/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


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, 543 ms]
(4) QTRS
(5) DependencyPairsProof [EQUIVALENT, 2694 ms]
(6) QDP
(7) QDPOrderProof [EQUIVALENT, 3201 ms]
(8) QDP
(9) DependencyGraphProof [EQUIVALENT, 11 ms]
(10) AND
    (11) QDP
        (12) QDPOrderProof [EQUIVALENT, 92 ms]
        (13) QDP
        (14) QDPOrderProof [EQUIVALENT, 81 ms]
        (15) QDP
        (16) MRRProof [EQUIVALENT, 6231 ms]
        (17) QDP
        (18) MRRProof [EQUIVALENT, 777 ms]
        (19) QDP
        (20) MRRProof [EQUIVALENT, 364 ms]
        (21) QDP
        (22) QDPOrderProof [EQUIVALENT, 40 ms]
        (23) QDP
        (24) MRRProof [EQUIVALENT, 269 ms]
        (25) QDP
        (26) MRRProof [EQUIVALENT, 136 ms]
        (27) QDP
        (28) MRRProof [EQUIVALENT, 115 ms]
        (29) QDP
        (30) MRRProof [EQUIVALENT, 451 ms]
        (31) QDP
        (32) DependencyGraphProof [EQUIVALENT, 0 ms]
        (33) TRUE
    (34) QDP
        (35) QDPOrderProof [EQUIVALENT, 650 ms]
        (36) QDP
        (37) DependencyGraphProof [EQUIVALENT, 0 ms]
        (38) AND
            (39) QDP
                (40) QDPOrderProof [EQUIVALENT, 70 ms]
                (41) QDP
                (42) MRRProof [EQUIVALENT, 7062 ms]
                (43) QDP
                (44) MRRProof [EQUIVALENT, 1688 ms]
                (45) QDP
                (46) MRRProof [EQUIVALENT, 247 ms]
                (47) QDP
                (48) MRRProof [EQUIVALENT, 219 ms]
                (49) QDP
                (50) MRRProof [EQUIVALENT, 180 ms]
                (51) QDP
                (52) MRRProof [EQUIVALENT, 186 ms]
                (53) QDP
                (54) MRRProof [EQUIVALENT, 144 ms]
                (55) QDP
                (56) DependencyGraphProof [EQUIVALENT, 0 ms]
                (57) QDP
                (58) QDPOrderProof [EQUIVALENT, 458 ms]
                (59) QDP
                (60) PisEmptyProof [EQUIVALENT, 0 ms]
                (61) YES
            (62) QDP
                (63) QDPOrderProof [EQUIVALENT, 70 ms]
                (64) QDP
                (65) DependencyGraphProof [EQUIVALENT, 0 ms]
                (66) AND
                    (67) QDP
                        (68) QDPOrderProof [EQUIVALENT, 0 ms]
                        (69) QDP
                        (70) MRRProof [EQUIVALENT, 928 ms]
                        (71) QDP
                        (72) MRRProof [EQUIVALENT, 2755 ms]
                        (73) QDP
                        (74) MRRProof [EQUIVALENT, 3003 ms]
                        (75) QDP
                        (76) MRRProof [EQUIVALENT, 1249 ms]
                        (77) QDP
                        (78) MRRProof [EQUIVALENT, 418 ms]
                        (79) QDP
                        (80) MRRProof [EQUIVALENT, 721 ms]
                        (81) QDP
                        (82) PisEmptyProof [EQUIVALENT, 0 ms]
                        (83) YES
                    (84) QDP
                        (85) QDPOrderProof [EQUIVALENT, 0 ms]
                        (86) QDP
                        (87) QDPOrderProof [EQUIVALENT, 0 ms]
                        (88) QDP
                        (89) QDPOrderProof [EQUIVALENT, 72 ms]
                        (90) QDP
                        (91) MRRProof [EQUIVALENT, 3966 ms]
                        (92) QDP
                        (93) MRRProof [EQUIVALENT, 2364 ms]
                        (94) QDP
                        (95) MRRProof [EQUIVALENT, 1668 ms]
                        (96) QDP
                        (97) MRRProof [EQUIVALENT, 1047 ms]
                        (98) QDP
                        (99) MRRProof [EQUIVALENT, 173 ms]
                        (100) QDP
                        (101) MRRProof [EQUIVALENT, 116 ms]
                        (102) QDP
                        (103) MRRProof [EQUIVALENT, 98 ms]
                        (104) QDP
                        (105) DependencyGraphProof [EQUIVALENT, 0 ms]
                        (106) TRUE
            (107) QDP
                (108) QDPOrderProof [EQUIVALENT, 82 ms]
                (109) QDP
                (110) QDPOrderProof [EQUIVALENT, 81 ms]
                (111) QDP
                (112) QDPOrderProof [EQUIVALENT, 75 ms]
                (113) QDP
                (114) QDPOrderProof [EQUIVALENT, 0 ms]
                (115) QDP
                (116) QDPOrderProof [EQUIVALENT, 11 ms]
                (117) QDP
                (118) QDPOrderProof [EQUIVALENT, 45 ms]
                (119) QDP
                (120) QDPOrderProof [EQUIVALENT, 0 ms]
                (121) QDP
                (122) MRRProof [EQUIVALENT, 3313 ms]
                (123) QDP
                (124) QDPOrderProof [EQUIVALENT, 46 ms]
                (125) QDP
                (126) MRRProof [EQUIVALENT, 598 ms]
                (127) QDP
                (128) MRRProof [EQUIVALENT, 235 ms]
                (129) QDP
                (130) MRRProof [EQUIVALENT, 155 ms]
                (131) QDP
                (132) MRRProof [EQUIVALENT, 470 ms]
                (133) QDP
                (134) MRRProof [EQUIVALENT, 174 ms]
                (135) QDP
                (136) DependencyGraphProof [EQUIVALENT, 0 ms]
                (137) TRUE
            (138) QDP
                (139) QDPOrderProof [EQUIVALENT, 77 ms]
                (140) QDP
                (141) QDPOrderProof [EQUIVALENT, 0 ms]
                (142) QDP
                (143) QDPOrderProof [EQUIVALENT, 34 ms]
                (144) QDP
                (145) QDPOrderProof [EQUIVALENT, 72 ms]
                (146) QDP
                (147) QDPOrderProof [EQUIVALENT, 0 ms]
                (148) QDP
                (149) MRRProof [EQUIVALENT, 6446 ms]
                (150) QDP
                (151) MRRProof [EQUIVALENT, 1452 ms]
                (152) QDP
                (153) MRRProof [EQUIVALENT, 1326 ms]
                (154) QDP
                (155) MRRProof [EQUIVALENT, 269 ms]
                (156) QDP
                (157) MRRProof [EQUIVALENT, 165 ms]
                (158) QDP
                (159) MRRProof [EQUIVALENT, 108 ms]
                (160) QDP
                (161) PisEmptyProof [EQUIVALENT, 0 ms]
                (162) YES


----------------------------------------

(0)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   0(1(0(2(2(0(3(x1))))))) -> 0(1(3(2(0(2(0(x1)))))))
   0(4(5(4(3(3(5(x1))))))) -> 0(4(3(4(5(3(5(x1)))))))
   2(1(0(4(5(2(4(x1))))))) -> 2(1(4(2(5(0(4(x1)))))))
   4(5(2(4(2(1(5(x1))))))) -> 4(5(2(2(4(1(5(x1)))))))
   3(3(3(0(0(2(4(4(x1)))))))) -> 3(3(2(3(0(0(4(4(x1))))))))
   4(0(0(5(4(3(3(0(x1)))))))) -> 4(0(3(5(3(4(0(0(x1))))))))
   1(1(3(4(3(1(4(3(5(x1))))))))) -> 1(1(3(4(1(3(4(3(5(x1)))))))))
   4(1(2(3(0(0(0(4(0(x1))))))))) -> 4(1(3(2(0(0(0(4(0(x1)))))))))
   1(2(3(3(4(3(2(1(5(2(x1)))))))))) -> 0(5(0(2(5(2(0(2(1(3(x1))))))))))
   5(2(3(0(1(1(2(3(3(3(x1)))))))))) -> 5(3(4(5(0(5(4(2(2(3(x1))))))))))
   0(0(2(0(0(3(2(5(1(1(4(x1))))))))))) -> 3(3(0(4(3(3(1(5(1(3(x1))))))))))
   0(0(4(0(5(3(4(0(3(1(1(x1))))))))))) -> 2(4(0(4(1(0(0(3(4(5(x1))))))))))
   0(1(2(5(4(2(1(0(0(1(4(x1))))))))))) -> 5(4(5(4(1(4(4(4(5(4(x1))))))))))
   0(1(3(5(5(2(0(2(3(1(2(x1))))))))))) -> 3(4(5(1(4(5(1(0(5(5(x1))))))))))
   0(4(2(1(2(0(3(3(5(4(3(x1))))))))))) -> 1(5(0(4(4(4(4(3(3(4(x1))))))))))
   0(4(5(4(0(5(0(3(1(5(4(x1))))))))))) -> 2(3(3(2(5(1(2(4(3(4(x1))))))))))
   0(5(1(4(0(3(2(3(3(3(4(x1))))))))))) -> 3(5(4(2(5(0(1(3(4(3(x1))))))))))
   1(0(1(3(5(0(1(0(4(4(4(x1))))))))))) -> 4(5(4(4(0(4(0(0(5(5(x1))))))))))
   1(0(2(5(4(5(1(4(4(2(0(x1))))))))))) -> 1(2(1(2(3(4(4(3(3(3(x1))))))))))
   1(0(5(3(3(3(5(5(1(5(0(x1))))))))))) -> 5(1(2(4(2(4(2(2(1(3(x1))))))))))
   1(1(4(3(5(5(4(0(1(5(0(x1))))))))))) -> 5(0(3(4(2(5(4(5(3(2(x1))))))))))
   1(2(4(0(3(4(2(2(3(5(4(x1))))))))))) -> 4(5(5(3(1(1(5(0(0(3(x1))))))))))
   1(3(0(1(1(4(1(5(5(0(4(x1))))))))))) -> 4(2(0(5(0(4(5(3(1(5(x1))))))))))
   1(5(0(3(3(1(3(5(0(1(0(x1))))))))))) -> 3(0(2(1(0(4(2(2(0(5(x1))))))))))
   1(5(4(5(2(0(0(1(1(1(0(x1))))))))))) -> 5(4(4(4(2(3(1(2(5(1(x1))))))))))
   2(0(3(3(0(1(0(5(2(3(5(x1))))))))))) -> 5(3(5(4(1(2(2(3(1(1(x1))))))))))
   2(1(3(1(4(0(1(4(2(2(2(x1))))))))))) -> 1(2(3(5(4(5(0(5(3(0(x1))))))))))
   2(2(2(5(3(2(5(0(0(0(1(x1))))))))))) -> 2(5(0(5(2(2(2(3(2(0(x1))))))))))
   2(2(3(1(1(5(4(4(0(0(1(x1))))))))))) -> 2(0(0(1(1(2(0(5(4(2(x1))))))))))
   2(3(3(3(2(2(5(5(0(1(0(x1))))))))))) -> 2(2(2(2(3(4(0(5(2(5(x1))))))))))
   2(4(2(4(5(4(3(5(4(1(5(x1))))))))))) -> 5(1(0(4(4(5(1(1(5(1(x1))))))))))
   2(4(4(5(5(4(3(4(2(2(0(x1))))))))))) -> 3(0(3(2(0(4(5(3(0(4(x1))))))))))
   3(0(2(4(0(3(3(1(2(1(5(x1))))))))))) -> 0(2(4(3(5(5(5(4(1(0(x1))))))))))
   3(0(3(5(2(3(1(1(0(4(2(x1))))))))))) -> 2(5(4(5(3(4(1(5(2(4(x1))))))))))
   3(1(1(1(3(4(1(3(1(2(0(x1))))))))))) -> 0(5(0(3(3(4(0(1(3(1(x1))))))))))
   3(1(1(3(4(0(2(3(3(1(5(x1))))))))))) -> 4(2(5(3(2(0(2(2(3(4(x1))))))))))
   3(2(5(2(1(3(1(3(0(1(1(x1))))))))))) -> 5(0(5(4(0(3(1(4(2(0(x1))))))))))
   3(3(0(2(4(5(4(4(0(0(3(x1))))))))))) -> 3(2(0(3(2(0(1(2(2(1(x1))))))))))
   3(3(0(5(4(2(3(3(5(4(1(x1))))))))))) -> 4(3(0(5(2(2(2(4(4(2(x1))))))))))
   3(4(1(2(0(3(4(1(5(2(3(x1))))))))))) -> 2(1(4(2(3(0(2(2(5(4(x1))))))))))
   3(5(0(1(5(2(3(3(5(0(0(x1))))))))))) -> 2(5(2(1(5(4(1(1(4(0(x1))))))))))
   3(5(1(3(4(4(0(2(5(5(3(x1))))))))))) -> 2(2(5(0(3(0(4(4(2(5(x1))))))))))
   3(5(2(5(4(1(0(1(0(5(0(x1))))))))))) -> 2(0(3(5(1(3(3(5(2(4(x1))))))))))
   4(0(5(1(5(0(5(5(1(2(5(x1))))))))))) -> 1(1(3(1(1(1(0(4(3(3(x1))))))))))
   4(1(2(1(2(4(0(0(3(2(1(x1))))))))))) -> 5(4(5(4(4(0(3(4(2(5(x1))))))))))
   4(1(3(1(5(1(5(4(2(4(5(x1))))))))))) -> 0(4(3(2(5(4(3(3(3(3(x1))))))))))
   4(1(4(1(3(4(3(2(5(0(4(x1))))))))))) -> 3(5(5(2(3(5(3(2(0(0(x1))))))))))
   4(2(3(2(1(5(4(1(1(3(3(x1))))))))))) -> 4(1(0(3(0(1(0(2(3(4(x1))))))))))
   4(2(5(2(1(5(2(0(2(5(3(x1))))))))))) -> 5(2(0(5(0(0(3(2(1(4(x1))))))))))
   4(3(2(0(1(3(3(3(5(0(3(x1))))))))))) -> 4(2(1(0(0(5(4(1(4(1(x1))))))))))
   4(3(3(2(4(2(0(2(3(0(3(x1))))))))))) -> 4(5(4(3(4(1(2(0(1(4(x1))))))))))
   4(3(4(0(5(1(3(0(1(0(1(x1))))))))))) -> 4(5(2(3(1(3(0(4(1(5(x1))))))))))
   4(3(4(1(4(1(1(2(0(4(0(x1))))))))))) -> 5(5(1(0(5(1(5(3(3(5(x1))))))))))
   4(4(3(0(4(1(1(0(5(3(3(x1))))))))))) -> 2(4(3(2(3(0(0(2(4(5(x1))))))))))
   5(1(2(5(3(5(1(1(3(3(3(x1))))))))))) -> 2(3(0(4(1(5(1(4(4(5(x1))))))))))
   5(3(2(2(2(5(1(3(4(3(0(x1))))))))))) -> 0(0(3(3(5(1(3(2(4(2(x1))))))))))
   5(4(1(0(2(1(4(1(0(4(2(x1))))))))))) -> 1(5(3(2(0(4(0(5(1(1(x1))))))))))
   5(5(4(5(3(3(3(0(2(4(5(x1))))))))))) -> 1(2(1(5(5(3(2(1(0(3(x1))))))))))
   0(5(5(4(3(3(5(1(3(4(4(2(x1)))))))))))) -> 0(5(4(5(3(3(5(1(3(4(4(2(x1))))))))))))
   3(1(2(2(1(0(2(0(4(3(2(0(x1)))))))))))) -> 3(1(2(2(1(0(0(2(4(3(2(0(x1))))))))))))
   1(2(2(2(0(1(4(2(3(1(3(5(1(x1))))))))))))) -> 1(2(2(2(0(1(4(3(2(1(3(5(1(x1)))))))))))))
   2(0(2(3(1(0(1(4(4(2(2(2(3(x1))))))))))))) -> 2(0(2(3(1(4(0(1(4(2(2(2(3(x1)))))))))))))
   4(2(3(1(3(4(4(1(5(5(0(1(4(x1))))))))))))) -> 4(2(3(5(4(0(4(1(1(3(5(1(4(x1)))))))))))))
   5(0(4(5(1(4(2(2(4(3(0(0(2(x1))))))))))))) -> 5(0(4(5(1(4(2(2(3(4(0(0(2(x1)))))))))))))
   4(2(0(1(2(4(2(1(0(1(0(2(1(1(x1)))))))))))))) -> 4(2(0(1(2(2(4(1(0(1(0(2(1(1(x1))))))))))))))
   0(1(4(0(1(1(2(3(2(2(5(5(3(5(1(x1))))))))))))))) -> 0(1(0(1(4(2(1(2(2(5(3(3(5(5(1(x1)))))))))))))))
   2(0(1(4(0(2(0(0(4(3(3(0(2(4(2(x1))))))))))))))) -> 2(0(1(4(0(2(0(0(4(3(0(3(2(4(2(x1)))))))))))))))
   3(0(1(5(1(1(3(1(0(3(1(5(0(0(5(x1))))))))))))))) -> 3(0(1(5(1(1(3(1(0(1(3(5(0(0(5(x1)))))))))))))))
   3(5(5(5(2(4(0(3(0(3(4(4(2(2(0(x1))))))))))))))) -> 3(5(2(5(4(5(3(4(0(2(2(4(0(0(3(x1)))))))))))))))
   3(1(1(2(4(2(5(0(4(4(5(4(1(3(4(1(x1)))))))))))))))) -> 3(1(1(2(4(2(5(0(4(5(4(4(1(3(4(1(x1))))))))))))))))
   3(5(1(4(5(5(5(2(3(1(2(5(0(0(1(4(x1)))))))))))))))) -> 3(5(5(1(3(5(5(0(5(1(2(4(0(2(1(4(x1))))))))))))))))
   1(4(1(1(2(4(3(3(1(4(4(3(4(5(5(4(3(x1))))))))))))))))) -> 1(4(1(1(2(3(4(3(1(4(4(3(4(5(5(4(3(x1)))))))))))))))))
   5(4(3(4(1(0(3(1(0(4(2(0(1(4(0(4(0(x1))))))))))))))))) -> 5(4(3(4(1(0(3(0(1(4(2(0(1(4(0(4(0(x1)))))))))))))))))
   0(5(3(4(2(5(4(1(0(4(0(3(1(0(2(1(4(1(x1)))))))))))))))))) -> 0(5(3(4(2(5(4(0(1(4(0(3(1(0(2(1(4(1(x1))))))))))))))))))
   3(4(5(5(0(3(4(3(2(5(1(0(4(0(4(1(1(0(x1)))))))))))))))))) -> 3(4(5(0(5(3(4(3(2(5(1(0(4(0(4(1(1(0(x1))))))))))))))))))
   4(3(3(2(5(4(2(0(5(2(1(2(0(1(5(2(2(5(x1)))))))))))))))))) -> 4(3(3(2(5(4(2(5(0(2(1(2(0(1(5(2(2(5(x1))))))))))))))))))
   5(1(1(3(3(1(0(2(5(0(3(0(0(1(5(4(3(0(x1)))))))))))))))))) -> 5(1(1(3(3(1(0(2(5(0(3(0(0(5(4(1(3(0(x1))))))))))))))))))
   3(4(1(5(3(3(0(5(4(1(5(5(5(0(3(3(3(4(5(x1))))))))))))))))))) -> 3(4(1(5(3(3(0(5(4(5(1(5(5(0(3(3(3(4(5(x1)))))))))))))))))))
   3(5(5(4(0(4(4(3(4(3(0(1(1(2(5(4(2(2(2(3(x1)))))))))))))))))))) -> 3(5(5(4(0(4(4(3(3(4(0(1(1(2(5(4(2(2(2(3(x1))))))))))))))))))))
   0(2(1(0(1(2(2(5(4(3(3(2(4(0(1(5(2(5(2(0(4(x1))))))))))))))))))))) -> 0(2(0(1(1(2(4(4(1(2(2(3(3(2(5(0(5(5(2(0(4(x1)))))))))))))))))))))
   5(2(3(0(1(4(0(4(5(3(4(5(3(5(2(1(1(4(4(5(4(x1))))))))))))))))))))) -> 5(2(3(0(1(4(0(4(5(3(4(5(3(2(5(1(1(4(4(5(4(x1)))))))))))))))))))))
   0(3(5(2(0(1(5(2(2(2(0(3(4(3(4(4(3(3(1(0(1(3(x1)))))))))))))))))))))) -> 0(3(5(2(0(1(5(2(2(2(0(3(4(3(4(4(3(3(0(1(1(3(x1))))))))))))))))))))))
   0(5(4(0(3(0(5(1(4(0(4(4(1(2(1(0(5(4(0(4(2(5(x1)))))))))))))))))))))) -> 0(5(4(3(0(0(5(4(1(4(4(0(1(2(1(0(5(4(0(4(2(5(x1))))))))))))))))))))))
   4(3(2(0(4(2(4(0(4(2(5(5(0(2(5(0(1(1(4(5(0(3(5(x1))))))))))))))))))))))) -> 4(3(2(4(4(0(0(4(2(2(0(5(0(5(5(2(4(1(1(0(5(3(5(x1)))))))))))))))))))))))
   4(5(3(5(0(3(1(4(5(0(4(4(2(0(4(2(3(3(5(3(5(0(2(x1))))))))))))))))))))))) -> 4(5(3(5(3(0(1(4(5(0(4(4(2(0(4(2(3(3(5(3(5(0(2(x1)))))))))))))))))))))))
   4(5(4(4(5(2(0(0(4(4(0(4(0(1(5(2(5(2(3(1(1(3(5(x1))))))))))))))))))))))) -> 4(5(4(4(5(2(0(0(4(4(0(4(0(1(5(2(2(5(3(1(1(3(5(x1)))))))))))))))))))))))
   0(1(3(1(5(1(2(3(0(3(2(1(2(0(2(2(1(0(3(5(1(3(4(4(0(x1))))))))))))))))))))))))) -> 0(1(3(1(5(2(1(3(0(3(2(1(2(0(2(2(1(0(3(5(1(3(4(4(0(x1)))))))))))))))))))))))))
   2(2(5(4(4(4(5(2(2(4(1(0(5(1(1(5(4(3(4(2(2(2(0(2(0(x1))))))))))))))))))))))))) -> 2(2(5(4(4(4(5(2(2(4(0(1(5(1(1(5(4(3(4(2(2(2(0(2(0(x1)))))))))))))))))))))))))
   0(0(2(2(4(4(2(5(4(5(0(3(4(3(5(2(1(2(4(3(1(1(2(5(5(5(4(x1))))))))))))))))))))))))))) -> 0(0(2(2(4(4(2(5(4(5(0(3(4(3(5(2(2(1(4(3(1(1(2(5(5(5(4(x1)))))))))))))))))))))))))))
   0(5(4(3(1(5(5(1(5(0(2(2(3(5(5(2(4(2(1(1(2(4(4(5(3(3(5(x1))))))))))))))))))))))))))) -> 0(5(4(3(1(5(5(1(5(0(2(2(3(5(5(2(4(2(1(1(4(2(4(5(3(3(5(x1)))))))))))))))))))))))))))
   1(1(5(3(1(2(2(5(3(1(5(4(5(0(5(5(1(1(4(2(0(4(1(4(4(2(0(x1))))))))))))))))))))))))))) -> 1(1(1(5(3(2(2(5(3(1(5(4(5(0(5(5(1(1(4(2(0(4(1(4(4(2(0(x1)))))))))))))))))))))))))))
   4(3(3(3(0(4(2(2(4(2(5(2(4(3(3(5(2(2(0(0(2(0(5(2(0(2(2(x1))))))))))))))))))))))))))) -> 4(3(3(3(0(4(2(2(4(2(5(4(2(3(3(5(2(2(0(0(2(0(5(2(0(2(2(x1)))))))))))))))))))))))))))
   4(4(5(2(3(4(1(2(5(5(3(5(3(4(4(5(4(1(5(2(5(4(4(1(0(4(5(x1))))))))))))))))))))))))))) -> 4(4(5(2(3(4(1(2(5(5(3(5(3(4(4(5(4(1(5(2(5(4(4(0(1(4(5(x1)))))))))))))))))))))))))))
   0(2(0(4(3(3(4(5(0(0(4(4(1(5(2(4(0(5(2(2(0(3(2(1(3(5(4(1(x1)))))))))))))))))))))))))))) -> 0(2(0(4(3(3(4(5(0(4(0(4(1(5(2(4(0(5(2(2(0(3(2(1(3(5(4(1(x1))))))))))))))))))))))))))))
   1(4(5(0(1(5(4(4(2(1(0(4(1(2(1(5(4(5(5(0(4(0(1(0(2(4(5(5(2(4(x1)))))))))))))))))))))))))))))) -> 1(4(5(0(1(5(4(4(2(1(4(0(1(2(1(5(4(5(5(0(4(0(1(0(2(4(5(5(2(4(x1))))))))))))))))))))))))))))))
   2(0(0(0(5(1(1(3(3(3(4(1(2(1(1(2(5(0(3(5(1(4(1(3(1(3(3(3(4(3(x1)))))))))))))))))))))))))))))) -> 2(0(0(0(5(1(1(3(3(3(4(1(2(1(1(2(5(0(3(5(4(1(1(3(1(3(3(3(4(3(x1))))))))))))))))))))))))))))))
   2(3(0(1(2(0(5(2(0(2(1(0(2(5(1(4(5(4(0(4(4(5(0(5(2(3(2(0(1(3(x1)))))))))))))))))))))))))))))) -> 2(3(0(1(2(0(5(2(0(2(0(1(2(5(1(4(5(4(0(4(4(5(0(5(2(3(2(0(1(3(x1))))))))))))))))))))))))))))))
   3(4(1(3(2(0(2(4(4(1(3(3(5(2(3(3(1(1(5(5(5(2(5(1(2(3(2(5(0(4(x1)))))))))))))))))))))))))))))) -> 3(4(1(3(2(0(2(4(4(1(3(3(5(2(3(3(1(5(1(5(5(2(5(1(2(3(2(5(0(4(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(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(5(1(2(3(4(3(3(2(1(x1)))))))))) -> 3(1(2(0(2(5(2(0(5(0(x1))))))))))
   3(3(3(2(1(1(0(3(2(5(x1)))))))))) -> 3(2(2(4(5(0(5(4(3(5(x1))))))))))
   4(1(1(5(2(3(0(0(2(0(0(x1))))))))))) -> 3(1(5(1(3(3(4(0(3(3(x1))))))))))
   1(1(3(0(4(3(5(0(4(0(0(x1))))))))))) -> 5(4(3(0(0(1(4(0(4(2(x1))))))))))
   4(1(0(0(1(2(4(5(2(1(0(x1))))))))))) -> 4(5(4(4(4(1(4(5(4(5(x1))))))))))
   2(1(3(2(0(2(5(5(3(1(0(x1))))))))))) -> 5(5(0(1(5(4(1(5(4(3(x1))))))))))
   3(4(5(3(3(0(2(1(2(4(0(x1))))))))))) -> 4(3(3(4(4(4(4(0(5(1(x1))))))))))
   4(5(1(3(0(5(0(4(5(4(0(x1))))))))))) -> 4(3(4(2(1(5(2(3(3(2(x1))))))))))
   4(3(3(3(2(3(0(4(1(5(0(x1))))))))))) -> 3(4(3(1(0(5(2(4(5(3(x1))))))))))
   4(4(4(0(1(0(5(3(1(0(1(x1))))))))))) -> 5(5(0(0(4(0(4(4(5(4(x1))))))))))
   0(2(4(4(1(5(4(5(2(0(1(x1))))))))))) -> 3(3(3(4(4(3(2(1(2(1(x1))))))))))
   0(5(1(5(5(3(3(3(5(0(1(x1))))))))))) -> 3(1(2(2(4(2(4(2(1(5(x1))))))))))
   0(5(1(0(4(5(5(3(4(1(1(x1))))))))))) -> 2(3(5(4(5(2(4(3(0(5(x1))))))))))
   4(5(3(2(2(4(3(0(4(2(1(x1))))))))))) -> 3(0(0(5(1(1(3(5(5(4(x1))))))))))
   4(0(5(5(1(4(1(1(0(3(1(x1))))))))))) -> 5(1(3(5(4(0(5(0(2(4(x1))))))))))
   0(1(0(5(3(1(3(3(0(5(1(x1))))))))))) -> 5(0(2(2(4(0(1(2(0(3(x1))))))))))
   0(1(1(1(0(0(2(5(4(5(1(x1))))))))))) -> 1(5(2(1(3(2(4(4(4(5(x1))))))))))
   5(3(2(5(0(1(0(3(3(0(2(x1))))))))))) -> 1(1(3(2(2(1(4(5(3(5(x1))))))))))
   2(2(2(4(1(0(4(1(3(1(2(x1))))))))))) -> 0(3(5(0(5(4(5(3(2(1(x1))))))))))
   1(0(0(0(5(2(3(5(2(2(2(x1))))))))))) -> 0(2(3(2(2(2(5(0(5(2(x1))))))))))
   1(0(0(4(4(5(1(1(3(2(2(x1))))))))))) -> 2(4(5(0(2(1(1(0(0(2(x1))))))))))
   0(1(0(5(5(2(2(3(3(3(2(x1))))))))))) -> 5(2(5(0(4(3(2(2(2(2(x1))))))))))
   5(1(4(5(3(4(5(4(2(4(2(x1))))))))))) -> 1(5(1(1(5(4(4(0(1(5(x1))))))))))
   0(2(2(4(3(4(5(5(4(4(2(x1))))))))))) -> 4(0(3(5(4(0(2(3(0(3(x1))))))))))
   5(1(2(1(3(3(0(4(2(0(3(x1))))))))))) -> 0(1(4(5(5(5(3(4(2(0(x1))))))))))
   2(4(0(1(1(3(2(5(3(0(3(x1))))))))))) -> 4(2(5(1(4(3(5(4(5(2(x1))))))))))
   0(2(1(3(1(4(3(1(1(1(3(x1))))))))))) -> 1(3(1(0(4(3(3(0(5(0(x1))))))))))
   5(1(3(3(2(0(4(3(1(1(3(x1))))))))))) -> 4(3(2(2(0(2(3(5(2(4(x1))))))))))
   1(1(0(3(1(3(1(2(5(2(3(x1))))))))))) -> 0(2(4(1(3(0(4(5(0(5(x1))))))))))
   3(0(0(4(4(5(4(2(0(3(3(x1))))))))))) -> 1(2(2(1(0(2(3(0(2(3(x1))))))))))
   1(4(5(3(3(2(4(5(0(3(3(x1))))))))))) -> 2(4(4(2(2(2(5(0(3(4(x1))))))))))
   3(2(5(1(4(3(0(2(1(4(3(x1))))))))))) -> 4(5(2(2(0(3(2(4(1(2(x1))))))))))
   0(0(5(3(3(2(5(1(0(5(3(x1))))))))))) -> 0(4(1(1(4(5(1(2(5(2(x1))))))))))
   3(5(5(2(0(4(4(3(1(5(3(x1))))))))))) -> 5(2(4(4(0(3(0(5(2(2(x1))))))))))
   0(5(0(1(0(1(4(5(2(5(3(x1))))))))))) -> 4(2(5(3(3(1(5(3(0(2(x1))))))))))
   5(2(1(5(5(0(5(1(5(0(4(x1))))))))))) -> 3(3(4(0(1(1(1(3(1(1(x1))))))))))
   1(2(3(0(0(4(2(1(2(1(4(x1))))))))))) -> 5(2(4(3(0(4(4(5(4(5(x1))))))))))
   5(4(2(4(5(1(5(1(3(1(4(x1))))))))))) -> 3(3(3(3(4(5(2(3(4(0(x1))))))))))
   4(0(5(2(3(4(3(1(4(1(4(x1))))))))))) -> 0(0(2(3(5(3(2(5(5(3(x1))))))))))
   3(3(1(1(4(5(1(2(3(2(4(x1))))))))))) -> 4(3(2(0(1(0(3(0(1(4(x1))))))))))
   3(5(2(0(2(5(1(2(5(2(4(x1))))))))))) -> 4(1(2(3(0(0(5(0(2(5(x1))))))))))
   3(0(5(3(3(3(1(0(2(3(4(x1))))))))))) -> 1(4(1(4(5(0(0(1(2(4(x1))))))))))
   3(0(3(2(0(2(4(2(3(3(4(x1))))))))))) -> 4(1(0(2(1(4(3(4(5(4(x1))))))))))
   1(0(1(0(3(1(5(0(4(3(4(x1))))))))))) -> 5(1(4(0(3(1(3(2(5(4(x1))))))))))
   0(4(0(2(1(1(4(1(4(3(4(x1))))))))))) -> 5(3(3(5(1(5(0(1(5(5(x1))))))))))
   3(3(5(0(1(1(4(0(3(4(4(x1))))))))))) -> 5(4(2(0(0(3(2(3(4(2(x1))))))))))
   3(3(3(1(1(5(3(5(2(1(5(x1))))))))))) -> 5(4(4(1(5(1(4(0(3(2(x1))))))))))
   0(3(4(3(1(5(2(2(2(3(5(x1))))))))))) -> 2(4(2(3(1(5(3(3(0(0(x1))))))))))
   2(4(0(1(4(1(2(0(1(4(5(x1))))))))))) -> 1(1(5(0(4(0(2(3(5(1(x1))))))))))
   5(4(2(0(3(3(3(5(4(5(5(x1))))))))))) -> 3(0(1(2(3(5(5(1(2(1(x1))))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.

----------------------------------------

(3) QTRSRRRProof (EQUIVALENT)
Used ordering:
Polynomial interpretation [POLO]:

   POL(0(x_1)) = 7 + x_1
   POL(1(x_1)) = 9 + x_1
   POL(2(x_1)) = 7 + x_1
   POL(3(x_1)) = 7 + x_1
   POL(4(x_1)) = 8 + x_1
   POL(5(x_1)) = 7 + x_1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   2(5(1(2(3(4(3(3(2(1(x1)))))))))) -> 3(1(2(0(2(5(2(0(5(0(x1))))))))))
   3(3(3(2(1(1(0(3(2(5(x1)))))))))) -> 3(2(2(4(5(0(5(4(3(5(x1))))))))))
   4(1(1(5(2(3(0(0(2(0(0(x1))))))))))) -> 3(1(5(1(3(3(4(0(3(3(x1))))))))))
   1(1(3(0(4(3(5(0(4(0(0(x1))))))))))) -> 5(4(3(0(0(1(4(0(4(2(x1))))))))))
   4(1(0(0(1(2(4(5(2(1(0(x1))))))))))) -> 4(5(4(4(4(1(4(5(4(5(x1))))))))))
   2(1(3(2(0(2(5(5(3(1(0(x1))))))))))) -> 5(5(0(1(5(4(1(5(4(3(x1))))))))))
   3(4(5(3(3(0(2(1(2(4(0(x1))))))))))) -> 4(3(3(4(4(4(4(0(5(1(x1))))))))))
   4(5(1(3(0(5(0(4(5(4(0(x1))))))))))) -> 4(3(4(2(1(5(2(3(3(2(x1))))))))))
   4(3(3(3(2(3(0(4(1(5(0(x1))))))))))) -> 3(4(3(1(0(5(2(4(5(3(x1))))))))))
   4(4(4(0(1(0(5(3(1(0(1(x1))))))))))) -> 5(5(0(0(4(0(4(4(5(4(x1))))))))))
   0(2(4(4(1(5(4(5(2(0(1(x1))))))))))) -> 3(3(3(4(4(3(2(1(2(1(x1))))))))))
   0(5(1(5(5(3(3(3(5(0(1(x1))))))))))) -> 3(1(2(2(4(2(4(2(1(5(x1))))))))))
   0(5(1(0(4(5(5(3(4(1(1(x1))))))))))) -> 2(3(5(4(5(2(4(3(0(5(x1))))))))))
   4(5(3(2(2(4(3(0(4(2(1(x1))))))))))) -> 3(0(0(5(1(1(3(5(5(4(x1))))))))))
   4(0(5(5(1(4(1(1(0(3(1(x1))))))))))) -> 5(1(3(5(4(0(5(0(2(4(x1))))))))))
   0(1(0(5(3(1(3(3(0(5(1(x1))))))))))) -> 5(0(2(2(4(0(1(2(0(3(x1))))))))))
   0(1(1(1(0(0(2(5(4(5(1(x1))))))))))) -> 1(5(2(1(3(2(4(4(4(5(x1))))))))))
   5(3(2(5(0(1(0(3(3(0(2(x1))))))))))) -> 1(1(3(2(2(1(4(5(3(5(x1))))))))))
   2(2(2(4(1(0(4(1(3(1(2(x1))))))))))) -> 0(3(5(0(5(4(5(3(2(1(x1))))))))))
   1(0(0(0(5(2(3(5(2(2(2(x1))))))))))) -> 0(2(3(2(2(2(5(0(5(2(x1))))))))))
   1(0(0(4(4(5(1(1(3(2(2(x1))))))))))) -> 2(4(5(0(2(1(1(0(0(2(x1))))))))))
   0(1(0(5(5(2(2(3(3(3(2(x1))))))))))) -> 5(2(5(0(4(3(2(2(2(2(x1))))))))))
   5(1(4(5(3(4(5(4(2(4(2(x1))))))))))) -> 1(5(1(1(5(4(4(0(1(5(x1))))))))))
   0(2(2(4(3(4(5(5(4(4(2(x1))))))))))) -> 4(0(3(5(4(0(2(3(0(3(x1))))))))))
   5(1(2(1(3(3(0(4(2(0(3(x1))))))))))) -> 0(1(4(5(5(5(3(4(2(0(x1))))))))))
   2(4(0(1(1(3(2(5(3(0(3(x1))))))))))) -> 4(2(5(1(4(3(5(4(5(2(x1))))))))))
   0(2(1(3(1(4(3(1(1(1(3(x1))))))))))) -> 1(3(1(0(4(3(3(0(5(0(x1))))))))))
   5(1(3(3(2(0(4(3(1(1(3(x1))))))))))) -> 4(3(2(2(0(2(3(5(2(4(x1))))))))))
   1(1(0(3(1(3(1(2(5(2(3(x1))))))))))) -> 0(2(4(1(3(0(4(5(0(5(x1))))))))))
   3(0(0(4(4(5(4(2(0(3(3(x1))))))))))) -> 1(2(2(1(0(2(3(0(2(3(x1))))))))))
   1(4(5(3(3(2(4(5(0(3(3(x1))))))))))) -> 2(4(4(2(2(2(5(0(3(4(x1))))))))))
   3(2(5(1(4(3(0(2(1(4(3(x1))))))))))) -> 4(5(2(2(0(3(2(4(1(2(x1))))))))))
   0(0(5(3(3(2(5(1(0(5(3(x1))))))))))) -> 0(4(1(1(4(5(1(2(5(2(x1))))))))))
   3(5(5(2(0(4(4(3(1(5(3(x1))))))))))) -> 5(2(4(4(0(3(0(5(2(2(x1))))))))))
   0(5(0(1(0(1(4(5(2(5(3(x1))))))))))) -> 4(2(5(3(3(1(5(3(0(2(x1))))))))))
   5(2(1(5(5(0(5(1(5(0(4(x1))))))))))) -> 3(3(4(0(1(1(1(3(1(1(x1))))))))))
   1(2(3(0(0(4(2(1(2(1(4(x1))))))))))) -> 5(2(4(3(0(4(4(5(4(5(x1))))))))))
   5(4(2(4(5(1(5(1(3(1(4(x1))))))))))) -> 3(3(3(3(4(5(2(3(4(0(x1))))))))))
   4(0(5(2(3(4(3(1(4(1(4(x1))))))))))) -> 0(0(2(3(5(3(2(5(5(3(x1))))))))))
   3(3(1(1(4(5(1(2(3(2(4(x1))))))))))) -> 4(3(2(0(1(0(3(0(1(4(x1))))))))))
   3(5(2(0(2(5(1(2(5(2(4(x1))))))))))) -> 4(1(2(3(0(0(5(0(2(5(x1))))))))))
   3(0(5(3(3(3(1(0(2(3(4(x1))))))))))) -> 1(4(1(4(5(0(0(1(2(4(x1))))))))))
   3(0(3(2(0(2(4(2(3(3(4(x1))))))))))) -> 4(1(0(2(1(4(3(4(5(4(x1))))))))))
   1(0(1(0(3(1(5(0(4(3(4(x1))))))))))) -> 5(1(4(0(3(1(3(2(5(4(x1))))))))))
   0(4(0(2(1(1(4(1(4(3(4(x1))))))))))) -> 5(3(3(5(1(5(0(1(5(5(x1))))))))))
   3(3(5(0(1(1(4(0(3(4(4(x1))))))))))) -> 5(4(2(0(0(3(2(3(4(2(x1))))))))))
   3(3(3(1(1(5(3(5(2(1(5(x1))))))))))) -> 5(4(4(1(5(1(4(0(3(2(x1))))))))))
   0(3(4(3(1(5(2(2(2(3(5(x1))))))))))) -> 2(4(2(3(1(5(3(3(0(0(x1))))))))))
   2(4(0(1(4(1(2(0(1(4(5(x1))))))))))) -> 1(1(5(0(4(0(2(3(5(1(x1))))))))))
   5(4(2(0(3(3(3(5(4(5(5(x1))))))))))) -> 3(0(1(2(3(5(5(1(2(1(x1))))))))))




----------------------------------------

(4)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(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(0(2(2(0(1(0(x1))))))) -> 0^1(2(0(2(3(1(0(x1)))))))
   3^1(0(2(2(0(1(0(x1))))))) -> 2^1(0(2(3(1(0(x1))))))
   3^1(0(2(2(0(1(0(x1))))))) -> 0^1(2(3(1(0(x1)))))
   3^1(0(2(2(0(1(0(x1))))))) -> 2^1(3(1(0(x1))))
   3^1(0(2(2(0(1(0(x1))))))) -> 3^1(1(0(x1)))
   5^1(3(3(4(5(4(0(x1))))))) -> 5^1(3(5(4(3(4(0(x1)))))))
   5^1(3(3(4(5(4(0(x1))))))) -> 3^1(5(4(3(4(0(x1))))))
   5^1(3(3(4(5(4(0(x1))))))) -> 5^1(4(3(4(0(x1)))))
   5^1(3(3(4(5(4(0(x1))))))) -> 4^1(3(4(0(x1))))
   5^1(3(3(4(5(4(0(x1))))))) -> 3^1(4(0(x1)))
   4^1(2(5(4(0(1(2(x1))))))) -> 4^1(0(5(2(4(1(2(x1)))))))
   4^1(2(5(4(0(1(2(x1))))))) -> 0^1(5(2(4(1(2(x1))))))
   4^1(2(5(4(0(1(2(x1))))))) -> 5^1(2(4(1(2(x1)))))
   4^1(2(5(4(0(1(2(x1))))))) -> 2^1(4(1(2(x1))))
   4^1(2(5(4(0(1(2(x1))))))) -> 4^1(1(2(x1)))
   5^1(1(2(4(2(5(4(x1))))))) -> 5^1(1(4(2(2(5(4(x1)))))))
   5^1(1(2(4(2(5(4(x1))))))) -> 1^1(4(2(2(5(4(x1))))))
   5^1(1(2(4(2(5(4(x1))))))) -> 4^1(2(2(5(4(x1)))))
   5^1(1(2(4(2(5(4(x1))))))) -> 2^1(2(5(4(x1))))
   4^1(4(2(0(0(3(3(3(x1)))))))) -> 4^1(4(0(0(3(2(3(3(x1))))))))
   4^1(4(2(0(0(3(3(3(x1)))))))) -> 4^1(0(0(3(2(3(3(x1)))))))
   4^1(4(2(0(0(3(3(3(x1)))))))) -> 0^1(0(3(2(3(3(x1))))))
   4^1(4(2(0(0(3(3(3(x1)))))))) -> 0^1(3(2(3(3(x1)))))
   4^1(4(2(0(0(3(3(3(x1)))))))) -> 3^1(2(3(3(x1))))
   4^1(4(2(0(0(3(3(3(x1)))))))) -> 2^1(3(3(x1)))
   0^1(3(3(4(5(0(0(4(x1)))))))) -> 0^1(0(4(3(5(3(0(4(x1))))))))
   0^1(3(3(4(5(0(0(4(x1)))))))) -> 0^1(4(3(5(3(0(4(x1)))))))
   0^1(3(3(4(5(0(0(4(x1)))))))) -> 4^1(3(5(3(0(4(x1))))))
   0^1(3(3(4(5(0(0(4(x1)))))))) -> 3^1(5(3(0(4(x1)))))
   0^1(3(3(4(5(0(0(4(x1)))))))) -> 5^1(3(0(4(x1))))
   0^1(3(3(4(5(0(0(4(x1)))))))) -> 3^1(0(4(x1)))
   5^1(3(4(1(3(4(3(1(1(x1))))))))) -> 5^1(3(4(3(1(4(3(1(1(x1)))))))))
   5^1(3(4(1(3(4(3(1(1(x1))))))))) -> 3^1(4(3(1(4(3(1(1(x1))))))))
   5^1(3(4(1(3(4(3(1(1(x1))))))))) -> 4^1(3(1(4(3(1(1(x1)))))))
   5^1(3(4(1(3(4(3(1(1(x1))))))))) -> 3^1(1(4(3(1(1(x1))))))
   5^1(3(4(1(3(4(3(1(1(x1))))))))) -> 1^1(4(3(1(1(x1)))))
   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 0^1(4(0(0(0(2(3(1(4(x1)))))))))
   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 4^1(0(0(0(2(3(1(4(x1))))))))
   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 0^1(0(0(2(3(1(4(x1)))))))
   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 0^1(0(2(3(1(4(x1))))))
   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 0^1(2(3(1(4(x1)))))
   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 2^1(3(1(4(x1))))
   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 3^1(1(4(x1)))
   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2^1(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 4^1(4(3(1(5(3(3(5(4(5(0(x1)))))))))))
   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 4^1(3(1(5(3(3(5(4(5(0(x1))))))))))
   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 3^1(1(5(3(3(5(4(5(0(x1)))))))))
   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 1^1(5(3(3(5(4(5(0(x1))))))))
   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 5^1(3(3(5(4(5(0(x1)))))))
   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 3^1(3(5(4(5(0(x1))))))
   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 3^1(5(4(5(0(x1)))))
   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 5^1(4(5(0(x1))))
   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 4^1(5(0(x1)))
   0^1(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0^1(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0^1(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 2^1(3(4(2(0(0(1(2(2(1(3(x1)))))))))))
   0^1(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 3^1(4(2(0(0(1(2(2(1(3(x1))))))))))
   0^1(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 4^1(2(0(0(1(2(2(1(3(x1)))))))))
   0^1(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 2^1(0(0(1(2(2(1(3(x1))))))))
   0^1(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0^1(0(1(2(2(1(3(x1)))))))
   1^1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1^1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1^1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 5^1(3(1(2(3(4(1(0(2(2(2(1(x1))))))))))))
   1^1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 3^1(1(2(3(4(1(0(2(2(2(1(x1)))))))))))
   1^1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1^1(2(3(4(1(0(2(2(2(1(x1))))))))))
   1^1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 2^1(3(4(1(0(2(2(2(1(x1)))))))))
   1^1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 3^1(4(1(0(2(2(2(1(x1))))))))
   3^1(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3^1(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   3^1(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 2^1(2(2(4(1(0(4(1(3(2(0(2(x1))))))))))))
   3^1(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 2^1(2(4(1(0(4(1(3(2(0(2(x1)))))))))))
   3^1(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 2^1(4(1(0(4(1(3(2(0(2(x1))))))))))
   3^1(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 4^1(1(0(4(1(3(2(0(2(x1)))))))))
   3^1(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 1^1(0(4(1(3(2(0(2(x1))))))))
   3^1(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 0^1(4(1(3(2(0(2(x1)))))))
   3^1(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 4^1(1(3(2(0(2(x1))))))
   4^1(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4^1(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   4^1(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 1^1(5(3(1(1(4(0(4(5(3(2(4(x1))))))))))))
   4^1(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 5^1(3(1(1(4(0(4(5(3(2(4(x1)))))))))))
   4^1(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 3^1(1(1(4(0(4(5(3(2(4(x1))))))))))
   4^1(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 1^1(1(4(0(4(5(3(2(4(x1)))))))))
   4^1(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 1^1(4(0(4(5(3(2(4(x1))))))))
   4^1(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4^1(0(4(5(3(2(4(x1)))))))
   4^1(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 0^1(4(5(3(2(4(x1))))))
   4^1(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4^1(5(3(2(4(x1)))))
   4^1(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 5^1(3(2(4(x1))))
   2^1(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2^1(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   2^1(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 0^1(0(4(3(2(2(4(1(5(4(0(5(x1))))))))))))
   2^1(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 0^1(4(3(2(2(4(1(5(4(0(5(x1)))))))))))
   2^1(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 4^1(3(2(2(4(1(5(4(0(5(x1))))))))))
   2^1(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 3^1(2(2(4(1(5(4(0(5(x1)))))))))
   1^1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1^1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1^1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1^1(2(0(1(0(1(4(2(2(1(0(2(4(x1)))))))))))))
   1^1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 2^1(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))
   1^1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 0^1(1(0(1(4(2(2(1(0(2(4(x1)))))))))))
   1^1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1^1(0(1(4(2(2(1(0(2(4(x1))))))))))
   1^1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 0^1(1(4(2(2(1(0(2(4(x1)))))))))
   1^1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1^1(4(2(2(1(0(2(4(x1))))))))
   1^1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 4^1(2(2(1(0(2(4(x1)))))))
   1^1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 2^1(2(1(0(2(4(x1))))))
   1^1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1^1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   1^1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 5^1(5(3(3(5(2(2(1(2(4(1(0(1(0(x1))))))))))))))
   1^1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 5^1(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))
   1^1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 3^1(3(5(2(2(1(2(4(1(0(1(0(x1))))))))))))
   1^1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 3^1(5(2(2(1(2(4(1(0(1(0(x1)))))))))))
   1^1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 5^1(2(2(1(2(4(1(0(1(0(x1))))))))))
   1^1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 2^1(2(1(2(4(1(0(1(0(x1)))))))))
   1^1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 2^1(1(2(4(1(0(1(0(x1))))))))
   1^1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1^1(2(4(1(0(1(0(x1)))))))
   1^1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 2^1(4(1(0(1(0(x1))))))
   1^1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 4^1(1(0(1(0(x1)))))
   1^1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1^1(0(1(0(x1))))
   1^1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 0^1(1(0(x1)))
   2^1(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2^1(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2^1(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 4^1(2(3(0(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))
   2^1(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2^1(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))
   2^1(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 3^1(0(3(4(0(0(2(0(4(1(0(2(x1))))))))))))
   2^1(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 0^1(3(4(0(0(2(0(4(1(0(2(x1)))))))))))
   5^1(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5^1(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   5^1(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 0^1(0(5(3(1(0(1(3(1(1(5(1(0(3(x1))))))))))))))
   5^1(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 0^1(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))
   5^1(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5^1(3(1(0(1(3(1(1(5(1(0(3(x1))))))))))))
   5^1(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 3^1(1(0(1(3(1(1(5(1(0(3(x1)))))))))))
   5^1(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 1^1(0(1(3(1(1(5(1(0(3(x1))))))))))
   0^1(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3^1(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   0^1(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 0^1(0(4(2(2(0(4(3(5(4(5(2(5(3(x1))))))))))))))
   0^1(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 0^1(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))
   0^1(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 4^1(2(2(0(4(3(5(4(5(2(5(3(x1))))))))))))
   0^1(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 2^1(2(0(4(3(5(4(5(2(5(3(x1)))))))))))
   0^1(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 2^1(0(4(3(5(4(5(2(5(3(x1))))))))))
   0^1(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 0^1(4(3(5(4(5(2(5(3(x1)))))))))
   0^1(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 4^1(3(5(4(5(2(5(3(x1))))))))
   0^1(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3^1(5(4(5(2(5(3(x1)))))))
   0^1(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 5^1(4(5(2(5(3(x1))))))
   0^1(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 4^1(5(2(5(3(x1)))))
   0^1(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 5^1(2(5(3(x1))))
   0^1(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 2^1(5(3(x1)))
   1^1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1^1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   1^1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 4^1(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1)))))))))))))))
   1^1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 3^1(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))
   1^1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1^1(4(4(5(4(0(5(2(4(2(1(1(3(x1)))))))))))))
   1^1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 4^1(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))
   1^1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 4^1(5(4(0(5(2(4(2(1(1(3(x1)))))))))))
   1^1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 5^1(4(0(5(2(4(2(1(1(3(x1))))))))))
   4^1(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4^1(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   4^1(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 1^1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1)))))))))))))))
   4^1(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 2^1(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))
   4^1(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 0^1(4(2(1(5(0(5(5(3(1(5(5(3(x1)))))))))))))
   4^1(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4^1(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))
   4^1(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 2^1(1(5(0(5(5(3(1(5(5(3(x1)))))))))))
   4^1(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 1^1(5(0(5(5(3(1(5(5(3(x1))))))))))
   4^1(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 5^1(0(5(5(3(1(5(5(3(x1)))))))))
   4^1(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 0^1(5(5(3(1(5(5(3(x1))))))))
   4^1(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 5^1(5(3(1(5(5(3(x1)))))))
   4^1(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 5^1(3(1(5(5(3(x1))))))
   4^1(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 3^1(1(5(5(3(x1)))))
   4^1(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 1^1(5(5(3(x1))))
   4^1(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 5^1(5(3(x1)))
   3^1(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3^1(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3^1(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 4^1(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1))))))))))))))))
   3^1(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 5^1(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))
   3^1(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 5^1(4(3(4(4(1(3(4(3(2(1(1(4(1(x1))))))))))))))
   3^1(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 4^1(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))
   3^1(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3^1(4(4(1(3(4(3(2(1(1(4(1(x1))))))))))))
   3^1(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 4^1(4(1(3(4(3(2(1(1(4(1(x1)))))))))))
   3^1(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 4^1(1(3(4(3(2(1(1(4(1(x1))))))))))
   3^1(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 1^1(3(4(3(2(1(1(4(1(x1)))))))))
   3^1(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3^1(4(3(2(1(1(4(1(x1))))))))
   3^1(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 4^1(3(2(1(1(4(1(x1)))))))
   3^1(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3^1(2(1(1(4(1(x1))))))
   0^1(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0^1(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   0^1(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 4^1(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1))))))))))))))))
   0^1(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0^1(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))
   0^1(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 4^1(1(0(2(4(1(0(3(0(1(4(3(4(5(x1))))))))))))))
   0^1(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 1^1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))
   0^1(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0^1(2(4(1(0(3(0(1(4(3(4(5(x1))))))))))))
   0^1(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 2^1(4(1(0(3(0(1(4(3(4(5(x1)))))))))))
   0^1(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 4^1(1(0(3(0(1(4(3(4(5(x1))))))))))
   0^1(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 1^1(0(3(0(1(4(3(4(5(x1)))))))))
   0^1(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0^1(3(0(1(4(3(4(5(x1))))))))
   1^1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1^1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   1^1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 4^1(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1)))))))))))))))))
   1^1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1^1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))
   1^1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 2^1(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1)))))))))))))))
   1^1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 0^1(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))
   1^1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1^1(3(0(4(1(0(4(5(2(4(3(5(0(x1)))))))))))))
   1^1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 3^1(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))
   1^1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 0^1(4(1(0(4(5(2(4(3(5(0(x1)))))))))))
   1^1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 4^1(1(0(4(5(2(4(3(5(0(x1))))))))))
   1^1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1^1(0(4(5(2(4(3(5(0(x1)))))))))
   1^1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 0^1(4(5(2(4(3(5(0(x1))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0^1(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 1^1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1)))))))))))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 1^1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 4^1(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1)))))))))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0^1(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 4^1(0(1(5(2(3(4(3(5(0(5(4(3(x1)))))))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0^1(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 1^1(5(2(3(4(3(5(0(5(4(3(x1)))))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 5^1(2(3(4(3(5(0(5(4(3(x1))))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 2^1(3(4(3(5(0(5(4(3(x1)))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 3^1(4(3(5(0(5(4(3(x1))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 4^1(3(5(0(5(4(3(x1)))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 3^1(5(0(5(4(3(x1))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 5^1(0(5(4(3(x1)))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0^1(5(4(3(x1))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5^1(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 2^1(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1)))))))))))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 2^1(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5^1(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1)))))))))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 1^1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 0^1(2(1(2(0(5(2(4(5(2(3(3(4(x1)))))))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 2^1(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 1^1(2(0(5(2(4(5(2(3(3(4(x1)))))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 2^1(0(5(2(4(5(2(3(3(4(x1))))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 0^1(5(2(4(5(2(3(3(4(x1)))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5^1(2(4(5(2(3(3(4(x1))))))))
   0^1(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0^1(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   0^1(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 3^1(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))
   0^1(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 1^1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))
   0^1(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 4^1(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))
   0^1(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 5^1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))
   5^1(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5^1(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   5^1(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 4^1(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))
   5^1(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 3^1(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))
   5^1(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 3^1(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1))))))))))))))))
   5^1(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 3^1(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))
   5^1(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 0^1(5(5(1(5(4(5(0(3(3(5(1(4(3(x1))))))))))))))
   5^1(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5^1(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))
   5^1(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5^1(1(5(4(5(0(3(3(5(1(4(3(x1))))))))))))
   5^1(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 1^1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))
   5^1(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5^1(4(5(0(3(3(5(1(4(3(x1))))))))))
   3^1(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3^1(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   3^1(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 2^1(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1)))))))))))))))))))
   3^1(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 2^1(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))
   3^1(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 2^1(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1)))))))))))))))))
   3^1(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 4^1(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))
   3^1(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 5^1(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1)))))))))))))))
   3^1(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 2^1(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))
   3^1(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 1^1(1(0(4(3(3(4(4(0(4(5(5(3(x1)))))))))))))
   3^1(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 1^1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))
   3^1(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 0^1(4(3(3(4(4(0(4(5(5(3(x1)))))))))))
   3^1(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 4^1(3(3(4(4(0(4(5(5(3(x1))))))))))
   3^1(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3^1(3(4(4(0(4(5(5(3(x1)))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4^1(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 0^1(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1))))))))))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 2^1(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 5^1(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1))))))))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 5^1(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 0^1(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1))))))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 5^1(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 2^1(3(3(2(2(1(4(4(2(1(1(0(2(0(x1))))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 3^1(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 3^1(2(2(1(4(4(2(1(1(0(2(0(x1))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 2^1(2(1(4(4(2(1(1(0(2(0(x1)))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 2^1(1(4(4(2(1(1(0(2(0(x1))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 1^1(4(4(2(1(1(0(2(0(x1)))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4^1(4(2(1(1(0(2(0(x1))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4^1(2(1(1(0(2(0(x1)))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 2^1(1(1(0(2(0(x1))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 1^1(1(0(2(0(x1)))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 1^1(0(2(0(x1))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 0^1(2(0(x1)))
   4^1(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4^1(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   4^1(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 5^1(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))
   4^1(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4^1(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))
   4^1(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4^1(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))
   4^1(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 1^1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))
   4^1(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 1^1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))
   4^1(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 5^1(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))
   4^1(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 2^1(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))
   3^1(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3^1(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   3^1(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 1^1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))
   3^1(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 1^1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))
   3^1(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 0^1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5^1(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 2^1(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1)))))))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 4^1(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 0^1(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1)))))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 4^1(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5^1(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1)))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 0^1(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 1^1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1)))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 2^1(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 1^1(0(4(4(1(4(5(0(0(3(4(5(0(x1)))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 0^1(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 4^1(4(1(4(5(0(0(3(4(5(0(x1)))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 4^1(1(4(5(0(0(3(4(5(0(x1))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 1^1(4(5(0(0(3(4(5(0(x1)))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 4^1(5(0(0(3(4(5(0(x1))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5^1(0(0(3(4(5(0(x1)))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 0^1(0(3(4(5(0(x1))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 0^1(3(4(5(0(x1)))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 3^1(4(5(0(x1))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5^1(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 3^1(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1))))))))))))))))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5^1(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 0^1(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1))))))))))))))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 1^1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 1^1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1))))))))))))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 4^1(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 2^1(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1))))))))))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5^1(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5^1(0(5(0(2(2(4(0(0(4(4(2(3(4(x1))))))))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 0^1(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5^1(0(2(2(4(0(0(4(4(2(3(4(x1))))))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 0^1(2(2(4(0(0(4(4(2(3(4(x1)))))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 2^1(2(4(0(0(4(4(2(3(4(x1))))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 2^1(4(0(0(4(4(2(3(4(x1)))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 4^1(0(0(4(4(2(3(4(x1))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 0^1(0(4(4(2(3(4(x1)))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 0^1(4(4(2(3(4(x1))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 4^1(4(2(3(4(x1)))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 4^1(2(3(4(x1))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 0^1(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1))))))))))))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 5^1(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 3^1(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1))))))))))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 5^1(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 3^1(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1))))))))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 3^1(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2^1(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1))))))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 4^1(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 0^1(2(4(4(0(5(4(1(0(3(5(3(5(4(x1))))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2^1(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 4^1(4(0(5(4(1(0(3(5(3(5(4(x1))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 4^1(0(5(4(1(0(3(5(3(5(4(x1)))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 0^1(5(4(1(0(3(5(3(5(4(x1))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 5^1(4(1(0(3(5(3(5(4(x1)))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 4^1(1(0(3(5(3(5(4(x1))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 1^1(0(3(5(3(5(4(x1)))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 0^1(3(5(3(5(4(x1))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 3^1(5(3(5(4(x1)))))
   5^1(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5^1(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5^1(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 3^1(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))
   5^1(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 1^1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))
   5^1(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 1^1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))
   5^1(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 3^1(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))
   5^1(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5^1(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))
   5^1(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 2^1(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 4^1(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1))))))))))))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 4^1(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 3^1(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1))))))))))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 1^1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 5^1(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1))))))))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 3^1(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0^1(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1))))))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 1^1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 2^1(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1))))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 2^1(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0^1(2(1(2(3(0(3(1(2(5(1(3(1(0(x1))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 2^1(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 1^1(2(3(0(3(1(2(5(1(3(1(0(x1))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 2^1(3(0(3(1(2(5(1(3(1(0(x1)))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 3^1(0(3(1(2(5(1(3(1(0(x1))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0^1(3(1(2(5(1(3(1(0(x1)))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 3^1(1(2(5(1(3(1(0(x1))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 1^1(2(5(1(3(1(0(x1)))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 2^1(5(1(3(1(0(x1))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0^1(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 2^1(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0^1(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 2^1(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 2^1(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 2^1(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 4^1(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 3^1(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 4^1(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 5^1(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 1^1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 1^1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 5^1(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 1^1(0(4(2(2(5(4(4(4(5(2(2(x1))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0^1(4(2(2(5(4(4(4(5(2(2(x1)))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4^1(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 5^1(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 5^1(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 5^1(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 2^1(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 1^1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 1^1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 3^1(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4^1(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 1^1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 2^1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))
   5^1(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5^1(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   5^1(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 3^1(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))
   5^1(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 3^1(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))
   5^1(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5^1(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))
   5^1(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 4^1(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))
   5^1(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 2^1(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))
   5^1(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 4^1(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 2^1(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1))))))))))))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 4^1(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 4^1(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1))))))))))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 1^1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 4^1(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1))))))))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0^1(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 2^1(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1))))))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 4^1(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 1^1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1))))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 1^1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 5^1(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 5^1(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0^1(5(4(5(1(3(5(2(2(3(5(1(1(1(x1))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 5^1(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 4^1(5(1(3(5(2(2(3(5(1(1(1(x1))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 5^1(1(3(5(2(2(3(5(1(1(1(x1)))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 1^1(3(5(2(2(3(5(1(1(1(x1))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 3^1(5(2(2(3(5(1(1(1(x1)))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 5^1(2(2(3(5(1(1(1(x1))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 2^1(2(3(5(1(1(1(x1)))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 2^1(3(5(1(1(1(x1))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 3^1(5(1(1(1(x1)))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 5^1(1(1(1(x1))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 1^1(1(1(x1)))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2^1(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 0^1(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2^1(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 5^1(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 0^1(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2^1(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 0^1(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 0^1(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2^1(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2^1(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 5^1(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 3^1(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 3^1(2(4(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2^1(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 4^1(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))
   5^1(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5^1(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   5^1(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 4^1(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))
   5^1(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 1^1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))
   5^1(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 0^1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 4^1(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 5^1(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 3^1(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1^1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 2^1(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 3^1(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 0^1(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 2^1(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 2^1(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 5^1(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 0^1(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 4^1(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 2^1(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1)))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 5^1(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1^1(4(0(4(0(5(4(3(3(4(0(2(0(x1)))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 4^1(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 0^1(4(0(5(4(3(3(4(0(2(0(x1)))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 4^1(0(5(4(3(3(4(0(2(0(x1))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 2^1(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 5^1(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 5^1(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4^1(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 2^1(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 0^1(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 1^1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 0^1(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4^1(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 0^1(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 5^1(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 5^1(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4^1(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 5^1(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 1^1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 2^1(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 1^1(0(4(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 0^1(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4^1(1(2(4(4(5(1(0(5(4(1(x1)))))))))))
   3^1(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3^1(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3^1(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 4^1(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))
   3^1(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3^1(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))
   3^1(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3^1(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))
   3^1(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3^1(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))
   3^1(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 1^1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))
   3^1(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3^1(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))
   3^1(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 1^1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))
   3^1(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 1^1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))
   3^1(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 4^1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 1^1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 0^1(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 2^1(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3^1(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 2^1(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 5^1(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 0^1(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 5^1(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 4^1(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 4^1(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 0^1(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 4^1(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 5^1(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 4^1(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 1^1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 5^1(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 2^1(1(0(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 1^1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 0^1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4^1(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 0^1(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 5^1(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 2^1(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 3^1(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 2^1(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 1^1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 5^1(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 2^1(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 5^1(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 5^1(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 1^1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 5^1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(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.

   5^1(3(3(4(5(4(0(x1))))))) -> 5^1(4(3(4(0(x1)))))
   5^1(3(3(4(5(4(0(x1))))))) -> 4^1(3(4(0(x1))))
   5^1(3(3(4(5(4(0(x1))))))) -> 3^1(4(0(x1)))
   5^1(1(2(4(2(5(4(x1))))))) -> 4^1(2(2(5(4(x1)))))
   5^1(1(2(4(2(5(4(x1))))))) -> 2^1(2(5(4(x1))))
   4^1(4(2(0(0(3(3(3(x1)))))))) -> 2^1(3(3(x1)))
   0^1(3(3(4(5(0(0(4(x1)))))))) -> 5^1(3(0(4(x1))))
   0^1(3(3(4(5(0(0(4(x1)))))))) -> 3^1(0(4(x1)))
   5^1(3(4(1(3(4(3(1(1(x1))))))))) -> 4^1(3(1(4(3(1(1(x1)))))))
   5^1(3(4(1(3(4(3(1(1(x1))))))))) -> 3^1(1(4(3(1(1(x1))))))
   5^1(3(4(1(3(4(3(1(1(x1))))))))) -> 1^1(4(3(1(1(x1)))))
   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 1^1(5(3(3(5(4(5(0(x1))))))))
   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 5^1(3(3(5(4(5(0(x1)))))))
   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 3^1(3(5(4(5(0(x1))))))
   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 3^1(5(4(5(0(x1)))))
   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 5^1(4(5(0(x1))))
   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 4^1(5(0(x1)))
   0^1(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 4^1(2(0(0(1(2(2(1(3(x1)))))))))
   0^1(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 2^1(0(0(1(2(2(1(3(x1))))))))
   0^1(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0^1(0(1(2(2(1(3(x1)))))))
   1^1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 5^1(3(1(2(3(4(1(0(2(2(2(1(x1))))))))))))
   1^1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 3^1(1(2(3(4(1(0(2(2(2(1(x1)))))))))))
   1^1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1^1(2(3(4(1(0(2(2(2(1(x1))))))))))
   1^1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 2^1(3(4(1(0(2(2(2(1(x1)))))))))
   1^1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 3^1(4(1(0(2(2(2(1(x1))))))))
   3^1(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 2^1(2(2(4(1(0(4(1(3(2(0(2(x1))))))))))))
   3^1(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 2^1(2(4(1(0(4(1(3(2(0(2(x1)))))))))))
   3^1(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 2^1(4(1(0(4(1(3(2(0(2(x1))))))))))
   3^1(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 4^1(1(0(4(1(3(2(0(2(x1)))))))))
   3^1(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 1^1(0(4(1(3(2(0(2(x1))))))))
   3^1(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 0^1(4(1(3(2(0(2(x1)))))))
   3^1(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 4^1(1(3(2(0(2(x1))))))
   4^1(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 5^1(3(1(1(4(0(4(5(3(2(4(x1)))))))))))
   4^1(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 3^1(1(1(4(0(4(5(3(2(4(x1))))))))))
   4^1(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 1^1(1(4(0(4(5(3(2(4(x1)))))))))
   4^1(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 1^1(4(0(4(5(3(2(4(x1))))))))
   4^1(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4^1(0(4(5(3(2(4(x1)))))))
   4^1(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 0^1(4(5(3(2(4(x1))))))
   4^1(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4^1(5(3(2(4(x1)))))
   4^1(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 5^1(3(2(4(x1))))
   1^1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1^1(2(0(1(0(1(4(2(2(1(0(2(4(x1)))))))))))))
   1^1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 2^1(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))
   1^1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 0^1(1(0(1(4(2(2(1(0(2(4(x1)))))))))))
   1^1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1^1(0(1(4(2(2(1(0(2(4(x1))))))))))
   1^1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 0^1(1(4(2(2(1(0(2(4(x1)))))))))
   1^1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1^1(4(2(2(1(0(2(4(x1))))))))
   1^1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 4^1(2(2(1(0(2(4(x1)))))))
   1^1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 2^1(2(1(0(2(4(x1))))))
   1^1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 5^1(5(3(3(5(2(2(1(2(4(1(0(1(0(x1))))))))))))))
   1^1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 5^1(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))
   1^1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 3^1(3(5(2(2(1(2(4(1(0(1(0(x1))))))))))))
   1^1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 3^1(5(2(2(1(2(4(1(0(1(0(x1)))))))))))
   1^1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 5^1(2(2(1(2(4(1(0(1(0(x1))))))))))
   1^1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 2^1(2(1(2(4(1(0(1(0(x1)))))))))
   1^1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 2^1(1(2(4(1(0(1(0(x1))))))))
   1^1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1^1(2(4(1(0(1(0(x1)))))))
   1^1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 2^1(4(1(0(1(0(x1))))))
   1^1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 4^1(1(0(1(0(x1)))))
   1^1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1^1(0(1(0(x1))))
   1^1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 0^1(1(0(x1)))
   2^1(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 0^1(3(4(0(0(2(0(4(1(0(2(x1)))))))))))
   5^1(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 1^1(0(1(3(1(1(5(1(0(3(x1))))))))))
   0^1(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 0^1(0(4(2(2(0(4(3(5(4(5(2(5(3(x1))))))))))))))
   0^1(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 0^1(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))
   0^1(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 4^1(2(2(0(4(3(5(4(5(2(5(3(x1))))))))))))
   0^1(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 2^1(2(0(4(3(5(4(5(2(5(3(x1)))))))))))
   0^1(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 2^1(0(4(3(5(4(5(2(5(3(x1))))))))))
   0^1(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 0^1(4(3(5(4(5(2(5(3(x1)))))))))
   0^1(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 4^1(3(5(4(5(2(5(3(x1))))))))
   0^1(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3^1(5(4(5(2(5(3(x1)))))))
   0^1(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 5^1(4(5(2(5(3(x1))))))
   0^1(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 4^1(5(2(5(3(x1)))))
   0^1(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 5^1(2(5(3(x1))))
   0^1(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 2^1(5(3(x1)))
   1^1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 4^1(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1)))))))))))))))
   1^1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 3^1(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))
   1^1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1^1(4(4(5(4(0(5(2(4(2(1(1(3(x1)))))))))))))
   1^1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 4^1(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))
   1^1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 4^1(5(4(0(5(2(4(2(1(1(3(x1)))))))))))
   1^1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 5^1(4(0(5(2(4(2(1(1(3(x1))))))))))
   4^1(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 2^1(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))
   4^1(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 0^1(4(2(1(5(0(5(5(3(1(5(5(3(x1)))))))))))))
   4^1(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4^1(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))
   4^1(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 2^1(1(5(0(5(5(3(1(5(5(3(x1)))))))))))
   4^1(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 1^1(5(0(5(5(3(1(5(5(3(x1))))))))))
   4^1(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 5^1(0(5(5(3(1(5(5(3(x1)))))))))
   4^1(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 0^1(5(5(3(1(5(5(3(x1))))))))
   4^1(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 5^1(5(3(1(5(5(3(x1)))))))
   4^1(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 5^1(3(1(5(5(3(x1))))))
   4^1(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 3^1(1(5(5(3(x1)))))
   4^1(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 1^1(5(5(3(x1))))
   4^1(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 5^1(5(3(x1)))
   3^1(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 4^1(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1))))))))))))))))
   3^1(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 5^1(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))
   3^1(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 5^1(4(3(4(4(1(3(4(3(2(1(1(4(1(x1))))))))))))))
   3^1(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 4^1(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))
   3^1(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3^1(4(4(1(3(4(3(2(1(1(4(1(x1))))))))))))
   3^1(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 4^1(4(1(3(4(3(2(1(1(4(1(x1)))))))))))
   3^1(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 4^1(1(3(4(3(2(1(1(4(1(x1))))))))))
   3^1(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 1^1(3(4(3(2(1(1(4(1(x1)))))))))
   3^1(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3^1(4(3(2(1(1(4(1(x1))))))))
   3^1(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 4^1(3(2(1(1(4(1(x1)))))))
   3^1(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3^1(2(1(1(4(1(x1))))))
   0^1(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0^1(2(4(1(0(3(0(1(4(3(4(5(x1))))))))))))
   0^1(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 2^1(4(1(0(3(0(1(4(3(4(5(x1)))))))))))
   0^1(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 4^1(1(0(3(0(1(4(3(4(5(x1))))))))))
   0^1(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 1^1(0(3(0(1(4(3(4(5(x1)))))))))
   0^1(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0^1(3(0(1(4(3(4(5(x1))))))))
   1^1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 4^1(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1)))))))))))))))))
   1^1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1^1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))
   1^1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 2^1(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1)))))))))))))))
   1^1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 0^1(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))
   1^1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1^1(3(0(4(1(0(4(5(2(4(3(5(0(x1)))))))))))))
   1^1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 3^1(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))
   1^1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 0^1(4(1(0(4(5(2(4(3(5(0(x1)))))))))))
   1^1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 4^1(1(0(4(5(2(4(3(5(0(x1))))))))))
   1^1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1^1(0(4(5(2(4(3(5(0(x1)))))))))
   1^1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 0^1(4(5(2(4(3(5(0(x1))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 1^1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 4^1(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1)))))))))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0^1(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 4^1(0(1(5(2(3(4(3(5(0(5(4(3(x1)))))))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0^1(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 1^1(5(2(3(4(3(5(0(5(4(3(x1)))))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 5^1(2(3(4(3(5(0(5(4(3(x1))))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 2^1(3(4(3(5(0(5(4(3(x1)))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 3^1(4(3(5(0(5(4(3(x1))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 4^1(3(5(0(5(4(3(x1)))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 3^1(5(0(5(4(3(x1))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 5^1(0(5(4(3(x1)))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0^1(5(4(3(x1))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 0^1(2(1(2(0(5(2(4(5(2(3(3(4(x1)))))))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 2^1(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 1^1(2(0(5(2(4(5(2(3(3(4(x1)))))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 2^1(0(5(2(4(5(2(3(3(4(x1))))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 0^1(5(2(4(5(2(3(3(4(x1)))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5^1(2(4(5(2(3(3(4(x1))))))))
   0^1(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 1^1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))
   0^1(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 4^1(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))
   0^1(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 5^1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))
   5^1(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 3^1(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1))))))))))))))))
   5^1(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 3^1(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))
   5^1(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 0^1(5(5(1(5(4(5(0(3(3(5(1(4(3(x1))))))))))))))
   5^1(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5^1(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))
   5^1(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5^1(1(5(4(5(0(3(3(5(1(4(3(x1))))))))))))
   5^1(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 1^1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))
   5^1(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5^1(4(5(0(3(3(5(1(4(3(x1))))))))))
   3^1(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 2^1(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1)))))))))))))))))))
   3^1(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 2^1(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))
   3^1(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 2^1(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1)))))))))))))))))
   3^1(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 4^1(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))
   3^1(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 5^1(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1)))))))))))))))
   3^1(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 2^1(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))
   3^1(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 1^1(1(0(4(3(3(4(4(0(4(5(5(3(x1)))))))))))))
   3^1(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 1^1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))
   3^1(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 0^1(4(3(3(4(4(0(4(5(5(3(x1)))))))))))
   3^1(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 4^1(3(3(4(4(0(4(5(5(3(x1))))))))))
   3^1(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3^1(3(4(4(0(4(5(5(3(x1)))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 3^1(2(2(1(4(4(2(1(1(0(2(0(x1))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 2^1(2(1(4(4(2(1(1(0(2(0(x1)))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 2^1(1(4(4(2(1(1(0(2(0(x1))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 1^1(4(4(2(1(1(0(2(0(x1)))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4^1(4(2(1(1(0(2(0(x1))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4^1(2(1(1(0(2(0(x1)))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 2^1(1(1(0(2(0(x1))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 1^1(1(0(2(0(x1)))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 1^1(0(2(0(x1))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 0^1(2(0(x1)))
   4^1(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 1^1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))
   4^1(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 5^1(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))
   4^1(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 2^1(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))
   3^1(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 1^1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))
   3^1(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 1^1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))
   3^1(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 0^1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 2^1(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 1^1(0(4(4(1(4(5(0(0(3(4(5(0(x1)))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 0^1(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 4^1(4(1(4(5(0(0(3(4(5(0(x1)))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 4^1(1(4(5(0(0(3(4(5(0(x1))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 1^1(4(5(0(0(3(4(5(0(x1)))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 4^1(5(0(0(3(4(5(0(x1))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5^1(0(0(3(4(5(0(x1)))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 0^1(0(3(4(5(0(x1))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 0^1(3(4(5(0(x1)))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 3^1(4(5(0(x1))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5^1(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 0^1(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1))))))))))))))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 1^1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 1^1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1))))))))))))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 4^1(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 2^1(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1))))))))))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5^1(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5^1(0(5(0(2(2(4(0(0(4(4(2(3(4(x1))))))))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 0^1(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5^1(0(2(2(4(0(0(4(4(2(3(4(x1))))))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 0^1(2(2(4(0(0(4(4(2(3(4(x1)))))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 2^1(2(4(0(0(4(4(2(3(4(x1))))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 2^1(4(0(0(4(4(2(3(4(x1)))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 4^1(0(0(4(4(2(3(4(x1))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 0^1(0(4(4(2(3(4(x1)))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 0^1(4(4(2(3(4(x1))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 4^1(4(2(3(4(x1)))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 4^1(2(3(4(x1))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 5^1(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 3^1(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1))))))))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 3^1(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2^1(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1))))))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 4^1(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 0^1(2(4(4(0(5(4(1(0(3(5(3(5(4(x1))))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2^1(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 4^1(4(0(5(4(1(0(3(5(3(5(4(x1))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 4^1(0(5(4(1(0(3(5(3(5(4(x1)))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 0^1(5(4(1(0(3(5(3(5(4(x1))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 5^1(4(1(0(3(5(3(5(4(x1)))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 4^1(1(0(3(5(3(5(4(x1))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 1^1(0(3(5(3(5(4(x1)))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 0^1(3(5(3(5(4(x1))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 3^1(5(3(5(4(x1)))))
   5^1(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 1^1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))
   5^1(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 1^1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))
   5^1(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 3^1(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))
   5^1(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5^1(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))
   5^1(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 2^1(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 1^1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 5^1(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1))))))))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 3^1(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0^1(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1))))))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 1^1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 2^1(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1))))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 2^1(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0^1(2(1(2(3(0(3(1(2(5(1(3(1(0(x1))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 2^1(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 1^1(2(3(0(3(1(2(5(1(3(1(0(x1))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 2^1(3(0(3(1(2(5(1(3(1(0(x1)))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 3^1(0(3(1(2(5(1(3(1(0(x1))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0^1(3(1(2(5(1(3(1(0(x1)))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 3^1(1(2(5(1(3(1(0(x1))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 1^1(2(5(1(3(1(0(x1)))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 2^1(5(1(3(1(0(x1))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 4^1(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 5^1(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 1^1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 1^1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 5^1(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 1^1(0(4(2(2(5(4(4(4(5(2(2(x1))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0^1(4(2(2(5(4(4(4(5(2(2(x1)))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 1^1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 3^1(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4^1(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 1^1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 2^1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))
   5^1(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 3^1(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))
   5^1(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5^1(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))
   5^1(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 4^1(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))
   5^1(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 2^1(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))
   5^1(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 4^1(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 4^1(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1))))))))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0^1(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 2^1(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1))))))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 4^1(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 1^1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1))))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 1^1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 5^1(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 5^1(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0^1(5(4(5(1(3(5(2(2(3(5(1(1(1(x1))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 5^1(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 4^1(5(1(3(5(2(2(3(5(1(1(1(x1))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 5^1(1(3(5(2(2(3(5(1(1(1(x1)))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 1^1(3(5(2(2(3(5(1(1(1(x1))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 3^1(5(2(2(3(5(1(1(1(x1)))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 5^1(2(2(3(5(1(1(1(x1))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 2^1(2(3(5(1(1(1(x1)))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 2^1(3(5(1(1(1(x1))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 3^1(5(1(1(1(x1)))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 5^1(1(1(1(x1))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 1^1(1(1(x1)))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 3^1(2(4(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2^1(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 4^1(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))
   5^1(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 0^1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 4^1(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 5^1(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 3^1(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1^1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 2^1(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 3^1(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 0^1(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 2^1(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 2^1(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 5^1(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 0^1(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 4^1(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 2^1(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1)))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 5^1(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1^1(4(0(4(0(5(4(3(3(4(0(2(0(x1)))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 4^1(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 0^1(4(0(5(4(3(3(4(0(2(0(x1)))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 4^1(0(5(4(3(3(4(0(2(0(x1))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 0^1(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4^1(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 0^1(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 5^1(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 5^1(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4^1(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 5^1(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 1^1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 2^1(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 1^1(0(4(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 0^1(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4^1(1(2(4(4(5(1(0(5(4(1(x1)))))))))))
   3^1(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 4^1(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))
   3^1(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3^1(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))
   3^1(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3^1(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))
   3^1(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3^1(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))
   3^1(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 1^1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))
   3^1(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3^1(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))
   3^1(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 1^1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))
   3^1(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 1^1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))
   3^1(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 4^1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 1^1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 0^1(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 2^1(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3^1(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 2^1(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 5^1(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 0^1(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 5^1(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 4^1(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 4^1(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 0^1(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 4^1(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 5^1(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 4^1(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 1^1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 5^1(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 2^1(1(0(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 1^1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 0^1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 2^1(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 1^1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 5^1(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 2^1(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 5^1(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 5^1(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 1^1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 5^1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(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)) = x_1
   POL(1(x_1)) = 1 + x_1
   POL(1^1(x_1)) = 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)) = 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:

   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))


----------------------------------------

(8)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   3^1(0(2(2(0(1(0(x1))))))) -> 0^1(2(0(2(3(1(0(x1)))))))
   3^1(0(2(2(0(1(0(x1))))))) -> 2^1(0(2(3(1(0(x1))))))
   3^1(0(2(2(0(1(0(x1))))))) -> 0^1(2(3(1(0(x1)))))
   3^1(0(2(2(0(1(0(x1))))))) -> 2^1(3(1(0(x1))))
   3^1(0(2(2(0(1(0(x1))))))) -> 3^1(1(0(x1)))
   5^1(3(3(4(5(4(0(x1))))))) -> 5^1(3(5(4(3(4(0(x1)))))))
   5^1(3(3(4(5(4(0(x1))))))) -> 3^1(5(4(3(4(0(x1))))))
   4^1(2(5(4(0(1(2(x1))))))) -> 4^1(0(5(2(4(1(2(x1)))))))
   4^1(2(5(4(0(1(2(x1))))))) -> 0^1(5(2(4(1(2(x1))))))
   4^1(2(5(4(0(1(2(x1))))))) -> 5^1(2(4(1(2(x1)))))
   4^1(2(5(4(0(1(2(x1))))))) -> 2^1(4(1(2(x1))))
   4^1(2(5(4(0(1(2(x1))))))) -> 4^1(1(2(x1)))
   5^1(1(2(4(2(5(4(x1))))))) -> 5^1(1(4(2(2(5(4(x1)))))))
   5^1(1(2(4(2(5(4(x1))))))) -> 1^1(4(2(2(5(4(x1))))))
   4^1(4(2(0(0(3(3(3(x1)))))))) -> 4^1(4(0(0(3(2(3(3(x1))))))))
   4^1(4(2(0(0(3(3(3(x1)))))))) -> 4^1(0(0(3(2(3(3(x1)))))))
   4^1(4(2(0(0(3(3(3(x1)))))))) -> 0^1(0(3(2(3(3(x1))))))
   4^1(4(2(0(0(3(3(3(x1)))))))) -> 0^1(3(2(3(3(x1)))))
   4^1(4(2(0(0(3(3(3(x1)))))))) -> 3^1(2(3(3(x1))))
   0^1(3(3(4(5(0(0(4(x1)))))))) -> 0^1(0(4(3(5(3(0(4(x1))))))))
   0^1(3(3(4(5(0(0(4(x1)))))))) -> 0^1(4(3(5(3(0(4(x1)))))))
   0^1(3(3(4(5(0(0(4(x1)))))))) -> 4^1(3(5(3(0(4(x1))))))
   0^1(3(3(4(5(0(0(4(x1)))))))) -> 3^1(5(3(0(4(x1)))))
   5^1(3(4(1(3(4(3(1(1(x1))))))))) -> 5^1(3(4(3(1(4(3(1(1(x1)))))))))
   5^1(3(4(1(3(4(3(1(1(x1))))))))) -> 3^1(4(3(1(4(3(1(1(x1))))))))
   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 0^1(4(0(0(0(2(3(1(4(x1)))))))))
   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 4^1(0(0(0(2(3(1(4(x1))))))))
   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 0^1(0(0(2(3(1(4(x1)))))))
   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 0^1(0(2(3(1(4(x1))))))
   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 0^1(2(3(1(4(x1)))))
   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 2^1(3(1(4(x1))))
   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 3^1(1(4(x1)))
   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2^1(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 4^1(4(3(1(5(3(3(5(4(5(0(x1)))))))))))
   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 4^1(3(1(5(3(3(5(4(5(0(x1))))))))))
   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 3^1(1(5(3(3(5(4(5(0(x1)))))))))
   0^1(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0^1(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0^1(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 2^1(3(4(2(0(0(1(2(2(1(3(x1)))))))))))
   0^1(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 3^1(4(2(0(0(1(2(2(1(3(x1))))))))))
   1^1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1^1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3^1(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3^1(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   4^1(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4^1(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   4^1(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 1^1(5(3(1(1(4(0(4(5(3(2(4(x1))))))))))))
   2^1(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2^1(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   2^1(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 0^1(0(4(3(2(2(4(1(5(4(0(5(x1))))))))))))
   2^1(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 0^1(4(3(2(2(4(1(5(4(0(5(x1)))))))))))
   2^1(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 4^1(3(2(2(4(1(5(4(0(5(x1))))))))))
   2^1(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 3^1(2(2(4(1(5(4(0(5(x1)))))))))
   1^1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1^1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1^1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1^1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2^1(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2^1(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2^1(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 4^1(2(3(0(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))
   2^1(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2^1(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))
   2^1(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 3^1(0(3(4(0(0(2(0(4(1(0(2(x1))))))))))))
   5^1(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5^1(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   5^1(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 0^1(0(5(3(1(0(1(3(1(1(5(1(0(3(x1))))))))))))))
   5^1(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 0^1(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))
   5^1(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5^1(3(1(0(1(3(1(1(5(1(0(3(x1))))))))))))
   5^1(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 3^1(1(0(1(3(1(1(5(1(0(3(x1)))))))))))
   0^1(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3^1(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1^1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1^1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4^1(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4^1(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   4^1(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 1^1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1)))))))))))))))
   3^1(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3^1(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0^1(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0^1(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   0^1(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 4^1(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1))))))))))))))))
   0^1(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0^1(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))
   0^1(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 4^1(1(0(2(4(1(0(3(0(1(4(3(4(5(x1))))))))))))))
   0^1(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 1^1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))
   1^1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1^1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0^1(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 1^1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1)))))))))))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5^1(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 2^1(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1)))))))))))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 2^1(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5^1(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1)))))))))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 1^1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))
   0^1(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0^1(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   0^1(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 3^1(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))
   5^1(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5^1(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   5^1(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 4^1(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))
   5^1(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 3^1(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))
   3^1(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3^1(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4^1(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 0^1(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1))))))))))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 2^1(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 5^1(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1))))))))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 5^1(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 0^1(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1))))))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 5^1(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 2^1(3(3(2(2(1(4(4(2(1(1(0(2(0(x1))))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 3^1(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))
   4^1(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4^1(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   4^1(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 5^1(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))
   4^1(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4^1(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))
   4^1(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4^1(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))
   4^1(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 1^1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))
   3^1(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3^1(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5^1(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 2^1(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1)))))))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 4^1(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 0^1(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1)))))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 4^1(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5^1(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1)))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 0^1(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 1^1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1)))))))))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5^1(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 3^1(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1))))))))))))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 0^1(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1))))))))))))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 5^1(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 3^1(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1))))))))))))))))))))
   5^1(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5^1(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5^1(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 3^1(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 4^1(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1))))))))))))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 4^1(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 3^1(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1))))))))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0^1(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 2^1(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0^1(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 2^1(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 2^1(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 2^1(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 4^1(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 3^1(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4^1(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 5^1(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 5^1(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 5^1(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 2^1(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 1^1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))
   5^1(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5^1(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   5^1(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 3^1(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 2^1(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1))))))))))))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 4^1(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 4^1(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1))))))))))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 1^1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2^1(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 0^1(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2^1(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 5^1(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 0^1(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2^1(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 0^1(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 0^1(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2^1(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2^1(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 5^1(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 3^1(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))
   5^1(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5^1(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   5^1(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 4^1(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))
   5^1(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 1^1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 2^1(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 5^1(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 5^1(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4^1(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 2^1(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 0^1(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 1^1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))
   3^1(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3^1(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4^1(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 0^1(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 5^1(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 2^1(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 3^1(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(9) DependencyGraphProof (EQUIVALENT)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 12 less nodes.
----------------------------------------

(10)
Complex Obligation (AND)

----------------------------------------

(11)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   1^1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1^1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1^1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1^1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1^1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1^1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   1^1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1^1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   1^1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1^1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(12) QDPOrderProof (EQUIVALENT)
We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.

   1^1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1^1(1(2(0(1(0(1(4(2(2(1(0(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(1^1(x_1)) = x_1
   POL(2(x_1)) = 1 + x_1
   POL(3(x_1)) = x_1
   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:

   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))


----------------------------------------

(13)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   1^1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1^1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1^1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1^1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   1^1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1^1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   1^1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1^1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(14) QDPOrderProof (EQUIVALENT)
We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.

   1^1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1^1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
The remaining pairs can at least be oriented weakly.
Used ordering:  Polynomial interpretation [POLO]:

   POL(0(x_1)) = 1
   POL(1(x_1)) = x_1
   POL(1^1(x_1)) = x_1
   POL(2(x_1)) = x_1
   POL(3(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:

   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))


----------------------------------------

(15)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   1^1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1^1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1^1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1^1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   1^1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1^1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(16) 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(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))

Used ordering: Polynomial interpretation [POLO]:

   POL(0(x_1)) = x_1
   POL(1(x_1)) = 2*x_1
   POL(1^1(x_1)) = 2*x_1
   POL(2(x_1)) = x_1
   POL(3(x_1)) = 1 + 2*x_1
   POL(4(x_1)) = x_1
   POL(5(x_1)) = x_1


----------------------------------------

(17)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   1^1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1^1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1^1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1^1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   1^1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1^1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(18) 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(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1^1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))

Strictly oriented rules of the TRS R:

   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))

Used ordering: Polynomial interpretation [POLO]:

   POL(0(x_1)) = 2*x_1
   POL(1(x_1)) = 2 + x_1
   POL(1^1(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)) = x_1


----------------------------------------

(19)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   1^1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1^1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1^1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1^1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(20) 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(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Used ordering: Polynomial interpretation [POLO]:

   POL(0(x_1)) = 2*x_1
   POL(1(x_1)) = 2 + 2*x_1
   POL(1^1(x_1)) = x_1
   POL(2(x_1)) = 2*x_1
   POL(3(x_1)) = 2*x_1
   POL(4(x_1)) = x_1
   POL(5(x_1)) = 2*x_1


----------------------------------------

(21)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   1^1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1^1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1^1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1^1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(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.

   1^1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1^1(5(3(1(2(3(4(1(0(2(2(2(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(1^1(x_1)) = x_1
   POL(2(x_1)) = 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:

   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))


----------------------------------------

(23)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   1^1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1^1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(24) 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(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))

Used ordering: Polynomial interpretation [POLO]:

   POL(0(x_1)) = x_1
   POL(1(x_1)) = 3 + 2*x_1
   POL(1^1(x_1)) = 2*x_1
   POL(2(x_1)) = 2*x_1
   POL(3(x_1)) = x_1
   POL(4(x_1)) = 2*x_1
   POL(5(x_1)) = 2*x_1


----------------------------------------

(25)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   1^1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1^1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(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:

   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))

Used ordering: Polynomial interpretation [POLO]:

   POL(0(x_1)) = x_1
   POL(1(x_1)) = 2*x_1
   POL(1^1(x_1)) = 2*x_1
   POL(2(x_1)) = 2*x_1
   POL(3(x_1)) = x_1
   POL(4(x_1)) = x_1
   POL(5(x_1)) = 2 + 2*x_1


----------------------------------------

(27)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   1^1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1^1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(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:

   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))

Used ordering: Polynomial interpretation [POLO]:

   POL(0(x_1)) = x_1
   POL(1(x_1)) = x_1
   POL(1^1(x_1)) = 2*x_1
   POL(2(x_1)) = 2*x_1
   POL(3(x_1)) = 2*x_1
   POL(4(x_1)) = x_1
   POL(5(x_1)) = 1 + 2*x_1


----------------------------------------

(29)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   1^1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1^1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(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:

   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))

Used ordering: Polynomial interpretation [POLO]:

   POL(0(x_1)) = x_1
   POL(1(x_1)) = x_1
   POL(1^1(x_1)) = 2*x_1
   POL(2(x_1)) = x_1
   POL(3(x_1)) = 2*x_1
   POL(4(x_1)) = 1 + 2*x_1
   POL(5(x_1)) = 1 + 2*x_1


----------------------------------------

(31)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   1^1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1^1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1^1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(32) DependencyGraphProof (EQUIVALENT)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 2 less nodes.
----------------------------------------

(33)
TRUE

----------------------------------------

(34)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   0^1(3(3(4(5(0(0(4(x1)))))))) -> 0^1(0(4(3(5(3(0(4(x1))))))))
   0^1(3(3(4(5(0(0(4(x1)))))))) -> 0^1(4(3(5(3(0(4(x1)))))))
   0^1(3(3(4(5(0(0(4(x1)))))))) -> 4^1(3(5(3(0(4(x1))))))
   4^1(2(5(4(0(1(2(x1))))))) -> 4^1(0(5(2(4(1(2(x1)))))))
   4^1(2(5(4(0(1(2(x1))))))) -> 0^1(5(2(4(1(2(x1))))))
   0^1(3(3(4(5(0(0(4(x1)))))))) -> 3^1(5(3(0(4(x1)))))
   3^1(0(2(2(0(1(0(x1))))))) -> 0^1(2(0(2(3(1(0(x1)))))))
   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 0^1(4(0(0(0(2(3(1(4(x1)))))))))
   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 4^1(0(0(0(2(3(1(4(x1))))))))
   4^1(2(5(4(0(1(2(x1))))))) -> 5^1(2(4(1(2(x1)))))
   5^1(3(3(4(5(4(0(x1))))))) -> 5^1(3(5(4(3(4(0(x1)))))))
   5^1(3(3(4(5(4(0(x1))))))) -> 3^1(5(4(3(4(0(x1))))))
   3^1(0(2(2(0(1(0(x1))))))) -> 2^1(0(2(3(1(0(x1))))))
   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2^1(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 4^1(4(3(1(5(3(3(5(4(5(0(x1)))))))))))
   4^1(2(5(4(0(1(2(x1))))))) -> 2^1(4(1(2(x1))))
   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 4^1(3(1(5(3(3(5(4(5(0(x1))))))))))
   4^1(2(5(4(0(1(2(x1))))))) -> 4^1(1(2(x1)))
   4^1(4(2(0(0(3(3(3(x1)))))))) -> 4^1(4(0(0(3(2(3(3(x1))))))))
   4^1(4(2(0(0(3(3(3(x1)))))))) -> 4^1(0(0(3(2(3(3(x1)))))))
   4^1(4(2(0(0(3(3(3(x1)))))))) -> 0^1(0(3(2(3(3(x1))))))
   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 0^1(0(0(2(3(1(4(x1)))))))
   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 0^1(0(2(3(1(4(x1))))))
   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 0^1(2(3(1(4(x1)))))
   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 2^1(3(1(4(x1))))
   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 3^1(1(5(3(3(5(4(5(0(x1)))))))))
   3^1(0(2(2(0(1(0(x1))))))) -> 0^1(2(3(1(0(x1)))))
   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 3^1(1(4(x1)))
   3^1(0(2(2(0(1(0(x1))))))) -> 2^1(3(1(0(x1))))
   2^1(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2^1(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   2^1(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 0^1(0(4(3(2(2(4(1(5(4(0(5(x1))))))))))))
   0^1(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0^1(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0^1(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 2^1(3(4(2(0(0(1(2(2(1(3(x1)))))))))))
   2^1(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 0^1(4(3(2(2(4(1(5(4(0(5(x1)))))))))))
   0^1(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 3^1(4(2(0(0(1(2(2(1(3(x1))))))))))
   3^1(0(2(2(0(1(0(x1))))))) -> 3^1(1(0(x1)))
   3^1(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3^1(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   3^1(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3^1(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3^1(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3^1(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   3^1(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3^1(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   3^1(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3^1(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   0^1(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3^1(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   0^1(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0^1(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   0^1(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 4^1(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1))))))))))))))))
   4^1(4(2(0(0(3(3(3(x1)))))))) -> 0^1(3(2(3(3(x1)))))
   0^1(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0^1(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))
   0^1(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 4^1(1(0(2(4(1(0(3(0(1(4(3(4(5(x1))))))))))))))
   4^1(4(2(0(0(3(3(3(x1)))))))) -> 3^1(2(3(3(x1))))
   4^1(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4^1(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   4^1(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4^1(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4^1(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 0^1(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1))))))))))))))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0^1(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   0^1(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0^1(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   0^1(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 3^1(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 4^1(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1))))))))))))))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 2^1(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))
   2^1(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 4^1(3(2(2(4(1(5(4(0(5(x1))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 5^1(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1))))))))))))))))))
   5^1(1(2(4(2(5(4(x1))))))) -> 5^1(1(4(2(2(5(4(x1)))))))
   5^1(3(4(1(3(4(3(1(1(x1))))))))) -> 5^1(3(4(3(1(4(3(1(1(x1)))))))))
   5^1(3(4(1(3(4(3(1(1(x1))))))))) -> 3^1(4(3(1(4(3(1(1(x1))))))))
   5^1(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5^1(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   5^1(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 0^1(0(5(3(1(0(1(3(1(1(5(1(0(3(x1))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 4^1(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 5^1(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))
   5^1(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 0^1(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 3^1(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1))))))))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0^1(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 2^1(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))
   2^1(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 3^1(2(2(4(1(5(4(0(5(x1)))))))))
   2^1(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2^1(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2^1(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 4^1(2(3(0(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 0^1(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0^1(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 2^1(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))
   2^1(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2^1(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))
   2^1(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 3^1(0(3(4(0(0(2(0(4(1(0(2(x1))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 0^1(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1))))))))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 2^1(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 5^1(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))
   5^1(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5^1(3(1(0(1(3(1(1(5(1(0(3(x1))))))))))))
   5^1(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 3^1(1(0(1(3(1(1(5(1(0(3(x1)))))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5^1(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 2^1(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1)))))))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 3^1(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2^1(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 0^1(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 2^1(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2^1(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 5^1(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 2^1(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 0^1(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 4^1(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 5^1(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5^1(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1)))))))))))))))
   5^1(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5^1(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   5^1(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 4^1(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 2^1(3(3(2(2(1(4(4(2(1(1(0(2(0(x1))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2^1(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 0^1(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 3^1(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 2^1(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1))))))))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 0^1(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 4^1(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 3^1(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))
   4^1(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4^1(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   4^1(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 5^1(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))
   5^1(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 3^1(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5^1(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 2^1(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1)))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2^1(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2^1(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 5^1(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 4^1(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))
   4^1(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4^1(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))
   4^1(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4^1(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4^1(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 5^1(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 0^1(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1)))))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 4^1(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1))))))))))))))))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 5^1(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 4^1(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 5^1(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5^1(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1)))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 0^1(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5^1(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 3^1(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1))))))))))))))))))))))
   5^1(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5^1(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5^1(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 3^1(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))
   5^1(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5^1(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   5^1(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 3^1(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))
   5^1(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5^1(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   5^1(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 4^1(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 2^1(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 3^1(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 2^1(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 5^1(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 5^1(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4^1(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 2^1(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 0^1(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4^1(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 0^1(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 5^1(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 2^1(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 3^1(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(35) QDPOrderProof (EQUIVALENT)
We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.

   0^1(3(3(4(5(0(0(4(x1)))))))) -> 4^1(3(5(3(0(4(x1))))))
   0^1(3(3(4(5(0(0(4(x1)))))))) -> 3^1(5(3(0(4(x1)))))
   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 4^1(0(0(0(2(3(1(4(x1))))))))
   4^1(2(5(4(0(1(2(x1))))))) -> 5^1(2(4(1(2(x1)))))
   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 4^1(4(3(1(5(3(3(5(4(5(0(x1)))))))))))
   4^1(2(5(4(0(1(2(x1))))))) -> 2^1(4(1(2(x1))))
   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 4^1(3(1(5(3(3(5(4(5(0(x1))))))))))
   4^1(2(5(4(0(1(2(x1))))))) -> 4^1(1(2(x1)))
   4^1(4(2(0(0(3(3(3(x1)))))))) -> 4^1(0(0(3(2(3(3(x1)))))))
   4^1(4(2(0(0(3(3(3(x1)))))))) -> 0^1(0(3(2(3(3(x1))))))
   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 0^1(0(0(2(3(1(4(x1)))))))
   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 0^1(0(2(3(1(4(x1))))))
   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 0^1(2(3(1(4(x1)))))
   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 2^1(3(1(4(x1))))
   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 3^1(1(5(3(3(5(4(5(0(x1)))))))))
   3^1(0(2(2(0(1(0(x1))))))) -> 0^1(2(3(1(0(x1)))))
   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 3^1(1(4(x1)))
   3^1(0(2(2(0(1(0(x1))))))) -> 2^1(3(1(0(x1))))
   2^1(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 0^1(0(4(3(2(2(4(1(5(4(0(5(x1))))))))))))
   2^1(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 0^1(4(3(2(2(4(1(5(4(0(5(x1)))))))))))
   0^1(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 3^1(4(2(0(0(1(2(2(1(3(x1))))))))))
   3^1(0(2(2(0(1(0(x1))))))) -> 3^1(1(0(x1)))
   0^1(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 4^1(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1))))))))))))))))
   4^1(4(2(0(0(3(3(3(x1)))))))) -> 0^1(3(2(3(3(x1)))))
   0^1(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0^1(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))
   0^1(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 4^1(1(0(2(4(1(0(3(0(1(4(3(4(5(x1))))))))))))))
   4^1(4(2(0(0(3(3(3(x1)))))))) -> 3^1(2(3(3(x1))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 4^1(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1))))))))))))))))))))))))
   2^1(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 4^1(3(2(2(4(1(5(4(0(5(x1))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 5^1(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1))))))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 4^1(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 5^1(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 3^1(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1))))))))))))))))))))))
   2^1(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 3^1(2(2(4(1(5(4(0(5(x1)))))))))
   2^1(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 4^1(2(3(0(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 0^1(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0^1(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 2^1(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))
   2^1(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2^1(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))
   2^1(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 3^1(0(3(4(0(0(2(0(4(1(0(2(x1))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 0^1(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1))))))))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 2^1(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 5^1(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))
   5^1(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5^1(3(1(0(1(3(1(1(5(1(0(3(x1))))))))))))
   5^1(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 3^1(1(0(1(3(1(1(5(1(0(3(x1)))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 3^1(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2^1(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 0^1(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 2^1(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2^1(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 5^1(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 2^1(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 0^1(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 4^1(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 5^1(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5^1(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1)))))))))))))))
   5^1(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 4^1(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 2^1(3(3(2(2(1(4(4(2(1(1(0(2(0(x1))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2^1(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 0^1(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 3^1(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 0^1(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 4^1(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 3^1(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))
   4^1(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 5^1(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))
   5^1(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 3^1(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2^1(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2^1(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 5^1(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 4^1(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))
   4^1(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4^1(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))
   4^1(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4^1(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 5^1(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 0^1(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1)))))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 4^1(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1))))))))))))))))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 5^1(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 4^1(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 5^1(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5^1(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1)))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 0^1(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))
   5^1(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 4^1(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 2^1(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 3^1(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 5^1(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 5^1(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4^1(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 2^1(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 0^1(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 5^1(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 2^1(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 3^1(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(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)) = x_1
   POL(1(x_1)) = 1 + x_1
   POL(2(x_1)) = 1 + x_1
   POL(2^1(x_1)) = 1 + x_1
   POL(3(x_1)) = x_1
   POL(3^1(x_1)) = x_1
   POL(4(x_1)) = 1 + x_1
   POL(4^1(x_1)) = x_1
   POL(5(x_1)) = 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:

   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))


----------------------------------------

(36)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   0^1(3(3(4(5(0(0(4(x1)))))))) -> 0^1(0(4(3(5(3(0(4(x1))))))))
   0^1(3(3(4(5(0(0(4(x1)))))))) -> 0^1(4(3(5(3(0(4(x1)))))))
   4^1(2(5(4(0(1(2(x1))))))) -> 4^1(0(5(2(4(1(2(x1)))))))
   4^1(2(5(4(0(1(2(x1))))))) -> 0^1(5(2(4(1(2(x1))))))
   3^1(0(2(2(0(1(0(x1))))))) -> 0^1(2(0(2(3(1(0(x1)))))))
   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 0^1(4(0(0(0(2(3(1(4(x1)))))))))
   5^1(3(3(4(5(4(0(x1))))))) -> 5^1(3(5(4(3(4(0(x1)))))))
   5^1(3(3(4(5(4(0(x1))))))) -> 3^1(5(4(3(4(0(x1))))))
   3^1(0(2(2(0(1(0(x1))))))) -> 2^1(0(2(3(1(0(x1))))))
   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2^1(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   4^1(4(2(0(0(3(3(3(x1)))))))) -> 4^1(4(0(0(3(2(3(3(x1))))))))
   2^1(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2^1(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   0^1(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0^1(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0^1(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 2^1(3(4(2(0(0(1(2(2(1(3(x1)))))))))))
   3^1(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3^1(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   3^1(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3^1(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3^1(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3^1(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   3^1(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3^1(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   3^1(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3^1(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   0^1(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3^1(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   0^1(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0^1(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   4^1(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4^1(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   4^1(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4^1(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4^1(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 0^1(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1))))))))))))))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0^1(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   0^1(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0^1(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   0^1(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 3^1(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 2^1(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))
   5^1(1(2(4(2(5(4(x1))))))) -> 5^1(1(4(2(2(5(4(x1)))))))
   5^1(3(4(1(3(4(3(1(1(x1))))))))) -> 5^1(3(4(3(1(4(3(1(1(x1)))))))))
   5^1(3(4(1(3(4(3(1(1(x1))))))))) -> 3^1(4(3(1(4(3(1(1(x1))))))))
   5^1(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5^1(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   5^1(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 0^1(0(5(3(1(0(1(3(1(1(5(1(0(3(x1))))))))))))))
   5^1(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 0^1(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0^1(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 2^1(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))
   2^1(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2^1(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5^1(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 2^1(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1)))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5^1(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5^1(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 2^1(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1))))))))))))))))))))))))))
   4^1(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4^1(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5^1(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 2^1(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1)))))))))))))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4^1(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5^1(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 3^1(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1))))))))))))))))))))))
   5^1(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5^1(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5^1(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 3^1(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))
   5^1(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5^1(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   5^1(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 3^1(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))
   5^1(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5^1(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 2^1(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4^1(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 0^1(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(37) DependencyGraphProof (EQUIVALENT)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 4 SCCs with 18 less nodes.
----------------------------------------

(38)
Complex Obligation (AND)

----------------------------------------

(39)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   2^1(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2^1(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2^1(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   2^1(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2^1(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(40) QDPOrderProof (EQUIVALENT)
We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.

   2^1(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2^1(0(0(4(3(2(2(4(1(5(4(0(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)) = 0
   POL(2(x_1)) = 1
   POL(2^1(x_1)) = x_1
   POL(3(x_1)) = 1
   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(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))


----------------------------------------

(41)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2^1(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   2^1(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2^1(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(42) 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(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(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)) = 2*x_1
   POL(2^1(x_1)) = 2*x_1
   POL(3(x_1)) = x_1
   POL(4(x_1)) = x_1
   POL(5(x_1)) = x_1


----------------------------------------

(43)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2^1(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   2^1(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2^1(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(44) 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(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))

Used ordering: Polynomial interpretation [POLO]:

   POL(0(x_1)) = 2*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)) = x_1
   POL(4(x_1)) = 2*x_1
   POL(5(x_1)) = x_1


----------------------------------------

(45)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2^1(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   2^1(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2^1(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(46) 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(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(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(2^1(x_1)) = 2*x_1
   POL(3(x_1)) = 2*x_1
   POL(4(x_1)) = x_1
   POL(5(x_1)) = 2 + 2*x_1


----------------------------------------

(47)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2^1(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   2^1(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2^1(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(48) 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(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))

Used ordering: Polynomial interpretation [POLO]:

   POL(0(x_1)) = x_1
   POL(1(x_1)) = 2*x_1
   POL(2(x_1)) = x_1
   POL(2^1(x_1)) = 2*x_1
   POL(3(x_1)) = 2 + 2*x_1
   POL(4(x_1)) = x_1
   POL(5(x_1)) = 2*x_1


----------------------------------------

(49)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2^1(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   2^1(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2^1(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(50) 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(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Used ordering: Polynomial interpretation [POLO]:

   POL(0(x_1)) = 2*x_1
   POL(1(x_1)) = 2 + 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)) = 2*x_1
   POL(5(x_1)) = 2*x_1


----------------------------------------

(51)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2^1(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   2^1(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2^1(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(52) 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(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))

Used ordering: Polynomial interpretation [POLO]:

   POL(0(x_1)) = 2 + 2*x_1
   POL(1(x_1)) = 2*x_1
   POL(2(x_1)) = x_1
   POL(2^1(x_1)) = x_1
   POL(3(x_1)) = x_1
   POL(4(x_1)) = 2*x_1
   POL(5(x_1)) = x_1


----------------------------------------

(53)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2^1(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   2^1(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2^1(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(54) 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(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))

Used ordering: Polynomial interpretation [POLO]:

   POL(0(x_1)) = x_1
   POL(1(x_1)) = x_1
   POL(2(x_1)) = x_1
   POL(2^1(x_1)) = x_1
   POL(3(x_1)) = 2*x_1
   POL(4(x_1)) = 1 + 2*x_1
   POL(5(x_1)) = 1 + 2*x_1


----------------------------------------

(55)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2^1(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   2^1(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2^1(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2^1(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2^1(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(56) DependencyGraphProof (EQUIVALENT)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes.
----------------------------------------

(57)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2^1(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(58) QDPOrderProof (EQUIVALENT)
We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.

   2^1(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2^1(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
The remaining pairs can at least be oriented weakly.
Used ordering:  Polynomial Order [NEGPOLO,POLO] with Interpretation:

POL( 2^1_1(x_1) ) = 2x_1 + 2
POL( 4_1(x_1) ) = max{0, 2x_1 - 1}
POL( 0_1(x_1) ) = max{0, -2}
POL( 2_1(x_1) ) = max{0, -2}
POL( 3_1(x_1) ) = x_1 + 2
POL( 1_1(x_1) ) = 2x_1 + 2
POL( 5_1(x_1) ) = x_1 + 1

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:

   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))


----------------------------------------

(59)
Obligation:
Q DP problem:
P is empty.
The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(60) PisEmptyProof (EQUIVALENT)
The TRS P is empty. Hence, there is no (P,Q,R) chain.
----------------------------------------

(61)
YES

----------------------------------------

(62)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   0^1(3(3(4(5(0(0(4(x1)))))))) -> 0^1(4(3(5(3(0(4(x1)))))))
   0^1(3(3(4(5(0(0(4(x1)))))))) -> 0^1(0(4(3(5(3(0(4(x1))))))))
   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 0^1(4(0(0(0(2(3(1(4(x1)))))))))
   0^1(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0^1(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0^1(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3^1(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   3^1(0(2(2(0(1(0(x1))))))) -> 0^1(2(0(2(3(1(0(x1)))))))
   0^1(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0^1(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0^1(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   0^1(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0^1(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   0^1(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 3^1(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))
   3^1(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3^1(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   3^1(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3^1(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3^1(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3^1(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   3^1(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3^1(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   3^1(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3^1(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0^1(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(63) QDPOrderProof (EQUIVALENT)
We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.

   3^1(0(2(2(0(1(0(x1))))))) -> 0^1(2(0(2(3(1(0(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)) = 0
   POL(1(x_1)) = 0
   POL(2(x_1)) = 1 + x_1
   POL(3(x_1)) = x_1
   POL(3^1(x_1)) = x_1
   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:

   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))


----------------------------------------

(64)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   0^1(3(3(4(5(0(0(4(x1)))))))) -> 0^1(4(3(5(3(0(4(x1)))))))
   0^1(3(3(4(5(0(0(4(x1)))))))) -> 0^1(0(4(3(5(3(0(4(x1))))))))
   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 0^1(4(0(0(0(2(3(1(4(x1)))))))))
   0^1(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0^1(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0^1(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3^1(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   0^1(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0^1(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0^1(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   0^1(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0^1(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   0^1(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 3^1(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))
   3^1(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3^1(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   3^1(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3^1(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3^1(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3^1(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   3^1(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3^1(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   3^1(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3^1(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0^1(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(65) DependencyGraphProof (EQUIVALENT)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 2 less nodes.
----------------------------------------

(66)
Complex Obligation (AND)

----------------------------------------

(67)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   3^1(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3^1(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3^1(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3^1(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   3^1(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3^1(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   3^1(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3^1(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   3^1(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3^1(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(68) QDPOrderProof (EQUIVALENT)
We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.

   3^1(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3^1(2(2(2(4(1(0(4(1(3(2(0(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)) = 1 + x_1
   POL(3(x_1)) = 0
   POL(3^1(x_1)) = x_1
   POL(4(x_1)) = 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(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))


----------------------------------------

(69)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   3^1(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3^1(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3^1(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3^1(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   3^1(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3^1(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   3^1(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3^1(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(70) 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(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))

Used ordering: Polynomial interpretation [POLO]:

   POL(0(x_1)) = x_1
   POL(1(x_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)) = x_1


----------------------------------------

(71)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   3^1(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3^1(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3^1(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3^1(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   3^1(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3^1(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   3^1(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3^1(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(72) 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(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3^1(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3^1(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))

Strictly oriented rules of the TRS R:

   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(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)) = x_1
   POL(3(x_1)) = x_1
   POL(3^1(x_1)) = x_1
   POL(4(x_1)) = x_1
   POL(5(x_1)) = 2*x_1


----------------------------------------

(73)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   3^1(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3^1(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3^1(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3^1(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   3^1(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3^1(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(74) 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(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(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)) = 2*x_1
   POL(3(x_1)) = x_1
   POL(3^1(x_1)) = 2*x_1
   POL(4(x_1)) = x_1
   POL(5(x_1)) = 2*x_1


----------------------------------------

(75)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   3^1(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3^1(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3^1(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3^1(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   3^1(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3^1(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(76) 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(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3^1(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))

Strictly oriented rules of the TRS R:

   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(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)) = 1 + 2*x_1
   POL(3(x_1)) = x_1
   POL(3^1(x_1)) = x_1
   POL(4(x_1)) = 1 + 2*x_1
   POL(5(x_1)) = 1 + 2*x_1


----------------------------------------

(77)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   3^1(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3^1(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3^1(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3^1(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(78) 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(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(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)) = x_1
   POL(4(x_1)) = x_1
   POL(5(x_1)) = 2 + x_1


----------------------------------------

(79)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   3^1(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3^1(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3^1(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3^1(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(80) 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(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3^1(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3^1(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3^1(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))

Strictly oriented rules of the TRS R:

   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))

Used ordering: Polynomial interpretation [POLO]:

   POL(0(x_1)) = x_1
   POL(1(x_1)) = 2*x_1
   POL(2(x_1)) = x_1
   POL(3(x_1)) = 1 + 3*x_1
   POL(3^1(x_1)) = 2*x_1
   POL(4(x_1)) = 1 + x_1
   POL(5(x_1)) = x_1


----------------------------------------

(81)
Obligation:
Q DP problem:
P is empty.
The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(82) PisEmptyProof (EQUIVALENT)
The TRS P is empty. Hence, there is no (P,Q,R) chain.
----------------------------------------

(83)
YES

----------------------------------------

(84)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   0^1(3(3(4(5(0(0(4(x1)))))))) -> 0^1(0(4(3(5(3(0(4(x1))))))))
   0^1(3(3(4(5(0(0(4(x1)))))))) -> 0^1(4(3(5(3(0(4(x1)))))))
   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 0^1(4(0(0(0(2(3(1(4(x1)))))))))
   0^1(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0^1(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0^1(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0^1(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0^1(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   0^1(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0^1(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0^1(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(85) QDPOrderProof (EQUIVALENT)
We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.

   0^1(3(3(4(5(0(0(4(x1)))))))) -> 0^1(4(3(5(3(0(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(2(x_1)) = x_1
   POL(3(x_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:

   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))


----------------------------------------

(86)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   0^1(3(3(4(5(0(0(4(x1)))))))) -> 0^1(0(4(3(5(3(0(4(x1))))))))
   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 0^1(4(0(0(0(2(3(1(4(x1)))))))))
   0^1(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0^1(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0^1(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0^1(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0^1(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   0^1(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0^1(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0^1(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(87) QDPOrderProof (EQUIVALENT)
We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.

   0^1(3(3(4(5(0(0(4(x1)))))))) -> 0^1(0(4(3(5(3(0(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)) = x_1
   POL(1(x_1)) = 0
   POL(2(x_1)) = 1
   POL(3(x_1)) = 1
   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:

   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))


----------------------------------------

(88)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 0^1(4(0(0(0(2(3(1(4(x1)))))))))
   0^1(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0^1(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0^1(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0^1(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0^1(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   0^1(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0^1(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0^1(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(89) QDPOrderProof (EQUIVALENT)
We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.

   0^1(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0^1(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(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)) = 0
   POL(2(x_1)) = 0
   POL(3(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(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))


----------------------------------------

(90)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 0^1(4(0(0(0(2(3(1(4(x1)))))))))
   0^1(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0^1(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0^1(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0^1(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0^1(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0^1(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(91) 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(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0^1(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0^1(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0^1(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0^1(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))

Strictly oriented rules of the TRS R:

   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))

Used ordering: Polynomial interpretation [POLO]:

   POL(0(x_1)) = 2*x_1
   POL(0^1(x_1)) = x_1
   POL(1(x_1)) = 2 + x_1
   POL(2(x_1)) = 2*x_1
   POL(3(x_1)) = x_1
   POL(4(x_1)) = x_1
   POL(5(x_1)) = x_1


----------------------------------------

(92)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 0^1(4(0(0(0(2(3(1(4(x1)))))))))
   0^1(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0^1(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0^1(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(93) 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(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0^1(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))

Strictly oriented rules of the TRS R:

   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))

Used ordering: Polynomial interpretation [POLO]:

   POL(0(x_1)) = 1 + 2*x_1
   POL(0^1(x_1)) = x_1
   POL(1(x_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)) = x_1


----------------------------------------

(94)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 0^1(4(0(0(0(2(3(1(4(x1)))))))))
   0^1(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0^1(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0^1(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(95) 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(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(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)) = 1 + 2*x_1
   POL(2(x_1)) = 2*x_1
   POL(3(x_1)) = x_1
   POL(4(x_1)) = 2*x_1
   POL(5(x_1)) = 2*x_1


----------------------------------------

(96)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 0^1(4(0(0(0(2(3(1(4(x1)))))))))
   0^1(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0^1(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0^1(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(97) 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(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))

Used ordering: Polynomial interpretation [POLO]:

   POL(0(x_1)) = x_1
   POL(0^1(x_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(5(x_1)) = 2 + 2*x_1


----------------------------------------

(98)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 0^1(4(0(0(0(2(3(1(4(x1)))))))))
   0^1(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0^1(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0^1(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(99) 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(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))

Used ordering: Polynomial interpretation [POLO]:

   POL(0(x_1)) = 2 + x_1
   POL(0^1(x_1)) = x_1
   POL(1(x_1)) = x_1
   POL(2(x_1)) = x_1
   POL(3(x_1)) = x_1
   POL(4(x_1)) = 2*x_1
   POL(5(x_1)) = x_1


----------------------------------------

(100)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 0^1(4(0(0(0(2(3(1(4(x1)))))))))
   0^1(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0^1(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0^1(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(101) 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(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))

Used ordering: Polynomial interpretation [POLO]:

   POL(0(x_1)) = x_1
   POL(0^1(x_1)) = 2*x_1
   POL(1(x_1)) = 2*x_1
   POL(2(x_1)) = 2*x_1
   POL(3(x_1)) = 2*x_1
   POL(4(x_1)) = x_1
   POL(5(x_1)) = 2 + 2*x_1


----------------------------------------

(102)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 0^1(4(0(0(0(2(3(1(4(x1)))))))))
   0^1(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0^1(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0^1(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(103) 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(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(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*x_1
   POL(2(x_1)) = x_1
   POL(3(x_1)) = 2*x_1
   POL(4(x_1)) = 2 + 2*x_1
   POL(5(x_1)) = x_1


----------------------------------------

(104)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   0^1(4(0(0(0(3(2(1(4(x1))))))))) -> 0^1(4(0(0(0(2(3(1(4(x1)))))))))
   0^1(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0^1(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0^1(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0^1(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(105) DependencyGraphProof (EQUIVALENT)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 3 less nodes.
----------------------------------------

(106)
TRUE

----------------------------------------

(107)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   5^1(1(2(4(2(5(4(x1))))))) -> 5^1(1(4(2(2(5(4(x1)))))))
   5^1(3(3(4(5(4(0(x1))))))) -> 5^1(3(5(4(3(4(0(x1)))))))
   5^1(3(4(1(3(4(3(1(1(x1))))))))) -> 5^1(3(4(3(1(4(3(1(1(x1)))))))))
   5^1(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5^1(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5^1(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5^1(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5^1(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5^1(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5^1(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   5^1(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5^1(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5^1(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5^1(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   5^1(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5^1(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(108) QDPOrderProof (EQUIVALENT)
We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.

   5^1(1(2(4(2(5(4(x1))))))) -> 5^1(1(4(2(2(5(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)) = 1
   POL(3(x_1)) = 0
   POL(4(x_1)) = 0
   POL(5(x_1)) = 0
   POL(5^1(x_1)) = x_1

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:

   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))


----------------------------------------

(109)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   5^1(3(3(4(5(4(0(x1))))))) -> 5^1(3(5(4(3(4(0(x1)))))))
   5^1(3(4(1(3(4(3(1(1(x1))))))))) -> 5^1(3(4(3(1(4(3(1(1(x1)))))))))
   5^1(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5^1(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5^1(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5^1(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5^1(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5^1(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5^1(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   5^1(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5^1(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5^1(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5^1(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   5^1(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5^1(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(110) QDPOrderProof (EQUIVALENT)
We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.

   5^1(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5^1(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
The remaining pairs can at least be oriented weakly.
Used ordering:  Polynomial interpretation [POLO]:

   POL(0(x_1)) = 1
   POL(1(x_1)) = 0
   POL(2(x_1)) = 1
   POL(3(x_1)) = 1
   POL(4(x_1)) = x_1
   POL(5(x_1)) = 0
   POL(5^1(x_1)) = x_1

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:

   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))


----------------------------------------

(111)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   5^1(3(3(4(5(4(0(x1))))))) -> 5^1(3(5(4(3(4(0(x1)))))))
   5^1(3(4(1(3(4(3(1(1(x1))))))))) -> 5^1(3(4(3(1(4(3(1(1(x1)))))))))
   5^1(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5^1(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5^1(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5^1(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5^1(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5^1(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5^1(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   5^1(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5^1(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5^1(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5^1(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(112) QDPOrderProof (EQUIVALENT)
We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.

   5^1(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5^1(0(0(5(3(1(0(1(3(1(1(5(1(0(3(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)) = 0
   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:

   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))


----------------------------------------

(113)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   5^1(3(3(4(5(4(0(x1))))))) -> 5^1(3(5(4(3(4(0(x1)))))))
   5^1(3(4(1(3(4(3(1(1(x1))))))))) -> 5^1(3(4(3(1(4(3(1(1(x1)))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5^1(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5^1(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5^1(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5^1(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5^1(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   5^1(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5^1(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5^1(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5^1(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(114) QDPOrderProof (EQUIVALENT)
We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.

   5^1(3(3(4(5(4(0(x1))))))) -> 5^1(3(5(4(3(4(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)) = 0
   POL(2(x_1)) = 0
   POL(3(x_1)) = x_1
   POL(4(x_1)) = 1
   POL(5(x_1)) = 0
   POL(5^1(x_1)) = x_1

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:

   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))


----------------------------------------

(115)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   5^1(3(4(1(3(4(3(1(1(x1))))))))) -> 5^1(3(4(3(1(4(3(1(1(x1)))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5^1(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5^1(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5^1(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5^1(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5^1(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   5^1(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5^1(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5^1(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5^1(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(116) QDPOrderProof (EQUIVALENT)
We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.

   5^1(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5^1(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(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)) = x_1
   POL(3(x_1)) = x_1
   POL(4(x_1)) = 1
   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(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))


----------------------------------------

(117)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   5^1(3(4(1(3(4(3(1(1(x1))))))))) -> 5^1(3(4(3(1(4(3(1(1(x1)))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5^1(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5^1(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5^1(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5^1(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5^1(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5^1(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5^1(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5^1(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(118) QDPOrderProof (EQUIVALENT)
We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.

   5^1(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5^1(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(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)) = 0
   POL(2(x_1)) = 1
   POL(3(x_1)) = x_1
   POL(4(x_1)) = 1 + x_1
   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(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))


----------------------------------------

(119)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   5^1(3(4(1(3(4(3(1(1(x1))))))))) -> 5^1(3(4(3(1(4(3(1(1(x1)))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5^1(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5^1(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5^1(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5^1(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5^1(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5^1(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(120) QDPOrderProof (EQUIVALENT)
We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.

   5^1(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5^1(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(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)) = 1
   POL(3(x_1)) = x_1
   POL(4(x_1)) = 0
   POL(5(x_1)) = 0
   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(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))


----------------------------------------

(121)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   5^1(3(4(1(3(4(3(1(1(x1))))))))) -> 5^1(3(4(3(1(4(3(1(1(x1)))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5^1(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5^1(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5^1(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5^1(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(122) 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(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))

Used ordering: Polynomial interpretation [POLO]:

   POL(0(x_1)) = 2*x_1
   POL(1(x_1)) = 1 + x_1
   POL(2(x_1)) = 2*x_1
   POL(3(x_1)) = x_1
   POL(4(x_1)) = x_1
   POL(5(x_1)) = x_1
   POL(5^1(x_1)) = x_1


----------------------------------------

(123)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   5^1(3(4(1(3(4(3(1(1(x1))))))))) -> 5^1(3(4(3(1(4(3(1(1(x1)))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5^1(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5^1(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5^1(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5^1(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(124) QDPOrderProof (EQUIVALENT)
We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.

   5^1(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5^1(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(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(3(x_1)) = x_1
   POL(4(x_1)) = x_1
   POL(5(x_1)) = 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(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))


----------------------------------------

(125)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   5^1(3(4(1(3(4(3(1(1(x1))))))))) -> 5^1(3(4(3(1(4(3(1(1(x1)))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5^1(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5^1(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5^1(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(126) 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(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5^1(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))

Strictly oriented rules of the TRS R:

   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(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)) = 2*x_1
   POL(5(x_1)) = x_1
   POL(5^1(x_1)) = x_1


----------------------------------------

(127)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   5^1(3(4(1(3(4(3(1(1(x1))))))))) -> 5^1(3(4(3(1(4(3(1(1(x1)))))))))
   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5^1(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(128) 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(3(4(1(3(4(3(1(1(x1))))))))) -> 5^1(3(4(3(1(4(3(1(1(x1)))))))))

Strictly oriented rules of the TRS R:

   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))

Used ordering: Polynomial interpretation [POLO]:

   POL(0(x_1)) = x_1
   POL(1(x_1)) = 2*x_1
   POL(2(x_1)) = 2 + 2*x_1
   POL(3(x_1)) = 2 + 2*x_1
   POL(4(x_1)) = 2 + 2*x_1
   POL(5(x_1)) = x_1
   POL(5^1(x_1)) = 2*x_1


----------------------------------------

(129)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5^1(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(130) 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(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Used ordering: Polynomial interpretation [POLO]:

   POL(0(x_1)) = 2*x_1
   POL(1(x_1)) = 2 + x_1
   POL(2(x_1)) = x_1
   POL(3(x_1)) = x_1
   POL(4(x_1)) = x_1
   POL(5(x_1)) = 2*x_1
   POL(5^1(x_1)) = 2*x_1


----------------------------------------

(131)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5^1(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(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 rules of the TRS R:

   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))

Used ordering: Polynomial interpretation [POLO]:

   POL(0(x_1)) = x_1
   POL(1(x_1)) = 2*x_1
   POL(2(x_1)) = 2*x_1
   POL(3(x_1)) = x_1
   POL(4(x_1)) = x_1
   POL(5(x_1)) = 2 + 2*x_1
   POL(5^1(x_1)) = 2*x_1


----------------------------------------

(133)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5^1(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(134) 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(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))

Used ordering: Polynomial interpretation [POLO]:

   POL(0(x_1)) = x_1
   POL(1(x_1)) = 2*x_1
   POL(2(x_1)) = x_1
   POL(3(x_1)) = 1 + 3*x_1
   POL(4(x_1)) = 1 + 2*x_1
   POL(5(x_1)) = 1 + 2*x_1
   POL(5^1(x_1)) = 2*x_1


----------------------------------------

(135)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   5^1(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5^1(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(136) DependencyGraphProof (EQUIVALENT)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node.
----------------------------------------

(137)
TRUE

----------------------------------------

(138)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   4^1(4(2(0(0(3(3(3(x1)))))))) -> 4^1(4(0(0(3(2(3(3(x1))))))))
   4^1(2(5(4(0(1(2(x1))))))) -> 4^1(0(5(2(4(1(2(x1)))))))
   4^1(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4^1(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   4^1(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4^1(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4^1(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4^1(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4^1(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4^1(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4^1(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(139) QDPOrderProof (EQUIVALENT)
We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.

   4^1(2(5(4(0(1(2(x1))))))) -> 4^1(0(5(2(4(1(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)) = 1
   POL(3(x_1)) = 0
   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:

   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))


----------------------------------------

(140)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   4^1(4(2(0(0(3(3(3(x1)))))))) -> 4^1(4(0(0(3(2(3(3(x1))))))))
   4^1(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4^1(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   4^1(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4^1(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4^1(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4^1(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4^1(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4^1(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4^1(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(141) 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(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4^1(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(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)) = 0
   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:

   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))


----------------------------------------

(142)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   4^1(4(2(0(0(3(3(3(x1)))))))) -> 4^1(4(0(0(3(2(3(3(x1))))))))
   4^1(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4^1(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4^1(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4^1(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4^1(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4^1(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4^1(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(143) QDPOrderProof (EQUIVALENT)
We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.

   4^1(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4^1(1(5(3(1(1(4(0(4(5(3(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)) = 1 + x_1
   POL(2(x_1)) = 0
   POL(3(x_1)) = 0
   POL(4(x_1)) = 0
   POL(4^1(x_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:

   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))


----------------------------------------

(144)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   4^1(4(2(0(0(3(3(3(x1)))))))) -> 4^1(4(0(0(3(2(3(3(x1))))))))
   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4^1(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4^1(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4^1(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4^1(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4^1(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(145) QDPOrderProof (EQUIVALENT)
We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.

   4^1(4(2(0(0(3(3(3(x1)))))))) -> 4^1(4(0(0(3(2(3(3(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
   POL(3(x_1)) = 0
   POL(4(x_1)) = x_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:

   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))


----------------------------------------

(146)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4^1(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4^1(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4^1(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4^1(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4^1(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(147) QDPOrderProof (EQUIVALENT)
We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.

   4^1(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4^1(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(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)) = 1
   POL(2(x_1)) = x_1
   POL(3(x_1)) = 0
   POL(4(x_1)) = 0
   POL(4^1(x_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:

   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))


----------------------------------------

(148)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   4^1(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4^1(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   4^1(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4^1(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4^1(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(149) 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(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4^1(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))

Strictly oriented rules of the TRS R:

   4(1(0(5(5(1(4(4(3(1(3(2(4(x1))))))))))))) -> 4(1(5(3(1(1(4(0(4(5(3(2(4(x1)))))))))))))
   1(5(3(5(5(2(2(3(2(1(1(0(4(1(0(x1))))))))))))))) -> 1(5(5(3(3(5(2(2(1(2(4(1(0(1(0(x1)))))))))))))))
   0(4(0(4(1(0(2(4(0(1(3(0(1(4(3(4(5(x1))))))))))))))))) -> 0(4(0(4(1(0(2(4(1(0(3(0(1(4(3(4(5(x1)))))))))))))))))
   1(4(1(2(0(1(3(0(4(0(1(4(5(2(4(3(5(0(x1)))))))))))))))))) -> 1(4(1(2(0(1(3(0(4(1(0(4(5(2(4(3(5(0(x1))))))))))))))))))
   4(0(2(5(2(5(1(0(4(2(3(3(4(5(2(2(1(0(1(2(0(x1))))))))))))))))))))) -> 4(0(2(5(5(0(5(2(3(3(2(2(1(4(4(2(1(1(0(2(0(x1)))))))))))))))))))))
   3(1(0(1(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1)))))))))))))))))))))) -> 3(1(1(0(3(3(4(4(3(4(3(0(2(2(2(5(1(0(2(5(3(0(x1))))))))))))))))))))))
   0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(2(1(5(1(3(1(0(x1))))))))))))))))))))))))) -> 0(4(4(3(1(5(3(0(1(2(2(0(2(1(2(3(0(3(1(2(5(1(3(1(0(x1)))))))))))))))))))))))))
   0(2(0(2(2(2(4(3(4(5(1(1(5(0(1(4(2(2(5(4(4(4(5(2(2(x1))))))))))))))))))))))))) -> 0(2(0(2(2(2(4(3(4(5(1(1(5(1(0(4(2(2(5(4(4(4(5(2(2(x1)))))))))))))))))))))))))
   4(5(5(5(2(1(1(3(4(2(1(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1))))))))))))))))))))))))))) -> 4(5(5(5(2(1(1(3(4(1(2(2(5(3(4(3(0(5(4(5(2(4(4(2(2(0(0(x1)))))))))))))))))))))))))))
   5(4(0(1(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1))))))))))))))))))))))))))) -> 5(4(1(0(4(4(5(2(5(1(4(5(4(4(3(5(3(5(5(2(1(4(3(2(5(4(4(x1)))))))))))))))))))))))))))
   3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(0(1(2(0(2(5(0(2(1(0(3(2(x1)))))))))))))))))))))))))))))) -> 3(1(0(2(3(2(5(0(5(4(4(0(4(5(4(1(5(2(1(0(2(0(2(5(0(2(1(0(3(2(x1))))))))))))))))))))))))))))))

Used ordering: Polynomial interpretation [POLO]:

   POL(0(x_1)) = 2*x_1
   POL(1(x_1)) = 2 + 2*x_1
   POL(2(x_1)) = 2*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)) = x_1


----------------------------------------

(150)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   4^1(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4^1(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4^1(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   5(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(151) 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(3(4(1(3(4(3(1(1(x1))))))))) -> 5(3(4(3(1(4(3(1(1(x1)))))))))
   5(0(0(5(1(3(0(1(3(1(1(5(1(0(3(x1))))))))))))))) -> 5(0(0(5(3(1(0(1(3(1(1(5(1(0(3(x1)))))))))))))))
   0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(1(3(5(1(1(x1))))))))))))))))))))))))))) -> 0(2(4(4(1(4(0(2(4(1(1(5(5(0(5(4(5(1(3(5(2(2(3(5(1(1(1(x1)))))))))))))))))))))))))))

Used ordering: Polynomial interpretation [POLO]:

   POL(0(x_1)) = 1 + 2*x_1
   POL(1(x_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(4^1(x_1)) = 2*x_1
   POL(5(x_1)) = x_1


----------------------------------------

(152)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   4^1(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4^1(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4^1(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   4(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(153) 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(1(0(0(5(2(1(3(2(5(5(5(4(1(5(3(x1)))))))))))))))) -> 4(1(2(0(4(2(1(5(0(5(5(3(1(5(5(3(x1))))))))))))))))

Used ordering: Polynomial interpretation [POLO]:

   POL(0(x_1)) = x_1
   POL(1(x_1)) = 2*x_1
   POL(2(x_1)) = 2 + 2*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)) = x_1


----------------------------------------

(154)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   4^1(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4^1(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   4^1(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4^1(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(155) 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(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4^1(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1))))))))))))))))))))))))))))))

Strictly oriented rules of the TRS R:

   3(2(2(2(4(4(1(0(1(3(2(0(2(x1))))))))))))) -> 3(2(2(2(4(1(0(4(1(3(2(0(2(x1)))))))))))))
   0(3(4(5(1(0(0(3(0(5(2(0(1(3(3(1(1(5(x1)))))))))))))))))) -> 0(3(1(4(5(0(0(3(0(5(2(0(1(3(3(1(1(5(x1))))))))))))))))))
   5(4(3(3(3(0(5(5(5(1(4(5(0(3(3(5(1(4(3(x1))))))))))))))))))) -> 5(4(3(3(3(0(5(5(1(5(4(5(0(3(3(5(1(4(3(x1)))))))))))))))))))
   5(2(4(0(4(5(0(1(2(1(4(4(0(4(1(5(0(3(0(4(5(0(x1)))))))))))))))))))))) -> 5(2(4(0(4(5(0(1(2(1(0(4(4(1(4(5(0(0(3(4(5(0(x1))))))))))))))))))))))
   5(3(0(5(4(1(1(0(5(2(0(5(5(2(4(0(4(2(4(0(2(3(4(x1))))))))))))))))))))))) -> 5(3(5(0(1(1(4(2(5(5(0(5(0(2(2(4(0(0(4(4(2(3(4(x1)))))))))))))))))))))))
   3(4(3(3(3(1(3(1(4(1(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1)))))))))))))))))))))))))))))) -> 3(4(3(3(3(1(3(1(1(4(5(3(0(5(2(1(1(2(1(4(3(3(3(1(1(5(0(0(0(2(x1))))))))))))))))))))))))))))))
   4(0(5(2(3(2(1(5(2(5(5(5(1(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(3(x1)))))))))))))))))))))))))))))) -> 4(0(5(2(3(2(1(5(2(5(5(1(5(1(3(3(2(5(3(3(1(4(4(2(0(2(3(1(4(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)) = 2*x_1
   POL(3(x_1)) = 2*x_1
   POL(4(x_1)) = 2*x_1
   POL(4^1(x_1)) = x_1
   POL(5(x_1)) = 2*x_1


----------------------------------------

(156)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   4^1(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4^1(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(157) 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(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4^1(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))

Strictly oriented rules of the TRS R:

   4(2(5(4(0(1(2(x1))))))) -> 4(0(5(2(4(1(2(x1)))))))
   0(3(3(4(5(0(0(4(x1)))))))) -> 0(0(4(3(5(3(0(4(x1))))))))
   0(2(2(4(4(3(0(3(0(4(2(5(5(5(3(x1))))))))))))))) -> 3(0(0(4(2(2(0(4(3(5(4(5(2(5(3(x1)))))))))))))))
   1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(4(0(0(5(4(3(3(4(0(2(0(x1)))))))))))))))))))))))))))) -> 1(4(5(3(1(2(3(0(2(2(5(0(4(2(5(1(4(0(4(0(5(4(3(3(4(0(2(0(x1))))))))))))))))))))))))))))
   4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(4(0(1(2(4(4(5(1(0(5(4(1(x1)))))))))))))))))))))))))))))) -> 4(2(5(5(4(2(0(1(0(4(0(5(5(4(5(1(2(1(0(4(1(2(4(4(5(1(0(5(4(1(x1))))))))))))))))))))))))))))))

Used ordering: Polynomial interpretation [POLO]:

   POL(0(x_1)) = 2 + 3*x_1
   POL(1(x_1)) = x_1
   POL(2(x_1)) = x_1
   POL(3(x_1)) = x_1
   POL(4(x_1)) = 1 + 3*x_1
   POL(4^1(x_1)) = x_1
   POL(5(x_1)) = x_1


----------------------------------------

(158)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   4^1(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4^1(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))

The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(159) 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(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4^1(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))

Strictly oriented rules of the TRS R:

   4(5(4(4(1(1(2(5(3(5(4(3(5(4(0(4(1(0(3(2(5(x1))))))))))))))))))))) -> 4(5(4(4(1(1(5(2(3(5(4(3(5(4(0(4(1(0(3(2(5(x1)))))))))))))))))))))
   5(3(1(1(3(2(5(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1))))))))))))))))))))))) -> 5(3(1(1(3(5(2(2(5(1(0(4(0(4(4(0(0(2(5(4(4(5(4(x1)))))))))))))))))))))))

Used ordering: Polynomial interpretation [POLO]:

   POL(0(x_1)) = x_1
   POL(1(x_1)) = x_1
   POL(2(x_1)) = 1 + 2*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)) = 3 + 3*x_1


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(160)
Obligation:
Q DP problem:
P is empty.
The TRS R consists of the following rules:

   3(0(2(2(0(1(0(x1))))))) -> 0(2(0(2(3(1(0(x1)))))))
   5(3(3(4(5(4(0(x1))))))) -> 5(3(5(4(3(4(0(x1)))))))
   5(1(2(4(2(5(4(x1))))))) -> 5(1(4(2(2(5(4(x1)))))))
   4(4(2(0(0(3(3(3(x1)))))))) -> 4(4(0(0(3(2(3(3(x1))))))))
   0(4(0(0(0(3(2(1(4(x1))))))))) -> 0(4(0(0(0(2(3(1(4(x1)))))))))
   2(4(4(3(1(5(3(3(4(5(5(0(x1)))))))))))) -> 2(4(4(3(1(5(3(3(5(4(5(0(x1))))))))))))
   0(2(3(4(0(2(0(1(2(2(1(3(x1)))))))))))) -> 0(2(3(4(2(0(0(1(2(2(1(3(x1))))))))))))
   1(5(3(1(3(2(4(1(0(2(2(2(1(x1))))))))))))) -> 1(5(3(1(2(3(4(1(0(2(2(2(1(x1)))))))))))))
   2(0(0(3(4(2(2(4(1(5(4(0(5(x1))))))))))))) -> 2(0(0(4(3(2(2(4(1(5(4(0(5(x1)))))))))))))
   1(1(2(0(1(0(1(2(4(2(1(0(2(4(x1)))))))))))))) -> 1(1(2(0(1(0(1(4(2(2(1(0(2(4(x1))))))))))))))
   2(4(2(0(3(3(4(0(0(2(0(4(1(0(2(x1))))))))))))))) -> 2(4(2(3(0(3(4(0(0(2(0(4(1(0(2(x1)))))))))))))))
   1(4(3(1(4(5(4(4(0(5(2(4(2(1(1(3(x1)))))))))))))))) -> 1(4(3(1(4(4(5(4(0(5(2(4(2(1(1(3(x1))))))))))))))))
   3(4(5(5(4(3(4(4(1(3(3(4(2(1(1(4(1(x1))))))))))))))))) -> 3(4(5(5(4(3(4(4(1(3(4(3(2(1(1(4(1(x1)))))))))))))))))
   0(1(1(4(0(4(0(1(5(2(3(4(3(0(5(5(4(3(x1)))))))))))))))))) -> 0(1(1(4(0(4(0(1(5(2(3(4(3(5(0(5(4(3(x1))))))))))))))))))
   5(2(2(5(1(0(2(1(2(5(0(2(4(5(2(3(3(4(x1)))))))))))))))))) -> 5(2(2(5(1(0(2(1(2(0(5(2(4(5(2(3(3(4(x1))))))))))))))))))
   3(2(2(2(4(5(2(1(1(0(3(4(3(4(4(0(4(5(5(3(x1)))))))))))))))))))) -> 3(2(2(2(4(5(2(1(1(0(4(3(3(4(4(0(4(5(5(3(x1))))))))))))))))))))
   2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(3(0(5(3(5(4(x1))))))))))))))))))))))) -> 2(0(5(3(5(3(3(2(4(0(2(4(4(0(5(4(1(0(3(5(3(5(4(x1)))))))))))))))))))))))
   5(3(3(5(4(4(2(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1))))))))))))))))))))))))))) -> 5(3(3(5(4(2(4(1(1(2(4(2(5(5(3(2(2(0(5(1(5(5(1(3(4(5(0(x1)))))))))))))))))))))))))))
   2(2(0(2(5(0(2(0(0(2(2(5(3(3(4(2(5(2(4(2(2(4(0(3(3(3(4(x1))))))))))))))))))))))))))) -> 2(2(0(2(5(0(2(0(0(2(2(5(3(3(2(4(5(2(4(2(2(4(0(3(3(3(4(x1)))))))))))))))))))))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(161) PisEmptyProof (EQUIVALENT)
The TRS P is empty. Hence, there is no (P,Q,R) chain.
----------------------------------------

(162)
YES