YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 483 ms]
(4) QTRS
(5) QTRSRRRProof [EQUIVALENT, 119 ms]
(6) QTRS
(7) DependencyPairsProof [EQUIVALENT, 2311 ms]
(8) QDP
(9) QDPOrderProof [EQUIVALENT, 2594 ms]
(10) QDP
(11) DependencyGraphProof [EQUIVALENT, 0 ms]
(12) AND
    (13) QDP
        (14) QDPOrderProof [EQUIVALENT, 657 ms]
        (15) QDP
        (16) DependencyGraphProof [EQUIVALENT, 0 ms]
        (17) AND
            (18) QDP
                (19) QDPOrderProof [EQUIVALENT, 139 ms]
                (20) QDP
                (21) QDPOrderProof [EQUIVALENT, 132 ms]
                (22) QDP
                (23) DependencyGraphProof [EQUIVALENT, 0 ms]
                (24) AND
                    (25) QDP
                        (26) QDPOrderProof [EQUIVALENT, 66 ms]
                        (27) QDP
                        (28) MRRProof [EQUIVALENT, 1693 ms]
                        (29) QDP
                        (30) MRRProof [EQUIVALENT, 2868 ms]
                        (31) QDP
                        (32) MRRProof [EQUIVALENT, 297 ms]
                        (33) QDP
                        (34) MRRProof [EQUIVALENT, 1535 ms]
                        (35) QDP
                        (36) MRRProof [EQUIVALENT, 220 ms]
                        (37) QDP
                        (38) MRRProof [EQUIVALENT, 184 ms]
                        (39) QDP
                        (40) MRRProof [EQUIVALENT, 99 ms]
                        (41) QDP
                        (42) DependencyGraphProof [EQUIVALENT, 0 ms]
                        (43) TRUE
                    (44) QDP
                        (45) QDPOrderProof [EQUIVALENT, 125 ms]
                        (46) QDP
                        (47) DependencyGraphProof [EQUIVALENT, 0 ms]
                        (48) AND
                            (49) QDP
                                (50) QDPOrderProof [EQUIVALENT, 87 ms]
                                (51) QDP
                                (52) QDPOrderProof [EQUIVALENT, 73 ms]
                                (53) QDP
                                (54) QDPOrderProof [EQUIVALENT, 79 ms]
                                (55) QDP
                                (56) QDPOrderProof [EQUIVALENT, 74 ms]
                                (57) QDP
                                (58) MRRProof [EQUIVALENT, 4424 ms]
                                (59) QDP
                                (60) MRRProof [EQUIVALENT, 2264 ms]
                                (61) QDP
                                (62) MRRProof [EQUIVALENT, 1792 ms]
                                (63) QDP
                                (64) MRRProof [EQUIVALENT, 307 ms]
                                (65) QDP
                                (66) MRRProof [EQUIVALENT, 233 ms]
                                (67) QDP
                                (68) MRRProof [EQUIVALENT, 83 ms]
                                (69) QDP
                                (70) MRRProof [EQUIVALENT, 67 ms]
                                (71) QDP
                                (72) DependencyGraphProof [EQUIVALENT, 0 ms]
                                (73) QDP
                                (74) QDPOrderProof [EQUIVALENT, 113 ms]
                                (75) QDP
                                (76) PisEmptyProof [EQUIVALENT, 0 ms]
                                (77) YES
                            (78) QDP
                                (79) QDPOrderProof [EQUIVALENT, 69 ms]
                                (80) QDP
                                (81) QDPOrderProof [EQUIVALENT, 70 ms]
                                (82) QDP
                                (83) QDPOrderProof [EQUIVALENT, 74 ms]
                                (84) QDP
                                (85) QDPOrderProof [EQUIVALENT, 68 ms]
                                (86) QDP
                                (87) QDPOrderProof [EQUIVALENT, 55 ms]
                                (88) QDP
                                (89) MRRProof [EQUIVALENT, 2886 ms]
                                (90) QDP
                                (91) QDPOrderProof [EQUIVALENT, 44 ms]
                                (92) QDP
                                (93) MRRProof [EQUIVALENT, 2131 ms]
                                (94) QDP
                                (95) MRRProof [EQUIVALENT, 358 ms]
                                (96) QDP
                                (97) MRRProof [EQUIVALENT, 198 ms]
                                (98) QDP
                                (99) MRRProof [EQUIVALENT, 127 ms]
                                (100) QDP
                                (101) MRRProof [EQUIVALENT, 279 ms]
                                (102) QDP
                                (103) MRRProof [EQUIVALENT, 117 ms]
                                (104) QDP
                                (105) MRRProof [EQUIVALENT, 82 ms]
                                (106) QDP
                                (107) DependencyGraphProof [EQUIVALENT, 0 ms]
                                (108) TRUE
            (109) QDP
                (110) QDPOrderProof [EQUIVALENT, 67 ms]
                (111) QDP
                (112) QDPOrderProof [EQUIVALENT, 63 ms]
                (113) QDP
                (114) MRRProof [EQUIVALENT, 3104 ms]
                (115) QDP
                (116) MRRProof [EQUIVALENT, 5710 ms]
                (117) QDP
                (118) MRRProof [EQUIVALENT, 2050 ms]
                (119) QDP
                (120) MRRProof [EQUIVALENT, 454 ms]
                (121) QDP
                (122) MRRProof [EQUIVALENT, 227 ms]
                (123) QDP
                (124) MRRProof [EQUIVALENT, 131 ms]
                (125) QDP
                (126) MRRProof [EQUIVALENT, 224 ms]
                (127) QDP
                (128) MRRProof [EQUIVALENT, 119 ms]
                (129) QDP
                (130) MRRProof [EQUIVALENT, 74 ms]
                (131) QDP
                (132) PisEmptyProof [EQUIVALENT, 0 ms]
                (133) YES
            (134) QDP
                (135) QDPOrderProof [EQUIVALENT, 75 ms]
                (136) QDP
                (137) QDPOrderProof [EQUIVALENT, 57 ms]
                (138) QDP
                (139) MRRProof [EQUIVALENT, 3045 ms]
                (140) QDP
                (141) MRRProof [EQUIVALENT, 2300 ms]
                (142) QDP
                (143) MRRProof [EQUIVALENT, 1539 ms]
                (144) QDP
                (145) MRRProof [EQUIVALENT, 179 ms]
                (146) QDP
                (147) MRRProof [EQUIVALENT, 188 ms]
                (148) QDP
                (149) MRRProof [EQUIVALENT, 112 ms]
                (150) QDP
                (151) MRRProof [EQUIVALENT, 130 ms]
                (152) QDP
                (153) MRRProof [EQUIVALENT, 87 ms]
                (154) QDP
                (155) DependencyGraphProof [EQUIVALENT, 0 ms]
                (156) TRUE
    (157) QDP
        (158) QDPOrderProof [EQUIVALENT, 87 ms]
        (159) QDP
        (160) QDPOrderProof [EQUIVALENT, 70 ms]
        (161) QDP
        (162) MRRProof [EQUIVALENT, 3633 ms]
        (163) QDP
        (164) MRRProof [EQUIVALENT, 1671 ms]
        (165) QDP
        (166) MRRProof [EQUIVALENT, 877 ms]
        (167) QDP
        (168) QDPOrderProof [EQUIVALENT, 40 ms]
        (169) QDP
        (170) MRRProof [EQUIVALENT, 383 ms]
        (171) QDP
        (172) MRRProof [EQUIVALENT, 877 ms]
        (173) QDP
        (174) MRRProof [EQUIVALENT, 276 ms]
        (175) QDP
        (176) MRRProof [EQUIVALENT, 153 ms]
        (177) QDP
        (178) MRRProof [EQUIVALENT, 159 ms]
        (179) QDP
        (180) PisEmptyProof [EQUIVALENT, 0 ms]
        (181) YES


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

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

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

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

Q is empty.

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

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

   POL(0(x_1)) = 5 + x_1
   POL(1(x_1)) = 8 + x_1
   POL(2(x_1)) = 9 + x_1
   POL(3(x_1)) = 9 + x_1
   POL(4(x_1)) = 9 + 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:

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




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

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

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

Q is empty.

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

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

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

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




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

(6)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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

Q is empty.

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

(7) DependencyPairsProof (EQUIVALENT)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
----------------------------------------

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

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

The TRS R consists of the following rules:

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

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

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


The following pairs can be oriented strictly and are deleted.

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


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

(10)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

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

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

(11) DependencyGraphProof (EQUIVALENT)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 54 less nodes.
----------------------------------------

(12)
Complex Obligation (AND)

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

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

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

The TRS R consists of the following rules:

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

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

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

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


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

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

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

The TRS R consists of the following rules:

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

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

(16) DependencyGraphProof (EQUIVALENT)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 3 SCCs with 22 less nodes.
----------------------------------------

(17)
Complex Obligation (AND)

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

(18)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

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

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

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


The following pairs can be oriented strictly and are deleted.

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

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

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


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

(20)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

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

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

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


The following pairs can be oriented strictly and are deleted.

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

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

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


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

(22)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

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

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

(23) DependencyGraphProof (EQUIVALENT)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 3 less nodes.
----------------------------------------

(24)
Complex Obligation (AND)

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

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

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

The TRS R consists of the following rules:

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

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

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


The following pairs can be oriented strictly and are deleted.

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

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


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

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

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

The TRS R consists of the following rules:

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

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

Strictly oriented rules of the TRS R:

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

Used ordering: Polynomial interpretation [POLO]:

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


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

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

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

The TRS R consists of the following rules:

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

Used ordering: Polynomial interpretation [POLO]:

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


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

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

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

The TRS R consists of the following rules:

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

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

(32) MRRProof (EQUIVALENT)
By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented.


Strictly oriented rules of the TRS R:

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

Used ordering: Polynomial interpretation [POLO]:

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


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

(33)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

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

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

(34) 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(4(2(2(5(2(3(3(2(0(1(0(x1)))))))))))) -> 2(4(2(5(2(2(3(3(2(0(1(0(x1))))))))))))

Used ordering: Polynomial interpretation [POLO]:

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


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

(35)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

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

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

(36) MRRProof (EQUIVALENT)
By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented.


Strictly oriented rules of the TRS R:

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

Used ordering: Polynomial interpretation [POLO]:

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


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

(37)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

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

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

(38) MRRProof (EQUIVALENT)
By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented.


Strictly oriented rules of the TRS R:

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

Used ordering: Polynomial interpretation [POLO]:

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


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

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

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

The TRS R consists of the following rules:

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

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

(40) MRRProof (EQUIVALENT)
By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented.

Strictly oriented dependency pairs:

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

Strictly oriented rules of the TRS R:

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

Used ordering: Polynomial interpretation [POLO]:

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


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

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

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

The TRS R consists of the following rules:

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

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

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

(43)
TRUE

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

(44)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

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

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

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


The following pairs can be oriented strictly and are deleted.

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

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

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


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

(46)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

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

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

(47) DependencyGraphProof (EQUIVALENT)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 1 less node.
----------------------------------------

(48)
Complex Obligation (AND)

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

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

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

The TRS R consists of the following rules:

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

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

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


The following pairs can be oriented strictly and are deleted.

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

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

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

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


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

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

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

The TRS R consists of the following rules:

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

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

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


The following pairs can be oriented strictly and are deleted.

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

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

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


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

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

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

The TRS R consists of the following rules:

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

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

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


The following pairs can be oriented strictly and are deleted.

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

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

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


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

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

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

The TRS R consists of the following rules:

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

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

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


The following pairs can be oriented strictly and are deleted.

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

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


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

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

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

The TRS R consists of the following rules:

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

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

(58) 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(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
   0(2(4(4(0(1(1(3(2(3(0(2(3(2(3(0(2(0(x1)))))))))))))))))) -> 0(2(4(4(1(0(0(1(3(2(3(2(3(3(2(2(0(0(x1))))))))))))))))))
   5(4(1(0(5(1(1(5(2(3(4(4(5(4(0(3(4(0(5(x1))))))))))))))))))) -> 5(4(1(0(5(1(1(5(2(3(4(4(5(4(3(0(4(0(5(x1)))))))))))))))))))
   1(2(2(1(2(2(0(2(0(3(0(5(2(3(3(0(2(5(2(0(1(x1))))))))))))))))))))) -> 1(2(2(1(2(2(0(2(3(0(0(5(3(2(3(0(5(2(1(0(2(x1)))))))))))))))))))))
   4(1(5(2(2(2(1(0(2(1(3(3(1(4(0(2(0(2(5(4(2(3(x1)))))))))))))))))))))) -> 4(2(1(5(2(2(1(3(1(2(0(3(1(4(2(0(0(5(2(4(2(3(x1))))))))))))))))))))))

Used ordering: Polynomial interpretation [POLO]:

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


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

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

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

The TRS R consists of the following rules:

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

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

(60) 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(0(4(1(3(1(5(0(2(4(4(5(x1)))))))))))) -> 1^1(0(4(1(1(3(5(0(2(4(4(5(x1))))))))))))
   1^1(1(3(5(2(1(1(3(5(0(5(0(3(x1))))))))))))) -> 1^1(1(1(1(3(5(2(5(3(0(0(5(3(x1)))))))))))))

Strictly oriented rules of the TRS R:

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

Used ordering: Polynomial interpretation [POLO]:

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


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

(61)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

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

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

(62) 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(0(1(5(5(0(2(0(5(5(2(4(1(1(1(3(3(3(5(0(3(1(1(4(3(2(0(2(5(4(x1)))))))))))))))))))))))))))))) -> 1^1(0(1(5(0(0(5(2(5(5(2(4(1(1(1(3(3(3(0(5(3(1(1(4(3(2(0(2(4(5(x1))))))))))))))))))))))))))))))

Strictly oriented rules of the TRS R:

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


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

(63)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

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

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

(64) 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(1(0(5(0(0(3(4(0(4(1(3(2(2(3(3(5(3(3(0(5(x1))))))))))))))))))))) -> 1^1(1(0(5(0(0(3(0(4(4(1(3(2(2(3(3(5(3(3(0(5(x1)))))))))))))))))))))

Strictly oriented rules of the TRS R:

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

Used ordering: Polynomial interpretation [POLO]:

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


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

(65)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

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

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

(66) MRRProof (EQUIVALENT)
By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented.


Strictly oriented rules of the TRS R:

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


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

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

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

The TRS R consists of the following rules:

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

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

(68) 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(4(2(2(5(2(3(3(2(0(1(0(x1)))))))))))) -> 2(4(2(5(2(2(3(3(2(0(1(0(x1))))))))))))

Used ordering: Polynomial interpretation [POLO]:

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


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

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

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

The TRS R consists of the following rules:

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

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

Used ordering: Polynomial interpretation [POLO]:

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


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

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

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

The TRS R consists of the following rules:

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

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

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

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

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

The TRS R consists of the following rules:

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

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

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


The following pairs can be oriented strictly and are deleted.

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

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

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


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

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

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

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

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

(77)
YES

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

(78)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

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

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

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


The following pairs can be oriented strictly and are deleted.

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

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

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


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

(80)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

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

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

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


The following pairs can be oriented strictly and are deleted.

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

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

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


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

(82)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

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

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

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


The following pairs can be oriented strictly and are deleted.

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

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

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


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

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

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

The TRS R consists of the following rules:

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

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

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

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


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

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

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

The TRS R consists of the following rules:

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

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

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

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


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

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

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

The TRS R consists of the following rules:

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

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

(89) MRRProof (EQUIVALENT)
By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented.

Strictly oriented dependency pairs:

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

Strictly oriented rules of the TRS R:

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

Used ordering: Polynomial interpretation [POLO]:

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


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

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

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

The TRS R consists of the following rules:

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

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

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


The following pairs can be oriented strictly and are deleted.

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

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

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


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

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

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

The TRS R consists of the following rules:

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

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


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

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

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

The TRS R consists of the following rules:

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

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

Used ordering: Polynomial interpretation [POLO]:

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


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

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

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

The TRS R consists of the following rules:

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

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


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

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

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

The TRS R consists of the following rules:

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

Used ordering: Polynomial interpretation [POLO]:

   POL(0(x_1)) = 2*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)) = 3 + x_1
   POL(5(x_1)) = 2*x_1


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

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

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

The TRS R consists of the following rules:

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

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

Used ordering: Polynomial interpretation [POLO]:

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


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

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

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

The TRS R consists of the following rules:

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

Used ordering: Polynomial interpretation [POLO]:

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


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

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

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

The TRS R consists of the following rules:

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

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

(105) 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(0(4(1(3(1(5(0(2(4(4(5(x1)))))))))))) -> 1(0(4(1(1(3(5(0(2(4(4(5(x1))))))))))))
   0(3(1(3(3(1(5(5(0(2(3(3(0(0(0(x1))))))))))))))) -> 0(3(1(3(1(3(5(5(0(2(3(3(0(0(0(x1)))))))))))))))
   5(0(4(4(3(1(3(1(0(0(2(2(2(2(5(5(4(1(2(x1))))))))))))))))))) -> 5(0(4(4(3(1(1(3(0(0(2(2(2(2(5(5(4(1(2(x1)))))))))))))))))))
   4(1(2(5(5(0(0(3(3(4(4(3(1(1(0(3(5(3(5(3(5(0(4(3(1(2(3(0(1(x1))))))))))))))))))))))))))))) -> 4(1(2(5(5(0(0(3(3(4(4(1(3(1(0(3(5(3(5(3(5(0(4(3(1(2(3(0(1(x1)))))))))))))))))))))))))))))

Used ordering: Polynomial interpretation [POLO]:

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


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

(106)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

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

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

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

(108)
TRUE

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

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

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

The TRS R consists of the following rules:

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

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

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

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

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


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

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

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

The TRS R consists of the following rules:

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

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

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


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

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

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

The TRS R consists of the following rules:

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

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

(114) 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(5(4(0(0(4(5(4(4(2(5(1(5(2(1(x1))))))))))))))) -> 5(5(4(0(0(4(5(4(2(4(5(1(5(2(1(x1)))))))))))))))
   2(4(0(4(1(1(4(0(1(1(0(1(0(4(4(2(3(3(3(5(3(x1))))))))))))))))))))) -> 2(4(0(4(1(4(1(0(1(1(0(1(0(4(2(4(3(3(3(5(3(x1)))))))))))))))))))))
   3(0(0(2(4(2(4(3(1(0(2(0(0(3(0(0(5(1(1(1(5(5(3(1(1(4(3(1(3(x1))))))))))))))))))))))))))))) -> 3(0(0(2(2(4(4(3(1(0(2(0(0(3(0(0(5(1(1(1(5(5(3(1(1(4(3(1(3(x1)))))))))))))))))))))))))))))

Used ordering: Polynomial interpretation [POLO]:

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


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

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

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

The TRS R consists of the following rules:

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

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

(116) 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(0(1(1(0(3(4(1(2(1(2(3(1(4(2(1(4(2(3(4(1(2(x1)))))))))))))))))))))) -> 4(0(1(1(0(3(4(1(2(1(2(3(1(4(2(1(4(2(4(3(1(2(x1))))))))))))))))))))))
   2(4(4(4(0(5(3(1(0(4(3(3(4(3(4(0(1(1(4(5(0(2(5(4(0(1(x1)))))))))))))))))))))))))) -> 2(4(4(4(0(5(3(1(4(0(3(3(4(4(3(0(1(1(4(2(5(5(0(4(0(1(x1))))))))))))))))))))))))))
   1(0(1(5(5(0(2(0(5(5(2(4(1(1(1(3(3(3(5(0(3(1(1(4(3(2(0(2(5(4(x1)))))))))))))))))))))))))))))) -> 1(0(1(5(0(0(5(2(5(5(2(4(1(1(1(3(3(3(0(5(3(1(1(4(3(2(0(2(4(5(x1))))))))))))))))))))))))))))))

Used ordering: Polynomial interpretation [POLO]:

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


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

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

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

The TRS R consists of the following rules:

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

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

(118) 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(3(4(1(0(3(4(5(5(3(0(2(2(2(4(0(1(4(2(2(4(0(2(1(3(4(5(3(x1)))))))))))))))))))))))))))) -> 0^1(3(4(1(0(3(4(5(5(3(0(2(2(2(0(4(1(4(2(2(4(0(2(1(3(4(5(3(x1))))))))))))))))))))))))))))

Strictly oriented rules of the TRS R:

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

Used ordering: Polynomial interpretation [POLO]:

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


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

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

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

The TRS R consists of the following rules:

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

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

(120) 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(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
   0(2(4(4(0(1(1(3(2(3(0(2(3(2(3(0(2(0(x1)))))))))))))))))) -> 0(2(4(4(1(0(0(1(3(2(3(2(3(3(2(2(0(0(x1))))))))))))))))))
   5(4(1(0(5(1(1(5(2(3(4(4(5(4(0(3(4(0(5(x1))))))))))))))))))) -> 5(4(1(0(5(1(1(5(2(3(4(4(5(4(3(0(4(0(5(x1)))))))))))))))))))
   1(2(2(1(2(2(0(2(0(3(0(5(2(3(3(0(2(5(2(0(1(x1))))))))))))))))))))) -> 1(2(2(1(2(2(0(2(3(0(0(5(3(2(3(0(5(2(1(0(2(x1)))))))))))))))))))))
   4(1(5(2(2(2(1(0(2(1(3(3(1(4(0(2(0(2(5(4(2(3(x1)))))))))))))))))))))) -> 4(2(1(5(2(2(1(3(1(2(0(3(1(4(2(0(0(5(2(4(2(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)) = x_1
   POL(2(x_1)) = 2*x_1
   POL(3(x_1)) = 1 + 2*x_1
   POL(4(x_1)) = 2*x_1
   POL(5(x_1)) = x_1


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

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

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

The TRS R consists of the following rules:

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

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

Strictly oriented rules of the TRS R:

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

Used ordering: Polynomial interpretation [POLO]:

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


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

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

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

The TRS R consists of the following rules:

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

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

(124) 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(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0^1(1(3(3(2(3(2(0(0(0(4(x1)))))))))))

Strictly oriented rules of the TRS R:

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


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

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

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

The TRS R consists of the following rules:

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

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


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

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

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

The TRS R consists of the following rules:

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

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

Used ordering: Polynomial interpretation [POLO]:

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


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

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

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

The TRS R consists of the following rules:

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

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

Strictly oriented rules of the TRS R:

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


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

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

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

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

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

(133)
YES

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

(134)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

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

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

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


The following pairs can be oriented strictly and are deleted.

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

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


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

(136)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

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

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

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


The following pairs can be oriented strictly and are deleted.

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

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


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

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

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

The TRS R consists of the following rules:

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

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

(139) 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(0(1(1(0(3(4(1(2(1(2(3(1(4(2(1(4(2(3(4(1(2(x1)))))))))))))))))))))) -> 4(0(1(1(0(3(4(1(2(1(2(3(1(4(2(1(4(2(4(3(1(2(x1))))))))))))))))))))))
   2(4(4(4(0(5(3(1(0(4(3(3(4(3(4(0(1(1(4(5(0(2(5(4(0(1(x1)))))))))))))))))))))))))) -> 2(4(4(4(0(5(3(1(4(0(3(3(4(4(3(0(1(1(4(2(5(5(0(4(0(1(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(3(x_1)) = 2*x_1
   POL(4(x_1)) = 2 + 2*x_1
   POL(5(x_1)) = x_1
   POL(5^1(x_1)) = x_1


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

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

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

The TRS R consists of the following rules:

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

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

(141) 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(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
   0(2(4(4(0(1(1(3(2(3(0(2(3(2(3(0(2(0(x1)))))))))))))))))) -> 0(2(4(4(1(0(0(1(3(2(3(2(3(3(2(2(0(0(x1))))))))))))))))))
   1(2(2(1(2(2(0(2(0(3(0(5(2(3(3(0(2(5(2(0(1(x1))))))))))))))))))))) -> 1(2(2(1(2(2(0(2(3(0(0(5(3(2(3(0(5(2(1(0(2(x1)))))))))))))))))))))
   4(1(5(2(2(2(1(0(2(1(3(3(1(4(0(2(0(2(5(4(2(3(x1)))))))))))))))))))))) -> 4(2(1(5(2(2(1(3(1(2(0(3(1(4(2(0(0(5(2(4(2(3(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)) = 1 + 2*x_1
   POL(4(x_1)) = 2*x_1
   POL(5(x_1)) = x_1
   POL(5^1(x_1)) = 2*x_1


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

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

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

The TRS R consists of the following rules:

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

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

(143) MRRProof (EQUIVALENT)
By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented.

Strictly oriented dependency pairs:

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

Strictly oriented rules of the TRS R:

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

Used ordering: Polynomial interpretation [POLO]:

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


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

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

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

The TRS R consists of the following rules:

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

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

(145) 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(4(2(2(5(2(3(3(2(0(1(0(x1)))))))))))) -> 2(4(2(5(2(2(3(3(2(0(1(0(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)) = 2*x_1
   POL(5(x_1)) = 2 + 2*x_1
   POL(5^1(x_1)) = 2*x_1


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

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

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

The TRS R consists of the following rules:

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

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

(147) MRRProof (EQUIVALENT)
By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented.


Strictly oriented rules of the TRS R:

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


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

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

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

The TRS R consists of the following rules:

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

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

Used ordering: Polynomial interpretation [POLO]:

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


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

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

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

The TRS R consists of the following rules:

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

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

Strictly oriented rules of the TRS R:

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

Used ordering: Polynomial interpretation [POLO]:

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


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

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

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

The TRS R consists of the following rules:

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

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

Strictly oriented rules of the TRS R:

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


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

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

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

The TRS R consists of the following rules:

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

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

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

(156)
TRUE

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

(157)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

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

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

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


The following pairs can be oriented strictly and are deleted.

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

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

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


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

(159)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

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

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

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


The following pairs can be oriented strictly and are deleted.

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

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

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


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

(161)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

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

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

(162) 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(1(1(0(3(4(1(2(1(2(3(1(4(2(1(4(2(3(4(1(2(x1)))))))))))))))))))))) -> 4^1(0(1(1(0(3(4(1(2(1(2(3(1(4(2(1(4(2(4(3(1(2(x1))))))))))))))))))))))

Strictly oriented rules of the TRS R:

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


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

(163)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

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

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

(164) 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(5(4(0(0(4(5(4(4(2(5(1(5(2(1(x1))))))))))))))) -> 5(5(4(0(0(4(5(4(2(4(5(1(5(2(1(x1)))))))))))))))
   0(1(3(4(0(0(4(4(1(5(1(2(0(0(2(5(2(4(5(x1))))))))))))))))))) -> 0(1(3(0(4(0(4(4(1(5(1(2(0(0(2(5(2(4(5(x1)))))))))))))))))))
   2(4(0(4(1(1(4(0(1(1(0(1(0(4(4(2(3(3(3(5(3(x1))))))))))))))))))))) -> 2(4(0(4(1(4(1(0(1(1(0(1(0(4(2(4(3(3(3(5(3(x1)))))))))))))))))))))
   1(1(0(5(0(0(3(4(0(4(1(3(2(2(3(3(5(3(3(0(5(x1))))))))))))))))))))) -> 1(1(0(5(0(0(3(0(4(4(1(3(2(2(3(3(5(3(3(0(5(x1)))))))))))))))))))))
   0(3(4(1(0(3(4(5(5(3(0(2(2(2(4(0(1(4(2(2(4(0(2(1(3(4(5(3(x1)))))))))))))))))))))))))))) -> 0(3(4(1(0(3(4(5(5(3(0(2(2(2(0(4(1(4(2(2(4(0(2(1(3(4(5(3(x1))))))))))))))))))))))))))))
   3(0(0(2(4(2(4(3(1(0(2(0(0(3(0(0(5(1(1(1(5(5(3(1(1(4(3(1(3(x1))))))))))))))))))))))))))))) -> 3(0(0(2(2(4(4(3(1(0(2(0(0(3(0(0(5(1(1(1(5(5(3(1(1(4(3(1(3(x1)))))))))))))))))))))))))))))

Used ordering: Polynomial interpretation [POLO]:

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


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

(165)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

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

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

(166) 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(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
   1(1(3(5(2(1(1(3(5(0(5(0(3(x1))))))))))))) -> 1(1(1(1(3(5(2(5(3(0(0(5(3(x1)))))))))))))
   3(5(4(1(4(2(2(2(5(0(5(2(4(0(2(x1))))))))))))))) -> 3(5(4(1(4(2(2(2(0(5(5(2(4(0(2(x1)))))))))))))))
   5(0(2(3(0(3(3(4(5(0(0(4(0(4(2(4(2(3(5(x1))))))))))))))))))) -> 5(0(2(3(0(3(3(4(0(5(0(4(0(4(2(4(2(3(5(x1)))))))))))))))))))
   4(4(1(4(2(5(0(3(2(2(5(5(3(4(0(0(3(4(1(2(5(4(2(1(x1)))))))))))))))))))))))) -> 4(4(1(4(2(0(5(3(2(2(5(5(3(4(0(0(3(4(1(2(5(4(2(1(x1))))))))))))))))))))))))

Used ordering: Polynomial interpretation [POLO]:

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


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

(167)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

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

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

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


The following pairs can be oriented strictly and are deleted.

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

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

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


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

(169)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

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

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

(170) 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(4(2(2(5(2(3(3(2(0(1(0(x1)))))))))))) -> 2(4(2(5(2(2(3(3(2(0(1(0(x1))))))))))))
   1(2(2(1(2(2(0(2(0(3(0(5(2(3(3(0(2(5(2(0(1(x1))))))))))))))))))))) -> 1(2(2(1(2(2(0(2(3(0(0(5(3(2(3(0(5(2(1(0(2(x1)))))))))))))))))))))
   4(1(5(2(2(2(1(0(2(1(3(3(1(4(0(2(0(2(5(4(2(3(x1)))))))))))))))))))))) -> 4(2(1(5(2(2(1(3(1(2(0(3(1(4(2(0(0(5(2(4(2(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)) = 2*x_1
   POL(3(x_1)) = x_1
   POL(4(x_1)) = 2*x_1
   POL(4^1(x_1)) = 2*x_1
   POL(5(x_1)) = 2 + x_1


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

(171)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

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

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

(172) 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(1(2(5(5(0(0(3(3(4(4(3(1(1(0(3(5(3(5(3(5(0(4(3(1(2(3(0(1(x1))))))))))))))))))))))))))))) -> 4^1(1(2(5(5(0(0(3(3(4(4(1(3(1(0(3(5(3(5(3(5(0(4(3(1(2(3(0(1(x1)))))))))))))))))))))))))))))

Strictly oriented rules of the TRS R:

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

Used ordering: Polynomial interpretation [POLO]:

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


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

(173)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

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

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

(174) MRRProof (EQUIVALENT)
By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented.


Strictly oriented rules of the TRS R:

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

Used ordering: Polynomial interpretation [POLO]:

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


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

(175)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

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

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

(176) 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(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
   5(4(1(0(5(1(1(5(2(3(4(4(5(4(0(3(4(0(5(x1))))))))))))))))))) -> 5(4(1(0(5(1(1(5(2(3(4(4(5(4(3(0(4(0(5(x1)))))))))))))))))))

Used ordering: Polynomial interpretation [POLO]:

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


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

(177)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

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

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

(178) 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(1(2(0(3(1(0(5(3(0(2(2(5(1(x1)))))))))))))) -> 4^1(1(2(0(3(1(0(5(3(2(0(2(5(1(x1))))))))))))))
   4^1(2(2(3(5(0(1(0(5(0(2(0(0(3(2(5(5(1(x1)))))))))))))))))) -> 4^1(2(2(3(5(0(1(0(5(2(0(0(0(3(2(5(5(1(x1))))))))))))))))))

Strictly oriented rules of the TRS R:

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


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

(179)
Obligation:
Q DP problem:
P is empty.
The TRS R consists of the following rules:

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

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

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

(181)
YES