/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 550 ms] (4) QTRS (5) DependencyPairsProof [EQUIVALENT, 1616 ms] (6) QDP (7) QDPOrderProof [EQUIVALENT, 3121 ms] (8) QDP (9) QDPOrderProof [EQUIVALENT, 1708 ms] (10) QDP (11) QDPOrderProof [EQUIVALENT, 1418 ms] (12) QDP (13) QDPOrderProof [EQUIVALENT, 1010 ms] (14) QDP (15) QDPOrderProof [EQUIVALENT, 1200 ms] (16) QDP (17) QDPOrderProof [EQUIVALENT, 1469 ms] (18) QDP (19) DependencyGraphProof [EQUIVALENT, 0 ms] (20) AND (21) QDP (22) QDPOrderProof [EQUIVALENT, 0 ms] (23) QDP (24) QDPOrderProof [EQUIVALENT, 59 ms] (25) QDP (26) MRRProof [EQUIVALENT, 4247 ms] (27) QDP (28) MRRProof [EQUIVALENT, 1210 ms] (29) QDP (30) MRRProof [EQUIVALENT, 1303 ms] (31) QDP (32) MRRProof [EQUIVALENT, 2663 ms] (33) QDP (34) PisEmptyProof [EQUIVALENT, 0 ms] (35) YES (36) QDP (37) QDPOrderProof [EQUIVALENT, 72 ms] (38) QDP (39) QDPOrderProof [EQUIVALENT, 82 ms] (40) QDP (41) QDPOrderProof [EQUIVALENT, 91 ms] (42) QDP (43) QDPOrderProof [EQUIVALENT, 83 ms] (44) QDP (45) QDPOrderProof [EQUIVALENT, 85 ms] (46) QDP (47) MRRProof [EQUIVALENT, 2175 ms] (48) QDP (49) QDPOrderProof [EQUIVALENT, 63 ms] (50) QDP (51) MRRProof [EQUIVALENT, 1297 ms] (52) QDP (53) MRRProof [EQUIVALENT, 1451 ms] (54) QDP (55) MRRProof [EQUIVALENT, 1892 ms] (56) QDP (57) DependencyGraphProof [EQUIVALENT, 0 ms] (58) TRUE (59) QDP (60) QDPOrderProof [EQUIVALENT, 109 ms] (61) QDP (62) QDPOrderProof [EQUIVALENT, 118 ms] (63) QDP (64) QDPOrderProof [EQUIVALENT, 149 ms] (65) QDP (66) DependencyGraphProof [EQUIVALENT, 0 ms] (67) AND (68) QDP (69) QDPOrderProof [EQUIVALENT, 70 ms] (70) QDP (71) QDPOrderProof [EQUIVALENT, 76 ms] (72) QDP (73) QDPOrderProof [EQUIVALENT, 79 ms] (74) QDP (75) MRRProof [EQUIVALENT, 1466 ms] (76) QDP (77) MRRProof [EQUIVALENT, 1239 ms] (78) QDP (79) MRRProof [EQUIVALENT, 1420 ms] (80) QDP (81) MRRProof [EQUIVALENT, 5056 ms] (82) QDP (83) DependencyGraphProof [EQUIVALENT, 0 ms] (84) TRUE (85) QDP (86) QDPOrderProof [EQUIVALENT, 70 ms] (87) QDP (88) MRRProof [EQUIVALENT, 2298 ms] (89) QDP (90) QDPOrderProof [EQUIVALENT, 55 ms] (91) QDP (92) MRRProof [EQUIVALENT, 1002 ms] (93) QDP (94) MRRProof [EQUIVALENT, 874 ms] (95) QDP (96) MRRProof [EQUIVALENT, 1867 ms] (97) QDP (98) MRRProof [EQUIVALENT, 2669 ms] (99) QDP (100) MRRProof [EQUIVALENT, 916 ms] (101) QDP (102) DependencyGraphProof [EQUIVALENT, 0 ms] (103) TRUE (104) QDP (105) QDPOrderProof [EQUIVALENT, 57 ms] (106) QDP (107) QDPOrderProof [EQUIVALENT, 71 ms] (108) QDP (109) QDPOrderProof [EQUIVALENT, 63 ms] (110) QDP (111) QDPOrderProof [EQUIVALENT, 65 ms] (112) QDP (113) MRRProof [EQUIVALENT, 646 ms] (114) QDP (115) MRRProof [EQUIVALENT, 1203 ms] (116) QDP (117) MRRProof [EQUIVALENT, 1119 ms] (118) QDP (119) MRRProof [EQUIVALENT, 779 ms] (120) QDP (121) MRRProof [EQUIVALENT, 1150 ms] (122) QDP (123) MRRProof [EQUIVALENT, 1471 ms] (124) QDP (125) MRRProof [EQUIVALENT, 1643 ms] (126) QDP (127) QDPOrderProof [EQUIVALENT, 999 ms] (128) QDP (129) PisEmptyProof [EQUIVALENT, 0 ms] (130) YES (131) QDP (132) MRRProof [EQUIVALENT, 6330 ms] (133) QDP (134) QDPOrderProof [EQUIVALENT, 50 ms] (135) QDP (136) PisEmptyProof [EQUIVALENT, 0 ms] (137) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: 0(1(1(2(3(3(x1)))))) -> 0(1(1(3(2(3(x1)))))) 4(4(2(0(3(1(2(3(x1)))))))) -> 4(2(4(0(3(1(2(3(x1)))))))) 4(5(0(1(4(2(5(3(x1)))))))) -> 4(5(0(2(3(4(1(5(x1)))))))) 0(1(0(2(5(0(5(3(0(x1))))))))) -> 0(3(5(5(0(0(2(1(0(x1))))))))) 1(1(0(2(3(3(2(2(5(x1))))))))) -> 1(1(3(2(3(2(0(2(5(x1))))))))) 2(3(4(1(2(2(2(1(4(x1))))))))) -> 2(3(2(4(1(2(2(1(4(x1))))))))) 5(5(3(1(1(4(1(2(0(x1))))))))) -> 5(5(3(1(1(1(4(2(0(x1))))))))) 1(0(3(4(5(1(1(3(4(0(x1)))))))))) -> 0(2(3(0(0(0(1(0(3(3(x1)))))))))) 1(1(2(5(4(1(4(3(5(1(x1)))))))))) -> 1(4(4(3(5(1(0(0(1(4(x1)))))))))) 2(2(2(4(4(1(1(5(3(5(x1)))))))))) -> 3(0(0(2(2(2(1(0(2(0(x1)))))))))) 4(1(5(3(1(2(2(4(3(4(x1)))))))))) -> 2(4(2(2(1(5(3(3(4(0(x1)))))))))) 4(2(1(0(3(5(2(4(4(4(x1)))))))))) -> 4(0(1(0(3(1(3(0(0(5(x1)))))))))) 0(0(3(5(4(5(0(3(5(0(2(x1))))))))))) -> 0(0(3(5(4(0(5(5(3(0(2(x1))))))))))) 0(1(2(0(4(2(4(3(3(0(5(x1))))))))))) -> 0(1(0(5(2(2(1(5(0(4(x1)))))))))) 0(1(3(0(4(2(5(1(3(5(3(x1))))))))))) -> 3(4(3(1(4(0(5(2(4(2(x1)))))))))) 0(4(4(3(1(4(3(1(2(0(0(x1))))))))))) -> 2(1(2(3(1(1(3(3(3(2(x1)))))))))) 0(5(0(0(5(2(0(4(0(4(0(x1))))))))))) -> 0(5(0(0(5(2(4(0(0(4(0(x1))))))))))) 0(5(3(5(1(4(0(5(3(2(4(x1))))))))))) -> 2(3(2(0(2(3(5(5(5(4(x1)))))))))) 1(0(4(1(0(2(4(1(1(1(4(x1))))))))))) -> 5(5(2(2(3(4(2(4(3(5(x1)))))))))) 1(0(5(3(2(4(2(0(2(4(0(x1))))))))))) -> 0(1(1(1(0(4(0(1(2(5(x1)))))))))) 1(1(5(4(1(0(4(0(0(1(3(x1))))))))))) -> 4(2(0(2(4(1(3(2(1(5(x1)))))))))) 1(2(3(5(1(4(3(2(5(0(2(x1))))))))))) -> 4(0(0(5(2(2(0(2(1(5(x1)))))))))) 1(3(5(0(0(1(1(1(4(0(1(x1))))))))))) -> 0(4(5(0(5(0(5(1(3(0(x1)))))))))) 1(4(0(5(5(5(1(0(3(2(1(x1))))))))))) -> 3(2(0(1(5(2(4(2(1(1(x1)))))))))) 1(4(2(5(0(4(2(1(2(3(5(x1))))))))))) -> 2(4(5(3(0(4(5(0(0(5(x1)))))))))) 1(4(4(0(5(0(4(2(1(3(2(x1))))))))))) -> 3(3(1(4(5(5(1(4(5(2(x1)))))))))) 1(5(5(5(5(3(4(2(5(1(2(x1))))))))))) -> 4(1(0(4(5(2(4(3(0(3(x1)))))))))) 2(0(0(1(3(4(1(0(2(4(5(x1))))))))))) -> 3(4(4(0(0(4(3(2(1(5(x1)))))))))) 2(0(4(1(2(4(2(0(3(5(5(x1))))))))))) -> 1(2(2(0(3(3(0(4(1(4(x1)))))))))) 2(0(5(0(3(3(3(1(3(3(1(x1))))))))))) -> 5(2(0(5(0(5(3(5(5(3(x1)))))))))) 2(2(3(1(0(1(3(5(2(3(1(x1))))))))))) -> 5(3(3(4(1(1(0(0(1(2(x1)))))))))) 2(3(5(3(0(3(4(5(2(1(2(x1))))))))))) -> 5(5(5(1(2(3(5(3(0(4(x1)))))))))) 2(3(5(4(5(1(5(5(3(5(1(x1))))))))))) -> 5(3(2(0(5(3(1(5(5(4(x1)))))))))) 2(4(3(0(1(2(0(1(4(2(4(x1))))))))))) -> 0(5(4(5(2(3(2(1(0(3(x1)))))))))) 2(5(5(1(1(0(3(0(5(4(4(x1))))))))))) -> 2(5(5(1(1(3(0(5(0(4(4(x1))))))))))) 2(5(5(4(4(4(4(4(5(1(4(x1))))))))))) -> 4(4(0(5(3(5(4(2(2(3(x1)))))))))) 3(0(1(5(0(0(4(1(0(4(5(x1))))))))))) -> 3(0(1(3(2(0(0(4(0(3(x1)))))))))) 3(3(0(1(2(0(4(1(5(1(1(x1))))))))))) -> 4(1(0(3(3(2(4(0(3(1(x1)))))))))) 3(3(0(3(2(0(1(4(2(2(4(x1))))))))))) -> 5(1(3(3(2(3(0(5(5(0(x1)))))))))) 3(4(2(4(3(0(4(1(2(5(2(x1))))))))))) -> 3(2(4(4(3(0(4(1(2(5(2(x1))))))))))) 3(5(1(2(1(0(2(4(5(0(2(x1))))))))))) -> 1(3(0(5(2(0(1(5(5(5(x1)))))))))) 4(0(1(0(1(4(3(0(0(1(0(x1))))))))))) -> 4(4(4(2(0(2(3(0(5(3(x1)))))))))) 4(1(4(3(0(3(5(2(5(3(4(x1))))))))))) -> 5(2(4(1(4(3(0(2(4(4(x1)))))))))) 4(1(4(3(2(2(5(4(5(3(1(x1))))))))))) -> 5(3(2(4(3(2(4(2(3(0(x1)))))))))) 4(3(5(1(4(1(5(5(4(2(0(x1))))))))))) -> 5(4(4(3(2(2(1(0(0(3(x1)))))))))) 5(0(2(3(5(3(1(2(2(1(3(x1))))))))))) -> 4(5(5(1(0(1(4(2(5(0(x1)))))))))) 5(0(4(4(5(5(3(4(1(1(2(x1))))))))))) -> 1(1(4(5(3(4(0(2(4(3(x1)))))))))) 5(3(1(1(4(0(1(5(5(1(2(x1))))))))))) -> 5(5(4(4(1(3(2(4(3(3(x1)))))))))) 5(4(2(0(3(4(3(5(4(1(2(x1))))))))))) -> 5(2(2(5(1(0(2(2(2(2(x1)))))))))) 5(5(0(1(0(0(4(1(2(2(4(x1))))))))))) -> 1(5(1(4(4(4(0(1(2(0(x1)))))))))) 5(5(2(1(0(0(5(1(5(1(2(x1))))))))))) -> 1(5(1(0(0(5(3(0(3(0(x1)))))))))) 5(5(2(5(3(2(3(1(4(0(0(x1))))))))))) -> 4(0(4(3(0(3(1(0(4(2(x1)))))))))) 0(2(3(3(3(1(3(0(4(2(3(2(x1)))))))))))) -> 1(5(3(1(5(4(4(1(4(4(x1)))))))))) 1(1(2(2(2(0(4(0(5(2(2(1(x1)))))))))))) -> 4(1(0(5(3(3(5(4(5(4(x1)))))))))) 1(2(1(2(1(2(5(1(1(4(3(1(x1)))))))))))) -> 1(2(1(1(5(1(4(2(3(1(2(1(x1)))))))))))) 1(3(1(5(4(3(1(5(3(2(4(5(x1)))))))))))) -> 1(3(1(5(4(3(1(5(2(3(4(5(x1)))))))))))) 1(3(1(5(5(1(1(4(0(1(3(0(x1)))))))))))) -> 4(0(1(4(1(3(3(0(3(2(x1)))))))))) 3(0(2(5(5(0(3(0(4(4(0(0(x1)))))))))))) -> 2(0(4(1(5(3(4(4(2(1(x1)))))))))) 3(0(5(2(0(2(2(2(0(2(5(1(x1)))))))))))) -> 5(4(4(4(5(0(3(2(1(1(x1)))))))))) 3(4(2(0(0(3(4(2(0(0(2(0(x1)))))))))))) -> 3(0(0(4(3(2(0(0(4(2(2(0(x1)))))))))))) 3(4(4(0(0(3(4(0(3(0(2(0(x1)))))))))))) -> 5(4(1(1(4(3(1(5(1(5(x1)))))))))) 3(4(5(2(0(2(0(3(0(5(4(5(x1)))))))))))) -> 1(5(4(2(4(3(4(3(3(2(x1)))))))))) 5(0(2(0(1(1(5(4(0(3(1(1(x1)))))))))))) -> 0(4(2(3(4(3(4(4(3(4(x1)))))))))) 5(1(5(0(2(1(2(3(0(2(5(3(x1)))))))))))) -> 4(4(2(1(4(3(0(3(4(2(x1)))))))))) 0(2(2(4(0(3(2(5(2(5(2(3(1(x1))))))))))))) -> 0(2(2(4(0(3(5(2(2(5(2(3(1(x1))))))))))))) 4(3(3(2(0(3(2(5(5(1(4(3(0(x1))))))))))))) -> 4(3(3(2(3(0(2(5(5(1(4(3(0(x1))))))))))))) 2(5(1(2(0(1(1(2(0(3(5(0(5(3(x1)))))))))))))) -> 2(5(1(2(0(1(1(0(2(3(5(0(5(3(x1)))))))))))))) 4(5(5(4(4(2(5(4(4(0(2(3(1(3(x1)))))))))))))) -> 4(5(5(4(4(2(5(4(0(4(2(3(1(3(x1)))))))))))))) 2(3(1(4(1(2(3(1(2(1(2(3(3(3(2(x1))))))))))))))) -> 2(3(1(4(1(2(3(1(2(2(1(3(3(3(2(x1))))))))))))))) 2(0(3(1(1(1(1(0(2(2(4(4(4(2(0(3(3(x1))))))))))))))))) -> 2(0(3(1(1(1(1(0(2(2(4(4(4(0(2(3(3(x1))))))))))))))))) 3(1(0(5(2(1(4(0(4(5(1(1(3(0(3(5(0(x1))))))))))))))))) -> 3(1(0(5(2(1(4(0(4(5(1(3(1(0(3(5(0(x1))))))))))))))))) 4(2(2(2(2(2(1(5(3(4(3(1(1(3(3(1(2(x1))))))))))))))))) -> 4(2(2(2(2(2(1(5(3(3(4(1(1(3(3(1(2(x1))))))))))))))))) 3(4(1(0(0(1(1(2(0(0(1(4(4(4(4(1(5(3(x1)))))))))))))))))) -> 3(4(0(0(1(1(1(2(0(0(1(4(4(4(4(1(5(3(x1)))))))))))))))))) 5(5(0(1(3(4(2(2(4(2(5(2(2(3(1(2(5(1(x1)))))))))))))))))) -> 5(5(0(1(3(4(2(2(2(4(5(2(2(3(1(2(5(1(x1)))))))))))))))))) 0(2(5(2(4(4(1(1(4(4(4(1(2(1(4(3(4(4(3(x1))))))))))))))))))) -> 0(2(5(2(4(4(1(1(4(4(4(1(2(4(1(3(4(4(3(x1))))))))))))))))))) 0(3(4(0(4(2(1(3(2(0(5(1(5(2(1(2(2(0(0(x1))))))))))))))))))) -> 0(3(4(0(4(2(1(3(2(0(5(5(1(2(1(2(2(0(0(x1))))))))))))))))))) 4(0(2(5(4(5(5(0(3(4(0(5(5(4(4(0(4(5(0(3(x1)))))))))))))))))))) -> 4(0(2(5(4(5(5(0(4(3(0(5(5(4(4(0(4(5(0(3(x1)))))))))))))))))))) 4(1(3(0(5(1(1(0(0(0(4(3(5(4(5(3(0(5(3(3(x1)))))))))))))))))))) -> 4(1(3(0(5(1(1(0(0(0(4(3(4(5(5(3(0(5(3(3(x1)))))))))))))))))))) 1(0(4(1(1(5(1(5(5(0(5(0(0(0(0(4(0(0(3(2(4(x1))))))))))))))))))))) -> 1(0(4(1(5(1(1(5(5(0(5(0(0(0(0(4(0(0(3(2(4(x1))))))))))))))))))))) 4(0(4(3(1(4(5(4(4(4(2(4(4(5(2(0(0(0(4(1(3(x1))))))))))))))))))))) -> 4(0(4(3(1(5(4(4(4(4(2(4(4(5(2(0(0(0(4(1(3(x1))))))))))))))))))))) 1(4(4(3(1(0(5(1(2(5(2(1(4(2(0(4(5(3(0(0(1(4(x1)))))))))))))))))))))) -> 1(4(4(3(1(0(5(1(2(5(2(1(4(2(0(5(4(3(0(0(1(4(x1)))))))))))))))))))))) 2(5(3(1(1(5(4(5(5(2(3(1(3(5(2(2(1(0(4(1(1(3(x1)))))))))))))))))))))) -> 2(5(3(1(1(5(4(5(5(2(3(1(3(5(2(1(2(0(4(1(1(3(x1)))))))))))))))))))))) 5(1(0(5(4(0(3(0(1(1(5(1(2(3(1(2(4(2(0(2(3(4(x1)))))))))))))))))))))) -> 5(1(0(5(4(0(3(0(1(1(5(2(1(3(1(2(4(2(0(2(3(4(x1)))))))))))))))))))))) 2(3(4(5(2(4(3(5(2(3(5(4(2(1(4(5(3(2(1(2(5(5(0(x1))))))))))))))))))))))) -> 2(3(4(5(2(4(3(5(2(3(5(4(2(1(4(5(3(2(2(1(5(5(0(x1))))))))))))))))))))))) 1(5(0(5(0(2(0(2(1(5(4(1(0(1(1(1(3(3(0(1(4(5(3(5(2(3(3(x1))))))))))))))))))))))))))) -> 1(5(0(5(0(2(0(2(1(5(4(1(0(1(1(3(1(3(0(1(4(5(3(5(2(3(3(x1))))))))))))))))))))))))))) 4(5(0(1(0(4(2(4(0(4(0(1(4(5(2(4(3(5(0(1(1(3(3(3(2(2(2(x1))))))))))))))))))))))))))) -> 4(5(0(1(0(4(2(4(0(4(0(1(4(5(2(4(3(5(0(1(3(1(3(3(2(2(2(x1))))))))))))))))))))))))))) 1(0(4(0(1(3(1(3(2(5(4(1(1(5(0(5(1(4(2(1(4(1(1(1(4(4(1(2(x1)))))))))))))))))))))))))))) -> 1(0(0(4(1(3(1(3(2(5(4(1(1(5(0(5(1(4(2(1(4(1(1(1(4(4(1(2(x1)))))))))))))))))))))))))))) 4(2(4(1(1(3(4(2(0(3(0(3(1(5(0(4(1(2(1(2(0(5(5(4(5(0(4(4(x1)))))))))))))))))))))))))))) -> 4(2(4(1(1(3(4(2(0(3(0(3(1(5(0(4(1(2(1(2(0(5(4(5(5(0(4(4(x1)))))))))))))))))))))))))))) 3(3(2(0(1(2(4(5(2(1(2(1(3(0(3(4(4(1(0(4(2(2(5(2(5(0(4(0(3(x1))))))))))))))))))))))))))))) -> 3(3(2(0(1(2(4(5(2(1(2(1(3(0(3(4(4(1(0(4(2(5(2(2(5(0(4(0(3(x1))))))))))))))))))))))))))))) 4(0(3(0(2(0(0(0(4(3(3(4(0(2(0(0(1(3(2(3(0(4(2(2(2(4(4(5(0(5(x1)))))))))))))))))))))))))))))) -> 4(0(3(0(2(0(0(0(4(3(3(4(0(2(0(0(1(3(2(3(0(2(4(2(2(4(4(5(0(5(x1)))))))))))))))))))))))))))))) 4(5(5(4(4(2(0(1(3(5(5(0(0(4(0(4(1(1(0(0(4(4(5(3(5(5(1(4(0(3(x1)))))))))))))))))))))))))))))) -> 4(5(5(4(2(4(0(1(3(5(5(0(0(4(0(4(1(1(0(0(4(4(5(3(5(5(1(4(0(3(x1)))))))))))))))))))))))))))))) Q is empty. ---------------------------------------- (1) QTRS Reverse (EQUIVALENT) We applied the QTRS Reverse Processor [REVERSE]. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(4(3(1(1(5(4(3(0(1(x1)))))))))) -> 3(3(0(1(0(0(0(3(2(0(x1)))))))))) 1(5(3(4(1(4(5(2(1(1(x1)))))))))) -> 4(1(0(0(1(5(3(4(4(1(x1)))))))))) 5(3(5(1(1(4(4(2(2(2(x1)))))))))) -> 0(2(0(1(2(2(2(0(0(3(x1)))))))))) 4(3(4(2(2(1(3(5(1(4(x1)))))))))) -> 0(4(3(3(5(1(2(2(4(2(x1)))))))))) 4(4(4(2(5(3(0(1(2(4(x1)))))))))) -> 5(0(0(3(1(3(0(1(0(4(x1)))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 5(0(3(3(4(2(4(0(2(1(0(x1))))))))))) -> 4(0(5(1(2(2(5(0(1(0(x1)))))))))) 3(5(3(1(5(2(4(0(3(1(0(x1))))))))))) -> 2(4(2(5(0(4(1(3(4(3(x1)))))))))) 0(0(2(1(3(4(1(3(4(4(0(x1))))))))))) -> 2(3(3(3(1(1(3(2(1(2(x1)))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(2(3(5(0(4(1(5(3(5(0(x1))))))))))) -> 4(5(5(5(3(2(0(2(3(2(x1)))))))))) 4(1(1(1(4(2(0(1(4(0(1(x1))))))))))) -> 5(3(4(2(4(3(2(2(5(5(x1)))))))))) 0(4(2(0(2(4(2(3(5(0(1(x1))))))))))) -> 5(2(1(0(4(0(1(1(1(0(x1)))))))))) 3(1(0(0(4(0(1(4(5(1(1(x1))))))))))) -> 5(1(2(3(1(4(2(0(2(4(x1)))))))))) 2(0(5(2(3(4(1(5(3(2(1(x1))))))))))) -> 5(1(2(0(2(2(5(0(0(4(x1)))))))))) 1(0(4(1(1(1(0(0(5(3(1(x1))))))))))) -> 0(3(1(5(0(5(0(5(4(0(x1)))))))))) 1(2(3(0(1(5(5(5(0(4(1(x1))))))))))) -> 1(1(2(4(2(5(1(0(2(3(x1)))))))))) 5(3(2(1(2(4(0(5(2(4(1(x1))))))))))) -> 5(0(0(5(4(0(3(5(4(2(x1)))))))))) 2(3(1(2(4(0(5(0(4(4(1(x1))))))))))) -> 2(5(4(1(5(5(4(1(3(3(x1)))))))))) 2(1(5(2(4(3(5(5(5(5(1(x1))))))))))) -> 3(0(3(4(2(5(4(0(1(4(x1)))))))))) 5(4(2(0(1(4(3(1(0(0(2(x1))))))))))) -> 5(1(2(3(4(0(0(4(4(3(x1)))))))))) 5(5(3(0(2(4(2(1(4(0(2(x1))))))))))) -> 4(1(4(0(3(3(0(2(2(1(x1)))))))))) 1(3(3(1(3(3(3(0(5(0(2(x1))))))))))) -> 3(5(5(3(5(0(5(0(2(5(x1)))))))))) 1(3(2(5(3(1(0(1(3(2(2(x1))))))))))) -> 2(1(0(0(1(1(4(3(3(5(x1)))))))))) 2(1(2(5(4(3(0(3(5(3(2(x1))))))))))) -> 4(0(3(5(3(2(1(5(5(5(x1)))))))))) 1(5(3(5(5(1(5(4(5(3(2(x1))))))))))) -> 4(5(5(1(3(5(0(2(3(5(x1)))))))))) 4(2(4(1(0(2(1(0(3(4(2(x1))))))))))) -> 3(0(1(2(3(2(5(4(5(0(x1)))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 4(1(5(4(4(4(4(4(5(5(2(x1))))))))))) -> 3(2(2(4(5(3(5(0(4(4(x1)))))))))) 5(4(0(1(4(0(0(5(1(0(3(x1))))))))))) -> 3(0(4(0(0(2(3(1(0(3(x1)))))))))) 1(1(5(1(4(0(2(1(0(3(3(x1))))))))))) -> 1(3(0(4(2(3(3(0(1(4(x1)))))))))) 4(2(2(4(1(0(2(3(0(3(3(x1))))))))))) -> 0(5(5(0(3(2(3(3(1(5(x1)))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2(0(5(4(2(0(1(2(1(5(3(x1))))))))))) -> 5(5(5(1(0(2(5(0(3(1(x1)))))))))) 0(1(0(0(3(4(1(0(1(0(4(x1))))))))))) -> 3(5(0(3(2(0(2(4(4(4(x1)))))))))) 4(3(5(2(5(3(0(3(4(1(4(x1))))))))))) -> 4(4(2(0(3(4(1(4(2(5(x1)))))))))) 1(3(5(4(5(2(2(3(4(1(4(x1))))))))))) -> 0(3(2(4(2(3(4(2(3(5(x1)))))))))) 0(2(4(5(5(1(4(1(5(3(4(x1))))))))))) -> 3(0(0(1(2(2(3(4(4(5(x1)))))))))) 3(1(2(2(1(3(5(3(2(0(5(x1))))))))))) -> 0(5(2(4(1(0(1(5(5(4(x1)))))))))) 2(1(1(4(3(5(5(4(4(0(5(x1))))))))))) -> 3(4(2(0(4(3(5(4(1(1(x1)))))))))) 2(1(5(5(1(0(4(1(1(3(5(x1))))))))))) -> 3(3(4(2(3(1(4(4(5(5(x1)))))))))) 2(1(4(5(3(4(3(0(2(4(5(x1))))))))))) -> 2(2(2(2(0(1(5(2(2(5(x1)))))))))) 4(2(2(1(4(0(0(1(0(5(5(x1))))))))))) -> 0(2(1(0(4(4(4(1(5(1(x1)))))))))) 2(1(5(1(5(0(0(1(2(5(5(x1))))))))))) -> 0(3(0(3(5(0(0(1(5(1(x1)))))))))) 0(0(4(1(3(2(3(5(2(5(5(x1))))))))))) -> 2(4(0(1(3(0(3(4(0(4(x1)))))))))) 2(3(2(4(0(3(1(3(3(3(2(0(x1)))))))))))) -> 4(4(1(4(4(5(1(3(5(1(x1)))))))))) 1(2(2(5(0(4(0(2(2(2(1(1(x1)))))))))))) -> 4(5(4(5(3(3(5(0(1(4(x1)))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(3(1(0(4(1(1(5(5(1(3(1(x1)))))))))))) -> 2(3(0(3(3(1(4(1(0(4(x1)))))))))) 0(0(4(4(0(3(0(5(5(2(0(3(x1)))))))))))) -> 1(2(4(4(3(5(1(4(0(2(x1)))))))))) 1(5(2(0(2(2(2(0(2(5(0(3(x1)))))))))))) -> 1(1(2(3(0(5(4(4(4(5(x1)))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0(2(0(3(0(4(3(0(0(4(4(3(x1)))))))))))) -> 5(1(5(1(3(4(1(1(4(5(x1)))))))))) 5(4(5(0(3(0(2(0(2(5(4(3(x1)))))))))))) -> 2(3(3(4(3(4(2(4(5(1(x1)))))))))) 1(1(3(0(4(5(1(1(0(2(0(5(x1)))))))))))) -> 4(3(4(4(3(4(3(2(4(0(x1)))))))))) 3(5(2(0(3(2(1(2(0(5(1(5(x1)))))))))))) -> 2(4(3(0(3(4(1(2(4(4(x1)))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 5 + x_1 POL(1(x_1)) = 6 + x_1 POL(2(x_1)) = 7 + x_1 POL(3(x_1)) = 6 + x_1 POL(4(x_1)) = 7 + x_1 POL(5(x_1)) = 5 + x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 0(4(3(1(1(5(4(3(0(1(x1)))))))))) -> 3(3(0(1(0(0(0(3(2(0(x1)))))))))) 1(5(3(4(1(4(5(2(1(1(x1)))))))))) -> 4(1(0(0(1(5(3(4(4(1(x1)))))))))) 5(3(5(1(1(4(4(2(2(2(x1)))))))))) -> 0(2(0(1(2(2(2(0(0(3(x1)))))))))) 4(3(4(2(2(1(3(5(1(4(x1)))))))))) -> 0(4(3(3(5(1(2(2(4(2(x1)))))))))) 4(4(4(2(5(3(0(1(2(4(x1)))))))))) -> 5(0(0(3(1(3(0(1(0(4(x1)))))))))) 5(0(3(3(4(2(4(0(2(1(0(x1))))))))))) -> 4(0(5(1(2(2(5(0(1(0(x1)))))))))) 3(5(3(1(5(2(4(0(3(1(0(x1))))))))))) -> 2(4(2(5(0(4(1(3(4(3(x1)))))))))) 0(0(2(1(3(4(1(3(4(4(0(x1))))))))))) -> 2(3(3(3(1(1(3(2(1(2(x1)))))))))) 4(2(3(5(0(4(1(5(3(5(0(x1))))))))))) -> 4(5(5(5(3(2(0(2(3(2(x1)))))))))) 4(1(1(1(4(2(0(1(4(0(1(x1))))))))))) -> 5(3(4(2(4(3(2(2(5(5(x1)))))))))) 0(4(2(0(2(4(2(3(5(0(1(x1))))))))))) -> 5(2(1(0(4(0(1(1(1(0(x1)))))))))) 3(1(0(0(4(0(1(4(5(1(1(x1))))))))))) -> 5(1(2(3(1(4(2(0(2(4(x1)))))))))) 2(0(5(2(3(4(1(5(3(2(1(x1))))))))))) -> 5(1(2(0(2(2(5(0(0(4(x1)))))))))) 1(0(4(1(1(1(0(0(5(3(1(x1))))))))))) -> 0(3(1(5(0(5(0(5(4(0(x1)))))))))) 1(2(3(0(1(5(5(5(0(4(1(x1))))))))))) -> 1(1(2(4(2(5(1(0(2(3(x1)))))))))) 5(3(2(1(2(4(0(5(2(4(1(x1))))))))))) -> 5(0(0(5(4(0(3(5(4(2(x1)))))))))) 2(3(1(2(4(0(5(0(4(4(1(x1))))))))))) -> 2(5(4(1(5(5(4(1(3(3(x1)))))))))) 2(1(5(2(4(3(5(5(5(5(1(x1))))))))))) -> 3(0(3(4(2(5(4(0(1(4(x1)))))))))) 5(4(2(0(1(4(3(1(0(0(2(x1))))))))))) -> 5(1(2(3(4(0(0(4(4(3(x1)))))))))) 5(5(3(0(2(4(2(1(4(0(2(x1))))))))))) -> 4(1(4(0(3(3(0(2(2(1(x1)))))))))) 1(3(3(1(3(3(3(0(5(0(2(x1))))))))))) -> 3(5(5(3(5(0(5(0(2(5(x1)))))))))) 1(3(2(5(3(1(0(1(3(2(2(x1))))))))))) -> 2(1(0(0(1(1(4(3(3(5(x1)))))))))) 2(1(2(5(4(3(0(3(5(3(2(x1))))))))))) -> 4(0(3(5(3(2(1(5(5(5(x1)))))))))) 1(5(3(5(5(1(5(4(5(3(2(x1))))))))))) -> 4(5(5(1(3(5(0(2(3(5(x1)))))))))) 4(2(4(1(0(2(1(0(3(4(2(x1))))))))))) -> 3(0(1(2(3(2(5(4(5(0(x1)))))))))) 4(1(5(4(4(4(4(4(5(5(2(x1))))))))))) -> 3(2(2(4(5(3(5(0(4(4(x1)))))))))) 5(4(0(1(4(0(0(5(1(0(3(x1))))))))))) -> 3(0(4(0(0(2(3(1(0(3(x1)))))))))) 1(1(5(1(4(0(2(1(0(3(3(x1))))))))))) -> 1(3(0(4(2(3(3(0(1(4(x1)))))))))) 4(2(2(4(1(0(2(3(0(3(3(x1))))))))))) -> 0(5(5(0(3(2(3(3(1(5(x1)))))))))) 2(0(5(4(2(0(1(2(1(5(3(x1))))))))))) -> 5(5(5(1(0(2(5(0(3(1(x1)))))))))) 0(1(0(0(3(4(1(0(1(0(4(x1))))))))))) -> 3(5(0(3(2(0(2(4(4(4(x1)))))))))) 4(3(5(2(5(3(0(3(4(1(4(x1))))))))))) -> 4(4(2(0(3(4(1(4(2(5(x1)))))))))) 1(3(5(4(5(2(2(3(4(1(4(x1))))))))))) -> 0(3(2(4(2(3(4(2(3(5(x1)))))))))) 0(2(4(5(5(1(4(1(5(3(4(x1))))))))))) -> 3(0(0(1(2(2(3(4(4(5(x1)))))))))) 3(1(2(2(1(3(5(3(2(0(5(x1))))))))))) -> 0(5(2(4(1(0(1(5(5(4(x1)))))))))) 2(1(1(4(3(5(5(4(4(0(5(x1))))))))))) -> 3(4(2(0(4(3(5(4(1(1(x1)))))))))) 2(1(5(5(1(0(4(1(1(3(5(x1))))))))))) -> 3(3(4(2(3(1(4(4(5(5(x1)))))))))) 2(1(4(5(3(4(3(0(2(4(5(x1))))))))))) -> 2(2(2(2(0(1(5(2(2(5(x1)))))))))) 4(2(2(1(4(0(0(1(0(5(5(x1))))))))))) -> 0(2(1(0(4(4(4(1(5(1(x1)))))))))) 2(1(5(1(5(0(0(1(2(5(5(x1))))))))))) -> 0(3(0(3(5(0(0(1(5(1(x1)))))))))) 0(0(4(1(3(2(3(5(2(5(5(x1))))))))))) -> 2(4(0(1(3(0(3(4(0(4(x1)))))))))) 2(3(2(4(0(3(1(3(3(3(2(0(x1)))))))))))) -> 4(4(1(4(4(5(1(3(5(1(x1)))))))))) 1(2(2(5(0(4(0(2(2(2(1(1(x1)))))))))))) -> 4(5(4(5(3(3(5(0(1(4(x1)))))))))) 0(3(1(0(4(1(1(5(5(1(3(1(x1)))))))))))) -> 2(3(0(3(3(1(4(1(0(4(x1)))))))))) 0(0(4(4(0(3(0(5(5(2(0(3(x1)))))))))))) -> 1(2(4(4(3(5(1(4(0(2(x1)))))))))) 1(5(2(0(2(2(2(0(2(5(0(3(x1)))))))))))) -> 1(1(2(3(0(5(4(4(4(5(x1)))))))))) 0(2(0(3(0(4(3(0(0(4(4(3(x1)))))))))))) -> 5(1(5(1(3(4(1(1(4(5(x1)))))))))) 5(4(5(0(3(0(2(0(2(5(4(3(x1)))))))))))) -> 2(3(3(4(3(4(2(4(5(1(x1)))))))))) 1(1(3(0(4(5(1(1(0(2(0(5(x1)))))))))))) -> 4(3(4(4(3(4(3(2(4(0(x1)))))))))) 3(5(2(0(3(2(1(2(0(5(1(5(x1)))))))))))) -> 2(4(3(0(3(4(1(2(4(4(x1)))))))))) ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. ---------------------------------------- (5) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (6) Obligation: Q DP problem: The TRS P consists of the following rules: 3^1(3(2(1(1(0(x1)))))) -> 3^1(2(3(1(1(0(x1)))))) 3^1(3(2(1(1(0(x1)))))) -> 2^1(3(1(1(0(x1))))) 3^1(3(2(1(1(0(x1)))))) -> 3^1(1(1(0(x1)))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 3^1(2(1(3(0(4(2(4(x1)))))))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 2^1(1(3(0(4(2(4(x1))))))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 1^1(3(0(4(2(4(x1)))))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 3^1(0(4(2(4(x1))))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 0^1(4(2(4(x1)))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 4^1(2(4(x1))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 2^1(4(x1)) 3^1(5(2(4(1(0(5(4(x1)))))))) -> 5^1(1(4(3(2(0(5(4(x1)))))))) 3^1(5(2(4(1(0(5(4(x1)))))))) -> 1^1(4(3(2(0(5(4(x1))))))) 3^1(5(2(4(1(0(5(4(x1)))))))) -> 4^1(3(2(0(5(4(x1)))))) 3^1(5(2(4(1(0(5(4(x1)))))))) -> 3^1(2(0(5(4(x1))))) 3^1(5(2(4(1(0(5(4(x1)))))))) -> 2^1(0(5(4(x1)))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 0^1(1(2(0(0(5(5(3(0(x1))))))))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 1^1(2(0(0(5(5(3(0(x1)))))))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 2^1(0(0(5(5(3(0(x1))))))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 0^1(0(5(5(3(0(x1)))))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 0^1(5(5(3(0(x1))))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 5^1(5(3(0(x1)))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 5^1(3(0(x1))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 3^1(0(x1)) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 5^1(2(0(2(3(2(3(1(1(x1))))))))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 2^1(0(2(3(2(3(1(1(x1)))))))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 0^1(2(3(2(3(1(1(x1))))))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 2^1(3(2(3(1(1(x1)))))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 3^1(2(3(1(1(x1))))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 2^1(3(1(1(x1)))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 3^1(1(1(x1))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 4^1(1(2(2(1(4(2(3(2(x1))))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 1^1(2(2(1(4(2(3(2(x1)))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 2^1(2(1(4(2(3(2(x1))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 2^1(1(4(2(3(2(x1)))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 1^1(4(2(3(2(x1))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 4^1(2(3(2(x1)))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 2^1(3(2(x1))) 0^1(2(1(4(1(1(3(5(5(x1))))))))) -> 0^1(2(4(1(1(1(3(5(5(x1))))))))) 0^1(2(1(4(1(1(3(5(5(x1))))))))) -> 2^1(4(1(1(1(3(5(5(x1)))))))) 0^1(2(1(4(1(1(3(5(5(x1))))))))) -> 4^1(1(1(1(3(5(5(x1))))))) 0^1(2(1(4(1(1(3(5(5(x1))))))))) -> 1^1(1(1(3(5(5(x1)))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2^1(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 0^1(3(5(5(0(4(5(3(0(0(x1)))))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 3^1(5(5(0(4(5(3(0(0(x1))))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 5^1(5(0(4(5(3(0(0(x1)))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 5^1(0(4(5(3(0(0(x1))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 0^1(4(5(3(0(0(x1)))))) 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0^1(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 4^1(0(0(4(2(5(0(0(5(0(x1)))))))))) 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0^1(0(4(2(5(0(0(5(0(x1))))))))) 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0^1(4(2(5(0(0(5(0(x1)))))))) 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 4^1(2(5(0(0(5(0(x1))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4^1(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4^1(0(5(0(3(1(1(5(5(2(x1)))))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 0^1(5(0(3(1(1(5(5(2(x1))))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 5^1(0(3(1(1(5(5(2(x1)))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 0^1(3(1(1(5(5(2(x1))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 3^1(1(1(5(5(2(x1)))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2^1(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 5^1(2(1(4(0(3(4(4(2(3(x1)))))))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2^1(1(4(0(3(4(4(2(3(x1))))))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 1^1(4(0(3(4(4(2(3(x1)))))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 4^1(0(3(4(4(2(3(x1))))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 0^1(3(4(4(2(3(x1)))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 3^1(4(4(2(3(x1))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 4^1(4(2(3(x1)))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 4^1(2(3(x1))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2^1(3(x1)) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1^1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 2^1(1(3(2(4(1(5(1(1(2(1(x1))))))))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1^1(3(2(4(1(5(1(1(2(1(x1)))))))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 3^1(2(4(1(5(1(1(2(1(x1))))))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 2^1(4(1(5(1(1(2(1(x1)))))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 4^1(1(5(1(1(2(1(x1))))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1^1(5(1(1(2(1(x1)))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 5^1(1(1(2(1(x1))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1^1(1(2(1(x1)))) 5^1(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5^1(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 5^1(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 4^1(3(2(5(1(3(4(5(1(3(1(x1))))))))))) 5^1(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 3^1(2(5(1(3(4(5(1(3(1(x1)))))))))) 5^1(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 2^1(5(1(3(4(5(1(3(1(x1))))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0^1(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 2^1(2(4(0(0(2(3(4(0(0(3(x1))))))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 2^1(4(0(0(2(3(4(0(0(3(x1)))))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 4^1(0(0(2(3(4(0(0(3(x1))))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0^1(0(2(3(4(0(0(3(x1)))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0^1(2(3(4(0(0(3(x1))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 2^1(3(4(0(0(3(x1)))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 3^1(4(0(0(3(x1))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 4^1(0(0(3(x1)))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0^1(0(3(x1))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0^1(3(x1)) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1^1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 3^1(2(5(2(2(5(3(0(4(2(2(0(x1)))))))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 2^1(5(2(2(5(3(0(4(2(2(0(x1))))))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 5^1(2(2(5(3(0(4(2(2(0(x1)))))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 2^1(2(5(3(0(4(2(2(0(x1))))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 2^1(5(3(0(4(2(2(0(x1)))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 5^1(3(0(4(2(2(0(x1))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0^1(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 3^1(4(1(5(5(2(0(3(2(3(3(4(x1)))))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 4^1(1(5(5(2(0(3(2(3(3(4(x1))))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 1^1(5(5(2(0(3(2(3(3(4(x1)))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 5^1(5(2(0(3(2(3(3(4(x1))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 5^1(2(0(3(2(3(3(4(x1)))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 2^1(0(3(2(3(3(4(x1))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0^1(3(2(3(3(4(x1)))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 3^1(2(3(3(4(x1))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3^1(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 5^1(0(5(3(2(0(1(1(0(2(1(5(2(x1))))))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 0^1(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 5^1(3(2(0(1(1(0(2(1(5(2(x1))))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3^1(2(0(1(1(0(2(1(5(2(x1)))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 2^1(0(1(1(0(2(1(5(2(x1))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 0^1(1(1(0(2(1(5(2(x1)))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3^1(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 1^1(3(2(4(0(4(5(2(4(4(5(5(4(x1))))))))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3^1(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 2^1(4(0(4(5(2(4(4(5(5(4(x1))))))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 4^1(0(4(5(2(4(4(5(5(4(x1)))))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 0^1(4(5(2(4(4(5(5(4(x1))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2^1(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 3^1(3(3(1(2(2(1(3(2(1(4(1(3(2(x1)))))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 3^1(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 3^1(1(2(2(1(3(2(1(4(1(3(2(x1)))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 1^1(2(2(1(3(2(1(4(1(3(2(x1))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2^1(2(1(3(2(1(4(1(3(2(x1)))))))))) 3^1(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3^1(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 3^1(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3^1(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1)))))))))))))))) 3^1(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 2^1(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))) 3^1(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 0^1(4(4(4(2(2(0(1(1(1(1(3(0(2(x1)))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0^1(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 5^1(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1)))))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 3^1(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0^1(1(3(1(5(4(0(4(1(2(5(0(1(3(x1)))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 1^1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 3^1(1(5(4(0(4(1(2(5(0(1(3(x1)))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2^1(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 1^1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1)))))))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 3^1(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 3^1(1(1(4(3(3(5(1(2(2(2(2(2(4(x1)))))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 1^1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 1^1(4(3(3(5(1(2(2(2(2(2(4(x1)))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 4^1(3(3(5(1(2(2(2(2(2(4(x1))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 3^1(3(5(1(2(2(2(2(2(4(x1)))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3^1(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 5^1(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1))))))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 1^1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 4^1(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1))))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 4^1(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 4^1(4(1(0(0(2(1(1(1(0(0(4(3(x1))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 4^1(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 1^1(0(0(2(1(1(1(0(0(4(3(x1))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 0^1(0(2(1(1(1(0(0(4(3(x1)))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 0^1(2(1(1(1(0(0(4(3(x1))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 2^1(1(1(1(0(0(4(3(x1)))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 1^1(1(1(0(0(4(3(x1))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 1^1(1(0(0(4(3(x1)))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 1^1(0(0(4(3(x1))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 0^1(0(4(3(x1)))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 0^1(4(3(x1))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1^1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 5^1(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1))))))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 2^1(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1^1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1))))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 3^1(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 2^1(2(5(4(2(2(2(4(3(1(0(5(5(x1))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 2^1(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 5^1(4(2(2(2(4(3(1(0(5(5(x1))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 4^1(2(2(2(4(3(1(0(5(5(x1)))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 2^1(2(2(4(3(1(0(5(5(x1))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3^1(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 4^1(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1)))))))))))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 4^1(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3^1(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1)))))))))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 1^1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 4^1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1)))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0^1(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0^1(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1)))))))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 2^1(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 2^1(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1)))))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 1^1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 2^1(1(5(5(0(2(3(1(2(4(0(4(3(0(x1)))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 1^1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 5^1(5(0(2(3(1(2(4(0(4(3(0(x1)))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3^1(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 0^1(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1))))))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 5^1(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 4^1(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1))))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 0^1(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 4^1(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 4^1(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 5^1(5(0(3(4(0(5(5(4(5(2(0(4(x1))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 5^1(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 0^1(3(4(0(5(5(4(5(2(0(4(x1))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3^1(4(0(5(5(4(5(2(0(4(x1)))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 4^1(0(5(5(4(5(2(0(4(x1))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3^1(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3^1(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1))))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 5^1(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 0^1(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3^1(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 5^1(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 5^1(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 4^1(3(4(0(0(0(1(1(5(0(3(1(4(x1))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 2^1(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1)))))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 3^1(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1)))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4^1(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1)))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(0(0(5(0(5(5(1(1(5(1(4(0(1(x1)))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(5(0(5(5(1(1(5(1(4(0(1(x1)))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 5^1(0(5(5(1(1(5(1(4(0(1(x1))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(5(5(1(1(5(1(4(0(1(x1)))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 5^1(5(1(1(5(1(4(0(1(x1))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 5^1(1(1(5(1(4(0(1(x1)))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 1^1(1(5(1(4(0(1(x1))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 1^1(5(1(4(0(1(x1)))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 5^1(1(4(0(1(x1))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 1^1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1)))))))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 0^1(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1)))))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 0^1(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 0^1(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1)))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 2^1(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 5^1(4(4(2(4(4(4(4(5(1(3(4(0(4(x1)))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(2(4(4(4(4(5(1(3(4(0(4(x1)))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 2^1(4(4(4(4(5(1(3(4(0(4(x1))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(4(4(4(5(1(3(4(0(4(x1)))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(4(4(5(1(3(4(0(4(x1))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(4(5(1(3(4(0(4(x1)))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(5(1(3(4(0(4(x1))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 5^1(1(3(4(0(4(x1)))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4^1(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 1^1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1))))))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 0^1(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 0^1(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1))))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 3^1(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4^1(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 5^1(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3^1(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 1^1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1))))))))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 1^1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 4^1(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1))))))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 0^1(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 2^1(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1))))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 1^1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4^1(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 3^1(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1))))))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 2^1(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 0^1(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1))))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 2^1(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4^1(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 2^1(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 1^1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 3^1(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 1^1(2(5(1(1(0(3(0(4(5(0(1(5(x1))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 2^1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))) 0^1(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0^1(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 0^1(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 5^1(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1)))))))))))))))))))))) 0^1(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 5^1(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))) 0^1(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 1^1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1)))))))))))))))))))) 0^1(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 2^1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1)))))))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 2^1(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 5^1(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1)))))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 5^1(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1)))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 4^1(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 1^1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1)))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 0^1(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1)))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 1^1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1)))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2^1(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2^1(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1)))))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2^1(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 3^1(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1)))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 3^1(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 1^1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1)))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 3^1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 1^1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 1^1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 1^1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 1^1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 1^1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2^1(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 1^1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 5^1(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 0^1(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 5^1(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 1^1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 1^1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(5(2(3(1(3(1(4(0(0(1(x1))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 5^1(2(3(1(3(1(4(0(0(1(x1)))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2^1(3(1(3(1(4(0(0(1(x1))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 3^1(1(3(1(4(0(0(1(x1)))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 1^1(3(1(4(0(0(1(x1))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 3^1(1(4(0(0(1(x1)))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 1^1(4(0(0(1(x1))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(0(0(1(x1)))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 0^1(0(1(x1))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4^1(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4^1(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1))))))))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 0^1(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 5^1(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1))))))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 5^1(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4^1(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3^1(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 0^1(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1)))))))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 4^1(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 0^1(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1)))))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 5^1(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 2^1(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1)))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 2^1(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 5^1(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1)))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5^1(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 0^1(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1))))))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5^1(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 4^1(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1))))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 4^1(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 2^1(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 2^1(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 4^1(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 2^1(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 4^1(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 1^1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 5^1(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 5^1(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3^1(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 5^1(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 4^1(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 4^1(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 1^1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 1^1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 4^1(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 4^1(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 5^1(5(3(1(0(4(2(4(5(5(4(x1))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 5^1(3(1(0(4(2(4(5(5(4(x1)))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3^1(1(0(4(2(4(5(5(4(x1))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 1^1(0(4(2(4(5(5(4(x1)))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(4(2(4(5(5(4(x1))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 4^1(2(4(5(5(4(x1)))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 2^1(4(5(5(4(x1))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (7) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. 0^1(2(1(4(1(1(3(5(5(x1))))))))) -> 1^1(1(1(3(5(5(x1)))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1^1(5(1(1(2(1(x1)))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1^1(1(2(1(x1)))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 1^1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 1^1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1)))))))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 1^1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 1^1(1(1(0(0(4(3(x1))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 1^1(1(0(0(4(3(x1)))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 1^1(1(5(1(4(0(1(x1))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 1^1(5(1(4(0(1(x1)))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 1^1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1))))))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 1^1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 1^1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1)))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 1^1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 1^1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1)))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 1^1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 1^1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 1^1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 1^1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 1^1(3(1(4(0(0(1(x1))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 1^1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = x_1 POL(0^1(x_1)) = 1 POL(1(x_1)) = 0 POL(1^1(x_1)) = x_1 POL(2(x_1)) = 1 POL(2^1(x_1)) = 1 POL(3(x_1)) = x_1 POL(3^1(x_1)) = 1 POL(4(x_1)) = 1 POL(4^1(x_1)) = 1 POL(5(x_1)) = x_1 POL(5^1(x_1)) = 1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) ---------------------------------------- (8) Obligation: Q DP problem: The TRS P consists of the following rules: 3^1(3(2(1(1(0(x1)))))) -> 3^1(2(3(1(1(0(x1)))))) 3^1(3(2(1(1(0(x1)))))) -> 2^1(3(1(1(0(x1))))) 3^1(3(2(1(1(0(x1)))))) -> 3^1(1(1(0(x1)))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 3^1(2(1(3(0(4(2(4(x1)))))))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 2^1(1(3(0(4(2(4(x1))))))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 1^1(3(0(4(2(4(x1)))))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 3^1(0(4(2(4(x1))))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 0^1(4(2(4(x1)))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 4^1(2(4(x1))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 2^1(4(x1)) 3^1(5(2(4(1(0(5(4(x1)))))))) -> 5^1(1(4(3(2(0(5(4(x1)))))))) 3^1(5(2(4(1(0(5(4(x1)))))))) -> 1^1(4(3(2(0(5(4(x1))))))) 3^1(5(2(4(1(0(5(4(x1)))))))) -> 4^1(3(2(0(5(4(x1)))))) 3^1(5(2(4(1(0(5(4(x1)))))))) -> 3^1(2(0(5(4(x1))))) 3^1(5(2(4(1(0(5(4(x1)))))))) -> 2^1(0(5(4(x1)))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 0^1(1(2(0(0(5(5(3(0(x1))))))))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 1^1(2(0(0(5(5(3(0(x1)))))))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 2^1(0(0(5(5(3(0(x1))))))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 0^1(0(5(5(3(0(x1)))))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 0^1(5(5(3(0(x1))))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 5^1(5(3(0(x1)))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 5^1(3(0(x1))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 3^1(0(x1)) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 5^1(2(0(2(3(2(3(1(1(x1))))))))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 2^1(0(2(3(2(3(1(1(x1)))))))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 0^1(2(3(2(3(1(1(x1))))))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 2^1(3(2(3(1(1(x1)))))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 3^1(2(3(1(1(x1))))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 2^1(3(1(1(x1)))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 3^1(1(1(x1))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 4^1(1(2(2(1(4(2(3(2(x1))))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 1^1(2(2(1(4(2(3(2(x1)))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 2^1(2(1(4(2(3(2(x1))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 2^1(1(4(2(3(2(x1)))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 1^1(4(2(3(2(x1))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 4^1(2(3(2(x1)))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 2^1(3(2(x1))) 0^1(2(1(4(1(1(3(5(5(x1))))))))) -> 0^1(2(4(1(1(1(3(5(5(x1))))))))) 0^1(2(1(4(1(1(3(5(5(x1))))))))) -> 2^1(4(1(1(1(3(5(5(x1)))))))) 0^1(2(1(4(1(1(3(5(5(x1))))))))) -> 4^1(1(1(1(3(5(5(x1))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2^1(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 0^1(3(5(5(0(4(5(3(0(0(x1)))))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 3^1(5(5(0(4(5(3(0(0(x1))))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 5^1(5(0(4(5(3(0(0(x1)))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 5^1(0(4(5(3(0(0(x1))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 0^1(4(5(3(0(0(x1)))))) 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0^1(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 4^1(0(0(4(2(5(0(0(5(0(x1)))))))))) 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0^1(0(4(2(5(0(0(5(0(x1))))))))) 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0^1(4(2(5(0(0(5(0(x1)))))))) 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 4^1(2(5(0(0(5(0(x1))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4^1(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4^1(0(5(0(3(1(1(5(5(2(x1)))))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 0^1(5(0(3(1(1(5(5(2(x1))))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 5^1(0(3(1(1(5(5(2(x1)))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 0^1(3(1(1(5(5(2(x1))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 3^1(1(1(5(5(2(x1)))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2^1(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 5^1(2(1(4(0(3(4(4(2(3(x1)))))))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2^1(1(4(0(3(4(4(2(3(x1))))))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 1^1(4(0(3(4(4(2(3(x1)))))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 4^1(0(3(4(4(2(3(x1))))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 0^1(3(4(4(2(3(x1)))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 3^1(4(4(2(3(x1))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 4^1(4(2(3(x1)))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 4^1(2(3(x1))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2^1(3(x1)) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1^1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 2^1(1(3(2(4(1(5(1(1(2(1(x1))))))))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1^1(3(2(4(1(5(1(1(2(1(x1)))))))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 3^1(2(4(1(5(1(1(2(1(x1))))))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 2^1(4(1(5(1(1(2(1(x1)))))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 4^1(1(5(1(1(2(1(x1))))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 5^1(1(1(2(1(x1))))) 5^1(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5^1(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 5^1(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 4^1(3(2(5(1(3(4(5(1(3(1(x1))))))))))) 5^1(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 3^1(2(5(1(3(4(5(1(3(1(x1)))))))))) 5^1(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 2^1(5(1(3(4(5(1(3(1(x1))))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0^1(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 2^1(2(4(0(0(2(3(4(0(0(3(x1))))))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 2^1(4(0(0(2(3(4(0(0(3(x1)))))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 4^1(0(0(2(3(4(0(0(3(x1))))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0^1(0(2(3(4(0(0(3(x1)))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0^1(2(3(4(0(0(3(x1))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 2^1(3(4(0(0(3(x1)))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 3^1(4(0(0(3(x1))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 4^1(0(0(3(x1)))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0^1(0(3(x1))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0^1(3(x1)) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1^1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 3^1(2(5(2(2(5(3(0(4(2(2(0(x1)))))))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 2^1(5(2(2(5(3(0(4(2(2(0(x1))))))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 5^1(2(2(5(3(0(4(2(2(0(x1)))))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 2^1(2(5(3(0(4(2(2(0(x1))))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 2^1(5(3(0(4(2(2(0(x1)))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 5^1(3(0(4(2(2(0(x1))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0^1(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 3^1(4(1(5(5(2(0(3(2(3(3(4(x1)))))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 4^1(1(5(5(2(0(3(2(3(3(4(x1))))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 1^1(5(5(2(0(3(2(3(3(4(x1)))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 5^1(5(2(0(3(2(3(3(4(x1))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 5^1(2(0(3(2(3(3(4(x1)))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 2^1(0(3(2(3(3(4(x1))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0^1(3(2(3(3(4(x1)))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 3^1(2(3(3(4(x1))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3^1(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 5^1(0(5(3(2(0(1(1(0(2(1(5(2(x1))))))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 0^1(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 5^1(3(2(0(1(1(0(2(1(5(2(x1))))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3^1(2(0(1(1(0(2(1(5(2(x1)))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 2^1(0(1(1(0(2(1(5(2(x1))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 0^1(1(1(0(2(1(5(2(x1)))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3^1(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 1^1(3(2(4(0(4(5(2(4(4(5(5(4(x1))))))))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3^1(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 2^1(4(0(4(5(2(4(4(5(5(4(x1))))))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 4^1(0(4(5(2(4(4(5(5(4(x1)))))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 0^1(4(5(2(4(4(5(5(4(x1))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2^1(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 3^1(3(3(1(2(2(1(3(2(1(4(1(3(2(x1)))))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 3^1(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 3^1(1(2(2(1(3(2(1(4(1(3(2(x1)))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 1^1(2(2(1(3(2(1(4(1(3(2(x1))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2^1(2(1(3(2(1(4(1(3(2(x1)))))))))) 3^1(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3^1(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 3^1(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3^1(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1)))))))))))))))) 3^1(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 2^1(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))) 3^1(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 0^1(4(4(4(2(2(0(1(1(1(1(3(0(2(x1)))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0^1(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 5^1(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1)))))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 3^1(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0^1(1(3(1(5(4(0(4(1(2(5(0(1(3(x1)))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 3^1(1(5(4(0(4(1(2(5(0(1(3(x1)))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2^1(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 3^1(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 3^1(1(1(4(3(3(5(1(2(2(2(2(2(4(x1)))))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 1^1(4(3(3(5(1(2(2(2(2(2(4(x1)))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 4^1(3(3(5(1(2(2(2(2(2(4(x1))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 3^1(3(5(1(2(2(2(2(2(4(x1)))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3^1(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 5^1(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1))))))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 1^1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 4^1(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1))))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 4^1(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 4^1(4(1(0(0(2(1(1(1(0(0(4(3(x1))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 4^1(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 1^1(0(0(2(1(1(1(0(0(4(3(x1))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 0^1(0(2(1(1(1(0(0(4(3(x1)))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 0^1(2(1(1(1(0(0(4(3(x1))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 2^1(1(1(1(0(0(4(3(x1)))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 1^1(0(0(4(3(x1))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 0^1(0(4(3(x1)))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 0^1(4(3(x1))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1^1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 5^1(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1))))))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 2^1(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1^1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1))))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 3^1(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 2^1(2(5(4(2(2(2(4(3(1(0(5(5(x1))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 2^1(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 5^1(4(2(2(2(4(3(1(0(5(5(x1))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 4^1(2(2(2(4(3(1(0(5(5(x1)))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 2^1(2(2(4(3(1(0(5(5(x1))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3^1(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 4^1(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1)))))))))))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 4^1(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3^1(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1)))))))))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 1^1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 4^1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1)))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0^1(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0^1(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1)))))))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 2^1(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 2^1(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1)))))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 1^1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 2^1(1(5(5(0(2(3(1(2(4(0(4(3(0(x1)))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 1^1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 5^1(5(0(2(3(1(2(4(0(4(3(0(x1)))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3^1(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 0^1(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1))))))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 5^1(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 4^1(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1))))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 0^1(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 4^1(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 4^1(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 5^1(5(0(3(4(0(5(5(4(5(2(0(4(x1))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 5^1(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 0^1(3(4(0(5(5(4(5(2(0(4(x1))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3^1(4(0(5(5(4(5(2(0(4(x1)))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 4^1(0(5(5(4(5(2(0(4(x1))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3^1(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3^1(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1))))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 5^1(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 0^1(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3^1(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 5^1(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 5^1(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 4^1(3(4(0(0(0(1(1(5(0(3(1(4(x1))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 2^1(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1)))))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 3^1(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1)))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4^1(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1)))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(0(0(5(0(5(5(1(1(5(1(4(0(1(x1)))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(5(0(5(5(1(1(5(1(4(0(1(x1)))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 5^1(0(5(5(1(1(5(1(4(0(1(x1))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(5(5(1(1(5(1(4(0(1(x1)))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 5^1(5(1(1(5(1(4(0(1(x1))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 5^1(1(1(5(1(4(0(1(x1)))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 5^1(1(4(0(1(x1))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 1^1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1)))))))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 0^1(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1)))))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 0^1(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 0^1(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1)))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 2^1(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 5^1(4(4(2(4(4(4(4(5(1(3(4(0(4(x1)))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(2(4(4(4(4(5(1(3(4(0(4(x1)))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 2^1(4(4(4(4(5(1(3(4(0(4(x1))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(4(4(4(5(1(3(4(0(4(x1)))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(4(4(5(1(3(4(0(4(x1))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(4(5(1(3(4(0(4(x1)))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(5(1(3(4(0(4(x1))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 5^1(1(3(4(0(4(x1)))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4^1(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 1^1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1))))))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 0^1(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 0^1(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1))))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 3^1(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4^1(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 5^1(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3^1(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 1^1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 4^1(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1))))))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 0^1(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 2^1(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1))))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 1^1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4^1(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 3^1(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1))))))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 2^1(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 0^1(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1))))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 2^1(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4^1(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 2^1(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 3^1(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 1^1(2(5(1(1(0(3(0(4(5(0(1(5(x1))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 2^1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))) 0^1(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0^1(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 0^1(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 5^1(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1)))))))))))))))))))))) 0^1(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 5^1(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))) 0^1(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 1^1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1)))))))))))))))))))) 0^1(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 2^1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1)))))))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 2^1(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 5^1(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1)))))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 5^1(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1)))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 4^1(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 0^1(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1)))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1)))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2^1(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2^1(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1)))))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2^1(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 3^1(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1)))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 3^1(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 3^1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 1^1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 1^1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 1^1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2^1(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 5^1(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 0^1(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 5^1(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 1^1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(5(2(3(1(3(1(4(0(0(1(x1))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 5^1(2(3(1(3(1(4(0(0(1(x1)))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2^1(3(1(3(1(4(0(0(1(x1))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 3^1(1(3(1(4(0(0(1(x1)))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 3^1(1(4(0(0(1(x1)))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 1^1(4(0(0(1(x1))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(0(0(1(x1)))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 0^1(0(1(x1))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4^1(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4^1(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1))))))))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 0^1(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 5^1(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1))))))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 5^1(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4^1(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3^1(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 0^1(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1)))))))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 4^1(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 0^1(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1)))))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 5^1(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 2^1(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1)))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 2^1(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 5^1(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1)))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5^1(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 0^1(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1))))))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5^1(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 4^1(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1))))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 4^1(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 2^1(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 2^1(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 4^1(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 2^1(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 4^1(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 1^1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 5^1(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 5^1(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3^1(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 5^1(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 4^1(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 4^1(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 1^1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 4^1(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 4^1(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 5^1(5(3(1(0(4(2(4(5(5(4(x1))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 5^1(3(1(0(4(2(4(5(5(4(x1)))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3^1(1(0(4(2(4(5(5(4(x1))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 1^1(0(4(2(4(5(5(4(x1)))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(4(2(4(5(5(4(x1))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 4^1(2(4(5(5(4(x1)))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 2^1(4(5(5(4(x1))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (9) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 1^1(2(0(0(5(5(3(0(x1)))))))) 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 4^1(0(0(4(2(5(0(0(5(0(x1)))))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4^1(0(5(0(3(1(1(5(5(2(x1)))))))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 4^1(0(3(4(4(2(3(x1))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 4^1(0(0(2(3(4(0(0(3(x1))))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 4^1(0(0(3(x1)))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 4^1(0(4(5(2(4(4(5(5(4(x1)))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 1^1(0(0(2(1(1(1(0(0(4(3(x1))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 1^1(0(0(4(3(x1))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 4^1(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1))))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 4^1(0(5(5(4(5(2(0(4(x1))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4^1(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1)))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 1^1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1))))))))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 4^1(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(0(0(1(x1)))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4^1(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1))))))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 4^1(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 4^1(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 4^1(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 4^1(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 4^1(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 1^1(0(4(2(4(5(5(4(x1)))))))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 0 POL(0^1(x_1)) = 1 POL(1(x_1)) = 1 POL(1^1(x_1)) = x_1 POL(2(x_1)) = x_1 POL(2^1(x_1)) = 1 POL(3(x_1)) = 1 POL(3^1(x_1)) = 1 POL(4(x_1)) = 1 POL(4^1(x_1)) = x_1 POL(5(x_1)) = 1 POL(5^1(x_1)) = 1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) ---------------------------------------- (10) Obligation: Q DP problem: The TRS P consists of the following rules: 3^1(3(2(1(1(0(x1)))))) -> 3^1(2(3(1(1(0(x1)))))) 3^1(3(2(1(1(0(x1)))))) -> 2^1(3(1(1(0(x1))))) 3^1(3(2(1(1(0(x1)))))) -> 3^1(1(1(0(x1)))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 3^1(2(1(3(0(4(2(4(x1)))))))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 2^1(1(3(0(4(2(4(x1))))))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 1^1(3(0(4(2(4(x1)))))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 3^1(0(4(2(4(x1))))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 0^1(4(2(4(x1)))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 4^1(2(4(x1))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 2^1(4(x1)) 3^1(5(2(4(1(0(5(4(x1)))))))) -> 5^1(1(4(3(2(0(5(4(x1)))))))) 3^1(5(2(4(1(0(5(4(x1)))))))) -> 1^1(4(3(2(0(5(4(x1))))))) 3^1(5(2(4(1(0(5(4(x1)))))))) -> 4^1(3(2(0(5(4(x1)))))) 3^1(5(2(4(1(0(5(4(x1)))))))) -> 3^1(2(0(5(4(x1))))) 3^1(5(2(4(1(0(5(4(x1)))))))) -> 2^1(0(5(4(x1)))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 0^1(1(2(0(0(5(5(3(0(x1))))))))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 2^1(0(0(5(5(3(0(x1))))))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 0^1(0(5(5(3(0(x1)))))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 0^1(5(5(3(0(x1))))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 5^1(5(3(0(x1)))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 5^1(3(0(x1))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 3^1(0(x1)) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 5^1(2(0(2(3(2(3(1(1(x1))))))))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 2^1(0(2(3(2(3(1(1(x1)))))))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 0^1(2(3(2(3(1(1(x1))))))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 2^1(3(2(3(1(1(x1)))))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 3^1(2(3(1(1(x1))))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 2^1(3(1(1(x1)))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 3^1(1(1(x1))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 4^1(1(2(2(1(4(2(3(2(x1))))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 1^1(2(2(1(4(2(3(2(x1)))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 2^1(2(1(4(2(3(2(x1))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 2^1(1(4(2(3(2(x1)))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 1^1(4(2(3(2(x1))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 4^1(2(3(2(x1)))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 2^1(3(2(x1))) 0^1(2(1(4(1(1(3(5(5(x1))))))))) -> 0^1(2(4(1(1(1(3(5(5(x1))))))))) 0^1(2(1(4(1(1(3(5(5(x1))))))))) -> 2^1(4(1(1(1(3(5(5(x1)))))))) 0^1(2(1(4(1(1(3(5(5(x1))))))))) -> 4^1(1(1(1(3(5(5(x1))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2^1(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 0^1(3(5(5(0(4(5(3(0(0(x1)))))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 3^1(5(5(0(4(5(3(0(0(x1))))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 5^1(5(0(4(5(3(0(0(x1)))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 5^1(0(4(5(3(0(0(x1))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 0^1(4(5(3(0(0(x1)))))) 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0^1(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0^1(0(4(2(5(0(0(5(0(x1))))))))) 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0^1(4(2(5(0(0(5(0(x1)))))))) 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 4^1(2(5(0(0(5(0(x1))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4^1(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 0^1(5(0(3(1(1(5(5(2(x1))))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 5^1(0(3(1(1(5(5(2(x1)))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 0^1(3(1(1(5(5(2(x1))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 3^1(1(1(5(5(2(x1)))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2^1(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 5^1(2(1(4(0(3(4(4(2(3(x1)))))))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2^1(1(4(0(3(4(4(2(3(x1))))))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 1^1(4(0(3(4(4(2(3(x1)))))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 0^1(3(4(4(2(3(x1)))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 3^1(4(4(2(3(x1))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 4^1(4(2(3(x1)))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 4^1(2(3(x1))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2^1(3(x1)) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1^1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 2^1(1(3(2(4(1(5(1(1(2(1(x1))))))))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1^1(3(2(4(1(5(1(1(2(1(x1)))))))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 3^1(2(4(1(5(1(1(2(1(x1))))))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 2^1(4(1(5(1(1(2(1(x1)))))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 4^1(1(5(1(1(2(1(x1))))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 5^1(1(1(2(1(x1))))) 5^1(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5^1(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 5^1(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 4^1(3(2(5(1(3(4(5(1(3(1(x1))))))))))) 5^1(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 3^1(2(5(1(3(4(5(1(3(1(x1)))))))))) 5^1(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 2^1(5(1(3(4(5(1(3(1(x1))))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0^1(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 2^1(2(4(0(0(2(3(4(0(0(3(x1))))))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 2^1(4(0(0(2(3(4(0(0(3(x1)))))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0^1(0(2(3(4(0(0(3(x1)))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0^1(2(3(4(0(0(3(x1))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 2^1(3(4(0(0(3(x1)))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 3^1(4(0(0(3(x1))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0^1(0(3(x1))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0^1(3(x1)) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1^1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 3^1(2(5(2(2(5(3(0(4(2(2(0(x1)))))))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 2^1(5(2(2(5(3(0(4(2(2(0(x1))))))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 5^1(2(2(5(3(0(4(2(2(0(x1)))))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 2^1(2(5(3(0(4(2(2(0(x1))))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 2^1(5(3(0(4(2(2(0(x1)))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 5^1(3(0(4(2(2(0(x1))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0^1(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 3^1(4(1(5(5(2(0(3(2(3(3(4(x1)))))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 4^1(1(5(5(2(0(3(2(3(3(4(x1))))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 1^1(5(5(2(0(3(2(3(3(4(x1)))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 5^1(5(2(0(3(2(3(3(4(x1))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 5^1(2(0(3(2(3(3(4(x1)))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 2^1(0(3(2(3(3(4(x1))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0^1(3(2(3(3(4(x1)))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 3^1(2(3(3(4(x1))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3^1(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 5^1(0(5(3(2(0(1(1(0(2(1(5(2(x1))))))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 0^1(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 5^1(3(2(0(1(1(0(2(1(5(2(x1))))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3^1(2(0(1(1(0(2(1(5(2(x1)))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 2^1(0(1(1(0(2(1(5(2(x1))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 0^1(1(1(0(2(1(5(2(x1)))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3^1(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 1^1(3(2(4(0(4(5(2(4(4(5(5(4(x1))))))))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3^1(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 2^1(4(0(4(5(2(4(4(5(5(4(x1))))))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 0^1(4(5(2(4(4(5(5(4(x1))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2^1(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 3^1(3(3(1(2(2(1(3(2(1(4(1(3(2(x1)))))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 3^1(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 3^1(1(2(2(1(3(2(1(4(1(3(2(x1)))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 1^1(2(2(1(3(2(1(4(1(3(2(x1))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2^1(2(1(3(2(1(4(1(3(2(x1)))))))))) 3^1(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3^1(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 3^1(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3^1(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1)))))))))))))))) 3^1(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 2^1(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))) 3^1(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 0^1(4(4(4(2(2(0(1(1(1(1(3(0(2(x1)))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0^1(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 5^1(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1)))))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 3^1(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0^1(1(3(1(5(4(0(4(1(2(5(0(1(3(x1)))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 3^1(1(5(4(0(4(1(2(5(0(1(3(x1)))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2^1(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 3^1(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 3^1(1(1(4(3(3(5(1(2(2(2(2(2(4(x1)))))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 1^1(4(3(3(5(1(2(2(2(2(2(4(x1)))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 4^1(3(3(5(1(2(2(2(2(2(4(x1))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 3^1(3(5(1(2(2(2(2(2(4(x1)))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3^1(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 5^1(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1))))))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 1^1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 4^1(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1))))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 4^1(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 4^1(4(1(0(0(2(1(1(1(0(0(4(3(x1))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 4^1(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 0^1(0(2(1(1(1(0(0(4(3(x1)))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 0^1(2(1(1(1(0(0(4(3(x1))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 2^1(1(1(1(0(0(4(3(x1)))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 0^1(0(4(3(x1)))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 0^1(4(3(x1))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1^1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 5^1(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1))))))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 2^1(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1^1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1))))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 3^1(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 2^1(2(5(4(2(2(2(4(3(1(0(5(5(x1))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 2^1(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 5^1(4(2(2(2(4(3(1(0(5(5(x1))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 4^1(2(2(2(4(3(1(0(5(5(x1)))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 2^1(2(2(4(3(1(0(5(5(x1))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3^1(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 4^1(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1)))))))))))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 4^1(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3^1(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1)))))))))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 1^1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 4^1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1)))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0^1(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0^1(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1)))))))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 2^1(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 2^1(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1)))))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 1^1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 2^1(1(5(5(0(2(3(1(2(4(0(4(3(0(x1)))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 1^1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 5^1(5(0(2(3(1(2(4(0(4(3(0(x1)))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3^1(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 0^1(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1))))))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 5^1(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 0^1(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 4^1(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 4^1(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 5^1(5(0(3(4(0(5(5(4(5(2(0(4(x1))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 5^1(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 0^1(3(4(0(5(5(4(5(2(0(4(x1))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3^1(4(0(5(5(4(5(2(0(4(x1)))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3^1(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3^1(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1))))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 5^1(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 0^1(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3^1(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 5^1(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 5^1(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 4^1(3(4(0(0(0(1(1(5(0(3(1(4(x1))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 2^1(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1)))))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 3^1(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1)))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(0(0(5(0(5(5(1(1(5(1(4(0(1(x1)))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(5(0(5(5(1(1(5(1(4(0(1(x1)))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 5^1(0(5(5(1(1(5(1(4(0(1(x1))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(5(5(1(1(5(1(4(0(1(x1)))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 5^1(5(1(1(5(1(4(0(1(x1))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 5^1(1(1(5(1(4(0(1(x1)))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 5^1(1(4(0(1(x1))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 1^1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1)))))))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 0^1(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1)))))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 0^1(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 0^1(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1)))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 2^1(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 5^1(4(4(2(4(4(4(4(5(1(3(4(0(4(x1)))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(2(4(4(4(4(5(1(3(4(0(4(x1)))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 2^1(4(4(4(4(5(1(3(4(0(4(x1))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(4(4(4(5(1(3(4(0(4(x1)))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(4(4(5(1(3(4(0(4(x1))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(4(5(1(3(4(0(4(x1)))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(5(1(3(4(0(4(x1))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 5^1(1(3(4(0(4(x1)))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4^1(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 0^1(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 0^1(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1))))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 3^1(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4^1(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 5^1(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3^1(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 1^1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 0^1(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 2^1(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1))))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 1^1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4^1(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 3^1(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1))))))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 2^1(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 0^1(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1))))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 2^1(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4^1(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 2^1(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 3^1(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 1^1(2(5(1(1(0(3(0(4(5(0(1(5(x1))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 2^1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))) 0^1(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0^1(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 0^1(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 5^1(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1)))))))))))))))))))))) 0^1(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 5^1(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))) 0^1(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 1^1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1)))))))))))))))))))) 0^1(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 2^1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1)))))))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 2^1(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 5^1(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1)))))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 5^1(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1)))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 4^1(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 0^1(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1)))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1)))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2^1(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2^1(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1)))))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2^1(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 3^1(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1)))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 3^1(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 3^1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 1^1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 1^1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 1^1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2^1(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 5^1(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 0^1(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 5^1(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 1^1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(5(2(3(1(3(1(4(0(0(1(x1))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 5^1(2(3(1(3(1(4(0(0(1(x1)))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2^1(3(1(3(1(4(0(0(1(x1))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 3^1(1(3(1(4(0(0(1(x1)))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 3^1(1(4(0(0(1(x1)))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 1^1(4(0(0(1(x1))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 0^1(0(1(x1))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4^1(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 0^1(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 5^1(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1))))))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 5^1(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4^1(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3^1(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 0^1(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1)))))))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 0^1(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1)))))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 5^1(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 2^1(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1)))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 2^1(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 5^1(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1)))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5^1(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 0^1(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1))))))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5^1(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 4^1(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1))))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 4^1(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 2^1(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 2^1(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 2^1(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 4^1(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 1^1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 5^1(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 5^1(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3^1(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 5^1(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 4^1(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 1^1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 5^1(5(3(1(0(4(2(4(5(5(4(x1))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 5^1(3(1(0(4(2(4(5(5(4(x1)))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3^1(1(0(4(2(4(5(5(4(x1))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(4(2(4(5(5(4(x1))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 4^1(2(4(5(5(4(x1)))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 2^1(4(5(5(4(x1))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (11) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. 3^1(5(2(4(1(0(5(4(x1)))))))) -> 1^1(4(3(2(0(5(4(x1))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 1^1(2(2(1(4(2(3(2(x1)))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 1^1(4(2(3(2(x1))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 1^1(4(0(3(4(4(2(3(x1)))))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1^1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 1^1(2(2(1(3(2(1(4(1(3(2(x1))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 1^1(4(3(3(5(1(2(2(2(2(2(4(x1)))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 1^1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 1^1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 1^1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 1^1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1)))))))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 1^1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 1^1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 1^1(2(5(1(1(0(3(0(4(5(0(1(5(x1))))))))))))) 0^1(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 1^1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1)))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 1^1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 1^1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 1^1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 1^1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 1^1(4(0(0(1(x1))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 1^1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 0 POL(0^1(x_1)) = 1 POL(1(x_1)) = 0 POL(1^1(x_1)) = x_1 POL(2(x_1)) = 0 POL(2^1(x_1)) = 1 POL(3(x_1)) = 1 POL(3^1(x_1)) = 1 POL(4(x_1)) = 0 POL(4^1(x_1)) = 1 POL(5(x_1)) = 1 POL(5^1(x_1)) = 1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) ---------------------------------------- (12) Obligation: Q DP problem: The TRS P consists of the following rules: 3^1(3(2(1(1(0(x1)))))) -> 3^1(2(3(1(1(0(x1)))))) 3^1(3(2(1(1(0(x1)))))) -> 2^1(3(1(1(0(x1))))) 3^1(3(2(1(1(0(x1)))))) -> 3^1(1(1(0(x1)))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 3^1(2(1(3(0(4(2(4(x1)))))))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 2^1(1(3(0(4(2(4(x1))))))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 1^1(3(0(4(2(4(x1)))))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 3^1(0(4(2(4(x1))))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 0^1(4(2(4(x1)))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 4^1(2(4(x1))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 2^1(4(x1)) 3^1(5(2(4(1(0(5(4(x1)))))))) -> 5^1(1(4(3(2(0(5(4(x1)))))))) 3^1(5(2(4(1(0(5(4(x1)))))))) -> 4^1(3(2(0(5(4(x1)))))) 3^1(5(2(4(1(0(5(4(x1)))))))) -> 3^1(2(0(5(4(x1))))) 3^1(5(2(4(1(0(5(4(x1)))))))) -> 2^1(0(5(4(x1)))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 0^1(1(2(0(0(5(5(3(0(x1))))))))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 2^1(0(0(5(5(3(0(x1))))))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 0^1(0(5(5(3(0(x1)))))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 0^1(5(5(3(0(x1))))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 5^1(5(3(0(x1)))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 5^1(3(0(x1))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 3^1(0(x1)) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 5^1(2(0(2(3(2(3(1(1(x1))))))))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 2^1(0(2(3(2(3(1(1(x1)))))))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 0^1(2(3(2(3(1(1(x1))))))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 2^1(3(2(3(1(1(x1)))))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 3^1(2(3(1(1(x1))))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 2^1(3(1(1(x1)))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 3^1(1(1(x1))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 4^1(1(2(2(1(4(2(3(2(x1))))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 2^1(2(1(4(2(3(2(x1))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 2^1(1(4(2(3(2(x1)))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 4^1(2(3(2(x1)))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 2^1(3(2(x1))) 0^1(2(1(4(1(1(3(5(5(x1))))))))) -> 0^1(2(4(1(1(1(3(5(5(x1))))))))) 0^1(2(1(4(1(1(3(5(5(x1))))))))) -> 2^1(4(1(1(1(3(5(5(x1)))))))) 0^1(2(1(4(1(1(3(5(5(x1))))))))) -> 4^1(1(1(1(3(5(5(x1))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2^1(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 0^1(3(5(5(0(4(5(3(0(0(x1)))))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 3^1(5(5(0(4(5(3(0(0(x1))))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 5^1(5(0(4(5(3(0(0(x1)))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 5^1(0(4(5(3(0(0(x1))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 0^1(4(5(3(0(0(x1)))))) 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0^1(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0^1(0(4(2(5(0(0(5(0(x1))))))))) 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0^1(4(2(5(0(0(5(0(x1)))))))) 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 4^1(2(5(0(0(5(0(x1))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4^1(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 0^1(5(0(3(1(1(5(5(2(x1))))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 5^1(0(3(1(1(5(5(2(x1)))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 0^1(3(1(1(5(5(2(x1))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 3^1(1(1(5(5(2(x1)))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2^1(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 5^1(2(1(4(0(3(4(4(2(3(x1)))))))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2^1(1(4(0(3(4(4(2(3(x1))))))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 0^1(3(4(4(2(3(x1)))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 3^1(4(4(2(3(x1))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 4^1(4(2(3(x1)))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 4^1(2(3(x1))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2^1(3(x1)) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 2^1(1(3(2(4(1(5(1(1(2(1(x1))))))))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1^1(3(2(4(1(5(1(1(2(1(x1)))))))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 3^1(2(4(1(5(1(1(2(1(x1))))))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 2^1(4(1(5(1(1(2(1(x1)))))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 4^1(1(5(1(1(2(1(x1))))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 5^1(1(1(2(1(x1))))) 5^1(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5^1(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 5^1(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 4^1(3(2(5(1(3(4(5(1(3(1(x1))))))))))) 5^1(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 3^1(2(5(1(3(4(5(1(3(1(x1)))))))))) 5^1(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 2^1(5(1(3(4(5(1(3(1(x1))))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0^1(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 2^1(2(4(0(0(2(3(4(0(0(3(x1))))))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 2^1(4(0(0(2(3(4(0(0(3(x1)))))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0^1(0(2(3(4(0(0(3(x1)))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0^1(2(3(4(0(0(3(x1))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 2^1(3(4(0(0(3(x1)))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 3^1(4(0(0(3(x1))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0^1(0(3(x1))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0^1(3(x1)) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1^1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 3^1(2(5(2(2(5(3(0(4(2(2(0(x1)))))))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 2^1(5(2(2(5(3(0(4(2(2(0(x1))))))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 5^1(2(2(5(3(0(4(2(2(0(x1)))))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 2^1(2(5(3(0(4(2(2(0(x1))))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 2^1(5(3(0(4(2(2(0(x1)))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 5^1(3(0(4(2(2(0(x1))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0^1(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 3^1(4(1(5(5(2(0(3(2(3(3(4(x1)))))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 4^1(1(5(5(2(0(3(2(3(3(4(x1))))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 1^1(5(5(2(0(3(2(3(3(4(x1)))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 5^1(5(2(0(3(2(3(3(4(x1))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 5^1(2(0(3(2(3(3(4(x1)))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 2^1(0(3(2(3(3(4(x1))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0^1(3(2(3(3(4(x1)))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 3^1(2(3(3(4(x1))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3^1(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 5^1(0(5(3(2(0(1(1(0(2(1(5(2(x1))))))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 0^1(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 5^1(3(2(0(1(1(0(2(1(5(2(x1))))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3^1(2(0(1(1(0(2(1(5(2(x1)))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 2^1(0(1(1(0(2(1(5(2(x1))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 0^1(1(1(0(2(1(5(2(x1)))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3^1(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 1^1(3(2(4(0(4(5(2(4(4(5(5(4(x1))))))))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3^1(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 2^1(4(0(4(5(2(4(4(5(5(4(x1))))))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 0^1(4(5(2(4(4(5(5(4(x1))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2^1(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 3^1(3(3(1(2(2(1(3(2(1(4(1(3(2(x1)))))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 3^1(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 3^1(1(2(2(1(3(2(1(4(1(3(2(x1)))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2^1(2(1(3(2(1(4(1(3(2(x1)))))))))) 3^1(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3^1(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 3^1(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3^1(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1)))))))))))))))) 3^1(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 2^1(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))) 3^1(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 0^1(4(4(4(2(2(0(1(1(1(1(3(0(2(x1)))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0^1(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 5^1(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1)))))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 3^1(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0^1(1(3(1(5(4(0(4(1(2(5(0(1(3(x1)))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 3^1(1(5(4(0(4(1(2(5(0(1(3(x1)))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2^1(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 3^1(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 3^1(1(1(4(3(3(5(1(2(2(2(2(2(4(x1)))))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 4^1(3(3(5(1(2(2(2(2(2(4(x1))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 3^1(3(5(1(2(2(2(2(2(4(x1)))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3^1(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 5^1(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1))))))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 4^1(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1))))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 4^1(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 4^1(4(1(0(0(2(1(1(1(0(0(4(3(x1))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 4^1(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 0^1(0(2(1(1(1(0(0(4(3(x1)))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 0^1(2(1(1(1(0(0(4(3(x1))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 2^1(1(1(1(0(0(4(3(x1)))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 0^1(0(4(3(x1)))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 0^1(4(3(x1))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1^1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 5^1(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1))))))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 2^1(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1^1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1))))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 3^1(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 2^1(2(5(4(2(2(2(4(3(1(0(5(5(x1))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 2^1(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 5^1(4(2(2(2(4(3(1(0(5(5(x1))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 4^1(2(2(2(4(3(1(0(5(5(x1)))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 2^1(2(2(4(3(1(0(5(5(x1))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3^1(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 4^1(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1)))))))))))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 4^1(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3^1(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1)))))))))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 4^1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1)))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0^1(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0^1(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1)))))))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 2^1(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 2^1(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1)))))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 2^1(1(5(5(0(2(3(1(2(4(0(4(3(0(x1)))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 1^1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 5^1(5(0(2(3(1(2(4(0(4(3(0(x1)))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3^1(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 0^1(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1))))))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 5^1(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 0^1(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 4^1(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 4^1(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 5^1(5(0(3(4(0(5(5(4(5(2(0(4(x1))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 5^1(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 0^1(3(4(0(5(5(4(5(2(0(4(x1))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3^1(4(0(5(5(4(5(2(0(4(x1)))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3^1(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3^1(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1))))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 5^1(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 0^1(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3^1(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 5^1(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 5^1(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 4^1(3(4(0(0(0(1(1(5(0(3(1(4(x1))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 2^1(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1)))))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 3^1(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1)))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(0(0(5(0(5(5(1(1(5(1(4(0(1(x1)))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(5(0(5(5(1(1(5(1(4(0(1(x1)))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 5^1(0(5(5(1(1(5(1(4(0(1(x1))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(5(5(1(1(5(1(4(0(1(x1)))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 5^1(5(1(1(5(1(4(0(1(x1))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 5^1(1(1(5(1(4(0(1(x1)))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 5^1(1(4(0(1(x1))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 0^1(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1)))))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 0^1(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 0^1(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1)))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 2^1(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 5^1(4(4(2(4(4(4(4(5(1(3(4(0(4(x1)))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(2(4(4(4(4(5(1(3(4(0(4(x1)))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 2^1(4(4(4(4(5(1(3(4(0(4(x1))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(4(4(4(5(1(3(4(0(4(x1)))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(4(4(5(1(3(4(0(4(x1))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(4(5(1(3(4(0(4(x1)))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(5(1(3(4(0(4(x1))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 5^1(1(3(4(0(4(x1)))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4^1(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 0^1(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 0^1(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1))))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 3^1(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4^1(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 5^1(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3^1(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 0^1(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 2^1(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4^1(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 3^1(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1))))))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 2^1(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 0^1(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1))))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 2^1(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4^1(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 2^1(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 3^1(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 2^1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))) 0^1(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0^1(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 0^1(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 5^1(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1)))))))))))))))))))))) 0^1(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 5^1(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))) 0^1(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 2^1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1)))))))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 2^1(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 5^1(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1)))))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 5^1(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1)))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 4^1(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 0^1(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1)))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1)))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2^1(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2^1(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1)))))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2^1(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 3^1(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1)))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 3^1(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 3^1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2^1(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 5^1(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 0^1(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 5^1(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(5(2(3(1(3(1(4(0(0(1(x1))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 5^1(2(3(1(3(1(4(0(0(1(x1)))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2^1(3(1(3(1(4(0(0(1(x1))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 3^1(1(3(1(4(0(0(1(x1)))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 3^1(1(4(0(0(1(x1)))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 0^1(0(1(x1))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4^1(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 0^1(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 5^1(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1))))))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 5^1(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4^1(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3^1(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 0^1(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1)))))))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 0^1(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1)))))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 5^1(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 2^1(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1)))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 2^1(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 5^1(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1)))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5^1(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 0^1(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1))))))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5^1(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 4^1(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1))))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 4^1(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 2^1(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 2^1(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 2^1(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 4^1(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 1^1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 5^1(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 5^1(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3^1(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 5^1(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 4^1(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 5^1(5(3(1(0(4(2(4(5(5(4(x1))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 5^1(3(1(0(4(2(4(5(5(4(x1)))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3^1(1(0(4(2(4(5(5(4(x1))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(4(2(4(5(5(4(x1))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 4^1(2(4(5(5(4(x1)))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 2^1(4(5(5(4(x1))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (13) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 4^1(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(5(1(3(4(0(4(x1))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4^1(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(5(2(3(1(3(1(4(0(0(1(x1))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4^1(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1))))))))))))))))))))))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 0 POL(0^1(x_1)) = 1 POL(1(x_1)) = 1 POL(1^1(x_1)) = 1 POL(2(x_1)) = 1 POL(2^1(x_1)) = 1 POL(3(x_1)) = 1 POL(3^1(x_1)) = 1 POL(4(x_1)) = 1 POL(4^1(x_1)) = x_1 POL(5(x_1)) = 0 POL(5^1(x_1)) = 1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) ---------------------------------------- (14) Obligation: Q DP problem: The TRS P consists of the following rules: 3^1(3(2(1(1(0(x1)))))) -> 3^1(2(3(1(1(0(x1)))))) 3^1(3(2(1(1(0(x1)))))) -> 2^1(3(1(1(0(x1))))) 3^1(3(2(1(1(0(x1)))))) -> 3^1(1(1(0(x1)))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 3^1(2(1(3(0(4(2(4(x1)))))))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 2^1(1(3(0(4(2(4(x1))))))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 1^1(3(0(4(2(4(x1)))))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 3^1(0(4(2(4(x1))))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 0^1(4(2(4(x1)))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 4^1(2(4(x1))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 2^1(4(x1)) 3^1(5(2(4(1(0(5(4(x1)))))))) -> 5^1(1(4(3(2(0(5(4(x1)))))))) 3^1(5(2(4(1(0(5(4(x1)))))))) -> 4^1(3(2(0(5(4(x1)))))) 3^1(5(2(4(1(0(5(4(x1)))))))) -> 3^1(2(0(5(4(x1))))) 3^1(5(2(4(1(0(5(4(x1)))))))) -> 2^1(0(5(4(x1)))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 0^1(1(2(0(0(5(5(3(0(x1))))))))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 2^1(0(0(5(5(3(0(x1))))))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 0^1(0(5(5(3(0(x1)))))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 0^1(5(5(3(0(x1))))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 5^1(5(3(0(x1)))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 5^1(3(0(x1))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 3^1(0(x1)) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 5^1(2(0(2(3(2(3(1(1(x1))))))))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 2^1(0(2(3(2(3(1(1(x1)))))))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 0^1(2(3(2(3(1(1(x1))))))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 2^1(3(2(3(1(1(x1)))))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 3^1(2(3(1(1(x1))))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 2^1(3(1(1(x1)))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 3^1(1(1(x1))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 4^1(1(2(2(1(4(2(3(2(x1))))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 2^1(2(1(4(2(3(2(x1))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 2^1(1(4(2(3(2(x1)))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 4^1(2(3(2(x1)))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 2^1(3(2(x1))) 0^1(2(1(4(1(1(3(5(5(x1))))))))) -> 0^1(2(4(1(1(1(3(5(5(x1))))))))) 0^1(2(1(4(1(1(3(5(5(x1))))))))) -> 2^1(4(1(1(1(3(5(5(x1)))))))) 0^1(2(1(4(1(1(3(5(5(x1))))))))) -> 4^1(1(1(1(3(5(5(x1))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2^1(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 0^1(3(5(5(0(4(5(3(0(0(x1)))))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 3^1(5(5(0(4(5(3(0(0(x1))))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 5^1(5(0(4(5(3(0(0(x1)))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 5^1(0(4(5(3(0(0(x1))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 0^1(4(5(3(0(0(x1)))))) 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0^1(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0^1(0(4(2(5(0(0(5(0(x1))))))))) 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0^1(4(2(5(0(0(5(0(x1)))))))) 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 4^1(2(5(0(0(5(0(x1))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4^1(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 0^1(5(0(3(1(1(5(5(2(x1))))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 5^1(0(3(1(1(5(5(2(x1)))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 0^1(3(1(1(5(5(2(x1))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 3^1(1(1(5(5(2(x1)))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2^1(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 5^1(2(1(4(0(3(4(4(2(3(x1)))))))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2^1(1(4(0(3(4(4(2(3(x1))))))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 0^1(3(4(4(2(3(x1)))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 3^1(4(4(2(3(x1))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 4^1(4(2(3(x1)))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 4^1(2(3(x1))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2^1(3(x1)) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 2^1(1(3(2(4(1(5(1(1(2(1(x1))))))))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1^1(3(2(4(1(5(1(1(2(1(x1)))))))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 3^1(2(4(1(5(1(1(2(1(x1))))))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 2^1(4(1(5(1(1(2(1(x1)))))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 4^1(1(5(1(1(2(1(x1))))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 5^1(1(1(2(1(x1))))) 5^1(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5^1(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 5^1(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 4^1(3(2(5(1(3(4(5(1(3(1(x1))))))))))) 5^1(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 3^1(2(5(1(3(4(5(1(3(1(x1)))))))))) 5^1(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 2^1(5(1(3(4(5(1(3(1(x1))))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0^1(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 2^1(2(4(0(0(2(3(4(0(0(3(x1))))))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 2^1(4(0(0(2(3(4(0(0(3(x1)))))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0^1(0(2(3(4(0(0(3(x1)))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0^1(2(3(4(0(0(3(x1))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 2^1(3(4(0(0(3(x1)))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 3^1(4(0(0(3(x1))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0^1(0(3(x1))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0^1(3(x1)) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1^1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 3^1(2(5(2(2(5(3(0(4(2(2(0(x1)))))))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 2^1(5(2(2(5(3(0(4(2(2(0(x1))))))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 5^1(2(2(5(3(0(4(2(2(0(x1)))))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 2^1(2(5(3(0(4(2(2(0(x1))))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 2^1(5(3(0(4(2(2(0(x1)))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 5^1(3(0(4(2(2(0(x1))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0^1(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 3^1(4(1(5(5(2(0(3(2(3(3(4(x1)))))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 4^1(1(5(5(2(0(3(2(3(3(4(x1))))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 1^1(5(5(2(0(3(2(3(3(4(x1)))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 5^1(5(2(0(3(2(3(3(4(x1))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 5^1(2(0(3(2(3(3(4(x1)))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 2^1(0(3(2(3(3(4(x1))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0^1(3(2(3(3(4(x1)))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 3^1(2(3(3(4(x1))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3^1(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 5^1(0(5(3(2(0(1(1(0(2(1(5(2(x1))))))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 0^1(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 5^1(3(2(0(1(1(0(2(1(5(2(x1))))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3^1(2(0(1(1(0(2(1(5(2(x1)))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 2^1(0(1(1(0(2(1(5(2(x1))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 0^1(1(1(0(2(1(5(2(x1)))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3^1(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 1^1(3(2(4(0(4(5(2(4(4(5(5(4(x1))))))))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3^1(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 2^1(4(0(4(5(2(4(4(5(5(4(x1))))))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 0^1(4(5(2(4(4(5(5(4(x1))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2^1(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 3^1(3(3(1(2(2(1(3(2(1(4(1(3(2(x1)))))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 3^1(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 3^1(1(2(2(1(3(2(1(4(1(3(2(x1)))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2^1(2(1(3(2(1(4(1(3(2(x1)))))))))) 3^1(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3^1(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 3^1(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3^1(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1)))))))))))))))) 3^1(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 2^1(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))) 3^1(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 0^1(4(4(4(2(2(0(1(1(1(1(3(0(2(x1)))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0^1(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 5^1(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1)))))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 3^1(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0^1(1(3(1(5(4(0(4(1(2(5(0(1(3(x1)))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 3^1(1(5(4(0(4(1(2(5(0(1(3(x1)))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2^1(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 3^1(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 3^1(1(1(4(3(3(5(1(2(2(2(2(2(4(x1)))))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 4^1(3(3(5(1(2(2(2(2(2(4(x1))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 3^1(3(5(1(2(2(2(2(2(4(x1)))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3^1(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 5^1(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1))))))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 4^1(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1))))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 4^1(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 4^1(4(1(0(0(2(1(1(1(0(0(4(3(x1))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 4^1(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 0^1(0(2(1(1(1(0(0(4(3(x1)))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 0^1(2(1(1(1(0(0(4(3(x1))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 2^1(1(1(1(0(0(4(3(x1)))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 0^1(0(4(3(x1)))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 0^1(4(3(x1))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1^1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 5^1(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1))))))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 2^1(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1^1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1))))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 3^1(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 2^1(2(5(4(2(2(2(4(3(1(0(5(5(x1))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 2^1(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 5^1(4(2(2(2(4(3(1(0(5(5(x1))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 4^1(2(2(2(4(3(1(0(5(5(x1)))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 2^1(2(2(4(3(1(0(5(5(x1))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3^1(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 4^1(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1)))))))))))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 4^1(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3^1(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1)))))))))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 4^1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1)))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0^1(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0^1(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1)))))))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 2^1(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 2^1(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1)))))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 2^1(1(5(5(0(2(3(1(2(4(0(4(3(0(x1)))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 1^1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 5^1(5(0(2(3(1(2(4(0(4(3(0(x1)))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3^1(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 0^1(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1))))))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 5^1(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 0^1(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 4^1(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 5^1(5(0(3(4(0(5(5(4(5(2(0(4(x1))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 5^1(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 0^1(3(4(0(5(5(4(5(2(0(4(x1))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3^1(4(0(5(5(4(5(2(0(4(x1)))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3^1(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3^1(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1))))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 5^1(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 0^1(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3^1(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 5^1(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 5^1(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 4^1(3(4(0(0(0(1(1(5(0(3(1(4(x1))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 2^1(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1)))))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 3^1(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1)))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(0(0(5(0(5(5(1(1(5(1(4(0(1(x1)))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(5(0(5(5(1(1(5(1(4(0(1(x1)))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 5^1(0(5(5(1(1(5(1(4(0(1(x1))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(5(5(1(1(5(1(4(0(1(x1)))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 5^1(5(1(1(5(1(4(0(1(x1))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 5^1(1(1(5(1(4(0(1(x1)))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 5^1(1(4(0(1(x1))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 0^1(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1)))))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 0^1(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 0^1(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1)))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 2^1(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 5^1(4(4(2(4(4(4(4(5(1(3(4(0(4(x1)))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(2(4(4(4(4(5(1(3(4(0(4(x1)))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 2^1(4(4(4(4(5(1(3(4(0(4(x1))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(4(4(4(5(1(3(4(0(4(x1)))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(4(4(5(1(3(4(0(4(x1))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(4(5(1(3(4(0(4(x1)))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 5^1(1(3(4(0(4(x1)))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4^1(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 0^1(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 0^1(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1))))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 3^1(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 5^1(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3^1(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 0^1(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 2^1(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4^1(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 3^1(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1))))))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 2^1(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 0^1(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1))))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 2^1(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4^1(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 2^1(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 3^1(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 2^1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))) 0^1(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0^1(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 0^1(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 5^1(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1)))))))))))))))))))))) 0^1(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 5^1(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))) 0^1(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 2^1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1)))))))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 2^1(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 5^1(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1)))))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 5^1(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1)))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 4^1(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 0^1(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1)))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1)))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2^1(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2^1(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1)))))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2^1(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 3^1(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1)))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 3^1(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 3^1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2^1(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 5^1(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 0^1(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 5^1(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 5^1(2(3(1(3(1(4(0(0(1(x1)))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2^1(3(1(3(1(4(0(0(1(x1))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 3^1(1(3(1(4(0(0(1(x1)))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 3^1(1(4(0(0(1(x1)))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 0^1(0(1(x1))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4^1(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 0^1(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 5^1(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1))))))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 5^1(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3^1(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 0^1(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1)))))))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 0^1(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1)))))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 5^1(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 2^1(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1)))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 2^1(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 5^1(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1)))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5^1(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 0^1(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1))))))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5^1(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 4^1(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1))))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 4^1(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 2^1(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 2^1(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 2^1(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 4^1(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 1^1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 5^1(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 5^1(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3^1(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 5^1(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 4^1(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 5^1(5(3(1(0(4(2(4(5(5(4(x1))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 5^1(3(1(0(4(2(4(5(5(4(x1)))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3^1(1(0(4(2(4(5(5(4(x1))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(4(2(4(5(5(4(x1))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 4^1(2(4(5(5(4(x1)))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 2^1(4(5(5(4(x1))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (15) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 2^1(1(3(2(4(1(5(1(1(2(1(x1))))))))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1^1(3(2(4(1(5(1(1(2(1(x1)))))))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 3^1(2(4(1(5(1(1(2(1(x1))))))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 2^1(4(1(5(1(1(2(1(x1)))))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 4^1(1(5(1(1(2(1(x1))))))) 1^1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 5^1(1(1(2(1(x1))))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 0 POL(0^1(x_1)) = 0 POL(1(x_1)) = 0 POL(1^1(x_1)) = x_1 POL(2(x_1)) = 0 POL(2^1(x_1)) = 0 POL(3(x_1)) = x_1 POL(3^1(x_1)) = 0 POL(4(x_1)) = 1 POL(4^1(x_1)) = 0 POL(5(x_1)) = 0 POL(5^1(x_1)) = 0 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) ---------------------------------------- (16) Obligation: Q DP problem: The TRS P consists of the following rules: 3^1(3(2(1(1(0(x1)))))) -> 3^1(2(3(1(1(0(x1)))))) 3^1(3(2(1(1(0(x1)))))) -> 2^1(3(1(1(0(x1))))) 3^1(3(2(1(1(0(x1)))))) -> 3^1(1(1(0(x1)))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 3^1(2(1(3(0(4(2(4(x1)))))))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 2^1(1(3(0(4(2(4(x1))))))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 1^1(3(0(4(2(4(x1)))))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 3^1(0(4(2(4(x1))))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 0^1(4(2(4(x1)))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 4^1(2(4(x1))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 2^1(4(x1)) 3^1(5(2(4(1(0(5(4(x1)))))))) -> 5^1(1(4(3(2(0(5(4(x1)))))))) 3^1(5(2(4(1(0(5(4(x1)))))))) -> 4^1(3(2(0(5(4(x1)))))) 3^1(5(2(4(1(0(5(4(x1)))))))) -> 3^1(2(0(5(4(x1))))) 3^1(5(2(4(1(0(5(4(x1)))))))) -> 2^1(0(5(4(x1)))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 0^1(1(2(0(0(5(5(3(0(x1))))))))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 2^1(0(0(5(5(3(0(x1))))))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 0^1(0(5(5(3(0(x1)))))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 0^1(5(5(3(0(x1))))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 5^1(5(3(0(x1)))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 5^1(3(0(x1))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 3^1(0(x1)) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 5^1(2(0(2(3(2(3(1(1(x1))))))))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 2^1(0(2(3(2(3(1(1(x1)))))))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 0^1(2(3(2(3(1(1(x1))))))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 2^1(3(2(3(1(1(x1)))))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 3^1(2(3(1(1(x1))))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 2^1(3(1(1(x1)))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 3^1(1(1(x1))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 4^1(1(2(2(1(4(2(3(2(x1))))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 2^1(2(1(4(2(3(2(x1))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 2^1(1(4(2(3(2(x1)))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 4^1(2(3(2(x1)))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 2^1(3(2(x1))) 0^1(2(1(4(1(1(3(5(5(x1))))))))) -> 0^1(2(4(1(1(1(3(5(5(x1))))))))) 0^1(2(1(4(1(1(3(5(5(x1))))))))) -> 2^1(4(1(1(1(3(5(5(x1)))))))) 0^1(2(1(4(1(1(3(5(5(x1))))))))) -> 4^1(1(1(1(3(5(5(x1))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2^1(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 0^1(3(5(5(0(4(5(3(0(0(x1)))))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 3^1(5(5(0(4(5(3(0(0(x1))))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 5^1(5(0(4(5(3(0(0(x1)))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 5^1(0(4(5(3(0(0(x1))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 0^1(4(5(3(0(0(x1)))))) 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0^1(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0^1(0(4(2(5(0(0(5(0(x1))))))))) 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0^1(4(2(5(0(0(5(0(x1)))))))) 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 4^1(2(5(0(0(5(0(x1))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4^1(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 0^1(5(0(3(1(1(5(5(2(x1))))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 5^1(0(3(1(1(5(5(2(x1)))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 0^1(3(1(1(5(5(2(x1))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 3^1(1(1(5(5(2(x1)))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2^1(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 5^1(2(1(4(0(3(4(4(2(3(x1)))))))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2^1(1(4(0(3(4(4(2(3(x1))))))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 0^1(3(4(4(2(3(x1)))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 3^1(4(4(2(3(x1))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 4^1(4(2(3(x1)))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 4^1(2(3(x1))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2^1(3(x1)) 5^1(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5^1(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 5^1(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 4^1(3(2(5(1(3(4(5(1(3(1(x1))))))))))) 5^1(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 3^1(2(5(1(3(4(5(1(3(1(x1)))))))))) 5^1(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 2^1(5(1(3(4(5(1(3(1(x1))))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0^1(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 2^1(2(4(0(0(2(3(4(0(0(3(x1))))))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 2^1(4(0(0(2(3(4(0(0(3(x1)))))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0^1(0(2(3(4(0(0(3(x1)))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0^1(2(3(4(0(0(3(x1))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 2^1(3(4(0(0(3(x1)))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 3^1(4(0(0(3(x1))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0^1(0(3(x1))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0^1(3(x1)) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1^1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 3^1(2(5(2(2(5(3(0(4(2(2(0(x1)))))))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 2^1(5(2(2(5(3(0(4(2(2(0(x1))))))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 5^1(2(2(5(3(0(4(2(2(0(x1)))))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 2^1(2(5(3(0(4(2(2(0(x1))))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 2^1(5(3(0(4(2(2(0(x1)))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 5^1(3(0(4(2(2(0(x1))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0^1(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 3^1(4(1(5(5(2(0(3(2(3(3(4(x1)))))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 4^1(1(5(5(2(0(3(2(3(3(4(x1))))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 1^1(5(5(2(0(3(2(3(3(4(x1)))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 5^1(5(2(0(3(2(3(3(4(x1))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 5^1(2(0(3(2(3(3(4(x1)))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 2^1(0(3(2(3(3(4(x1))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0^1(3(2(3(3(4(x1)))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 3^1(2(3(3(4(x1))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3^1(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 5^1(0(5(3(2(0(1(1(0(2(1(5(2(x1))))))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 0^1(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 5^1(3(2(0(1(1(0(2(1(5(2(x1))))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3^1(2(0(1(1(0(2(1(5(2(x1)))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 2^1(0(1(1(0(2(1(5(2(x1))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 0^1(1(1(0(2(1(5(2(x1)))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3^1(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 1^1(3(2(4(0(4(5(2(4(4(5(5(4(x1))))))))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3^1(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 2^1(4(0(4(5(2(4(4(5(5(4(x1))))))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 0^1(4(5(2(4(4(5(5(4(x1))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2^1(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 3^1(3(3(1(2(2(1(3(2(1(4(1(3(2(x1)))))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 3^1(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 3^1(1(2(2(1(3(2(1(4(1(3(2(x1)))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2^1(2(1(3(2(1(4(1(3(2(x1)))))))))) 3^1(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3^1(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 3^1(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3^1(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1)))))))))))))))) 3^1(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 2^1(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))) 3^1(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 0^1(4(4(4(2(2(0(1(1(1(1(3(0(2(x1)))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0^1(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 5^1(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1)))))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 3^1(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0^1(1(3(1(5(4(0(4(1(2(5(0(1(3(x1)))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 3^1(1(5(4(0(4(1(2(5(0(1(3(x1)))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2^1(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 3^1(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 3^1(1(1(4(3(3(5(1(2(2(2(2(2(4(x1)))))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 4^1(3(3(5(1(2(2(2(2(2(4(x1))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 3^1(3(5(1(2(2(2(2(2(4(x1)))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3^1(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 5^1(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1))))))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 4^1(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1))))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 4^1(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 4^1(4(1(0(0(2(1(1(1(0(0(4(3(x1))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 4^1(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 0^1(0(2(1(1(1(0(0(4(3(x1)))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 0^1(2(1(1(1(0(0(4(3(x1))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 2^1(1(1(1(0(0(4(3(x1)))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 0^1(0(4(3(x1)))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 0^1(4(3(x1))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1^1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 5^1(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1))))))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 2^1(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1^1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1))))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 3^1(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 2^1(2(5(4(2(2(2(4(3(1(0(5(5(x1))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 2^1(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 5^1(4(2(2(2(4(3(1(0(5(5(x1))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 4^1(2(2(2(4(3(1(0(5(5(x1)))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 2^1(2(2(4(3(1(0(5(5(x1))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3^1(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 4^1(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1)))))))))))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 4^1(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3^1(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1)))))))))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 4^1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1)))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0^1(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0^1(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1)))))))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 2^1(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 2^1(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1)))))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 2^1(1(5(5(0(2(3(1(2(4(0(4(3(0(x1)))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 1^1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 5^1(5(0(2(3(1(2(4(0(4(3(0(x1)))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3^1(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 0^1(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1))))))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 5^1(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 0^1(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 4^1(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 5^1(5(0(3(4(0(5(5(4(5(2(0(4(x1))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 5^1(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 0^1(3(4(0(5(5(4(5(2(0(4(x1))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3^1(4(0(5(5(4(5(2(0(4(x1)))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3^1(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3^1(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1))))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 5^1(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 0^1(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3^1(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 5^1(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 5^1(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 4^1(3(4(0(0(0(1(1(5(0(3(1(4(x1))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 2^1(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1)))))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 3^1(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1)))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(0(0(5(0(5(5(1(1(5(1(4(0(1(x1)))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(5(0(5(5(1(1(5(1(4(0(1(x1)))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 5^1(0(5(5(1(1(5(1(4(0(1(x1))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(5(5(1(1(5(1(4(0(1(x1)))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 5^1(5(1(1(5(1(4(0(1(x1))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 5^1(1(1(5(1(4(0(1(x1)))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 5^1(1(4(0(1(x1))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 0^1(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1)))))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 0^1(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 0^1(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1)))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 2^1(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 5^1(4(4(2(4(4(4(4(5(1(3(4(0(4(x1)))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(2(4(4(4(4(5(1(3(4(0(4(x1)))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 2^1(4(4(4(4(5(1(3(4(0(4(x1))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(4(4(4(5(1(3(4(0(4(x1)))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(4(4(5(1(3(4(0(4(x1))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(4(5(1(3(4(0(4(x1)))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 5^1(1(3(4(0(4(x1)))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4^1(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 0^1(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 0^1(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1))))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 3^1(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 5^1(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3^1(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 0^1(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 2^1(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4^1(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 3^1(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1))))))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 2^1(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 0^1(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1))))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 2^1(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4^1(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 2^1(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 3^1(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 2^1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))) 0^1(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0^1(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 0^1(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 5^1(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1)))))))))))))))))))))) 0^1(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 5^1(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))) 0^1(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 2^1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1)))))))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 2^1(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 5^1(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1)))))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 5^1(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1)))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 4^1(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 0^1(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1)))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1)))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2^1(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2^1(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1)))))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2^1(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 3^1(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1)))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 3^1(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 3^1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2^1(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 5^1(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 0^1(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 5^1(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 5^1(2(3(1(3(1(4(0(0(1(x1)))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2^1(3(1(3(1(4(0(0(1(x1))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 3^1(1(3(1(4(0(0(1(x1)))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 3^1(1(4(0(0(1(x1)))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 0^1(0(1(x1))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4^1(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 0^1(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 5^1(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1))))))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 5^1(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3^1(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 0^1(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1)))))))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 0^1(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1)))))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 5^1(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 2^1(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1)))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 2^1(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 5^1(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1)))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5^1(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 0^1(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1))))))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5^1(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 4^1(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1))))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 4^1(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 2^1(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 2^1(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 2^1(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 4^1(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 1^1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 5^1(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 5^1(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3^1(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 5^1(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 4^1(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 5^1(5(3(1(0(4(2(4(5(5(4(x1))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 5^1(3(1(0(4(2(4(5(5(4(x1)))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3^1(1(0(4(2(4(5(5(4(x1))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(4(2(4(5(5(4(x1))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 4^1(2(4(5(5(4(x1)))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 2^1(4(5(5(4(x1))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (17) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. 3^1(3(2(1(1(0(x1)))))) -> 2^1(3(1(1(0(x1))))) 3^1(3(2(1(1(0(x1)))))) -> 3^1(1(1(0(x1)))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 2^1(1(3(0(4(2(4(x1))))))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 1^1(3(0(4(2(4(x1)))))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 3^1(0(4(2(4(x1))))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 0^1(4(2(4(x1)))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 4^1(2(4(x1))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 2^1(4(x1)) 3^1(5(2(4(1(0(5(4(x1)))))))) -> 4^1(3(2(0(5(4(x1)))))) 3^1(5(2(4(1(0(5(4(x1)))))))) -> 3^1(2(0(5(4(x1))))) 3^1(5(2(4(1(0(5(4(x1)))))))) -> 2^1(0(5(4(x1)))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 0^1(0(5(5(3(0(x1)))))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 0^1(5(5(3(0(x1))))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 5^1(5(3(0(x1)))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 5^1(3(0(x1))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 3^1(0(x1)) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 2^1(0(2(3(2(3(1(1(x1)))))))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 0^1(2(3(2(3(1(1(x1))))))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 2^1(3(2(3(1(1(x1)))))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 3^1(2(3(1(1(x1))))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 2^1(3(1(1(x1)))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 3^1(1(1(x1))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 0^1(3(5(5(0(4(5(3(0(0(x1)))))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 3^1(5(5(0(4(5(3(0(0(x1))))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 5^1(5(0(4(5(3(0(0(x1)))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 5^1(0(4(5(3(0(0(x1))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 0^1(4(5(3(0(0(x1)))))) 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0^1(0(4(2(5(0(0(5(0(x1))))))))) 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0^1(4(2(5(0(0(5(0(x1)))))))) 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 4^1(2(5(0(0(5(0(x1))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 0^1(5(0(3(1(1(5(5(2(x1))))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 5^1(0(3(1(1(5(5(2(x1)))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 0^1(3(1(1(5(5(2(x1))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 3^1(1(1(5(5(2(x1)))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2^1(1(4(0(3(4(4(2(3(x1))))))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 0^1(3(4(4(2(3(x1)))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 3^1(4(4(2(3(x1))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 4^1(4(2(3(x1)))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 4^1(2(3(x1))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2^1(3(x1)) 5^1(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 4^1(3(2(5(1(3(4(5(1(3(1(x1))))))))))) 5^1(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 3^1(2(5(1(3(4(5(1(3(1(x1)))))))))) 5^1(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 2^1(5(1(3(4(5(1(3(1(x1))))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0^1(0(2(3(4(0(0(3(x1)))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0^1(2(3(4(0(0(3(x1))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 2^1(3(4(0(0(3(x1)))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 3^1(4(0(0(3(x1))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0^1(0(3(x1))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0^1(3(x1)) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 2^1(5(2(2(5(3(0(4(2(2(0(x1))))))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 5^1(2(2(5(3(0(4(2(2(0(x1)))))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 2^1(2(5(3(0(4(2(2(0(x1))))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 2^1(5(3(0(4(2(2(0(x1)))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 5^1(3(0(4(2(2(0(x1))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 4^1(1(5(5(2(0(3(2(3(3(4(x1))))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 1^1(5(5(2(0(3(2(3(3(4(x1)))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 5^1(5(2(0(3(2(3(3(4(x1))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 5^1(2(0(3(2(3(3(4(x1)))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 2^1(0(3(2(3(3(4(x1))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0^1(3(2(3(3(4(x1)))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 3^1(2(3(3(4(x1))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 5^1(0(5(3(2(0(1(1(0(2(1(5(2(x1))))))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 0^1(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 5^1(3(2(0(1(1(0(2(1(5(2(x1))))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3^1(2(0(1(1(0(2(1(5(2(x1)))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 2^1(0(1(1(0(2(1(5(2(x1))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 0^1(1(1(0(2(1(5(2(x1)))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 1^1(3(2(4(0(4(5(2(4(4(5(5(4(x1))))))))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3^1(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 2^1(4(0(4(5(2(4(4(5(5(4(x1))))))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 0^1(4(5(2(4(4(5(5(4(x1))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 3^1(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 3^1(1(2(2(1(3(2(1(4(1(3(2(x1)))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2^1(2(1(3(2(1(4(1(3(2(x1)))))))))) 3^1(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3^1(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1)))))))))))))))) 3^1(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 2^1(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))) 3^1(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 0^1(4(4(4(2(2(0(1(1(1(1(3(0(2(x1)))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 3^1(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0^1(1(3(1(5(4(0(4(1(2(5(0(1(3(x1)))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 3^1(1(5(4(0(4(1(2(5(0(1(3(x1)))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 3^1(1(1(4(3(3(5(1(2(2(2(2(2(4(x1)))))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 4^1(3(3(5(1(2(2(2(2(2(4(x1))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 3^1(3(5(1(2(2(2(2(2(4(x1)))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 5^1(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1))))))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 4^1(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1))))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 4^1(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 4^1(4(1(0(0(2(1(1(1(0(0(4(3(x1))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 4^1(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 0^1(0(2(1(1(1(0(0(4(3(x1)))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 0^1(2(1(1(1(0(0(4(3(x1))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 2^1(1(1(1(0(0(4(3(x1)))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 0^1(0(4(3(x1)))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 0^1(4(3(x1))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 2^1(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1^1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1))))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 3^1(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 2^1(2(5(4(2(2(2(4(3(1(0(5(5(x1))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 2^1(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 5^1(4(2(2(2(4(3(1(0(5(5(x1))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 4^1(2(2(2(4(3(1(0(5(5(x1)))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 2^1(2(2(4(3(1(0(5(5(x1))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 4^1(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1)))))))))))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 4^1(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3^1(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1)))))))))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 4^1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1)))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0^1(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1)))))))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 2^1(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 2^1(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1)))))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 2^1(1(5(5(0(2(3(1(2(4(0(4(3(0(x1)))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 1^1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 5^1(5(0(2(3(1(2(4(0(4(3(0(x1)))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 0^1(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1))))))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 5^1(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 0^1(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 4^1(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 5^1(5(0(3(4(0(5(5(4(5(2(0(4(x1))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 5^1(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 0^1(3(4(0(5(5(4(5(2(0(4(x1))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3^1(4(0(5(5(4(5(2(0(4(x1)))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3^1(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1))))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 5^1(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 0^1(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3^1(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 5^1(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 5^1(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 4^1(3(4(0(0(0(1(1(5(0(3(1(4(x1))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1)))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(0(0(5(0(5(5(1(1(5(1(4(0(1(x1)))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(5(0(5(5(1(1(5(1(4(0(1(x1)))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 5^1(0(5(5(1(1(5(1(4(0(1(x1))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 0^1(5(5(1(1(5(1(4(0(1(x1)))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 5^1(5(1(1(5(1(4(0(1(x1))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 5^1(1(1(5(1(4(0(1(x1)))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 5^1(1(4(0(1(x1))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 0^1(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1)))))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 0^1(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 0^1(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1)))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 2^1(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 5^1(4(4(2(4(4(4(4(5(1(3(4(0(4(x1)))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(2(4(4(4(4(5(1(3(4(0(4(x1)))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 2^1(4(4(4(4(5(1(3(4(0(4(x1))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(4(4(4(5(1(3(4(0(4(x1)))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(4(4(5(1(3(4(0(4(x1))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 4^1(4(5(1(3(4(0(4(x1)))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 5^1(1(3(4(0(4(x1)))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 0^1(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 0^1(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1))))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 3^1(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 5^1(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 0^1(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 2^1(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 2^1(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 0^1(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1))))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 2^1(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4^1(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 2^1(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 3^1(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 2^1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))) 0^1(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 5^1(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))) 0^1(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 2^1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1)))))))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 2^1(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 5^1(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1)))))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 5^1(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1)))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 4^1(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 0^1(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1)))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1)))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 3^1(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 3^1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 0^1(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 5^1(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 5^1(2(3(1(3(1(4(0(0(1(x1)))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2^1(3(1(3(1(4(0(0(1(x1))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 3^1(1(3(1(4(0(0(1(x1)))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 3^1(1(4(0(0(1(x1)))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 0^1(0(1(x1))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 0^1(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 5^1(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1))))))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 5^1(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 0^1(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1)))))))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 0^1(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1)))))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 5^1(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 2^1(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1)))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 2^1(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 5^1(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1)))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 0^1(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1))))))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5^1(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 4^1(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1))))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 4^1(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 2^1(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 2^1(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 2^1(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 4^1(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 1^1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 5^1(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 5^1(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3^1(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 5^1(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 4^1(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(0(5(5(3(1(0(4(2(4(5(5(4(x1))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 5^1(5(3(1(0(4(2(4(5(5(4(x1))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 5^1(3(1(0(4(2(4(5(5(4(x1)))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3^1(1(0(4(2(4(5(5(4(x1))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 0^1(4(2(4(5(5(4(x1))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 4^1(2(4(5(5(4(x1)))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 2^1(4(5(5(4(x1))))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 1 + x_1 POL(0^1(x_1)) = x_1 POL(1(x_1)) = x_1 POL(1^1(x_1)) = x_1 POL(2(x_1)) = x_1 POL(2^1(x_1)) = x_1 POL(3(x_1)) = 1 + x_1 POL(3^1(x_1)) = 1 + x_1 POL(4(x_1)) = x_1 POL(4^1(x_1)) = x_1 POL(5(x_1)) = 1 + x_1 POL(5^1(x_1)) = 1 + x_1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) ---------------------------------------- (18) Obligation: Q DP problem: The TRS P consists of the following rules: 3^1(3(2(1(1(0(x1)))))) -> 3^1(2(3(1(1(0(x1)))))) 3^1(2(1(3(0(2(4(4(x1)))))))) -> 3^1(2(1(3(0(4(2(4(x1)))))))) 3^1(5(2(4(1(0(5(4(x1)))))))) -> 5^1(1(4(3(2(0(5(4(x1)))))))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 0^1(1(2(0(0(5(5(3(0(x1))))))))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 2^1(0(0(5(5(3(0(x1))))))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 5^1(2(0(2(3(2(3(1(1(x1))))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 4^1(1(2(2(1(4(2(3(2(x1))))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 2^1(2(1(4(2(3(2(x1))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 2^1(1(4(2(3(2(x1)))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 4^1(2(3(2(x1)))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 2^1(3(2(x1))) 0^1(2(1(4(1(1(3(5(5(x1))))))))) -> 0^1(2(4(1(1(1(3(5(5(x1))))))))) 0^1(2(1(4(1(1(3(5(5(x1))))))))) -> 2^1(4(1(1(1(3(5(5(x1)))))))) 0^1(2(1(4(1(1(3(5(5(x1))))))))) -> 4^1(1(1(1(3(5(5(x1))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2^1(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0^1(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4^1(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2^1(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 5^1(2(1(4(0(3(4(4(2(3(x1)))))))))) 5^1(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5^1(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0^1(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 2^1(2(4(0(0(2(3(4(0(0(3(x1))))))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 2^1(4(0(0(2(3(4(0(0(3(x1)))))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1^1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 3^1(2(5(2(2(5(3(0(4(2(2(0(x1)))))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0^1(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 3^1(4(1(5(5(2(0(3(2(3(3(4(x1)))))))))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3^1(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3^1(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2^1(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 3^1(3(3(1(2(2(1(3(2(1(4(1(3(2(x1)))))))))))))) 3^1(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3^1(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0^1(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 5^1(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1)))))))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2^1(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 3^1(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3^1(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1^1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 5^1(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1))))))))))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3^1(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0^1(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3^1(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3^1(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 2^1(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1)))))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 3^1(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4^1(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3^1(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4^1(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 3^1(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1))))))))))))))))))))) 0^1(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0^1(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 0^1(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 5^1(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1)))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2^1(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2^1(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1)))))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2^1(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 3^1(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1)))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2^1(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 5^1(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4^1(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3^1(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5^1(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (19) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 5 SCCs with 18 less nodes. ---------------------------------------- (20) Complex Obligation (AND) ---------------------------------------- (21) Obligation: Q DP problem: The TRS P consists of the following rules: 5^1(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5^1(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 5^1(2(0(2(3(2(3(1(1(x1))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5^1(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (22) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. 5^1(2(2(3(3(2(0(1(1(x1))))))))) -> 5^1(2(0(2(3(2(3(1(1(x1))))))))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 0 POL(1(x_1)) = 0 POL(2(x_1)) = 1 + x_1 POL(3(x_1)) = 0 POL(4(x_1)) = 0 POL(5(x_1)) = x_1 POL(5^1(x_1)) = x_1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) ---------------------------------------- (23) Obligation: Q DP problem: The TRS P consists of the following rules: 5^1(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5^1(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5^1(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (24) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. 5^1(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5^1(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 0 POL(1(x_1)) = 0 POL(2(x_1)) = 1 + x_1 POL(3(x_1)) = 1 POL(4(x_1)) = x_1 POL(5(x_1)) = 1 POL(5^1(x_1)) = x_1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) ---------------------------------------- (25) Obligation: Q DP problem: The TRS P consists of the following rules: 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5^1(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (26) MRRProof (EQUIVALENT) By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. Strictly oriented rules of the TRS R: 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 1 + 2*x_1 POL(1(x_1)) = x_1 POL(2(x_1)) = x_1 POL(3(x_1)) = 2*x_1 POL(4(x_1)) = x_1 POL(5(x_1)) = 3 + 3*x_1 POL(5^1(x_1)) = x_1 ---------------------------------------- (27) Obligation: Q DP problem: The TRS P consists of the following rules: 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5^1(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (28) MRRProof (EQUIVALENT) By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. Strictly oriented rules of the TRS R: 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 1 + 2*x_1 POL(1(x_1)) = 1 + x_1 POL(2(x_1)) = x_1 POL(3(x_1)) = 2 + 2*x_1 POL(4(x_1)) = x_1 POL(5(x_1)) = x_1 POL(5^1(x_1)) = 2*x_1 ---------------------------------------- (29) Obligation: Q DP problem: The TRS P consists of the following rules: 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5^1(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (30) MRRProof (EQUIVALENT) By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. Strictly oriented rules of the TRS R: 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 2*x_1 POL(1(x_1)) = 1 + 2*x_1 POL(2(x_1)) = 1 + 2*x_1 POL(3(x_1)) = 1 + 2*x_1 POL(4(x_1)) = x_1 POL(5(x_1)) = 3*x_1 POL(5^1(x_1)) = x_1 ---------------------------------------- (31) Obligation: Q DP problem: The TRS P consists of the following rules: 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5^1(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (32) MRRProof (EQUIVALENT) By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. Strictly oriented dependency pairs: 5^1(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5^1(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) Strictly oriented rules of the TRS R: 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 1 + 2*x_1 POL(1(x_1)) = x_1 POL(2(x_1)) = 2*x_1 POL(3(x_1)) = x_1 POL(4(x_1)) = 1 + 2*x_1 POL(5(x_1)) = 1 + 2*x_1 POL(5^1(x_1)) = x_1 ---------------------------------------- (33) Obligation: Q DP problem: P is empty. The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (34) PisEmptyProof (EQUIVALENT) The TRS P is empty. Hence, there is no (P,Q,R) chain. ---------------------------------------- (35) YES ---------------------------------------- (36) Obligation: Q DP problem: The TRS P consists of the following rules: 3^1(2(1(3(0(2(4(4(x1)))))))) -> 3^1(2(1(3(0(4(2(4(x1)))))))) 3^1(3(2(1(1(0(x1)))))) -> 3^1(2(3(1(1(0(x1)))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3^1(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3^1(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 3^1(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3^1(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3^1(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3^1(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3^1(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3^1(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3^1(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3^1(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (37) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. 3^1(3(2(1(1(0(x1)))))) -> 3^1(2(3(1(1(0(x1)))))) 3^1(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3^1(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3^1(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3^1(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 1 + x_1 POL(1(x_1)) = x_1 POL(2(x_1)) = 0 POL(3(x_1)) = 1 + x_1 POL(3^1(x_1)) = x_1 POL(4(x_1)) = 0 POL(5(x_1)) = x_1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) ---------------------------------------- (38) Obligation: Q DP problem: The TRS P consists of the following rules: 3^1(2(1(3(0(2(4(4(x1)))))))) -> 3^1(2(1(3(0(4(2(4(x1)))))))) 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3^1(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3^1(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3^1(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3^1(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3^1(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3^1(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3^1(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (39) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. 3^1(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3^1(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 1 + x_1 POL(1(x_1)) = x_1 POL(2(x_1)) = x_1 POL(3(x_1)) = x_1 POL(3^1(x_1)) = x_1 POL(4(x_1)) = 1 POL(5(x_1)) = x_1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) ---------------------------------------- (40) Obligation: Q DP problem: The TRS P consists of the following rules: 3^1(2(1(3(0(2(4(4(x1)))))))) -> 3^1(2(1(3(0(4(2(4(x1)))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3^1(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3^1(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3^1(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3^1(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3^1(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3^1(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (41) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. 3^1(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3^1(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 0 POL(1(x_1)) = 1 POL(2(x_1)) = 0 POL(3(x_1)) = 1 + x_1 POL(3^1(x_1)) = x_1 POL(4(x_1)) = 1 + x_1 POL(5(x_1)) = 0 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) ---------------------------------------- (42) Obligation: Q DP problem: The TRS P consists of the following rules: 3^1(2(1(3(0(2(4(4(x1)))))))) -> 3^1(2(1(3(0(4(2(4(x1)))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3^1(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3^1(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3^1(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3^1(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3^1(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (43) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. 3^1(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3^1(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = x_1 POL(1(x_1)) = 0 POL(2(x_1)) = 0 POL(3(x_1)) = 0 POL(3^1(x_1)) = x_1 POL(4(x_1)) = 1 + x_1 POL(5(x_1)) = x_1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) ---------------------------------------- (44) Obligation: Q DP problem: The TRS P consists of the following rules: 3^1(2(1(3(0(2(4(4(x1)))))))) -> 3^1(2(1(3(0(4(2(4(x1)))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3^1(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3^1(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3^1(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3^1(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (45) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. 3^1(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3^1(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = x_1 POL(1(x_1)) = 1 + x_1 POL(2(x_1)) = 0 POL(3(x_1)) = 1 POL(3^1(x_1)) = x_1 POL(4(x_1)) = x_1 POL(5(x_1)) = 0 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) ---------------------------------------- (46) Obligation: Q DP problem: The TRS P consists of the following rules: 3^1(2(1(3(0(2(4(4(x1)))))))) -> 3^1(2(1(3(0(4(2(4(x1)))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3^1(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3^1(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3^1(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (47) MRRProof (EQUIVALENT) By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. Strictly oriented dependency pairs: 3^1(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3^1(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) Strictly oriented rules of the TRS R: 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = x_1 POL(1(x_1)) = 1 + 2*x_1 POL(2(x_1)) = x_1 POL(3(x_1)) = 2*x_1 POL(3^1(x_1)) = x_1 POL(4(x_1)) = x_1 POL(5(x_1)) = 2*x_1 ---------------------------------------- (48) Obligation: Q DP problem: The TRS P consists of the following rules: 3^1(2(1(3(0(2(4(4(x1)))))))) -> 3^1(2(1(3(0(4(2(4(x1)))))))) 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3^1(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3^1(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3^1(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (49) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. 3^1(2(1(3(0(2(4(4(x1)))))))) -> 3^1(2(1(3(0(4(2(4(x1)))))))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = x_1 POL(1(x_1)) = x_1 POL(2(x_1)) = 1 + x_1 POL(3(x_1)) = x_1 POL(3^1(x_1)) = x_1 POL(4(x_1)) = 1 POL(5(x_1)) = 0 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) ---------------------------------------- (50) Obligation: Q DP problem: The TRS P consists of the following rules: 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3^1(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3^1(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3^1(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (51) MRRProof (EQUIVALENT) By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. Strictly oriented dependency pairs: 3^1(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3^1(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) Strictly oriented rules of the TRS R: 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = x_1 POL(1(x_1)) = 1 + 2*x_1 POL(2(x_1)) = 1 + 2*x_1 POL(3(x_1)) = 1 + 2*x_1 POL(3^1(x_1)) = 2*x_1 POL(4(x_1)) = x_1 POL(5(x_1)) = 2*x_1 ---------------------------------------- (52) Obligation: Q DP problem: The TRS P consists of the following rules: 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3^1(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3^1(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (53) MRRProof (EQUIVALENT) By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. Strictly oriented rules of the TRS R: 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 2 + 2*x_1 POL(1(x_1)) = 2 + 2*x_1 POL(2(x_1)) = 2 + 2*x_1 POL(3(x_1)) = 2 + 2*x_1 POL(3^1(x_1)) = 2*x_1 POL(4(x_1)) = x_1 POL(5(x_1)) = 2*x_1 ---------------------------------------- (54) Obligation: Q DP problem: The TRS P consists of the following rules: 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3^1(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3^1(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (55) MRRProof (EQUIVALENT) By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. Strictly oriented dependency pairs: 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3^1(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Strictly oriented rules of the TRS R: 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = x_1 POL(1(x_1)) = x_1 POL(2(x_1)) = 2*x_1 POL(3(x_1)) = x_1 POL(3^1(x_1)) = 3*x_1 POL(4(x_1)) = 2 + 2*x_1 POL(5(x_1)) = 2 + 2*x_1 ---------------------------------------- (56) Obligation: Q DP problem: The TRS P consists of the following rules: 3^1(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3^1(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3^1(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3^1(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3^1(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (57) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 3 less nodes. ---------------------------------------- (58) TRUE ---------------------------------------- (59) Obligation: Q DP problem: The TRS P consists of the following rules: 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2^1(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2^1(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2^1(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2^1(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2^1(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2^1(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1)))))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2^1(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 4^1(1(2(2(1(4(2(3(2(x1))))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 2^1(2(1(4(2(3(2(x1))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 2^1(1(4(2(3(2(x1)))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 4^1(2(3(2(x1)))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 2^1(3(2(x1))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2^1(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4^1(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 2^1(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1)))))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4^1(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4^1(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4^1(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (60) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 0 POL(1(x_1)) = 1 POL(2(x_1)) = 1 POL(2^1(x_1)) = 1 POL(3(x_1)) = 1 POL(4(x_1)) = 0 POL(4^1(x_1)) = x_1 POL(5(x_1)) = 0 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) ---------------------------------------- (61) Obligation: Q DP problem: The TRS P consists of the following rules: 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2^1(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2^1(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2^1(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2^1(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2^1(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2^1(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1)))))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2^1(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 4^1(1(2(2(1(4(2(3(2(x1))))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 2^1(2(1(4(2(3(2(x1))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 2^1(1(4(2(3(2(x1)))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 4^1(2(3(2(x1)))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 2^1(3(2(x1))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2^1(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))) 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4^1(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 2^1(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1)))))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4^1(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4^1(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4^1(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (62) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. 4^1(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4^1(4(0(5(0(3(1(1(5(5(2(x1))))))))))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 0 POL(1(x_1)) = 0 POL(2(x_1)) = 0 POL(2^1(x_1)) = 0 POL(3(x_1)) = 1 POL(4(x_1)) = x_1 POL(4^1(x_1)) = x_1 POL(5(x_1)) = 1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) ---------------------------------------- (63) Obligation: Q DP problem: The TRS P consists of the following rules: 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2^1(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2^1(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2^1(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2^1(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2^1(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2^1(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1)))))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2^1(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 4^1(1(2(2(1(4(2(3(2(x1))))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 2^1(2(1(4(2(3(2(x1))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 2^1(1(4(2(3(2(x1)))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 4^1(2(3(2(x1)))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 2^1(3(2(x1))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2^1(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 2^1(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1)))))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4^1(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4^1(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4^1(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (64) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2^1(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1)))))))))))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2^1(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 2^1(1(4(2(3(2(x1)))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 4^1(2(3(2(x1)))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 2^1(3(2(x1))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2^1(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 4^1(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = x_1 POL(1(x_1)) = x_1 POL(2(x_1)) = 1 + x_1 POL(2^1(x_1)) = 1 + x_1 POL(3(x_1)) = 1 + x_1 POL(4(x_1)) = x_1 POL(4^1(x_1)) = x_1 POL(5(x_1)) = 1 + x_1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) ---------------------------------------- (65) Obligation: Q DP problem: The TRS P consists of the following rules: 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2^1(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2^1(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2^1(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2^1(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2^1(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 4^1(1(2(2(1(4(2(3(2(x1))))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 2^1(2(1(4(2(3(2(x1))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 2^1(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1)))))))))))))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4^1(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4^1(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4^1(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (66) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 2 less nodes. ---------------------------------------- (67) Complex Obligation (AND) ---------------------------------------- (68) Obligation: Q DP problem: The TRS P consists of the following rules: 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2^1(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2^1(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2^1(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2^1(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2^1(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (69) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. 2^1(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2^1(0(3(5(5(0(4(5(3(0(0(x1))))))))))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = x_1 POL(1(x_1)) = 0 POL(2(x_1)) = x_1 POL(2^1(x_1)) = x_1 POL(3(x_1)) = 1 POL(4(x_1)) = 0 POL(5(x_1)) = 1 + x_1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) ---------------------------------------- (70) Obligation: Q DP problem: The TRS P consists of the following rules: 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2^1(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2^1(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2^1(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2^1(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (71) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. 2^1(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2^1(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 0 POL(1(x_1)) = x_1 POL(2(x_1)) = 0 POL(2^1(x_1)) = x_1 POL(3(x_1)) = 1 + x_1 POL(4(x_1)) = 1 POL(5(x_1)) = 0 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) ---------------------------------------- (72) Obligation: Q DP problem: The TRS P consists of the following rules: 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2^1(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2^1(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2^1(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (73) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. 2^1(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2^1(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2^1(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2^1(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = x_1 POL(1(x_1)) = 1 POL(2(x_1)) = 1 + x_1 POL(2^1(x_1)) = x_1 POL(3(x_1)) = 1 + x_1 POL(4(x_1)) = 0 POL(5(x_1)) = x_1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) ---------------------------------------- (74) Obligation: Q DP problem: The TRS P consists of the following rules: 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2^1(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (75) MRRProof (EQUIVALENT) By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. Strictly oriented rules of the TRS R: 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 1 + x_1 POL(1(x_1)) = x_1 POL(2(x_1)) = x_1 POL(2^1(x_1)) = 2*x_1 POL(3(x_1)) = 2*x_1 POL(4(x_1)) = x_1 POL(5(x_1)) = x_1 ---------------------------------------- (76) Obligation: Q DP problem: The TRS P consists of the following rules: 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2^1(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (77) MRRProof (EQUIVALENT) By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. Strictly oriented rules of the TRS R: 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = x_1 POL(1(x_1)) = 2 + 2*x_1 POL(2(x_1)) = x_1 POL(2^1(x_1)) = 2*x_1 POL(3(x_1)) = 1 + 2*x_1 POL(4(x_1)) = x_1 POL(5(x_1)) = 2*x_1 ---------------------------------------- (78) Obligation: Q DP problem: The TRS P consists of the following rules: 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2^1(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (79) MRRProof (EQUIVALENT) By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. Strictly oriented rules of the TRS R: 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 2*x_1 POL(1(x_1)) = 1 + 2*x_1 POL(2(x_1)) = 1 + 2*x_1 POL(2^1(x_1)) = x_1 POL(3(x_1)) = 1 + 2*x_1 POL(4(x_1)) = x_1 POL(5(x_1)) = 2*x_1 ---------------------------------------- (80) Obligation: Q DP problem: The TRS P consists of the following rules: 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2^1(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (81) MRRProof (EQUIVALENT) By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. Strictly oriented dependency pairs: 2^1(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2^1(5(2(1(4(0(3(4(4(2(3(x1))))))))))) Strictly oriented rules of the TRS R: 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 2 + 2*x_1 POL(1(x_1)) = x_1 POL(2(x_1)) = 1 + 2*x_1 POL(2^1(x_1)) = 2*x_1 POL(3(x_1)) = x_1 POL(4(x_1)) = 2 + 2*x_1 POL(5(x_1)) = 2 + 2*x_1 ---------------------------------------- (82) Obligation: Q DP problem: The TRS P consists of the following rules: 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2^1(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (83) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node. ---------------------------------------- (84) TRUE ---------------------------------------- (85) Obligation: Q DP problem: The TRS P consists of the following rules: 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 4^1(1(2(2(1(4(2(3(2(x1))))))))) 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4^1(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4^1(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4^1(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (86) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. 4^1(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4^1(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = x_1 POL(1(x_1)) = x_1 POL(2(x_1)) = 0 POL(3(x_1)) = x_1 POL(4(x_1)) = 0 POL(4^1(x_1)) = x_1 POL(5(x_1)) = 1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) ---------------------------------------- (87) Obligation: Q DP problem: The TRS P consists of the following rules: 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 4^1(1(2(2(1(4(2(3(2(x1))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4^1(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4^1(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (88) MRRProof (EQUIVALENT) By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. Strictly oriented dependency pairs: 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4^1(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) Strictly oriented rules of the TRS R: 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = x_1 POL(1(x_1)) = 1 + 2*x_1 POL(2(x_1)) = x_1 POL(3(x_1)) = 2*x_1 POL(4(x_1)) = x_1 POL(4^1(x_1)) = 2*x_1 POL(5(x_1)) = 2*x_1 ---------------------------------------- (89) Obligation: Q DP problem: The TRS P consists of the following rules: 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 4^1(1(2(2(1(4(2(3(2(x1))))))))) 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4^1(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4^1(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (90) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. 4^1(1(2(2(2(1(4(3(2(x1))))))))) -> 4^1(1(2(2(1(4(2(3(2(x1))))))))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 1 + x_1 POL(1(x_1)) = x_1 POL(2(x_1)) = 1 + x_1 POL(3(x_1)) = 0 POL(4(x_1)) = 1 POL(4^1(x_1)) = x_1 POL(5(x_1)) = 0 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) ---------------------------------------- (91) Obligation: Q DP problem: The TRS P consists of the following rules: 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4^1(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4^1(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (92) MRRProof (EQUIVALENT) By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. Strictly oriented rules of the TRS R: 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 2*x_1 POL(1(x_1)) = 1 + x_1 POL(2(x_1)) = x_1 POL(3(x_1)) = x_1 POL(4(x_1)) = x_1 POL(4^1(x_1)) = x_1 POL(5(x_1)) = 2*x_1 ---------------------------------------- (93) Obligation: Q DP problem: The TRS P consists of the following rules: 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4^1(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4^1(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (94) MRRProof (EQUIVALENT) By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. Strictly oriented rules of the TRS R: 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = x_1 POL(1(x_1)) = x_1 POL(2(x_1)) = 2 + 2*x_1 POL(3(x_1)) = 2 + 2*x_1 POL(4(x_1)) = x_1 POL(4^1(x_1)) = 2*x_1 POL(5(x_1)) = 2*x_1 ---------------------------------------- (95) Obligation: Q DP problem: The TRS P consists of the following rules: 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4^1(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4^1(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (96) MRRProof (EQUIVALENT) By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. Strictly oriented rules of the TRS R: 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 2 + x_1 POL(1(x_1)) = x_1 POL(2(x_1)) = x_1 POL(3(x_1)) = x_1 POL(4(x_1)) = x_1 POL(4^1(x_1)) = 2*x_1 POL(5(x_1)) = 2*x_1 ---------------------------------------- (97) Obligation: Q DP problem: The TRS P consists of the following rules: 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4^1(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4^1(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (98) MRRProof (EQUIVALENT) By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. Strictly oriented rules of the TRS R: 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 1 + x_1 POL(1(x_1)) = 2*x_1 POL(2(x_1)) = x_1 POL(3(x_1)) = 2*x_1 POL(4(x_1)) = x_1 POL(4^1(x_1)) = x_1 POL(5(x_1)) = 2*x_1 ---------------------------------------- (99) Obligation: Q DP problem: The TRS P consists of the following rules: 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4^1(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4^1(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (100) MRRProof (EQUIVALENT) By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. Strictly oriented rules of the TRS R: 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = x_1 POL(1(x_1)) = x_1 POL(2(x_1)) = 2*x_1 POL(3(x_1)) = x_1 POL(4(x_1)) = 1 + 2*x_1 POL(4^1(x_1)) = x_1 POL(5(x_1)) = 1 + 2*x_1 ---------------------------------------- (101) Obligation: Q DP problem: The TRS P consists of the following rules: 4^1(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4^1(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4^1(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4^1(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (102) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 2 less nodes. ---------------------------------------- (103) TRUE ---------------------------------------- (104) Obligation: Q DP problem: The TRS P consists of the following rules: 0^1(2(1(4(1(1(3(5(5(x1))))))))) -> 0^1(2(4(1(1(1(3(5(5(x1))))))))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 0^1(1(2(0(0(5(5(3(0(x1))))))))) 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0^1(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0^1(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0^1(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0^1(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0^1(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 0^1(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0^1(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (105) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. 0^1(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0^1(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 1 + x_1 POL(0^1(x_1)) = x_1 POL(1(x_1)) = 1 POL(2(x_1)) = 1 + x_1 POL(3(x_1)) = 1 POL(4(x_1)) = 1 POL(5(x_1)) = 1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) ---------------------------------------- (106) Obligation: Q DP problem: The TRS P consists of the following rules: 0^1(2(1(4(1(1(3(5(5(x1))))))))) -> 0^1(2(4(1(1(1(3(5(5(x1))))))))) 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 0^1(1(2(0(0(5(5(3(0(x1))))))))) 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0^1(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0^1(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0^1(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0^1(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 0^1(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0^1(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (107) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. 0^1(3(5(0(5(2(0(1(0(x1))))))))) -> 0^1(1(2(0(0(5(5(3(0(x1))))))))) 0^1(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0^1(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 0^1(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0^1(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 1 + x_1 POL(0^1(x_1)) = x_1 POL(1(x_1)) = 0 POL(2(x_1)) = 1 + x_1 POL(3(x_1)) = 1 + x_1 POL(4(x_1)) = x_1 POL(5(x_1)) = 1 + x_1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) ---------------------------------------- (108) Obligation: Q DP problem: The TRS P consists of the following rules: 0^1(2(1(4(1(1(3(5(5(x1))))))))) -> 0^1(2(4(1(1(1(3(5(5(x1))))))))) 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0^1(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0^1(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0^1(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (109) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. 0^1(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0^1(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 1 POL(0^1(x_1)) = x_1 POL(1(x_1)) = x_1 POL(2(x_1)) = x_1 POL(3(x_1)) = 1 + x_1 POL(4(x_1)) = x_1 POL(5(x_1)) = 1 + x_1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) ---------------------------------------- (110) Obligation: Q DP problem: The TRS P consists of the following rules: 0^1(2(1(4(1(1(3(5(5(x1))))))))) -> 0^1(2(4(1(1(1(3(5(5(x1))))))))) 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0^1(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0^1(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (111) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. 0^1(2(1(4(1(1(3(5(5(x1))))))))) -> 0^1(2(4(1(1(1(3(5(5(x1))))))))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 0 POL(0^1(x_1)) = x_1 POL(1(x_1)) = 1 POL(2(x_1)) = x_1 POL(3(x_1)) = 0 POL(4(x_1)) = 0 POL(5(x_1)) = 0 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) ---------------------------------------- (112) Obligation: Q DP problem: The TRS P consists of the following rules: 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0^1(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0^1(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (113) MRRProof (EQUIVALENT) By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. Strictly oriented dependency pairs: 0^1(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0^1(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) Strictly oriented rules of the TRS R: 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = x_1 POL(0^1(x_1)) = 3*x_1 POL(1(x_1)) = 1 + x_1 POL(2(x_1)) = x_1 POL(3(x_1)) = x_1 POL(4(x_1)) = x_1 POL(5(x_1)) = 3 + 2*x_1 ---------------------------------------- (114) Obligation: Q DP problem: The TRS P consists of the following rules: 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0^1(4(0(0(4(2(5(0(0(5(0(x1))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (115) MRRProof (EQUIVALENT) By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. Strictly oriented rules of the TRS R: 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 2*x_1 POL(0^1(x_1)) = 2*x_1 POL(1(x_1)) = 2 + 2*x_1 POL(2(x_1)) = x_1 POL(3(x_1)) = 2*x_1 POL(4(x_1)) = x_1 POL(5(x_1)) = 2*x_1 ---------------------------------------- (116) Obligation: Q DP problem: The TRS P consists of the following rules: 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0^1(4(0(0(4(2(5(0(0(5(0(x1))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (117) MRRProof (EQUIVALENT) By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. Strictly oriented rules of the TRS R: 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = x_1 POL(0^1(x_1)) = 2*x_1 POL(1(x_1)) = x_1 POL(2(x_1)) = 1 + 2*x_1 POL(3(x_1)) = 1 + 2*x_1 POL(4(x_1)) = x_1 POL(5(x_1)) = 2*x_1 ---------------------------------------- (118) Obligation: Q DP problem: The TRS P consists of the following rules: 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0^1(4(0(0(4(2(5(0(0(5(0(x1))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (119) MRRProof (EQUIVALENT) By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. Strictly oriented rules of the TRS R: 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 2 + 2*x_1 POL(0^1(x_1)) = 2*x_1 POL(1(x_1)) = 2 + 2*x_1 POL(2(x_1)) = 2 + 2*x_1 POL(3(x_1)) = 2 + 2*x_1 POL(4(x_1)) = x_1 POL(5(x_1)) = 2*x_1 ---------------------------------------- (120) Obligation: Q DP problem: The TRS P consists of the following rules: 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0^1(4(0(0(4(2(5(0(0(5(0(x1))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (121) MRRProof (EQUIVALENT) By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. Strictly oriented rules of the TRS R: 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 2 + 2*x_1 POL(0^1(x_1)) = 2*x_1 POL(1(x_1)) = 2*x_1 POL(2(x_1)) = x_1 POL(3(x_1)) = 2*x_1 POL(4(x_1)) = x_1 POL(5(x_1)) = 2*x_1 ---------------------------------------- (122) Obligation: Q DP problem: The TRS P consists of the following rules: 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0^1(4(0(0(4(2(5(0(0(5(0(x1))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (123) MRRProof (EQUIVALENT) By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. Strictly oriented rules of the TRS R: 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 2*x_1 POL(0^1(x_1)) = 2*x_1 POL(1(x_1)) = 2 + 2*x_1 POL(2(x_1)) = 2 + 2*x_1 POL(3(x_1)) = x_1 POL(4(x_1)) = x_1 POL(5(x_1)) = 2*x_1 ---------------------------------------- (124) Obligation: Q DP problem: The TRS P consists of the following rules: 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0^1(4(0(0(4(2(5(0(0(5(0(x1))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (125) MRRProof (EQUIVALENT) By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. Strictly oriented rules of the TRS R: 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = x_1 POL(0^1(x_1)) = x_1 POL(1(x_1)) = x_1 POL(2(x_1)) = 2*x_1 POL(3(x_1)) = x_1 POL(4(x_1)) = 1 + 2*x_1 POL(5(x_1)) = x_1 ---------------------------------------- (126) Obligation: Q DP problem: The TRS P consists of the following rules: 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0^1(4(0(0(4(2(5(0(0(5(0(x1))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (127) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. 0^1(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0^1(4(0(0(4(2(5(0(0(5(0(x1))))))))))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 2 + x_1 POL(0^1(x_1)) = 2*x_1 POL(1(x_1)) = 0 POL(2(x_1)) = 0 POL(3(x_1)) = 0 POL(4(x_1)) = 2*x_1 POL(5(x_1)) = 0 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) ---------------------------------------- (128) Obligation: Q DP problem: P is empty. The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (129) PisEmptyProof (EQUIVALENT) The TRS P is empty. Hence, there is no (P,Q,R) chain. ---------------------------------------- (130) YES ---------------------------------------- (131) Obligation: Q DP problem: The TRS P consists of the following rules: 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1^1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1^1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (132) MRRProof (EQUIVALENT) By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. Strictly oriented dependency pairs: 1^1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1^1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) Strictly oriented rules of the TRS R: 0(3(5(0(5(2(0(1(0(x1))))))))) -> 0(1(2(0(0(5(5(3(0(x1))))))))) 1(3(4(1(1(5(2(1(2(1(2(1(x1)))))))))))) -> 1(2(1(3(2(4(1(5(1(1(2(1(x1)))))))))))) 1(3(2(5(2(5(2(3(0(4(2(2(0(x1))))))))))))) -> 1(3(2(5(2(2(5(3(0(4(2(2(0(x1))))))))))))) 0(0(2(2(1(2(5(1(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) -> 0(0(2(2(1(2(1(5(5(0(2(3(1(2(4(0(4(3(0(x1))))))))))))))))))) 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(5(1(1(4(0(1(x1))))))))))))))))))))) -> 4(2(3(0(0(4(0(0(0(0(5(0(5(5(1(1(5(1(4(0(1(x1))))))))))))))))))))) 3(0(4(0(5(2(5(2(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) -> 3(0(4(0(5(2(2(5(2(4(0(1(4(4(3(0(3(1(2(1(2(5(4(2(1(0(2(3(3(x1))))))))))))))))))))))))))))) Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = x_1 POL(1(x_1)) = 2 + 2*x_1 POL(1^1(x_1)) = 3*x_1 POL(2(x_1)) = 2 + 2*x_1 POL(3(x_1)) = x_1 POL(4(x_1)) = x_1 POL(5(x_1)) = 1 + 2*x_1 ---------------------------------------- (133) Obligation: Q DP problem: The TRS P consists of the following rules: 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1^1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (134) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. 1^1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1^1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = x_1 POL(1(x_1)) = 1 + x_1 POL(1^1(x_1)) = x_1 POL(2(x_1)) = 1 + x_1 POL(3(x_1)) = x_1 POL(4(x_1)) = 1 POL(5(x_1)) = x_1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) ---------------------------------------- (135) Obligation: Q DP problem: P is empty. The TRS R consists of the following rules: 3(3(2(1(1(0(x1)))))) -> 3(2(3(1(1(0(x1)))))) 3(2(1(3(0(2(4(4(x1)))))))) -> 3(2(1(3(0(4(2(4(x1)))))))) 3(5(2(4(1(0(5(4(x1)))))))) -> 5(1(4(3(2(0(5(4(x1)))))))) 5(2(2(3(3(2(0(1(1(x1))))))))) -> 5(2(0(2(3(2(3(1(1(x1))))))))) 4(1(2(2(2(1(4(3(2(x1))))))))) -> 4(1(2(2(1(4(2(3(2(x1))))))))) 0(2(1(4(1(1(3(5(5(x1))))))))) -> 0(2(4(1(1(1(3(5(5(x1))))))))) 2(0(5(3(0(5(4(5(3(0(0(x1))))))))))) -> 2(0(3(5(5(0(4(5(3(0(0(x1))))))))))) 0(4(0(4(0(2(5(0(0(5(0(x1))))))))))) -> 0(4(0(0(4(2(5(0(0(5(0(x1))))))))))) 4(4(5(0(3(0(1(1(5(5(2(x1))))))))))) -> 4(4(0(5(0(3(1(1(5(5(2(x1))))))))))) 2(5(2(1(4(0(3(4(2(4(3(x1))))))))))) -> 2(5(2(1(4(0(3(4(4(2(3(x1))))))))))) 5(4(2(3(5(1(3(4(5(1(3(1(x1)))))))))))) -> 5(4(3(2(5(1(3(4(5(1(3(1(x1)))))))))))) 0(2(0(0(2(4(3(0(0(2(4(3(x1)))))))))))) -> 0(2(2(4(0(0(2(3(4(0(0(3(x1)))))))))))) 0(3(4(1(5(5(2(3(0(2(3(3(4(x1))))))))))))) -> 0(3(4(1(5(5(2(0(3(2(3(3(4(x1))))))))))))) 3(5(0(5(3(0(2(1(1(0(2(1(5(2(x1)))))))))))))) -> 3(5(0(5(3(2(0(1(1(0(2(1(5(2(x1)))))))))))))) 3(1(3(2(0(4(4(5(2(4(4(5(5(4(x1)))))))))))))) -> 3(1(3(2(4(0(4(5(2(4(4(5(5(4(x1)))))))))))))) 2(3(3(3(2(1(2(1(3(2(1(4(1(3(2(x1))))))))))))))) -> 2(3(3(3(1(2(2(1(3(2(1(4(1(3(2(x1))))))))))))))) 3(3(0(2(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) -> 3(3(2(0(4(4(4(2(2(0(1(1(1(1(3(0(2(x1))))))))))))))))) 0(5(3(0(3(1(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) -> 0(5(3(0(1(3(1(5(4(0(4(1(2(5(0(1(3(x1))))))))))))))))) 2(1(3(3(1(1(3(4(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) -> 2(1(3(3(1(1(4(3(3(5(1(2(2(2(2(2(4(x1))))))))))))))))) 3(5(1(4(4(4(4(1(0(0(2(1(1(0(0(1(4(3(x1)))))))))))))))))) -> 3(5(1(4(4(4(4(1(0(0(2(1(1(1(0(0(4(3(x1)))))))))))))))))) 1(5(2(1(3(2(2(5(2(4(2(2(4(3(1(0(5(5(x1)))))))))))))))))) -> 1(5(2(1(3(2(2(5(4(2(2(2(4(3(1(0(5(5(x1)))))))))))))))))) 3(4(4(3(4(1(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) -> 3(4(4(3(1(4(2(1(4(4(4(1(1(4(4(2(5(2(0(x1))))))))))))))))))) 3(0(5(4(0(4(4(5(5(0(4(3(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) -> 3(0(5(4(0(4(4(5(5(0(3(4(0(5(5(4(5(2(0(4(x1)))))))))))))))))))) 3(3(5(0(3(5(4(5(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) -> 3(3(5(0(3(5(5(4(3(4(0(0(0(1(1(5(0(3(1(4(x1)))))))))))))))))))) 3(1(4(0(0(0(2(5(4(4(2(4(4(4(5(4(1(3(4(0(4(x1))))))))))))))))))))) -> 3(1(4(0(0(0(2(5(4(4(2(4(4(4(4(5(1(3(4(0(4(x1))))))))))))))))))))) 4(1(0(0(3(5(4(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) -> 4(1(0(0(3(4(5(0(2(4(1(2(5(2(1(5(0(1(3(4(4(1(x1)))))))))))))))))))))) 3(1(1(4(0(1(2(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) -> 3(1(1(4(0(2(1(2(5(3(1(3(2(5(5(4(5(1(1(3(5(2(x1)))))))))))))))))))))) 4(3(2(0(2(4(2(1(3(2(1(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) -> 4(3(2(0(2(4(2(1(3(1(2(5(1(1(0(3(0(4(5(0(1(5(x1)))))))))))))))))))))) 0(5(5(2(1(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) -> 0(5(5(1(2(2(3(5(4(1(2(4(5(3(2(5(3(4(2(5(4(3(2(x1))))))))))))))))))))))) 3(3(2(5(3(5(4(1(0(3(3(1(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) -> 3(3(2(5(3(5(4(1(0(3(1(3(1(1(0(1(4(5(1(2(0(2(0(5(0(5(1(x1))))))))))))))))))))))))))) 2(2(2(3(3(3(1(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) -> 2(2(2(3(3(1(3(1(0(5(3(4(2(5(4(1(0(4(0(4(2(4(0(1(0(5(4(x1))))))))))))))))))))))))))) 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(0(4(0(1(x1)))))))))))))))))))))))))))) -> 2(1(4(4(1(1(1(4(1(2(4(1(5(0(5(1(1(4(5(2(3(1(3(1(4(0(0(1(x1)))))))))))))))))))))))))))) 4(4(0(5(4(5(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) -> 4(4(0(5(5(4(5(0(2(1(2(1(4(0(5(1(3(0(3(0(2(4(3(1(1(4(2(4(x1)))))))))))))))))))))))))))) 5(0(5(4(4(2(2(2(4(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) -> 5(0(5(4(4(2(2(4(2(0(3(2(3(1(0(0(2(0(4(3(3(4(0(0(0(2(0(3(0(4(x1)))))))))))))))))))))))))))))) 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(2(4(4(5(5(4(x1)))))))))))))))))))))))))))))) -> 3(0(4(1(5(5(3(5(4(4(0(0(1(1(4(0(4(0(0(5(5(3(1(0(4(2(4(5(5(4(x1)))))))))))))))))))))))))))))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (136) PisEmptyProof (EQUIVALENT) The TRS P is empty. Hence, there is no (P,Q,R) chain. ---------------------------------------- (137) YES