.65 Q DP problem: 590.70/152.65 The TRS P consists of the following rules: 590.70/152.65 590.70/152.65 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.65 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.65 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.65 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.65 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.65 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.65 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.65 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.65 0^1(1(4(4(x1)))) -> 4^1(1(4(x1))) 590.70/152.65 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.65 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.65 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.65 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.65 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.65 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.65 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.65 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.65 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.65 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.65 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.65 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 590.70/152.65 The TRS R consists of the following rules: 590.70/152.65 590.70/152.65 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.65 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.65 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.65 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.65 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.65 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.65 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.65 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.65 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.65 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.65 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.65 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.65 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.65 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.65 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.65 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.65 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.65 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.65 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.65 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.65 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.65 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.65 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.65 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.65 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.65 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.65 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.65 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.65 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.65 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.65 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.65 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.65 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.65 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.65 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.65 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.65 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.65 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.65 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.65 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.65 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.65 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.65 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.65 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.65 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.65 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.65 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.65 590.70/152.65 Q is empty. 590.70/152.65 We have to consider all minimal (P,Q,R)-chains. 590.70/152.65 ---------------------------------------- 590.70/152.65 590.70/152.65 (71) TransformationProof (EQUIVALENT) 590.70/152.65 By narrowing [LPAR04] the rule 0^1(1(4(4(x1)))) -> 4^1(1(4(x1))) at position [0] we obtained the following new rules [LPAR04]: 590.70/152.65 590.70/152.65 (0^1(1(4(4(1(1(0(1(x0)))))))) -> 4^1(1(5(0(4(1(1(1(x0)))))))),0^1(1(4(4(1(1(0(1(x0)))))))) -> 4^1(1(5(0(4(1(1(1(x0))))))))) 590.70/152.65 (0^1(1(4(4(0(1(2(4(x0)))))))) -> 4^1(1(4(0(2(2(1(4(x0)))))))),0^1(1(4(4(0(1(2(4(x0)))))))) -> 4^1(1(4(0(2(2(1(4(x0))))))))) 590.70/152.65 (0^1(1(4(4(0(1(2(4(x0)))))))) -> 4^1(1(0(4(2(5(1(4(x0)))))))),0^1(1(4(4(0(1(2(4(x0)))))))) -> 4^1(1(0(4(2(5(1(4(x0))))))))) 590.70/152.65 590.70/152.65 590.70/152.65 ---------------------------------------- 590.70/152.65 590.70/152.65 (72) 590.70/152.65 Obligation: 590.70/152.65 Q DP problem: 590.70/152.65 The TRS P consists of the following rules: 590.70/152.65 590.70/152.65 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.65 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.65 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.65 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.65 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.65 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.65 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.65 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.65 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.65 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.65 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.65 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.65 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.65 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.65 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.65 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.65 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.65 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.65 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.65 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(4(4(1(1(0(1(x0)))))))) -> 4^1(1(5(0(4(1(1(1(x0)))))))) 590.70/152.65 0^1(1(4(4(0(1(2(4(x0)))))))) -> 4^1(1(4(0(2(2(1(4(x0)))))))) 590.70/152.65 0^1(1(4(4(0(1(2(4(x0)))))))) -> 4^1(1(0(4(2(5(1(4(x0)))))))) 590.70/152.65 590.70/152.65 The TRS R consists of the following rules: 590.70/152.65 590.70/152.65 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.65 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.65 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.65 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.65 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.65 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.65 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.65 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.65 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.65 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.65 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.65 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.65 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.65 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.65 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.65 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.65 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.65 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.65 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.65 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.65 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.65 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.65 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.65 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.65 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.65 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.65 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.65 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.65 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.65 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.65 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.65 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.65 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.65 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.65 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.65 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.65 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.65 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.65 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.65 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.65 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.65 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.65 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.65 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.65 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.65 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.65 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.65 590.70/152.65 Q is empty. 590.70/152.65 We have to consider all minimal (P,Q,R)-chains. 590.70/152.65 ---------------------------------------- 590.70/152.65 590.70/152.65 (73) DependencyGraphProof (EQUIVALENT) 590.70/152.65 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes. 590.70/152.65 ---------------------------------------- 590.70/152.65 590.70/152.65 (74) 590.70/152.65 Obligation: 590.70/152.65 Q DP problem: 590.70/152.65 The TRS P consists of the following rules: 590.70/152.65 590.70/152.65 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.65 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.65 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.65 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.65 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.65 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.65 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.65 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.65 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.65 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.65 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.65 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.65 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.65 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.65 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.65 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.65 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.65 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.65 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.65 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.65 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 590.70/152.65 The TRS R consists of the following rules: 590.70/152.65 590.70/152.65 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.65 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.65 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.65 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.65 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.65 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.65 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.65 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.65 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.65 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.65 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.65 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.65 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.65 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.65 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.65 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.65 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.65 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.65 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.65 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.65 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.65 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.65 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.65 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.65 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.65 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.65 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.65 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.65 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.65 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.65 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.65 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.65 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.65 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.65 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.65 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.65 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.65 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.65 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.65 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.65 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.65 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.65 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.65 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.65 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.65 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.65 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.65 590.70/152.65 Q is empty. 590.70/152.65 We have to consider all minimal (P,Q,R)-chains. 590.70/152.65 ---------------------------------------- 590.70/152.65 590.70/152.65 (75) TransformationProof (EQUIVALENT) 590.70/152.65 By narrowing [LPAR04] the rule 0^1(1(2(4(0(x1))))) -> 0^1(4(x1)) at position [0] we obtained the following new rules [LPAR04]: 590.70/152.65 590.70/152.65 (0^1(1(2(4(0(1(1(0(1(x0))))))))) -> 0^1(5(0(4(1(1(1(x0))))))),0^1(1(2(4(0(1(1(0(1(x0))))))))) -> 0^1(5(0(4(1(1(1(x0)))))))) 590.70/152.65 (0^1(1(2(4(0(0(1(2(4(x0))))))))) -> 0^1(4(0(2(2(1(4(x0))))))),0^1(1(2(4(0(0(1(2(4(x0))))))))) -> 0^1(4(0(2(2(1(4(x0)))))))) 590.70/152.65 (0^1(1(2(4(0(0(1(2(4(x0))))))))) -> 0^1(0(4(2(5(1(4(x0))))))),0^1(1(2(4(0(0(1(2(4(x0))))))))) -> 0^1(0(4(2(5(1(4(x0)))))))) 590.70/152.65 590.70/152.65 590.70/152.65 ---------------------------------------- 590.70/152.65 590.70/152.65 (76) 590.70/152.65 Obligation: 590.70/152.65 Q DP problem: 590.70/152.65 The TRS P consists of the following rules: 590.70/152.65 590.70/152.65 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.65 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.65 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.65 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.65 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.65 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.65 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.65 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.65 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.65 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.65 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.65 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.65 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.65 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.65 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.65 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.65 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.65 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.65 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.65 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.65 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(2(4(0(1(1(0(1(x0))))))))) -> 0^1(5(0(4(1(1(1(x0))))))) 590.70/152.65 0^1(1(2(4(0(0(1(2(4(x0))))))))) -> 0^1(4(0(2(2(1(4(x0))))))) 590.70/152.65 0^1(1(2(4(0(0(1(2(4(x0))))))))) -> 0^1(0(4(2(5(1(4(x0))))))) 590.70/152.65 590.70/152.65 The TRS R consists of the following rules: 590.70/152.65 590.70/152.65 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.65 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.65 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.65 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.65 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.65 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.65 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.65 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.65 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.65 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.65 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.65 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.65 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.65 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.65 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.65 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.65 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.65 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.65 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.65 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.65 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.65 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.65 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.65 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.65 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.65 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.65 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.65 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.65 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.65 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.65 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.65 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.65 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.65 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.65 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.65 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.65 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.65 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.65 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.65 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.65 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.65 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.65 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.65 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.65 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.65 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.65 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.65 590.70/152.65 Q is empty. 590.70/152.65 We have to consider all minimal (P,Q,R)-chains. 590.70/152.65 ---------------------------------------- 590.70/152.65 590.70/152.65 (77) DependencyGraphProof (EQUIVALENT) 590.70/152.65 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes. 590.70/152.65 ---------------------------------------- 590.70/152.65 590.70/152.65 (78) 590.70/152.65 Obligation: 590.70/152.65 Q DP problem: 590.70/152.65 The TRS P consists of the following rules: 590.70/152.65 590.70/152.65 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.65 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.65 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.65 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.65 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.65 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.65 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.65 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.65 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.65 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.65 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.65 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.65 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.65 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.65 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.65 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.65 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.65 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.65 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.65 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.65 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 590.70/152.65 The TRS R consists of the following rules: 590.70/152.65 590.70/152.65 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.65 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.65 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.65 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.65 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.65 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.65 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.65 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.65 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.65 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.65 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.65 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.65 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.65 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.65 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.65 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.65 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.65 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.65 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.65 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.65 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.65 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.65 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.65 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.65 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.65 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.65 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.65 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.65 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.65 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.65 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.65 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.65 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.65 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.65 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.65 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.65 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.65 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.65 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.65 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.65 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.65 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.65 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.65 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.65 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.65 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.65 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.65 590.70/152.65 Q is empty. 590.70/152.65 We have to consider all minimal (P,Q,R)-chains. 590.70/152.65 ---------------------------------------- 590.70/152.65 590.70/152.65 (79) TransformationProof (EQUIVALENT) 590.70/152.65 By narrowing [LPAR04] the rule 4^1(0(1(2(4(x1))))) -> 1^1(4(x1)) at position [0] we obtained the following new rules [LPAR04]: 590.70/152.65 590.70/152.65 (4^1(0(1(2(4(1(1(0(1(x0))))))))) -> 1^1(5(0(4(1(1(1(x0))))))),4^1(0(1(2(4(1(1(0(1(x0))))))))) -> 1^1(5(0(4(1(1(1(x0)))))))) 590.70/152.65 (4^1(0(1(2(4(0(1(2(4(x0))))))))) -> 1^1(4(0(2(2(1(4(x0))))))),4^1(0(1(2(4(0(1(2(4(x0))))))))) -> 1^1(4(0(2(2(1(4(x0)))))))) 590.70/152.65 (4^1(0(1(2(4(0(1(2(4(x0))))))))) -> 1^1(0(4(2(5(1(4(x0))))))),4^1(0(1(2(4(0(1(2(4(x0))))))))) -> 1^1(0(4(2(5(1(4(x0)))))))) 590.70/152.65 590.70/152.65 590.70/152.65 ---------------------------------------- 590.70/152.65 590.70/152.65 (80) 590.70/152.65 Obligation: 590.70/152.65 Q DP problem: 590.70/152.65 The TRS P consists of the following rules: 590.70/152.65 590.70/152.65 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.65 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.65 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.65 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.65 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.65 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.65 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.65 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.65 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 4^1(x1) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 4^1(4(1(x1))) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 4^1(1(x1)) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 4^1(x1) 590.70/152.65 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(0(1(x1))))) -> 4^1(x1) 590.70/152.65 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(2(4(1(x1))))) -> 4^1(x1) 590.70/152.65 0^1(1(0(1(4(x1))))) -> 4^1(0(1(x1))) 590.70/152.65 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.65 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(0(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.65 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(0(1(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.65 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 4^1(1(2(x1))) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 4^1(4(1(x1))) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 4^1(1(x1)) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.65 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.65 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.65 0^1(1(4(5(4(x1))))) -> 4^1(1(4(x1))) 590.70/152.65 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 4^1(0(1(2(4(1(1(0(1(x0))))))))) -> 1^1(5(0(4(1(1(1(x0))))))) 590.70/152.65 4^1(0(1(2(4(0(1(2(4(x0))))))))) -> 1^1(4(0(2(2(1(4(x0))))))) 590.70/152.65 4^1(0(1(2(4(0(1(2(4(x0))))))))) -> 1^1(0(4(2(5(1(4(x0))))))) 590.70/152.65 590.70/152.65 The TRS R consists of the following rules: 590.70/152.65 590.70/152.65 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.65 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.65 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.65 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.65 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.65 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.65 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.65 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.65 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.65 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.65 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.65 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.65 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.65 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.65 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.65 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.65 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.65 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.65 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.65 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.65 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.65 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.65 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.65 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.65 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.65 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.65 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.65 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.65 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.65 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.65 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.65 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.65 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.65 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.65 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.65 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.65 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.65 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.65 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.65 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.65 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.65 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.65 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.65 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.65 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.65 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.65 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.65 590.70/152.65 Q is empty. 590.70/152.65 We have to consider all minimal (P,Q,R)-chains. 590.70/152.65 ---------------------------------------- 590.70/152.65 590.70/152.65 (81) DependencyGraphProof (EQUIVALENT) 590.70/152.65 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 18 less nodes. 590.70/152.65 ---------------------------------------- 590.70/152.65 590.70/152.65 (82) 590.70/152.65 Obligation: 590.70/152.65 Q DP problem: 590.70/152.65 The TRS P consists of the following rules: 590.70/152.65 590.70/152.65 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.65 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.65 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.65 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.65 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.65 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.65 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.65 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.65 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.65 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.65 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.65 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 590.70/152.65 The TRS R consists of the following rules: 590.70/152.65 590.70/152.65 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.65 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.65 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.65 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.65 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.65 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.65 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.65 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.65 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.65 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.65 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.65 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.65 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.65 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.65 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.65 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.65 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.65 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.65 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.65 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.65 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.65 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.65 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.65 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.65 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.65 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.65 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.65 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.65 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.65 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.65 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.65 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.65 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.65 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.65 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.65 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.65 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.65 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.65 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.65 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.65 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.65 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.65 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.65 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.65 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.65 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.65 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.65 590.70/152.65 Q is empty. 590.70/152.65 We have to consider all minimal (P,Q,R)-chains. 590.70/152.65 ---------------------------------------- 590.70/152.65 590.70/152.65 (83) TransformationProof (EQUIVALENT) 590.70/152.65 By narrowing [LPAR04] the rule 0^1(1(4(4(0(x1))))) -> 0^1(4(4(1(x1)))) at position [0] we obtained the following new rules [LPAR04]: 590.70/152.65 590.70/152.65 (0^1(1(4(4(0(1(0(1(x0)))))))) -> 0^1(4(5(0(4(1(1(1(x0)))))))),0^1(1(4(4(0(1(0(1(x0)))))))) -> 0^1(4(5(0(4(1(1(1(x0))))))))) 590.70/152.65 (0^1(1(4(4(0(0(1(0(x0)))))))) -> 0^1(4(4(2(0(3(0(1(1(x0))))))))),0^1(1(4(4(0(0(1(0(x0)))))))) -> 0^1(4(4(2(0(3(0(1(1(x0)))))))))) 590.70/152.65 (0^1(1(4(4(0(0(0(3(1(x0))))))))) -> 0^1(4(4(3(0(1(5(1(0(x0))))))))),0^1(1(4(4(0(0(0(3(1(x0))))))))) -> 0^1(4(4(3(0(1(5(1(0(x0)))))))))) 590.70/152.65 (0^1(1(4(4(0(0(1(2(4(x0))))))))) -> 0^1(4(4(5(1(4(0(2(1(x0))))))))),0^1(1(4(4(0(0(1(2(4(x0))))))))) -> 0^1(4(4(5(1(4(0(2(1(x0)))))))))) 590.70/152.65 (0^1(1(4(4(0(2(1(3(4(x0))))))))) -> 0^1(4(4(1(4(1(2(2(3(x0))))))))),0^1(1(4(4(0(2(1(3(4(x0))))))))) -> 0^1(4(4(1(4(1(2(2(3(x0)))))))))) 590.70/152.65 (0^1(1(4(4(0(0(1(4(4(x0))))))))) -> 0^1(4(4(1(4(1(3(0(4(x0))))))))),0^1(1(4(4(0(0(1(4(4(x0))))))))) -> 0^1(4(4(1(4(1(3(0(4(x0)))))))))) 590.70/152.65 590.70/152.65 590.70/152.65 ---------------------------------------- 590.70/152.65 590.70/152.65 (84) 590.70/152.65 Obligation: 590.70/152.65 Q DP problem: 590.70/152.65 The TRS P consists of the following rules: 590.70/152.65 590.70/152.65 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.65 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.65 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.65 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.65 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.65 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.65 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.65 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.65 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.65 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.65 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.65 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(4(4(0(1(0(1(x0)))))))) -> 0^1(4(5(0(4(1(1(1(x0)))))))) 590.70/152.65 0^1(1(4(4(0(0(1(0(x0)))))))) -> 0^1(4(4(2(0(3(0(1(1(x0))))))))) 590.70/152.65 0^1(1(4(4(0(0(0(3(1(x0))))))))) -> 0^1(4(4(3(0(1(5(1(0(x0))))))))) 590.70/152.65 0^1(1(4(4(0(0(1(2(4(x0))))))))) -> 0^1(4(4(5(1(4(0(2(1(x0))))))))) 590.70/152.65 0^1(1(4(4(0(2(1(3(4(x0))))))))) -> 0^1(4(4(1(4(1(2(2(3(x0))))))))) 590.70/152.65 0^1(1(4(4(0(0(1(4(4(x0))))))))) -> 0^1(4(4(1(4(1(3(0(4(x0))))))))) 590.70/152.65 590.70/152.65 The TRS R consists of the following rules: 590.70/152.65 590.70/152.65 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.65 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.65 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.65 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.65 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.65 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.65 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.65 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.65 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.65 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.65 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.65 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.65 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.65 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.65 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.65 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.65 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.65 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.65 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.65 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.65 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.65 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.65 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.65 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.65 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.65 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.65 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.65 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.65 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.65 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.65 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.65 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.65 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.65 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.65 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.65 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.65 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.65 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.65 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.65 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.65 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.65 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.65 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.65 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.65 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.65 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.65 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.65 590.70/152.65 Q is empty. 590.70/152.65 We have to consider all minimal (P,Q,R)-chains. 590.70/152.65 ---------------------------------------- 590.70/152.65 590.70/152.65 (85) DependencyGraphProof (EQUIVALENT) 590.70/152.65 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 6 less nodes. 590.70/152.65 ---------------------------------------- 590.70/152.65 590.70/152.65 (86) 590.70/152.65 Obligation: 590.70/152.65 Q DP problem: 590.70/152.65 The TRS P consists of the following rules: 590.70/152.65 590.70/152.65 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.65 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.65 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.65 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.65 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.65 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.65 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.65 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.65 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.65 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.65 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.65 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 590.70/152.65 The TRS R consists of the following rules: 590.70/152.65 590.70/152.65 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.65 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.65 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.65 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.65 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.65 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.65 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.65 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.65 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.65 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.65 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.65 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.65 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.65 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.65 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.65 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.65 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.65 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.65 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.65 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.65 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.65 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.65 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.65 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.65 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.65 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.65 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.65 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.65 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.65 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.65 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.65 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.65 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.65 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.65 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.65 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.65 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.65 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.65 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.65 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.65 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.65 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.65 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.65 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.65 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.65 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.65 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.65 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.65 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.65 590.70/152.65 Q is empty. 590.70/152.65 We have to consider all minimal (P,Q,R)-chains. 590.70/152.65 ---------------------------------------- 590.70/152.65 590.70/152.65 (87) TransformationProof (EQUIVALENT) 590.70/152.65 By narrowing [LPAR04] the rule 0^1(1(4(4(0(x1))))) -> 1^1(0(4(x1))) at position [0] we obtained the following new rules [LPAR04]: 590.70/152.65 590.70/152.65 (0^1(1(4(4(0(1(1(0(1(x0))))))))) -> 1^1(0(5(0(4(1(1(1(x0)))))))),0^1(1(4(4(0(1(1(0(1(x0))))))))) -> 1^1(0(5(0(4(1(1(1(x0))))))))) 590.70/152.65 (0^1(1(4(4(0(0(1(2(4(x0))))))))) -> 1^1(0(4(0(2(2(1(4(x0)))))))),0^1(1(4(4(0(0(1(2(4(x0))))))))) -> 1^1(0(4(0(2(2(1(4(x0))))))))) 590.70/152.65 (0^1(1(4(4(0(0(1(2(4(x0))))))))) -> 1^1(0(0(4(2(5(1(4(x0)))))))),0^1(1(4(4(0(0(1(2(4(x0))))))))) -> 1^1(0(0(4(2(5(1(4(x0))))))))) 590.70/152.65 590.70/152.65 590.70/152.65 ---------------------------------------- 590.70/152.65 590.70/152.65 (88) 590.70/152.65 Obligation: 590.70/152.65 Q DP problem: 590.70/152.65 The TRS P consists of the following rules: 590.70/152.65 590.70/152.65 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.65 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.65 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.65 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.65 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.65 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.65 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.65 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.65 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.65 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.65 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.65 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.65 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.65 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.65 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.65 0^1(1(4(4(0(1(1(0(1(x0))))))))) -> 1^1(0(5(0(4(1(1(1(x0)))))))) 590.70/152.65 0^1(1(4(4(0(0(1(2(4(x0))))))))) -> 1^1(0(4(0(2(2(1(4(x0)))))))) 590.70/152.65 0^1(1(4(4(0(0(1(2(4(x0))))))))) -> 1^1(0(0(4(2(5(1(4(x0)))))))) 590.70/152.65 590.70/152.65 The TRS R consists of the following rules: 590.70/152.65 590.70/152.65 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.65 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.65 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.65 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.65 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.65 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.65 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.65 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.65 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.65 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.65 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.65 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.65 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.65 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.66 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.66 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.66 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.66 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.66 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.66 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.66 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.66 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.66 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.66 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.66 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.66 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.66 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.66 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.66 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.66 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.66 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.66 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.66 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.66 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.66 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.66 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.66 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.66 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.66 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.66 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.66 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.66 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.66 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.66 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.66 590.70/152.66 Q is empty. 590.70/152.66 We have to consider all minimal (P,Q,R)-chains. 590.70/152.66 ---------------------------------------- 590.70/152.66 590.70/152.66 (89) DependencyGraphProof (EQUIVALENT) 590.70/152.66 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes. 590.70/152.66 ---------------------------------------- 590.70/152.66 590.70/152.66 (90) 590.70/152.66 Obligation: 590.70/152.66 Q DP problem: 590.70/152.66 The TRS P consists of the following rules: 590.70/152.66 590.70/152.66 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.66 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.66 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.66 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.66 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.66 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.66 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.66 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.66 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.66 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.66 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.66 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.66 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.66 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.66 590.70/152.66 The TRS R consists of the following rules: 590.70/152.66 590.70/152.66 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.66 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.66 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.66 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.66 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.66 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.66 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.66 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.66 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.66 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.66 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.66 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.66 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.66 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.66 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.66 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.66 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.66 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.66 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.66 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.66 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.66 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.66 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.66 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.66 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.66 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.66 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.66 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.66 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.66 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.66 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.66 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.66 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.66 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.66 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.66 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.66 590.70/152.66 Q is empty. 590.70/152.66 We have to consider all minimal (P,Q,R)-chains. 590.70/152.66 ---------------------------------------- 590.70/152.66 590.70/152.66 (91) TransformationProof (EQUIVALENT) 590.70/152.66 By narrowing [LPAR04] the rule 0^1(1(4(4(0(x1))))) -> 0^1(4(x1)) at position [0] we obtained the following new rules [LPAR04]: 590.70/152.66 590.70/152.66 (0^1(1(4(4(0(1(1(0(1(x0))))))))) -> 0^1(5(0(4(1(1(1(x0))))))),0^1(1(4(4(0(1(1(0(1(x0))))))))) -> 0^1(5(0(4(1(1(1(x0)))))))) 590.70/152.66 (0^1(1(4(4(0(0(1(2(4(x0))))))))) -> 0^1(4(0(2(2(1(4(x0))))))),0^1(1(4(4(0(0(1(2(4(x0))))))))) -> 0^1(4(0(2(2(1(4(x0)))))))) 590.70/152.66 (0^1(1(4(4(0(0(1(2(4(x0))))))))) -> 0^1(0(4(2(5(1(4(x0))))))),0^1(1(4(4(0(0(1(2(4(x0))))))))) -> 0^1(0(4(2(5(1(4(x0)))))))) 590.70/152.66 590.70/152.66 590.70/152.66 ---------------------------------------- 590.70/152.66 590.70/152.66 (92) 590.70/152.66 Obligation: 590.70/152.66 Q DP problem: 590.70/152.66 The TRS P consists of the following rules: 590.70/152.66 590.70/152.66 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.66 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.66 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.66 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.66 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.66 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.66 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.66 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.66 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.66 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.66 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.66 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.66 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.66 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.66 0^1(1(4(4(0(1(1(0(1(x0))))))))) -> 0^1(5(0(4(1(1(1(x0))))))) 590.70/152.66 0^1(1(4(4(0(0(1(2(4(x0))))))))) -> 0^1(4(0(2(2(1(4(x0))))))) 590.70/152.66 0^1(1(4(4(0(0(1(2(4(x0))))))))) -> 0^1(0(4(2(5(1(4(x0))))))) 590.70/152.66 590.70/152.66 The TRS R consists of the following rules: 590.70/152.66 590.70/152.66 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.66 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.66 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.66 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.66 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.66 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.66 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.66 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.66 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.66 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.66 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.66 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.66 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.66 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.66 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.66 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.66 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.66 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.66 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.66 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.66 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.66 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.66 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.66 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.66 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.66 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.66 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.66 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.66 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.66 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.66 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.66 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.66 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.66 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.66 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.66 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.66 590.70/152.66 Q is empty. 590.70/152.66 We have to consider all minimal (P,Q,R)-chains. 590.70/152.66 ---------------------------------------- 590.70/152.66 590.70/152.66 (93) DependencyGraphProof (EQUIVALENT) 590.70/152.66 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes. 590.70/152.66 ---------------------------------------- 590.70/152.66 590.70/152.66 (94) 590.70/152.66 Obligation: 590.70/152.66 Q DP problem: 590.70/152.66 The TRS P consists of the following rules: 590.70/152.66 590.70/152.66 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.66 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.66 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.66 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.66 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.66 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.66 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.66 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.66 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.66 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.66 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.66 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.66 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.66 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.66 590.70/152.66 The TRS R consists of the following rules: 590.70/152.66 590.70/152.66 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.66 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.66 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.66 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.66 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.66 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.66 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.66 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.66 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.66 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.66 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.66 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.66 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.66 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.66 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.66 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.66 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.66 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.66 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.66 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.66 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.66 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.66 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.66 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.66 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.66 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.66 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.66 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.66 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.66 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.66 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.66 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.66 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.66 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.66 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.66 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.66 590.70/152.66 Q is empty. 590.70/152.66 We have to consider all minimal (P,Q,R)-chains. 590.70/152.66 ---------------------------------------- 590.70/152.66 590.70/152.66 (95) TransformationProof (EQUIVALENT) 590.70/152.66 By narrowing [LPAR04] the rule 0^1(1(4(0(1(x1))))) -> 0^1(4(x1)) at position [0] we obtained the following new rules [LPAR04]: 590.70/152.66 590.70/152.66 (0^1(1(4(0(1(1(1(0(1(x0))))))))) -> 0^1(5(0(4(1(1(1(x0))))))),0^1(1(4(0(1(1(1(0(1(x0))))))))) -> 0^1(5(0(4(1(1(1(x0)))))))) 590.70/152.66 (0^1(1(4(0(1(0(1(2(4(x0))))))))) -> 0^1(4(0(2(2(1(4(x0))))))),0^1(1(4(0(1(0(1(2(4(x0))))))))) -> 0^1(4(0(2(2(1(4(x0)))))))) 590.70/152.66 (0^1(1(4(0(1(0(1(2(4(x0))))))))) -> 0^1(0(4(2(5(1(4(x0))))))),0^1(1(4(0(1(0(1(2(4(x0))))))))) -> 0^1(0(4(2(5(1(4(x0)))))))) 590.70/152.66 590.70/152.66 590.70/152.66 ---------------------------------------- 590.70/152.66 590.70/152.66 (96) 590.70/152.66 Obligation: 590.70/152.66 Q DP problem: 590.70/152.66 The TRS P consists of the following rules: 590.70/152.66 590.70/152.66 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.66 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.66 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.66 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.66 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.66 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.66 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.66 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.66 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.66 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.66 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.66 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.66 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.66 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.66 0^1(1(4(0(1(1(1(0(1(x0))))))))) -> 0^1(5(0(4(1(1(1(x0))))))) 590.70/152.66 0^1(1(4(0(1(0(1(2(4(x0))))))))) -> 0^1(4(0(2(2(1(4(x0))))))) 590.70/152.66 0^1(1(4(0(1(0(1(2(4(x0))))))))) -> 0^1(0(4(2(5(1(4(x0))))))) 590.70/152.66 590.70/152.66 The TRS R consists of the following rules: 590.70/152.66 590.70/152.66 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.66 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.66 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.66 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.66 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.66 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.66 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.66 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.66 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.66 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.66 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.66 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.66 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.66 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.66 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.66 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.66 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.66 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.66 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.66 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.66 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.66 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.66 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.66 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.66 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.66 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.66 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.66 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.66 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.66 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.66 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.66 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.66 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.66 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.66 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.66 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.66 590.70/152.66 Q is empty. 590.70/152.66 We have to consider all minimal (P,Q,R)-chains. 590.70/152.66 ---------------------------------------- 590.70/152.66 590.70/152.66 (97) DependencyGraphProof (EQUIVALENT) 590.70/152.66 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes. 590.70/152.66 ---------------------------------------- 590.70/152.66 590.70/152.66 (98) 590.70/152.66 Obligation: 590.70/152.66 Q DP problem: 590.70/152.66 The TRS P consists of the following rules: 590.70/152.66 590.70/152.66 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.66 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.66 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.66 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.66 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.66 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.66 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.66 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.66 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) 590.70/152.66 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.66 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.66 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.66 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.66 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.66 590.70/152.66 The TRS R consists of the following rules: 590.70/152.66 590.70/152.66 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.66 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.66 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.66 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.66 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.66 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.66 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.66 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.66 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.66 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.66 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.66 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.66 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.66 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.66 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.66 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.66 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.66 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.66 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.66 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.66 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.66 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.66 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.66 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.66 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.66 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.66 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.66 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.66 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.66 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.66 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.66 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.66 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.66 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.66 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.66 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.66 590.70/152.66 Q is empty. 590.70/152.66 We have to consider all minimal (P,Q,R)-chains. 590.70/152.66 ---------------------------------------- 590.70/152.66 590.70/152.66 (99) TransformationProof (EQUIVALENT) 590.70/152.66 By narrowing [LPAR04] the rule 0^1(1(2(4(1(x1))))) -> 1^1(4(x1)) at position [0] we obtained the following new rules [LPAR04]: 590.70/152.66 590.70/152.66 (0^1(1(2(4(1(1(1(0(1(x0))))))))) -> 1^1(5(0(4(1(1(1(x0))))))),0^1(1(2(4(1(1(1(0(1(x0))))))))) -> 1^1(5(0(4(1(1(1(x0)))))))) 590.70/152.66 (0^1(1(2(4(1(0(1(2(4(x0))))))))) -> 1^1(4(0(2(2(1(4(x0))))))),0^1(1(2(4(1(0(1(2(4(x0))))))))) -> 1^1(4(0(2(2(1(4(x0)))))))) 590.70/152.66 (0^1(1(2(4(1(0(1(2(4(x0))))))))) -> 1^1(0(4(2(5(1(4(x0))))))),0^1(1(2(4(1(0(1(2(4(x0))))))))) -> 1^1(0(4(2(5(1(4(x0)))))))) 590.70/152.66 590.70/152.66 590.70/152.66 ---------------------------------------- 590.70/152.66 590.70/152.66 (100) 590.70/152.66 Obligation: 590.70/152.66 Q DP problem: 590.70/152.66 The TRS P consists of the following rules: 590.70/152.66 590.70/152.66 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.66 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.66 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.66 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.66 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.66 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.66 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.66 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.66 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.66 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.66 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.66 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.66 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.66 0^1(1(2(4(1(1(1(0(1(x0))))))))) -> 1^1(5(0(4(1(1(1(x0))))))) 590.70/152.66 0^1(1(2(4(1(0(1(2(4(x0))))))))) -> 1^1(4(0(2(2(1(4(x0))))))) 590.70/152.66 0^1(1(2(4(1(0(1(2(4(x0))))))))) -> 1^1(0(4(2(5(1(4(x0))))))) 590.70/152.66 590.70/152.66 The TRS R consists of the following rules: 590.70/152.66 590.70/152.66 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.66 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.66 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.66 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.66 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.66 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.66 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.66 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.66 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.66 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.66 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.66 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.66 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.66 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.66 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.66 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.66 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.66 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.66 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.66 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.66 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.66 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.66 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.66 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.66 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.66 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.66 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.66 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.66 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.66 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.66 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.66 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.66 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.66 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.66 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.66 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.66 590.70/152.66 Q is empty. 590.70/152.66 We have to consider all minimal (P,Q,R)-chains. 590.70/152.66 ---------------------------------------- 590.70/152.66 590.70/152.66 (101) DependencyGraphProof (EQUIVALENT) 590.70/152.66 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes. 590.70/152.66 ---------------------------------------- 590.70/152.66 590.70/152.66 (102) 590.70/152.66 Obligation: 590.70/152.66 Q DP problem: 590.70/152.66 The TRS P consists of the following rules: 590.70/152.66 590.70/152.66 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.66 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.66 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.66 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.66 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.66 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.66 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.66 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.66 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.66 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.66 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.66 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.66 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.66 590.70/152.66 The TRS R consists of the following rules: 590.70/152.66 590.70/152.66 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.66 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.66 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.66 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.66 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.66 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.66 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.66 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.66 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.66 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.66 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.66 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.66 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.66 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.66 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.66 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.66 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.66 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.66 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.66 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.66 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.66 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.66 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.66 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.66 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.66 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.66 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.66 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.66 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.66 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.66 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.66 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.66 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.66 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.66 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.66 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.66 590.70/152.66 Q is empty. 590.70/152.66 We have to consider all minimal (P,Q,R)-chains. 590.70/152.66 ---------------------------------------- 590.70/152.66 590.70/152.66 (103) TransformationProof (EQUIVALENT) 590.70/152.66 By narrowing [LPAR04] the rule 0^1(1(1(2(4(x1))))) -> 1^1(4(x1)) at position [0] we obtained the following new rules [LPAR04]: 590.70/152.66 590.70/152.66 (0^1(1(1(2(4(1(1(0(1(x0))))))))) -> 1^1(5(0(4(1(1(1(x0))))))),0^1(1(1(2(4(1(1(0(1(x0))))))))) -> 1^1(5(0(4(1(1(1(x0)))))))) 590.70/152.66 (0^1(1(1(2(4(0(1(2(4(x0))))))))) -> 1^1(4(0(2(2(1(4(x0))))))),0^1(1(1(2(4(0(1(2(4(x0))))))))) -> 1^1(4(0(2(2(1(4(x0)))))))) 590.70/152.66 (0^1(1(1(2(4(0(1(2(4(x0))))))))) -> 1^1(0(4(2(5(1(4(x0))))))),0^1(1(1(2(4(0(1(2(4(x0))))))))) -> 1^1(0(4(2(5(1(4(x0)))))))) 590.70/152.66 590.70/152.66 590.70/152.66 ---------------------------------------- 590.70/152.66 590.70/152.66 (104) 590.70/152.66 Obligation: 590.70/152.66 Q DP problem: 590.70/152.66 The TRS P consists of the following rules: 590.70/152.66 590.70/152.66 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.66 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.66 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.66 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.66 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.66 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.66 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.66 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.66 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.66 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.66 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.66 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.66 0^1(1(1(2(4(1(1(0(1(x0))))))))) -> 1^1(5(0(4(1(1(1(x0))))))) 590.70/152.66 0^1(1(1(2(4(0(1(2(4(x0))))))))) -> 1^1(4(0(2(2(1(4(x0))))))) 590.70/152.66 0^1(1(1(2(4(0(1(2(4(x0))))))))) -> 1^1(0(4(2(5(1(4(x0))))))) 590.70/152.66 590.70/152.66 The TRS R consists of the following rules: 590.70/152.66 590.70/152.66 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.66 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.66 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.66 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.66 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.66 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.66 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.66 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.66 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.66 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.66 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.66 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.66 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.66 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.66 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.66 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.66 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.66 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.66 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.66 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.66 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.66 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.66 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.66 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.66 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.66 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.66 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.66 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.66 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.66 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.66 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.66 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.66 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.66 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.66 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.66 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.66 590.70/152.66 Q is empty. 590.70/152.66 We have to consider all minimal (P,Q,R)-chains. 590.70/152.66 ---------------------------------------- 590.70/152.66 590.70/152.66 (105) DependencyGraphProof (EQUIVALENT) 590.70/152.66 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes. 590.70/152.66 ---------------------------------------- 590.70/152.66 590.70/152.66 (106) 590.70/152.66 Obligation: 590.70/152.66 Q DP problem: 590.70/152.66 The TRS P consists of the following rules: 590.70/152.66 590.70/152.66 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) 590.70/152.66 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.66 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.66 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.66 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.66 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.66 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.66 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.66 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.66 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.66 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.66 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.66 590.70/152.66 The TRS R consists of the following rules: 590.70/152.66 590.70/152.66 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.66 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.66 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.66 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.66 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.66 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.66 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.66 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.66 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.66 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.66 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.66 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.66 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.66 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.66 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.66 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.66 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.66 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.66 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.66 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.66 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.66 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.66 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.66 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.66 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.66 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.66 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.66 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.66 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.66 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.66 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.66 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.66 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.66 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.66 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.66 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.66 590.70/152.66 Q is empty. 590.70/152.66 We have to consider all minimal (P,Q,R)-chains. 590.70/152.66 ---------------------------------------- 590.70/152.66 590.70/152.66 (107) TransformationProof (EQUIVALENT) 590.70/152.66 By narrowing [LPAR04] the rule 1^1(0(1(0(x1)))) -> 0^1(1(1(x1))) at position [0] we obtained the following new rules [LPAR04]: 590.70/152.66 590.70/152.66 (1^1(0(1(0(0(1(0(x0))))))) -> 0^1(1(2(0(3(0(1(1(x0)))))))),1^1(0(1(0(0(1(0(x0))))))) -> 0^1(1(2(0(3(0(1(1(x0))))))))) 590.70/152.66 (1^1(0(1(0(0(0(3(1(x0)))))))) -> 0^1(1(3(0(1(5(1(0(x0)))))))),1^1(0(1(0(0(0(3(1(x0)))))))) -> 0^1(1(3(0(1(5(1(0(x0))))))))) 590.70/152.66 (1^1(0(1(0(0(1(2(4(x0)))))))) -> 0^1(1(5(1(4(0(2(1(x0)))))))),1^1(0(1(0(0(1(2(4(x0)))))))) -> 0^1(1(5(1(4(0(2(1(x0))))))))) 590.70/152.66 (1^1(0(1(0(2(1(3(4(x0)))))))) -> 0^1(1(1(4(1(2(2(3(x0)))))))),1^1(0(1(0(2(1(3(4(x0)))))))) -> 0^1(1(1(4(1(2(2(3(x0))))))))) 590.70/152.66 (1^1(0(1(0(0(1(4(4(x0)))))))) -> 0^1(1(1(4(1(3(0(4(x0)))))))),1^1(0(1(0(0(1(4(4(x0)))))))) -> 0^1(1(1(4(1(3(0(4(x0))))))))) 590.70/152.66 590.70/152.66 590.70/152.66 ---------------------------------------- 590.70/152.66 590.70/152.66 (108) 590.70/152.66 Obligation: 590.70/152.66 Q DP problem: 590.70/152.66 The TRS P consists of the following rules: 590.70/152.66 590.70/152.66 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.66 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.66 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.66 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.66 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.66 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.66 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.66 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.66 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.66 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.66 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.66 1^1(0(1(0(0(1(0(x0))))))) -> 0^1(1(2(0(3(0(1(1(x0)))))))) 590.70/152.66 1^1(0(1(0(0(0(3(1(x0)))))))) -> 0^1(1(3(0(1(5(1(0(x0)))))))) 590.70/152.66 1^1(0(1(0(0(1(2(4(x0)))))))) -> 0^1(1(5(1(4(0(2(1(x0)))))))) 590.70/152.66 1^1(0(1(0(2(1(3(4(x0)))))))) -> 0^1(1(1(4(1(2(2(3(x0)))))))) 590.70/152.66 1^1(0(1(0(0(1(4(4(x0)))))))) -> 0^1(1(1(4(1(3(0(4(x0)))))))) 590.70/152.66 590.70/152.66 The TRS R consists of the following rules: 590.70/152.66 590.70/152.66 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.66 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.66 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.66 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.66 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.66 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.66 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.66 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.66 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.66 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.66 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.66 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.66 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.66 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.66 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.66 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.66 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.66 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.66 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.66 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.66 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.66 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.66 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.66 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.66 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.66 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.66 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.66 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.66 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.66 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.66 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.66 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.66 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.66 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.66 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.66 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.66 590.70/152.66 Q is empty. 590.70/152.66 We have to consider all minimal (P,Q,R)-chains. 590.70/152.66 ---------------------------------------- 590.70/152.66 590.70/152.66 (109) DependencyGraphProof (EQUIVALENT) 590.70/152.66 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 5 less nodes. 590.70/152.66 ---------------------------------------- 590.70/152.66 590.70/152.66 (110) 590.70/152.66 Obligation: 590.70/152.66 Q DP problem: 590.70/152.66 The TRS P consists of the following rules: 590.70/152.66 590.70/152.66 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.66 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.66 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.66 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.66 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.66 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.66 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.66 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.66 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.66 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.66 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.66 590.70/152.66 The TRS R consists of the following rules: 590.70/152.66 590.70/152.66 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.66 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.66 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.66 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.66 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.66 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.66 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.66 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.66 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.66 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.66 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.66 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.66 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.66 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.66 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.66 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.66 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.66 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.66 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.66 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.66 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.66 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.66 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.66 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.66 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.66 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.66 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.66 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.66 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.66 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.66 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.66 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.66 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.66 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.66 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.66 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.66 590.70/152.66 Q is empty. 590.70/152.66 We have to consider all minimal (P,Q,R)-chains. 590.70/152.66 ---------------------------------------- 590.70/152.66 590.70/152.66 (111) TransformationProof (EQUIVALENT) 590.70/152.66 By narrowing [LPAR04] the rule 0^1(1(2(2(4(x1))))) -> 1^1(4(1(2(x1)))) at position [0] we obtained the following new rules [LPAR04]: 590.70/152.66 590.70/152.66 (0^1(1(2(2(4(1(3(4(x0)))))))) -> 1^1(4(1(4(1(2(2(3(x0)))))))),0^1(1(2(2(4(1(3(4(x0)))))))) -> 1^1(4(1(4(1(2(2(3(x0))))))))) 590.70/152.66 590.70/152.66 590.70/152.66 ---------------------------------------- 590.70/152.66 590.70/152.66 (112) 590.70/152.66 Obligation: 590.70/152.66 Q DP problem: 590.70/152.66 The TRS P consists of the following rules: 590.70/152.66 590.70/152.66 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.66 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.66 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.66 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.66 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.66 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.66 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.66 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.66 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.66 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.66 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.66 0^1(1(2(2(4(1(3(4(x0)))))))) -> 1^1(4(1(4(1(2(2(3(x0)))))))) 590.70/152.66 590.70/152.66 The TRS R consists of the following rules: 590.70/152.66 590.70/152.66 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.66 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.66 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.66 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.66 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.66 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.66 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.66 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.66 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.66 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.66 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.66 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.66 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.66 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.66 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.66 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.66 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.66 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.66 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.66 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.66 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.66 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.66 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.66 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.66 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.66 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.66 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.66 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.66 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.66 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.66 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.66 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.66 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.66 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.66 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.66 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.66 590.70/152.66 Q is empty. 590.70/152.66 We have to consider all minimal (P,Q,R)-chains. 590.70/152.66 ---------------------------------------- 590.70/152.66 590.70/152.66 (113) DependencyGraphProof (EQUIVALENT) 590.70/152.66 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 590.70/152.66 ---------------------------------------- 590.70/152.66 590.70/152.66 (114) 590.70/152.66 Obligation: 590.70/152.66 Q DP problem: 590.70/152.66 The TRS P consists of the following rules: 590.70/152.66 590.70/152.66 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.66 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.66 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.66 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.66 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.66 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.66 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.66 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.66 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.66 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.66 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.66 590.70/152.66 The TRS R consists of the following rules: 590.70/152.66 590.70/152.66 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.66 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.66 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.66 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.66 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.66 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.66 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.66 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.66 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.66 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.66 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.66 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.66 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.66 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.66 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.66 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.66 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.66 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.66 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.66 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.66 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.66 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.66 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.66 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.66 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.66 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.66 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.66 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.66 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.66 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.66 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.66 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.66 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.66 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.66 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.66 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.66 590.70/152.66 Q is empty. 590.70/152.66 We have to consider all minimal (P,Q,R)-chains. 590.70/152.66 ---------------------------------------- 590.70/152.66 590.70/152.66 (115) TransformationProof (EQUIVALENT) 590.70/152.66 By narrowing [LPAR04] the rule 0^1(1(4(2(4(x1))))) -> 1^1(0(4(x1))) at position [0] we obtained the following new rules [LPAR04]: 590.70/152.66 590.70/152.66 (0^1(1(4(2(4(1(1(0(1(x0))))))))) -> 1^1(0(5(0(4(1(1(1(x0)))))))),0^1(1(4(2(4(1(1(0(1(x0))))))))) -> 1^1(0(5(0(4(1(1(1(x0))))))))) 590.70/152.66 (0^1(1(4(2(4(0(1(2(4(x0))))))))) -> 1^1(0(4(0(2(2(1(4(x0)))))))),0^1(1(4(2(4(0(1(2(4(x0))))))))) -> 1^1(0(4(0(2(2(1(4(x0))))))))) 590.70/152.66 (0^1(1(4(2(4(0(1(2(4(x0))))))))) -> 1^1(0(0(4(2(5(1(4(x0)))))))),0^1(1(4(2(4(0(1(2(4(x0))))))))) -> 1^1(0(0(4(2(5(1(4(x0))))))))) 590.70/152.66 590.70/152.66 590.70/152.66 ---------------------------------------- 590.70/152.66 590.70/152.66 (116) 590.70/152.66 Obligation: 590.70/152.66 Q DP problem: 590.70/152.66 The TRS P consists of the following rules: 590.70/152.66 590.70/152.66 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.66 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.66 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.66 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.66 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.66 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.66 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.66 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.66 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.66 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.66 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.66 0^1(1(4(2(4(1(1(0(1(x0))))))))) -> 1^1(0(5(0(4(1(1(1(x0)))))))) 590.70/152.66 0^1(1(4(2(4(0(1(2(4(x0))))))))) -> 1^1(0(4(0(2(2(1(4(x0)))))))) 590.70/152.66 0^1(1(4(2(4(0(1(2(4(x0))))))))) -> 1^1(0(0(4(2(5(1(4(x0)))))))) 590.70/152.66 590.70/152.66 The TRS R consists of the following rules: 590.70/152.66 590.70/152.66 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.66 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.66 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.66 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.66 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.66 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.66 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.66 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.66 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.66 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.66 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.66 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.66 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.66 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.66 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.66 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.66 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.66 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.66 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.66 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.66 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.66 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.66 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.66 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.66 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.66 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.66 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.66 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.66 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.66 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.66 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.66 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.66 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.66 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.66 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.66 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.66 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.66 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.66 590.70/152.66 Q is empty. 590.70/152.66 We have to consider all minimal (P,Q,R)-chains. 590.70/152.66 ---------------------------------------- 590.70/152.66 590.70/152.66 (117) DependencyGraphProof (EQUIVALENT) 590.70/152.66 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes. 590.70/152.66 ---------------------------------------- 590.70/152.66 590.70/152.66 (118) 590.70/152.66 Obligation: 590.70/152.66 Q DP problem: 590.70/152.66 The TRS P consists of the following rules: 590.70/152.66 590.70/152.66 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.66 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.66 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.66 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.66 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.66 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.66 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.66 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.66 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.66 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.66 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.66 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.66 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.66 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.66 590.70/152.66 The TRS R consists of the following rules: 590.70/152.66 590.70/152.66 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.66 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.66 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.66 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.66 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.66 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.66 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.66 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.66 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.66 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.66 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.66 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.66 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.66 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.66 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.66 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.66 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.66 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.66 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.66 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.66 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.66 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.66 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.66 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.67 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.67 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.67 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.67 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.67 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.67 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.67 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.67 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.67 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.67 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.67 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.67 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.67 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.67 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.67 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.67 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.67 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.67 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.67 590.70/152.67 Q is empty. 590.70/152.67 We have to consider all minimal (P,Q,R)-chains. 590.70/152.67 ---------------------------------------- 590.70/152.67 590.70/152.67 (119) TransformationProof (EQUIVALENT) 590.70/152.67 By narrowing [LPAR04] the rule 0^1(1(4(2(4(x1))))) -> 0^1(4(x1)) at position [0] we obtained the following new rules [LPAR04]: 590.70/152.67 590.70/152.67 (0^1(1(4(2(4(1(1(0(1(x0))))))))) -> 0^1(5(0(4(1(1(1(x0))))))),0^1(1(4(2(4(1(1(0(1(x0))))))))) -> 0^1(5(0(4(1(1(1(x0)))))))) 590.70/152.67 (0^1(1(4(2(4(0(1(2(4(x0))))))))) -> 0^1(4(0(2(2(1(4(x0))))))),0^1(1(4(2(4(0(1(2(4(x0))))))))) -> 0^1(4(0(2(2(1(4(x0)))))))) 590.70/152.67 (0^1(1(4(2(4(0(1(2(4(x0))))))))) -> 0^1(0(4(2(5(1(4(x0))))))),0^1(1(4(2(4(0(1(2(4(x0))))))))) -> 0^1(0(4(2(5(1(4(x0)))))))) 590.70/152.67 590.70/152.67 590.70/152.67 ---------------------------------------- 590.70/152.67 590.70/152.67 (120) 590.70/152.67 Obligation: 590.70/152.67 Q DP problem: 590.70/152.67 The TRS P consists of the following rules: 590.70/152.67 590.70/152.67 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.67 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.67 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.67 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.67 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.67 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.67 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.67 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.67 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.67 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.67 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.67 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.67 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.67 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.67 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.67 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.67 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.67 0^1(1(4(2(4(1(1(0(1(x0))))))))) -> 0^1(5(0(4(1(1(1(x0))))))) 590.70/152.67 0^1(1(4(2(4(0(1(2(4(x0))))))))) -> 0^1(4(0(2(2(1(4(x0))))))) 590.70/152.67 0^1(1(4(2(4(0(1(2(4(x0))))))))) -> 0^1(0(4(2(5(1(4(x0))))))) 590.70/152.67 590.70/152.67 The TRS R consists of the following rules: 590.70/152.67 590.70/152.67 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.67 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.67 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.67 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.67 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.67 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.67 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.67 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.67 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.67 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.67 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.67 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.67 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.67 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.67 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.67 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.67 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.67 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.67 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.67 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.67 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.67 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.67 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.67 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.67 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.67 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.67 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.67 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.67 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.67 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.67 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.67 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.67 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.67 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.67 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.67 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.67 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.67 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.67 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.67 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.67 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.67 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.67 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.67 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.67 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.67 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.67 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.67 590.70/152.67 Q is empty. 590.70/152.67 We have to consider all minimal (P,Q,R)-chains. 590.70/152.67 ---------------------------------------- 590.70/152.67 590.70/152.67 (121) DependencyGraphProof (EQUIVALENT) 590.70/152.67 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes. 590.70/152.67 ---------------------------------------- 590.70/152.67 590.70/152.67 (122) 590.70/152.67 Obligation: 590.70/152.67 Q DP problem: 590.70/152.67 The TRS P consists of the following rules: 590.70/152.67 590.70/152.67 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.67 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.67 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.67 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.67 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.67 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.67 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.67 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.67 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.67 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.67 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.67 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) 590.70/152.67 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.67 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.67 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.67 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.67 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.67 590.70/152.67 The TRS R consists of the following rules: 590.70/152.67 590.70/152.67 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.67 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.67 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.67 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.67 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.67 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.67 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.67 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.67 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.67 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.67 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.67 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.67 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.67 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.67 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.67 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.67 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.67 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.67 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.67 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.67 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.67 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.67 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.67 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.67 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.67 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.67 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.67 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.67 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.67 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.67 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.67 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.67 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.67 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.67 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.67 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.67 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.67 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.67 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.67 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.67 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.67 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.67 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.67 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.67 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.67 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.67 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.67 590.70/152.67 Q is empty. 590.70/152.67 We have to consider all minimal (P,Q,R)-chains. 590.70/152.67 ---------------------------------------- 590.70/152.67 590.70/152.67 (123) TransformationProof (EQUIVALENT) 590.70/152.67 By narrowing [LPAR04] the rule 0^1(1(4(2(4(x1))))) -> 1^1(4(x1)) at position [0] we obtained the following new rules [LPAR04]: 590.70/152.67 590.70/152.67 (0^1(1(4(2(4(1(1(0(1(x0))))))))) -> 1^1(5(0(4(1(1(1(x0))))))),0^1(1(4(2(4(1(1(0(1(x0))))))))) -> 1^1(5(0(4(1(1(1(x0)))))))) 590.70/152.67 (0^1(1(4(2(4(0(1(2(4(x0))))))))) -> 1^1(4(0(2(2(1(4(x0))))))),0^1(1(4(2(4(0(1(2(4(x0))))))))) -> 1^1(4(0(2(2(1(4(x0)))))))) 590.70/152.67 (0^1(1(4(2(4(0(1(2(4(x0))))))))) -> 1^1(0(4(2(5(1(4(x0))))))),0^1(1(4(2(4(0(1(2(4(x0))))))))) -> 1^1(0(4(2(5(1(4(x0)))))))) 590.70/152.67 590.70/152.67 590.70/152.67 ---------------------------------------- 590.70/152.67 590.70/152.67 (124) 590.70/152.67 Obligation: 590.70/152.67 Q DP problem: 590.70/152.67 The TRS P consists of the following rules: 590.70/152.67 590.70/152.67 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.67 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.67 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.67 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.67 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.67 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.67 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.67 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.67 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.67 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.67 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.67 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.67 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.67 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.67 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.67 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.67 0^1(1(4(2(4(1(1(0(1(x0))))))))) -> 1^1(5(0(4(1(1(1(x0))))))) 590.70/152.67 0^1(1(4(2(4(0(1(2(4(x0))))))))) -> 1^1(4(0(2(2(1(4(x0))))))) 590.70/152.67 0^1(1(4(2(4(0(1(2(4(x0))))))))) -> 1^1(0(4(2(5(1(4(x0))))))) 590.70/152.67 590.70/152.67 The TRS R consists of the following rules: 590.70/152.67 590.70/152.67 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.67 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.67 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.67 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.67 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.67 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.67 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.67 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.67 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.67 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.67 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.67 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.67 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.67 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.67 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.67 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.67 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.67 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.67 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.67 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.67 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.67 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.67 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.67 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.67 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.67 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.67 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.67 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.67 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.67 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.67 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.67 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.67 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.67 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.67 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.67 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.67 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.67 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.67 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.67 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.67 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.67 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.67 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.67 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.67 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.67 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.67 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.67 590.70/152.67 Q is empty. 590.70/152.67 We have to consider all minimal (P,Q,R)-chains. 590.70/152.67 ---------------------------------------- 590.70/152.67 590.70/152.67 (125) DependencyGraphProof (EQUIVALENT) 590.70/152.67 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes. 590.70/152.67 ---------------------------------------- 590.70/152.67 590.70/152.67 (126) 590.70/152.67 Obligation: 590.70/152.67 Q DP problem: 590.70/152.67 The TRS P consists of the following rules: 590.70/152.67 590.70/152.67 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.67 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.67 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.67 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.67 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.67 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.67 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.67 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.67 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.67 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.67 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.67 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.67 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.67 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.67 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.67 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.67 590.70/152.67 The TRS R consists of the following rules: 590.70/152.67 590.70/152.67 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.67 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.67 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.67 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.67 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.67 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.67 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.67 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.67 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.67 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.67 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.67 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.67 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.67 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.67 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.67 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.67 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.67 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.67 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.67 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.67 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.67 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.67 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.67 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.67 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.67 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.67 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.67 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.67 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.67 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.67 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.67 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.67 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.67 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.67 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.67 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.67 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.67 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.67 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.67 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.67 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.67 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.67 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.67 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.67 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.67 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.67 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.67 590.70/152.67 Q is empty. 590.70/152.67 We have to consider all minimal (P,Q,R)-chains. 590.70/152.67 ---------------------------------------- 590.70/152.67 590.70/152.67 (127) TransformationProof (EQUIVALENT) 590.70/152.67 By narrowing [LPAR04] the rule 0^1(1(0(4(4(x1))))) -> 0^1(4(x1)) at position [0] we obtained the following new rules [LPAR04]: 590.70/152.67 590.70/152.67 (0^1(1(0(4(4(1(1(0(1(x0))))))))) -> 0^1(5(0(4(1(1(1(x0))))))),0^1(1(0(4(4(1(1(0(1(x0))))))))) -> 0^1(5(0(4(1(1(1(x0)))))))) 590.70/152.67 (0^1(1(0(4(4(0(1(2(4(x0))))))))) -> 0^1(4(0(2(2(1(4(x0))))))),0^1(1(0(4(4(0(1(2(4(x0))))))))) -> 0^1(4(0(2(2(1(4(x0)))))))) 590.70/152.67 (0^1(1(0(4(4(0(1(2(4(x0))))))))) -> 0^1(0(4(2(5(1(4(x0))))))),0^1(1(0(4(4(0(1(2(4(x0))))))))) -> 0^1(0(4(2(5(1(4(x0)))))))) 590.70/152.67 590.70/152.67 590.70/152.67 ---------------------------------------- 590.70/152.67 590.70/152.67 (128) 590.70/152.67 Obligation: 590.70/152.67 Q DP problem: 590.70/152.67 The TRS P consists of the following rules: 590.70/152.67 590.70/152.67 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.67 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.67 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.67 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.67 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.67 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.67 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.67 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.67 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.67 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.67 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.67 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.67 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.67 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.67 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.67 0^1(1(0(4(4(1(1(0(1(x0))))))))) -> 0^1(5(0(4(1(1(1(x0))))))) 590.70/152.67 0^1(1(0(4(4(0(1(2(4(x0))))))))) -> 0^1(4(0(2(2(1(4(x0))))))) 590.70/152.67 0^1(1(0(4(4(0(1(2(4(x0))))))))) -> 0^1(0(4(2(5(1(4(x0))))))) 590.70/152.67 590.70/152.67 The TRS R consists of the following rules: 590.70/152.67 590.70/152.67 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.67 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.67 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.67 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.67 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.67 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.67 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.67 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.67 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.67 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.67 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.67 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.67 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.67 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.67 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.67 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.67 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.67 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.67 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.67 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.67 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.67 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.67 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.67 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.67 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.67 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.67 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.67 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.67 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.67 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.67 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.67 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.67 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.67 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.67 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.67 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.67 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.67 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.67 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.67 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.67 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.67 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.67 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.67 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.67 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.67 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.67 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.67 590.70/152.67 Q is empty. 590.70/152.67 We have to consider all minimal (P,Q,R)-chains. 590.70/152.67 ---------------------------------------- 590.70/152.67 590.70/152.67 (129) DependencyGraphProof (EQUIVALENT) 590.70/152.67 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes. 590.70/152.67 ---------------------------------------- 590.70/152.67 590.70/152.67 (130) 590.70/152.67 Obligation: 590.70/152.67 Q DP problem: 590.70/152.67 The TRS P consists of the following rules: 590.70/152.67 590.70/152.67 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.67 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.67 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.67 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.67 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.67 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.67 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.67 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.67 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.67 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.67 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.67 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.67 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) 590.70/152.67 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.67 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.67 590.70/152.67 The TRS R consists of the following rules: 590.70/152.67 590.70/152.67 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.67 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.67 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.67 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.67 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.67 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.67 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.67 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.67 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.67 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.67 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.67 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.67 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.67 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.67 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.67 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.67 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.67 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.67 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.67 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.67 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.67 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.67 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.67 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.67 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.67 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.67 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.67 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.67 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.67 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.67 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.67 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.67 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.67 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.67 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.67 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.67 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.67 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.67 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.67 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.67 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.67 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.67 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.67 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.67 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.67 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.67 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.67 590.70/152.67 Q is empty. 590.70/152.67 We have to consider all minimal (P,Q,R)-chains. 590.70/152.67 ---------------------------------------- 590.70/152.67 590.70/152.67 (131) TransformationProof (EQUIVALENT) 590.70/152.67 By narrowing [LPAR04] the rule 0^1(1(2(4(4(x1))))) -> 0^1(4(x1)) at position [0] we obtained the following new rules [LPAR04]: 590.70/152.67 590.70/152.67 (0^1(1(2(4(4(1(1(0(1(x0))))))))) -> 0^1(5(0(4(1(1(1(x0))))))),0^1(1(2(4(4(1(1(0(1(x0))))))))) -> 0^1(5(0(4(1(1(1(x0)))))))) 590.70/152.67 (0^1(1(2(4(4(0(1(2(4(x0))))))))) -> 0^1(4(0(2(2(1(4(x0))))))),0^1(1(2(4(4(0(1(2(4(x0))))))))) -> 0^1(4(0(2(2(1(4(x0)))))))) 590.70/152.67 (0^1(1(2(4(4(0(1(2(4(x0))))))))) -> 0^1(0(4(2(5(1(4(x0))))))),0^1(1(2(4(4(0(1(2(4(x0))))))))) -> 0^1(0(4(2(5(1(4(x0)))))))) 590.70/152.67 590.70/152.67 590.70/152.67 ---------------------------------------- 590.70/152.67 590.70/152.67 (132) 590.70/152.67 Obligation: 590.70/152.67 Q DP problem: 590.70/152.67 The TRS P consists of the following rules: 590.70/152.67 590.70/152.67 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.67 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.67 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.67 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.67 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.67 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.67 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.67 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.67 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.67 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.67 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.67 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.67 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.67 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.67 0^1(1(2(4(4(1(1(0(1(x0))))))))) -> 0^1(5(0(4(1(1(1(x0))))))) 590.70/152.67 0^1(1(2(4(4(0(1(2(4(x0))))))))) -> 0^1(4(0(2(2(1(4(x0))))))) 590.70/152.67 0^1(1(2(4(4(0(1(2(4(x0))))))))) -> 0^1(0(4(2(5(1(4(x0))))))) 590.70/152.67 590.70/152.67 The TRS R consists of the following rules: 590.70/152.67 590.70/152.67 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.67 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.67 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.67 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.67 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.67 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.67 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.67 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.67 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.67 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.67 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.67 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.67 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.67 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.67 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.67 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.67 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.67 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.67 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.67 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.67 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.67 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.67 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.67 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.67 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.67 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.67 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.67 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.67 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.67 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.67 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.67 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.67 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.67 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.67 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.67 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.67 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.67 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.67 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.67 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.67 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.67 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.67 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.67 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.67 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.67 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.67 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.67 590.70/152.67 Q is empty. 590.70/152.67 We have to consider all minimal (P,Q,R)-chains. 590.70/152.67 ---------------------------------------- 590.70/152.67 590.70/152.67 (133) DependencyGraphProof (EQUIVALENT) 590.70/152.67 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes. 590.70/152.67 ---------------------------------------- 590.70/152.67 590.70/152.67 (134) 590.70/152.67 Obligation: 590.70/152.67 Q DP problem: 590.70/152.67 The TRS P consists of the following rules: 590.70/152.67 590.70/152.67 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.67 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.67 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.67 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.67 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.67 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.67 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.67 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.67 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.67 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.67 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.67 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.67 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) 590.70/152.67 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.67 590.70/152.67 The TRS R consists of the following rules: 590.70/152.67 590.70/152.67 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.67 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.67 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.67 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.67 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.67 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.67 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.67 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.67 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.67 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.67 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.67 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.67 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.67 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.67 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.67 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.67 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.67 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.67 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.67 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.67 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.67 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.67 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.67 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.67 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.67 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.67 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.67 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.67 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.67 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.67 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.67 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.67 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.67 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.67 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.67 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.67 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.67 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.67 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.67 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.67 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.67 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.67 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.67 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.67 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.67 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.67 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.67 590.70/152.67 Q is empty. 590.70/152.67 We have to consider all minimal (P,Q,R)-chains. 590.70/152.67 ---------------------------------------- 590.70/152.67 590.70/152.67 (135) TransformationProof (EQUIVALENT) 590.70/152.67 By narrowing [LPAR04] the rule 0^1(1(4(5(4(x1))))) -> 0^1(4(1(4(x1)))) at position [0] we obtained the following new rules [LPAR04]: 590.70/152.67 590.70/152.67 (0^1(1(4(5(4(1(1(0(1(x0))))))))) -> 0^1(4(1(5(0(4(1(1(1(x0))))))))),0^1(1(4(5(4(1(1(0(1(x0))))))))) -> 0^1(4(1(5(0(4(1(1(1(x0)))))))))) 590.70/152.67 (0^1(1(4(5(4(0(1(2(4(x0))))))))) -> 0^1(4(1(4(0(2(2(1(4(x0))))))))),0^1(1(4(5(4(0(1(2(4(x0))))))))) -> 0^1(4(1(4(0(2(2(1(4(x0)))))))))) 590.70/152.67 (0^1(1(4(5(4(0(1(2(4(x0))))))))) -> 0^1(4(1(0(4(2(5(1(4(x0))))))))),0^1(1(4(5(4(0(1(2(4(x0))))))))) -> 0^1(4(1(0(4(2(5(1(4(x0)))))))))) 590.70/152.67 590.70/152.67 590.70/152.67 ---------------------------------------- 590.70/152.67 590.70/152.67 (136) 590.70/152.67 Obligation: 590.70/152.67 Q DP problem: 590.70/152.67 The TRS P consists of the following rules: 590.70/152.67 590.70/152.67 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.67 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.67 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.67 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.67 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.67 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.67 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.67 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.67 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.67 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.67 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.67 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.67 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.67 0^1(1(4(5(4(1(1(0(1(x0))))))))) -> 0^1(4(1(5(0(4(1(1(1(x0))))))))) 590.70/152.67 0^1(1(4(5(4(0(1(2(4(x0))))))))) -> 0^1(4(1(4(0(2(2(1(4(x0))))))))) 590.70/152.67 0^1(1(4(5(4(0(1(2(4(x0))))))))) -> 0^1(4(1(0(4(2(5(1(4(x0))))))))) 590.70/152.67 590.70/152.67 The TRS R consists of the following rules: 590.70/152.67 590.70/152.67 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.67 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.67 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.67 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.67 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.67 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.67 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.67 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.67 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.67 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.67 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.67 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.67 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.67 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.67 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.67 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.67 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.67 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.67 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.67 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.67 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.67 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.67 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.67 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.67 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.67 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.67 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.67 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.67 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.67 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.67 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.67 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.67 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.67 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.67 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.67 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.67 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.67 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.67 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.67 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.67 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.67 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.67 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.67 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.67 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.67 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.67 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.67 590.70/152.67 Q is empty. 590.70/152.67 We have to consider all minimal (P,Q,R)-chains. 590.70/152.67 ---------------------------------------- 590.70/152.67 590.70/152.67 (137) DependencyGraphProof (EQUIVALENT) 590.70/152.67 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes. 590.70/152.67 ---------------------------------------- 590.70/152.67 590.70/152.67 (138) 590.70/152.67 Obligation: 590.70/152.67 Q DP problem: 590.70/152.67 The TRS P consists of the following rules: 590.70/152.67 590.70/152.67 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.67 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.67 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.67 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.67 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.67 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.67 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.67 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.67 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.67 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.67 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.67 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.67 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) 590.70/152.67 590.70/152.67 The TRS R consists of the following rules: 590.70/152.67 590.70/152.67 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.67 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.67 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.67 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.67 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.67 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.67 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.67 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.67 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.67 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.67 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.67 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.67 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.67 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.67 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.67 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.67 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.67 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.67 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.70/152.67 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.70/152.67 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.67 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.70/152.67 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.70/152.67 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.70/152.67 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.70/152.67 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.70/152.67 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.70/152.67 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.70/152.67 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.70/152.67 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.70/152.67 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.70/152.67 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.70/152.67 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.70/152.67 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.70/152.67 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.70/152.67 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.70/152.67 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.70/152.67 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.70/152.67 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.70/152.67 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.70/152.67 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.70/152.67 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.70/152.67 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.70/152.67 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.70/152.67 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.70/152.67 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.70/152.67 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.70/152.67 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.70/152.67 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.70/152.67 590.70/152.67 Q is empty. 590.70/152.67 We have to consider all minimal (P,Q,R)-chains. 590.70/152.67 ---------------------------------------- 590.70/152.67 590.70/152.67 (139) TransformationProof (EQUIVALENT) 590.70/152.67 By narrowing [LPAR04] the rule 0^1(1(4(5(4(x1))))) -> 1^1(4(x1)) at position [0] we obtained the following new rules [LPAR04]: 590.70/152.67 590.70/152.67 (0^1(1(4(5(4(1(1(0(1(x0))))))))) -> 1^1(5(0(4(1(1(1(x0))))))),0^1(1(4(5(4(1(1(0(1(x0))))))))) -> 1^1(5(0(4(1(1(1(x0)))))))) 590.70/152.67 (0^1(1(4(5(4(0(1(2(4(x0))))))))) -> 1^1(4(0(2(2(1(4(x0))))))),0^1(1(4(5(4(0(1(2(4(x0))))))))) -> 1^1(4(0(2(2(1(4(x0)))))))) 590.70/152.67 (0^1(1(4(5(4(0(1(2(4(x0))))))))) -> 1^1(0(4(2(5(1(4(x0))))))),0^1(1(4(5(4(0(1(2(4(x0))))))))) -> 1^1(0(4(2(5(1(4(x0)))))))) 590.70/152.67 590.70/152.67 590.70/152.67 ---------------------------------------- 590.70/152.67 590.70/152.67 (140) 590.70/152.67 Obligation: 590.70/152.67 Q DP problem: 590.70/152.67 The TRS P consists of the following rules: 590.70/152.67 590.70/152.67 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.70/152.67 1^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.67 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.70/152.67 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.70/152.67 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(0(1(0(x1)))) -> 1^1(x1) 590.70/152.67 0^1(1(4(0(x1)))) -> 1^1(x1) 590.70/152.67 0^1(1(2(4(x1)))) -> 1^1(x1) 590.70/152.67 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.70/152.67 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.70/152.67 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.70/152.67 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.70/152.67 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.70/152.67 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.70/152.67 0^1(1(4(5(4(1(1(0(1(x0))))))))) -> 1^1(5(0(4(1(1(1(x0))))))) 590.70/152.67 0^1(1(4(5(4(0(1(2(4(x0))))))))) -> 1^1(4(0(2(2(1(4(x0))))))) 590.70/152.67 0^1(1(4(5(4(0(1(2(4(x0))))))))) -> 1^1(0(4(2(5(1(4(x0))))))) 590.70/152.67 590.70/152.67 The TRS R consists of the following rules: 590.70/152.67 590.70/152.67 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.67 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.70/152.67 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.70/152.67 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.70/152.67 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.70/152.67 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.70/152.67 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.70/152.67 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.70/152.67 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.70/152.67 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.70/152.67 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.70/152.67 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.70/152.67 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.70/152.67 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.70/152.67 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.70/152.67 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.70/152.67 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.70/152.67 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.70/152.67 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.70/152.67 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.70/152.67 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.70/152.67 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.70/152.67 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.94/152.67 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.94/152.67 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.94/152.67 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.94/152.67 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.94/152.67 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.94/152.67 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.94/152.67 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.94/152.67 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.94/152.67 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.94/152.67 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.94/152.67 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.94/152.67 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.94/152.67 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.94/152.67 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.94/152.67 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.94/152.67 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.94/152.67 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.94/152.67 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.94/152.67 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.94/152.67 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.94/152.67 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.94/152.67 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.94/152.67 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.94/152.67 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.94/152.67 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.94/152.67 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.94/152.67 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.94/152.67 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.94/152.67 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.94/152.67 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.94/152.67 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.94/152.67 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.94/152.67 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.94/152.67 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.94/152.67 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.94/152.67 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.94/152.67 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.94/152.67 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.94/152.67 590.94/152.67 Q is empty. 590.94/152.67 We have to consider all minimal (P,Q,R)-chains. 590.94/152.67 ---------------------------------------- 590.94/152.67 590.94/152.67 (141) DependencyGraphProof (EQUIVALENT) 590.94/152.67 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes. 590.94/152.67 ---------------------------------------- 590.94/152.67 590.94/152.67 (142) 590.94/152.67 Obligation: 590.94/152.67 Q DP problem: 590.94/152.67 The TRS P consists of the following rules: 590.94/152.67 590.94/152.67 1^1(0(1(0(x1)))) -> 1^1(x1) 590.94/152.67 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.94/152.67 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.94/152.67 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.94/152.67 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.94/152.67 0^1(0(1(0(x1)))) -> 1^1(x1) 590.94/152.67 0^1(1(4(0(x1)))) -> 1^1(x1) 590.94/152.67 0^1(1(2(4(x1)))) -> 1^1(x1) 590.94/152.67 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.94/152.67 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.94/152.67 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.94/152.67 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.94/152.67 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.94/152.67 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.94/152.67 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.94/152.67 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.94/152.67 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.94/152.67 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.94/152.67 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.94/152.67 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.94/152.67 590.94/152.67 The TRS R consists of the following rules: 590.94/152.67 590.94/152.67 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.94/152.67 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.94/152.67 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.94/152.67 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.94/152.67 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.94/152.67 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.94/152.67 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.94/152.67 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.94/152.67 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.94/152.67 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.94/152.67 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.94/152.67 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.94/152.67 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.94/152.67 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.94/152.67 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.94/152.67 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.94/152.67 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.94/152.67 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.94/152.67 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.94/152.67 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.94/152.67 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.94/152.67 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.94/152.67 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.94/152.67 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.94/152.67 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.94/152.67 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.94/152.67 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.94/152.67 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.94/152.67 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.94/152.67 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.94/152.67 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.94/152.67 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.94/152.67 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.94/152.67 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.94/152.67 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.94/152.67 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.94/152.67 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.94/152.67 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.94/152.67 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.94/152.67 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.94/152.67 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.94/152.67 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.94/152.67 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.94/152.67 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.94/152.67 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.94/152.67 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.94/152.67 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.94/152.67 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.94/152.67 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.94/152.67 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.94/152.67 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.94/152.67 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.94/152.67 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.94/152.67 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.94/152.67 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.94/152.67 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.94/152.67 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.94/152.67 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.94/152.67 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.94/152.67 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.94/152.67 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.94/152.67 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.94/152.67 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.94/152.67 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.94/152.67 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.94/152.67 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.94/152.67 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.94/152.67 590.94/152.67 Q is empty. 590.94/152.67 We have to consider all minimal (P,Q,R)-chains. 590.94/152.67 ---------------------------------------- 590.94/152.67 590.94/152.67 (143) QDPOrderProof (EQUIVALENT) 590.94/152.67 We use the reduction pair processor [LPAR04,JAR06]. 590.94/152.67 590.94/152.67 590.94/152.67 The following pairs can be oriented strictly and are deleted. 590.94/152.67 590.94/152.67 1^1(0(1(0(x1)))) -> 1^1(x1) 590.94/152.67 1^1(0(0(3(1(x1))))) -> 1^1(0(x1)) 590.94/152.67 1^1(0(0(3(1(x1))))) -> 0^1(x1) 590.94/152.67 0^1(1(0(0(x1)))) -> 1^1(0(x1)) 590.94/152.67 1^1(0(1(2(4(x1))))) -> 1^1(x1) 590.94/152.67 0^1(0(1(0(x1)))) -> 1^1(x1) 590.94/152.67 0^1(1(4(0(x1)))) -> 1^1(x1) 590.94/152.67 0^1(1(2(0(0(x1))))) -> 1^1(0(x1)) 590.94/152.67 0^1(1(2(4(0(x1))))) -> 1^1(x1) 590.94/152.67 0^1(1(4(4(0(x1))))) -> 1^1(x1) 590.94/152.67 0^1(1(0(1(4(x1))))) -> 0^1(1(x1)) 590.94/152.67 0^1(1(0(1(4(x1))))) -> 1^1(x1) 590.94/152.67 0^1(1(0(2(4(x1))))) -> 1^1(x1) 590.94/152.67 The remaining pairs can at least be oriented weakly. 590.94/152.67 Used ordering: Polynomial interpretation [POLO]: 590.94/152.67 590.94/152.67 POL(0(x_1)) = 1 + x_1 590.94/152.67 POL(0^1(x_1)) = 1 + x_1 590.94/152.67 POL(1(x_1)) = x_1 590.94/152.67 POL(1^1(x_1)) = 1 + x_1 590.94/152.67 POL(2(x_1)) = x_1 590.94/152.67 POL(3(x_1)) = x_1 590.94/152.67 POL(4(x_1)) = x_1 590.94/152.67 POL(5(x_1)) = 0 590.94/152.67 590.94/152.67 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 590.94/152.67 590.94/152.67 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.94/152.67 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.94/152.67 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.94/152.67 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.94/152.67 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.94/152.67 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.94/152.67 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.94/152.67 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.94/152.67 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.94/152.67 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.94/152.67 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.94/152.67 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.94/152.67 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.94/152.67 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.94/152.67 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.94/152.67 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.94/152.67 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.94/152.67 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.94/152.67 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.94/152.67 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.94/152.67 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.94/152.67 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.94/152.67 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.94/152.67 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.94/152.67 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.94/152.67 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.94/152.67 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.94/152.67 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.94/152.67 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.94/152.67 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.94/152.67 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.94/152.67 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.94/152.67 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.94/152.67 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.94/152.67 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.94/152.67 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.94/152.67 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.94/152.67 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.94/152.67 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.94/152.67 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.94/152.67 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.94/152.67 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.94/152.67 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.94/152.67 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.94/152.67 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.94/152.67 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.94/152.67 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.94/152.67 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.94/152.67 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.94/152.67 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.94/152.67 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.94/152.67 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.94/152.67 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.94/152.67 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.94/152.67 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.94/152.67 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.94/152.67 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.94/152.67 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.94/152.67 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.94/152.67 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.94/152.67 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.94/152.67 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.94/152.67 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.94/152.67 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.94/152.67 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.94/152.67 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.94/152.67 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.94/152.67 590.94/152.67 590.94/152.67 ---------------------------------------- 590.94/152.67 590.94/152.67 (144) 590.94/152.67 Obligation: 590.94/152.67 Q DP problem: 590.94/152.67 The TRS P consists of the following rules: 590.94/152.67 590.94/152.67 0^1(1(2(4(x1)))) -> 1^1(x1) 590.94/152.67 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.94/152.67 0^1(1(2(4(0(x1))))) -> 1^1(4(0(x1))) 590.94/152.67 0^1(1(2(2(4(x1))))) -> 1^1(x1) 590.94/152.67 0^1(1(4(2(4(x1))))) -> 1^1(x1) 590.94/152.67 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.94/152.67 0^1(1(2(4(4(x1))))) -> 1^1(x1) 590.94/152.67 590.94/152.67 The TRS R consists of the following rules: 590.94/152.67 590.94/152.67 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.94/152.67 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.94/152.67 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.94/152.67 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.94/152.67 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.94/152.67 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.94/152.67 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.94/152.67 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.94/152.67 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.94/152.67 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.94/152.67 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.94/152.67 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.94/152.67 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.94/152.67 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.94/152.67 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.94/152.67 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.94/152.67 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.94/152.67 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.94/152.67 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.94/152.67 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.94/152.67 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.94/152.67 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.94/152.67 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.94/152.67 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.94/152.67 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.94/152.67 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.94/152.67 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.94/152.67 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.94/152.67 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.94/152.67 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.94/152.67 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.94/152.67 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.94/152.67 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.94/152.67 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.94/152.67 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.94/152.67 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.94/152.67 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.94/152.67 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.94/152.67 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.94/152.67 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.94/152.67 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.94/152.67 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.94/152.67 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.94/152.67 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.94/152.67 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.94/152.67 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.94/152.67 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.94/152.67 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.94/152.67 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.94/152.67 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.94/152.67 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.94/152.67 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.94/152.67 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.94/152.67 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.94/152.67 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.94/152.67 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.94/152.67 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.94/152.67 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.94/152.67 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.94/152.67 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.94/152.67 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.94/152.67 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.94/152.67 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.94/152.67 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.94/152.67 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.94/152.67 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.94/152.67 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.94/152.67 590.94/152.67 Q is empty. 590.94/152.67 We have to consider all minimal (P,Q,R)-chains. 590.94/152.67 ---------------------------------------- 590.94/152.67 590.94/152.67 (145) DependencyGraphProof (EQUIVALENT) 590.94/152.67 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 5 less nodes. 590.94/152.67 ---------------------------------------- 590.94/152.67 590.94/152.67 (146) 590.94/152.67 Obligation: 590.94/152.67 Q DP problem: 590.94/152.67 The TRS P consists of the following rules: 590.94/152.67 590.94/152.67 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.94/152.67 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.94/152.67 590.94/152.67 The TRS R consists of the following rules: 590.94/152.67 590.94/152.67 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.94/152.67 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.94/152.67 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.94/152.67 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.94/152.67 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.94/152.67 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.94/152.67 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.94/152.67 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.94/152.67 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.94/152.67 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.94/152.67 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.94/152.67 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.94/152.67 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.94/152.67 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.94/152.67 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.94/152.67 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.94/152.67 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.94/152.67 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.94/152.67 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.94/152.67 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.94/152.67 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.94/152.67 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.94/152.67 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.94/152.67 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.94/152.67 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.94/152.67 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.94/152.67 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.94/152.67 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.94/152.67 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.94/152.67 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.94/152.67 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.94/152.67 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.94/152.67 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.94/152.67 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.94/152.67 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.94/152.67 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.94/152.67 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.94/152.67 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.94/152.67 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.94/152.67 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.94/152.67 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.94/152.67 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.94/152.67 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.94/152.67 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.94/152.67 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.94/152.67 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.94/152.67 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.94/152.67 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.94/152.67 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.94/152.67 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.94/152.67 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.94/152.67 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.94/152.67 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.94/152.67 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.94/152.67 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.94/152.67 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.94/152.67 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.94/152.67 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.94/152.67 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.94/152.67 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.94/152.67 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.94/152.67 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.94/152.67 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.94/152.67 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.94/152.67 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.94/152.67 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.94/152.67 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.94/152.67 590.94/152.67 Q is empty. 590.94/152.67 We have to consider all minimal (P,Q,R)-chains. 590.94/152.67 ---------------------------------------- 590.94/152.67 590.94/152.67 (147) QDPOrderProof (EQUIVALENT) 590.94/152.67 We use the reduction pair processor [LPAR04,JAR06]. 590.94/152.67 590.94/152.67 590.94/152.67 The following pairs can be oriented strictly and are deleted. 590.94/152.67 590.94/152.67 0^1(1(2(4(0(x1))))) -> 0^1(1(2(1(4(0(x1)))))) 590.94/152.67 The remaining pairs can at least be oriented weakly. 590.94/152.67 Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]: 590.94/152.67 590.94/152.67 <<< 590.94/152.67 POL(0^1(x_1)) = [[0A]] + [[0A, 0A, 0A]] * x_1 590.94/152.67 >>> 590.94/152.67 590.94/152.67 <<< 590.94/152.67 POL(1(x_1)) = [[-I], [-I], [0A]] + [[0A, -I, -I], [0A, -I, 0A], [-I, -I, -I]] * x_1 590.94/152.67 >>> 590.94/152.67 590.94/152.67 <<< 590.94/152.67 POL(2(x_1)) = [[0A], [-I], [-I]] + [[-I, -I, -I], [0A, -I, -I], [-I, -I, 0A]] * x_1 590.94/152.67 >>> 590.94/152.67 590.94/152.67 <<< 590.94/152.67 POL(4(x_1)) = [[0A], [-I], [0A]] + [[0A, -I, -I], [0A, 0A, -I], [0A, 0A, 0A]] * x_1 590.94/152.67 >>> 590.94/152.67 590.94/152.67 <<< 590.94/152.67 POL(0(x_1)) = [[0A], [1A], [0A]] + [[0A, 0A, -I], [0A, 0A, -I], [0A, 1A, 0A]] * x_1 590.94/152.67 >>> 590.94/152.67 590.94/152.67 <<< 590.94/152.67 POL(3(x_1)) = [[0A], [-I], [-I]] + [[-I, -I, -I], [-I, -I, -I], [-I, -I, -I]] * x_1 590.94/152.67 >>> 590.94/152.67 590.94/152.67 <<< 590.94/152.67 POL(5(x_1)) = [[0A], [-I], [-I]] + [[-I, -I, -I], [-I, -I, -I], [-I, -I, -I]] * x_1 590.94/152.67 >>> 590.94/152.67 590.94/152.67 590.94/152.67 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 590.94/152.67 590.94/152.67 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.94/152.67 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.94/152.67 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.94/152.67 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.94/152.67 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.94/152.67 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.94/152.67 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.94/152.67 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.94/152.67 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.94/152.67 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.94/152.67 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.94/152.67 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.94/152.67 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.94/152.67 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.94/152.67 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.94/152.67 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.94/152.67 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.94/152.67 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.94/152.67 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.94/152.67 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.94/152.67 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.94/152.67 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.94/152.67 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.94/152.67 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.94/152.67 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.94/152.67 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.94/152.67 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.94/152.67 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.94/152.67 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.94/152.67 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.94/152.67 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.94/152.67 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.94/152.67 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.94/152.67 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.94/152.67 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.94/152.67 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.94/152.67 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.94/152.67 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.94/152.67 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.94/152.67 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.94/152.67 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.94/152.67 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.94/152.67 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.94/152.67 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.94/152.67 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.94/152.67 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.94/152.67 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.94/152.67 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.94/152.67 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.94/152.67 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.94/152.67 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.94/152.67 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.94/152.67 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.94/152.67 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.94/152.67 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.94/152.67 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.94/152.67 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.94/152.67 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.94/152.67 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.94/152.67 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.94/152.67 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.94/152.67 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.94/152.67 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.94/152.67 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.94/152.67 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.94/152.67 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.94/152.67 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.94/152.67 590.94/152.67 590.94/152.67 ---------------------------------------- 590.94/152.67 590.94/152.67 (148) 590.94/152.67 Obligation: 590.94/152.67 Q DP problem: 590.94/152.67 The TRS P consists of the following rules: 590.94/152.67 590.94/152.67 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.94/152.67 590.94/152.67 The TRS R consists of the following rules: 590.94/152.67 590.94/152.67 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.94/152.67 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.94/152.67 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.94/152.67 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.94/152.67 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.94/152.67 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.94/152.67 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.94/152.67 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.94/152.67 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.94/152.67 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.94/152.68 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.94/152.68 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.94/152.68 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.94/152.68 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.94/152.68 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.94/152.68 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.94/152.68 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.94/152.68 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.94/152.68 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.94/152.68 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.94/152.68 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.94/152.68 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.94/152.68 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.94/152.68 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.94/152.68 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.94/152.68 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.94/152.68 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.94/152.68 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.94/152.68 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.94/152.68 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.94/152.68 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.94/152.68 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.94/152.68 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.94/152.68 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.94/152.68 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.94/152.68 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.94/152.68 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.94/152.68 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.94/152.68 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.94/152.68 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.94/152.68 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.94/152.68 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.94/152.68 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.94/152.68 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.94/152.68 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.94/152.68 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.94/152.68 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.94/152.68 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.94/152.68 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.94/152.68 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.94/152.68 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.94/152.68 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.94/152.68 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.94/152.68 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.94/152.68 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.94/152.68 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.94/152.68 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.94/152.68 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.94/152.68 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.94/152.68 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.94/152.68 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.94/152.68 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.94/152.68 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.94/152.68 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.94/152.68 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.94/152.68 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.94/152.68 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.94/152.68 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.94/152.68 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.94/152.68 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.94/152.68 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.94/152.68 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.94/152.68 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.94/152.68 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.94/152.68 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.94/152.68 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.94/152.68 590.94/152.68 Q is empty. 590.94/152.68 We have to consider all minimal (P,Q,R)-chains. 590.94/152.68 ---------------------------------------- 590.94/152.68 590.94/152.68 (149) QDPOrderProof (EQUIVALENT) 590.94/152.68 We use the reduction pair processor [LPAR04,JAR06]. 590.94/152.68 590.94/152.68 590.94/152.68 The following pairs can be oriented strictly and are deleted. 590.94/152.68 590.94/152.68 0^1(1(2(4(4(x1))))) -> 0^1(1(x1)) 590.94/152.68 The remaining pairs can at least be oriented weakly. 590.94/152.68 Used ordering: Polynomial Order [NEGPOLO,POLO] with Interpretation: 590.94/152.68 590.94/152.68 POL( 0^1_1(x_1) ) = max{0, 2x_1 - 2} 590.94/152.68 POL( 1_1(x_1) ) = max{0, x_1 - 2} 590.94/152.68 POL( 0_1(x_1) ) = max{0, -2} 590.94/152.68 POL( 2_1(x_1) ) = max{0, 2x_1 - 2} 590.94/152.68 POL( 3_1(x_1) ) = max{0, -2} 590.94/152.68 POL( 5_1(x_1) ) = max{0, -2} 590.94/152.68 POL( 4_1(x_1) ) = 2x_1 + 1 590.94/152.68 590.94/152.68 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 590.94/152.68 590.94/152.68 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.94/152.68 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.94/152.68 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.94/152.68 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.94/152.68 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.94/152.68 590.94/152.68 590.94/152.68 ---------------------------------------- 590.94/152.68 590.94/152.68 (150) 590.94/152.68 Obligation: 590.94/152.68 Q DP problem: 590.94/152.68 P is empty. 590.94/152.68 The TRS R consists of the following rules: 590.94/152.68 590.94/152.68 0(1(0(0(x1)))) -> 0(2(0(2(1(0(x1)))))) 590.94/152.68 0(0(1(0(x1)))) -> 0(0(0(2(1(x1))))) 590.94/152.68 1(0(1(0(x1)))) -> 2(0(3(0(1(1(x1)))))) 590.94/152.68 0(1(4(0(x1)))) -> 0(4(1(3(0(x1))))) 590.94/152.68 0(1(4(0(x1)))) -> 5(0(0(4(1(x1))))) 590.94/152.68 0(1(4(0(x1)))) -> 0(4(0(5(1(x1))))) 590.94/152.68 0(1(4(0(x1)))) -> 0(5(4(1(5(0(x1)))))) 590.94/152.68 0(1(4(0(x1)))) -> 0(4(5(1(5(0(x1)))))) 590.94/152.68 0(1(4(0(x1)))) -> 5(0(4(0(5(1(x1)))))) 590.94/152.68 0(1(2(4(x1)))) -> 4(0(5(2(1(x1))))) 590.94/152.68 0(1(2(4(x1)))) -> 0(5(2(4(1(x1))))) 590.94/152.68 0(1(2(4(x1)))) -> 0(2(5(4(1(x1))))) 590.94/152.68 0(1(2(4(x1)))) -> 4(1(3(0(2(x1))))) 590.94/152.68 0(1(2(4(x1)))) -> 4(1(5(0(2(x1))))) 590.94/152.68 0(1(2(4(x1)))) -> 4(0(2(1(2(x1))))) 590.94/152.68 0(1(2(4(x1)))) -> 5(0(4(1(2(x1))))) 590.94/152.68 0(1(2(4(x1)))) -> 4(1(2(0(3(x1))))) 590.94/152.68 0(1(2(4(x1)))) -> 0(2(2(1(4(x1))))) 590.94/152.68 0(1(2(4(x1)))) -> 0(1(2(3(4(x1))))) 590.94/152.68 0(1(2(4(x1)))) -> 0(2(1(5(4(x1))))) 590.94/152.68 0(1(2(4(x1)))) -> 4(1(2(0(5(x1))))) 590.94/152.68 0(1(2(4(x1)))) -> 0(2(1(4(5(x1))))) 590.94/152.68 0(1(2(4(x1)))) -> 4(0(2(5(1(2(x1)))))) 590.94/152.68 0(1(2(4(x1)))) -> 0(2(5(2(1(4(x1)))))) 590.94/152.68 0(1(2(4(x1)))) -> 4(1(2(0(3(4(x1)))))) 590.94/152.68 0(0(3(4(x1)))) -> 4(0(2(0(3(x1))))) 590.94/152.68 0(0(3(4(x1)))) -> 0(4(0(2(3(x1))))) 590.94/152.68 0(1(4(4(x1)))) -> 4(1(5(0(4(x1))))) 590.94/152.68 0(1(4(4(x1)))) -> 4(0(2(1(4(x1))))) 590.94/152.68 0(1(4(4(x1)))) -> 5(0(4(1(4(x1))))) 590.94/152.68 0(1(4(4(x1)))) -> 4(0(5(1(4(x1))))) 590.94/152.68 0(1(4(4(x1)))) -> 0(4(5(1(4(x1))))) 590.94/152.68 0(1(2(0(0(x1))))) -> 0(2(0(2(1(0(x1)))))) 590.94/152.68 0(1(2(4(0(x1))))) -> 0(1(2(1(4(0(x1)))))) 590.94/152.68 0(1(2(4(0(x1))))) -> 0(4(3(0(2(1(x1)))))) 590.94/152.68 0(1(2(4(0(x1))))) -> 2(0(1(3(0(4(x1)))))) 590.94/152.68 0(1(4(4(0(x1))))) -> 0(5(0(4(4(1(x1)))))) 590.94/152.68 0(1(4(4(0(x1))))) -> 4(0(2(1(0(4(x1)))))) 590.94/152.68 0(1(4(4(0(x1))))) -> 0(4(1(4(0(5(x1)))))) 590.94/152.68 4(1(1(0(1(x1))))) -> 5(0(4(1(1(1(x1)))))) 590.94/152.68 0(1(4(0(1(x1))))) -> 0(1(1(5(0(4(x1)))))) 590.94/152.68 0(0(3(1(1(x1))))) -> 0(2(0(1(3(1(x1)))))) 590.94/152.68 1(0(0(3(1(x1))))) -> 3(0(1(5(1(0(x1)))))) 590.94/152.68 0(0(1(4(1(x1))))) -> 0(0(4(1(1(5(x1)))))) 590.94/152.68 0(1(2(4(1(x1))))) -> 0(2(1(2(1(4(x1)))))) 590.94/152.68 0(1(2(4(1(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.94/152.68 0(0(3(4(1(x1))))) -> 0(4(0(1(2(3(x1)))))) 590.94/152.68 0(1(2(0(4(x1))))) -> 0(4(1(2(0(2(x1)))))) 590.94/152.68 0(1(0(1(4(x1))))) -> 0(1(3(4(0(1(x1)))))) 590.94/152.68 0(0(3(1(4(x1))))) -> 0(5(4(0(1(3(x1)))))) 590.94/152.68 0(0(3(1(4(x1))))) -> 0(2(0(1(3(4(x1)))))) 590.94/152.68 0(1(0(2(4(x1))))) -> 0(2(0(3(4(1(x1)))))) 590.94/152.68 0(1(0(2(4(x1))))) -> 4(0(2(0(5(1(x1)))))) 590.94/152.68 0(1(0(2(4(x1))))) -> 0(4(1(2(0(3(x1)))))) 590.94/152.68 0(0(1(2(4(x1))))) -> 0(0(2(4(1(2(x1)))))) 590.94/152.68 1(0(1(2(4(x1))))) -> 5(1(4(0(2(1(x1)))))) 590.94/152.68 4(0(1(2(4(x1))))) -> 4(0(2(2(1(4(x1)))))) 590.94/152.68 4(0(1(2(4(x1))))) -> 0(4(2(5(1(4(x1)))))) 590.94/152.68 0(1(1(2(4(x1))))) -> 0(5(1(2(1(4(x1)))))) 590.94/152.68 0(1(2(2(4(x1))))) -> 4(2(0(5(2(1(x1)))))) 590.94/152.68 0(1(2(2(4(x1))))) -> 5(0(2(2(4(1(x1)))))) 590.94/152.68 0(1(2(2(4(x1))))) -> 0(4(2(3(1(2(x1)))))) 590.94/152.68 0(1(2(2(4(x1))))) -> 0(2(1(4(1(2(x1)))))) 590.94/152.68 0(0(3(2(4(x1))))) -> 0(0(4(5(2(3(x1)))))) 590.94/152.68 0(1(4(2(4(x1))))) -> 5(0(2(4(4(1(x1)))))) 590.94/152.68 0(1(4(2(4(x1))))) -> 4(4(2(1(0(4(x1)))))) 590.94/152.68 0(1(4(2(4(x1))))) -> 5(4(0(2(1(4(x1)))))) 590.94/152.68 0(1(4(2(4(x1))))) -> 2(0(4(3(1(4(x1)))))) 590.94/152.68 0(1(4(2(4(x1))))) -> 5(0(2(4(1(4(x1)))))) 590.94/152.68 0(1(4(2(4(x1))))) -> 0(2(5(4(1(4(x1)))))) 590.94/152.68 1(2(1(3(4(x1))))) -> 1(4(1(2(2(3(x1)))))) 590.94/152.68 0(0(5(3(4(x1))))) -> 0(0(4(5(0(3(x1)))))) 590.94/152.68 0(0(5(3(4(x1))))) -> 0(4(1(3(0(5(x1)))))) 590.94/152.68 0(1(0(4(4(x1))))) -> 0(4(1(3(0(4(x1)))))) 590.94/152.68 1(0(1(4(4(x1))))) -> 1(4(1(3(0(4(x1)))))) 590.94/152.68 0(1(2(4(4(x1))))) -> 4(2(4(3(0(1(x1)))))) 590.94/152.68 0(1(2(4(4(x1))))) -> 2(4(1(3(0(4(x1)))))) 590.94/152.68 0(0(3(4(4(x1))))) -> 4(4(0(3(0(2(x1)))))) 590.94/152.68 0(0(3(4(4(x1))))) -> 0(5(4(0(3(4(x1)))))) 590.94/152.68 0(1(4(4(4(x1))))) -> 4(0(1(3(4(4(x1)))))) 590.94/152.68 0(1(2(5(4(x1))))) -> 0(5(4(1(2(3(x1)))))) 590.94/152.68 0(1(4(5(4(x1))))) -> 0(5(0(4(1(4(x1)))))) 590.94/152.68 590.94/152.68 Q is empty. 590.94/152.68 We have to consider all minimal (P,Q,R)-chains. 590.94/152.68 ---------------------------------------- 590.94/152.68 590.94/152.68 (151) PisEmptyProof (EQUIVALENT) 590.94/152.68 The TRS P is empty. Hence, there is no (P,Q,R) chain. 590.94/152.68 ---------------------------------------- 590.94/152.68 590.94/152.68 (152) 590.94/152.68 YES 590.98/152.74 EOF