1014.44/287.04	YES
1022.58/289.07	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
1022.58/289.07	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
1022.58/289.07	
1022.58/289.07	
1022.58/289.07	Termination w.r.t. Q of the given QTRS could be proven:
1022.58/289.07	
1022.58/289.07	(0) QTRS
1022.58/289.07	(1) QTRS Reverse [EQUIVALENT, 0 ms]
1022.58/289.07	(2) QTRS
1022.58/289.07	(3) QTRSRRRProof [EQUIVALENT, 724 ms]
1022.58/289.07	(4) QTRS
1022.58/289.07	(5) QTRSRRRProof [EQUIVALENT, 142 ms]
1022.58/289.07	(6) QTRS
1022.58/289.07	(7) DependencyPairsProof [EQUIVALENT, 2287 ms]
1022.58/289.07	(8) QDP
1022.58/289.07	(9) QDPOrderProof [EQUIVALENT, 2425 ms]
1022.58/289.07	(10) QDP
1022.58/289.07	(11) DependencyGraphProof [EQUIVALENT, 0 ms]
1022.58/289.07	(12) AND
1022.58/289.07	    (13) QDP
1022.58/289.07	        (14) QDPOrderProof [EQUIVALENT, 743 ms]
1022.58/289.07	        (15) QDP
1022.58/289.07	        (16) DependencyGraphProof [EQUIVALENT, 0 ms]
1022.58/289.07	        (17) AND
1022.58/289.07	            (18) QDP
1022.58/289.07	                (19) QDPOrderProof [EQUIVALENT, 119 ms]
1022.58/289.07	                (20) QDP
1022.58/289.07	                (21) QDPOrderProof [EQUIVALENT, 161 ms]
1022.58/289.07	                (22) QDP
1022.58/289.07	                (23) DependencyGraphProof [EQUIVALENT, 0 ms]
1022.58/289.07	                (24) AND
1022.58/289.07	                    (25) QDP
1022.58/289.07	                        (26) QDPOrderProof [EQUIVALENT, 64 ms]
1022.58/289.07	                        (27) QDP
1022.58/289.07	                        (28) MRRProof [EQUIVALENT, 2219 ms]
1022.58/289.07	                        (29) QDP
1022.58/289.07	                        (30) MRRProof [EQUIVALENT, 209 ms]
1022.58/289.07	                        (31) QDP
1022.58/289.07	                        (32) MRRProof [EQUIVALENT, 300 ms]
1022.58/289.07	                        (33) QDP
1022.58/289.07	                        (34) MRRProof [EQUIVALENT, 1698 ms]
1022.58/289.07	                        (35) QDP
1022.58/289.07	                        (36) MRRProof [EQUIVALENT, 1016 ms]
1022.58/289.07	                        (37) QDP
1022.58/289.07	                        (38) MRRProof [EQUIVALENT, 126 ms]
1022.58/289.07	                        (39) QDP
1022.58/289.07	                        (40) MRRProof [EQUIVALENT, 89 ms]
1022.58/289.07	                        (41) QDP
1022.58/289.07	                        (42) DependencyGraphProof [EQUIVALENT, 0 ms]
1022.58/289.07	                        (43) TRUE
1022.58/289.07	                    (44) QDP
1022.58/289.07	                        (45) QDPOrderProof [EQUIVALENT, 96 ms]
1022.58/289.07	                        (46) QDP
1022.58/289.07	                        (47) DependencyGraphProof [EQUIVALENT, 0 ms]
1022.58/289.07	                        (48) AND
1022.58/289.07	                            (49) QDP
1022.58/289.07	                                (50) QDPOrderProof [EQUIVALENT, 71 ms]
1022.58/289.07	                                (51) QDP
1022.58/289.07	                                (52) QDPOrderProof [EQUIVALENT, 0 ms]
1022.58/289.07	                                (53) QDP
1022.58/289.07	                                (54) QDPOrderProof [EQUIVALENT, 0 ms]
1022.58/289.07	                                (55) QDP
1022.58/289.07	                                (56) QDPOrderProof [EQUIVALENT, 0 ms]
1022.58/289.07	                                (57) QDP
1022.58/289.07	                                (58) MRRProof [EQUIVALENT, 3777 ms]
1022.58/289.07	                                (59) QDP
1022.58/289.07	                                (60) MRRProof [EQUIVALENT, 1540 ms]
1022.58/289.07	                                (61) QDP
1022.58/289.07	                                (62) MRRProof [EQUIVALENT, 3045 ms]
1022.58/289.07	                                (63) QDP
1022.58/289.07	                                (64) MRRProof [EQUIVALENT, 139 ms]
1022.58/289.07	                                (65) QDP
1022.58/289.07	                                (66) MRRProof [EQUIVALENT, 0 ms]
1022.58/289.07	                                (67) QDP
1022.58/289.07	                                (68) MRRProof [EQUIVALENT, 83 ms]
1022.58/289.07	                                (69) QDP
1022.58/289.07	                                (70) QDPOrderProof [EQUIVALENT, 232 ms]
1022.58/289.07	                                (71) QDP
1022.58/289.07	                                (72) MRRProof [EQUIVALENT, 71 ms]
1022.58/289.07	                                (73) QDP
1022.58/289.07	                                (74) DependencyGraphProof [EQUIVALENT, 0 ms]
1022.58/289.07	                                (75) TRUE
1022.58/289.07	                            (76) QDP
1022.58/289.07	                                (77) QDPOrderProof [EQUIVALENT, 64 ms]
1022.58/289.07	                                (78) QDP
1022.58/289.07	                                (79) QDPOrderProof [EQUIVALENT, 0 ms]
1022.58/289.07	                                (80) QDP
1022.58/289.07	                                (81) QDPOrderProof [EQUIVALENT, 0 ms]
1022.58/289.07	                                (82) QDP
1022.58/289.07	                                (83) QDPOrderProof [EQUIVALENT, 22 ms]
1022.58/289.07	                                (84) QDP
1022.58/289.07	                                (85) QDPOrderProof [EQUIVALENT, 0 ms]
1022.58/289.07	                                (86) QDP
1022.58/289.07	                                (87) MRRProof [EQUIVALENT, 9173 ms]
1022.58/289.07	                                (88) QDP
1022.58/289.07	                                (89) QDPOrderProof [EQUIVALENT, 0 ms]
1022.58/289.07	                                (90) QDP
1022.58/289.07	                                (91) MRRProof [EQUIVALENT, 1882 ms]
1022.58/289.07	                                (92) QDP
1022.58/289.07	                                (93) MRRProof [EQUIVALENT, 457 ms]
1022.58/289.07	                                (94) QDP
1022.58/289.07	                                (95) MRRProof [EQUIVALENT, 144 ms]
1022.58/289.07	                                (96) QDP
1022.58/289.07	                                (97) MRRProof [EQUIVALENT, 484 ms]
1022.58/289.07	                                (98) QDP
1022.58/289.07	                                (99) MRRProof [EQUIVALENT, 100 ms]
1022.58/289.07	                                (100) QDP
1022.58/289.07	                                (101) MRRProof [EQUIVALENT, 40 ms]
1022.58/289.07	                                (102) QDP
1022.58/289.07	                                (103) MRRProof [EQUIVALENT, 59 ms]
1022.58/289.07	                                (104) QDP
1022.58/289.07	                                (105) DependencyGraphProof [EQUIVALENT, 0 ms]
1022.58/289.07	                                (106) TRUE
1022.58/289.07	            (107) QDP
1022.58/289.07	                (108) QDPOrderProof [EQUIVALENT, 66 ms]
1022.58/289.07	                (109) QDP
1022.58/289.07	                (110) QDPOrderProof [EQUIVALENT, 67 ms]
1022.58/289.07	                (111) QDP
1022.58/289.07	                (112) MRRProof [EQUIVALENT, 693 ms]
1022.58/289.07	                (113) QDP
1022.58/289.07	                (114) MRRProof [EQUIVALENT, 3388 ms]
1022.58/289.07	                (115) QDP
1022.58/289.07	                (116) MRRProof [EQUIVALENT, 2015 ms]
1022.58/289.07	                (117) QDP
1022.58/289.07	                (118) MRRProof [EQUIVALENT, 398 ms]
1022.58/289.07	                (119) QDP
1022.58/289.07	                (120) MRRProof [EQUIVALENT, 545 ms]
1022.58/289.07	                (121) QDP
1022.58/289.07	                (122) MRRProof [EQUIVALENT, 129 ms]
1022.58/289.07	                (123) QDP
1022.58/289.07	                (124) MRRProof [EQUIVALENT, 101 ms]
1022.58/289.07	                (125) QDP
1022.58/289.07	                (126) MRRProof [EQUIVALENT, 65 ms]
1022.58/289.07	                (127) QDP
1022.58/289.07	                (128) MRRProof [EQUIVALENT, 0 ms]
1022.58/289.07	                (129) QDP
1022.58/289.07	                (130) PisEmptyProof [EQUIVALENT, 0 ms]
1022.58/289.07	                (131) YES
1022.58/289.07	            (132) QDP
1022.58/289.07	                (133) QDPOrderProof [EQUIVALENT, 66 ms]
1022.58/289.07	                (134) QDP
1022.58/289.07	                (135) QDPOrderProof [EQUIVALENT, 58 ms]
1022.58/289.07	                (136) QDP
1022.58/289.07	                (137) MRRProof [EQUIVALENT, 2191 ms]
1022.58/289.07	                (138) QDP
1022.58/289.07	                (139) MRRProof [EQUIVALENT, 441 ms]
1022.58/289.07	                (140) QDP
1022.58/289.07	                (141) MRRProof [EQUIVALENT, 90 ms]
1022.58/289.07	                (142) QDP
1022.58/289.07	                (143) MRRProof [EQUIVALENT, 140 ms]
1022.58/289.07	                (144) QDP
1022.58/289.07	                (145) MRRProof [EQUIVALENT, 432 ms]
1022.58/289.07	                (146) QDP
1022.58/289.07	                (147) MRRProof [EQUIVALENT, 347 ms]
1022.58/289.07	                (148) QDP
1022.58/289.07	                (149) MRRProof [EQUIVALENT, 0 ms]
1022.58/289.07	                (150) QDP
1022.58/289.07	                (151) MRRProof [EQUIVALENT, 0 ms]
1022.58/289.07	                (152) QDP
1022.58/289.07	                (153) DependencyGraphProof [EQUIVALENT, 0 ms]
1022.58/289.07	                (154) TRUE
1022.58/289.07	    (155) QDP
1022.58/289.07	        (156) QDPOrderProof [EQUIVALENT, 74 ms]
1022.58/289.07	        (157) QDP
1022.58/289.07	        (158) QDPOrderProof [EQUIVALENT, 24 ms]
1022.76/289.07	        (159) QDP
1022.76/289.07	        (160) MRRProof [EQUIVALENT, 2297 ms]
1022.76/289.07	        (161) QDP
1022.76/289.07	        (162) MRRProof [EQUIVALENT, 1761 ms]
1022.76/289.07	        (163) QDP
1022.76/289.07	        (164) MRRProof [EQUIVALENT, 261 ms]
1022.76/289.07	        (165) QDP
1022.76/289.07	        (166) QDPOrderProof [EQUIVALENT, 0 ms]
1022.76/289.07	        (167) QDP
1022.76/289.07	        (168) MRRProof [EQUIVALENT, 214 ms]
1022.76/289.07	        (169) QDP
1022.76/289.07	        (170) MRRProof [EQUIVALENT, 177 ms]
1022.76/289.07	        (171) QDP
1022.76/289.07	        (172) MRRProof [EQUIVALENT, 140 ms]
1022.76/289.07	        (173) QDP
1022.76/289.07	        (174) MRRProof [EQUIVALENT, 54 ms]
1022.76/289.07	        (175) QDP
1022.76/289.07	        (176) MRRProof [EQUIVALENT, 37 ms]
1022.76/289.07	        (177) QDP
1022.76/289.07	        (178) PisEmptyProof [EQUIVALENT, 0 ms]
1022.76/289.07	        (179) YES
1022.76/289.07	
1022.76/289.07	
1022.76/289.07	----------------------------------------
1022.76/289.07	
1022.76/289.07	(0)
1022.76/289.07	Obligation:
1022.76/289.07	Q restricted rewrite system:
1022.76/289.07	The TRS R consists of the following rules:
1022.76/289.07	
1022.76/289.07	   0(1(1(2(1(3(4(5(x1)))))))) -> 0(1(1(1(2(3(4(5(x1))))))))
1022.76/289.07	   1(5(2(2(5(3(3(1(x1)))))))) -> 1(5(2(2(3(5(3(1(x1))))))))
1022.76/289.07	   1(3(2(1(0(5(2(1(0(2(x1)))))))))) -> 1(1(5(0(0(2(2(3(1(2(x1))))))))))
1022.76/289.07	   2(5(3(0(1(1(3(2(0(2(x1)))))))))) -> 2(5(0(3(1(1(3(2(0(2(x1))))))))))
1022.76/289.08	   3(0(0(2(3(1(3(2(1(5(x1)))))))))) -> 3(0(0(2(3(1(2(3(1(5(x1))))))))))
1022.76/289.08	   4(0(4(4(0(3(4(0(2(3(x1)))))))))) -> 0(0(3(0(5(3(0(1(2(3(x1))))))))))
1022.76/289.08	   0(0(4(4(0(0(1(2(0(1(4(x1))))))))))) -> 4(1(2(2(1(0(0(4(0(2(x1))))))))))
1022.76/289.08	   0(4(4(3(2(4(0(5(5(3(4(x1))))))))))) -> 1(4(1(3(1(1(1(2(4(4(x1))))))))))
1022.76/289.08	   1(0(0(3(2(4(3(0(5(5(3(x1))))))))))) -> 5(2(0(4(1(4(0(0(1(1(x1))))))))))
1022.76/289.08	   1(0(2(5(0(3(2(4(1(0(2(x1))))))))))) -> 4(2(2(5(2(0(1(5(4(2(x1))))))))))
1022.76/289.08	   1(2(0(1(0(3(3(3(0(5(3(x1))))))))))) -> 1(2(1(5(1(0(2(1(2(5(x1))))))))))
1022.76/289.08	   1(3(1(0(4(5(2(3(4(2(5(x1))))))))))) -> 5(4(2(0(0(5(4(5(4(5(x1))))))))))
1022.76/289.08	   1(3(1(2(2(0(2(2(5(1(3(x1))))))))))) -> 1(3(3(3(2(3(5(4(1(4(x1))))))))))
1022.76/289.08	   1(3(4(0(2(4(1(2(4(3(5(x1))))))))))) -> 0(2(4(2(3(3(0(3(2(5(x1))))))))))
1022.76/289.08	   1(4(2(0(1(5(3(4(4(0(0(x1))))))))))) -> 1(2(1(4(5(1(5(4(2(4(x1))))))))))
1022.76/289.08	   1(4(5(1(4(2(5(3(2(3(2(x1))))))))))) -> 2(4(2(4(0(1(3(2(0(2(x1))))))))))
1022.76/289.08	   1(4(5(2(3(1(5(5(3(4(3(x1))))))))))) -> 5(3(4(1(4(0(2(2(2(2(x1))))))))))
1022.76/289.08	   1(5(5(3(4(1(3(1(5(5(0(x1))))))))))) -> 5(3(0(1(2(0(3(3(4(3(x1))))))))))
1022.76/289.08	   2(0(2(5(5(1(2(4(5(3(3(x1))))))))))) -> 2(3(5(2(0(0(4(2(1(5(x1))))))))))
1022.76/289.08	   2(0(4(3(0(0(0(1(4(4(5(x1))))))))))) -> 0(0(1(5(0(1(5(3(2(2(x1))))))))))
1022.76/289.08	   2(1(3(0(1(1(5(2(0(5(3(x1))))))))))) -> 4(0(3(5(0(2(2(1(1(0(x1))))))))))
1022.76/289.08	   2(2(3(1(3(1(1(3(4(2(0(x1))))))))))) -> 4(1(5(0(5(4(1(3(0(5(x1))))))))))
1022.76/289.08	   2(3(2(1(4(0(2(1(1(4(3(x1))))))))))) -> 1(4(2(4(5(2(2(0(5(1(x1))))))))))
1022.76/289.08	   2(3(3(3(4(4(1(0(0(4(5(x1))))))))))) -> 5(4(3(5(3(1(0(1(0(0(x1))))))))))
1022.76/289.08	   2(3(5(1(0(5(3(4(4(4(4(x1))))))))))) -> 3(3(4(5(2(4(2(4(4(2(x1))))))))))
1022.76/289.08	   2(4(3(2(2(4(5(0(0(2(2(x1))))))))))) -> 0(2(1(0(3(5(4(5(0(4(x1))))))))))
1022.76/289.08	   2(5(0(2(2(1(3(2(5(0(2(x1))))))))))) -> 2(1(1(2(4(4(2(4(2(0(x1))))))))))
1022.76/289.08	   2(5(3(2(4(1(0(0(1(0(5(x1))))))))))) -> 0(0(2(4(1(0(4(5(2(5(x1))))))))))
1022.76/289.08	   2(5(4(1(4(1(1(0(2(2(3(x1))))))))))) -> 2(4(1(2(0(3(0(0(2(4(x1))))))))))
1022.76/289.08	   3(0(4(4(2(1(1(4(3(3(4(x1))))))))))) -> 0(1(5(3(2(5(0(4(2(0(x1))))))))))
1022.76/289.08	   3(1(2(2(1(1(4(4(2(0(5(x1))))))))))) -> 0(2(1(2(4(3(3(0(0(0(x1))))))))))
1022.76/289.08	   3(2(0(3(0(5(0(5(5(3(5(x1))))))))))) -> 3(5(5(4(5(5(5(3(4(0(x1))))))))))
1022.76/289.08	   3(2(2(3(4(5(2(4(1(2(4(x1))))))))))) -> 1(3(1(2(0(4(3(4(3(2(x1))))))))))
1022.76/289.08	   3(2(4(0(3(1(4(4(0(4(5(x1))))))))))) -> 3(3(5(1(4(0(1(1(5(1(x1))))))))))
1022.76/289.08	   3(2(4(4(3(0(0(3(1(2(2(x1))))))))))) -> 5(5(3(5(0(4(3(2(0(4(x1))))))))))
1022.76/289.08	   3(3(1(0(1(0(1(0(5(3(0(x1))))))))))) -> 1(1(2(5(1(3(3(5(1(0(x1))))))))))
1022.76/289.08	   3(4(5(5(1(4(4(1(1(4(4(x1))))))))))) -> 5(3(2(1(3(2(5(4(4(5(x1))))))))))
1022.76/289.08	   3(5(3(2(3(3(4(0(0(2(4(x1))))))))))) -> 3(0(1(1(4(0(1(5(5(1(x1))))))))))
1022.76/289.08	   4(0(0(2(0(3(2(3(3(1(0(x1))))))))))) -> 4(0(0(0(2(3(2(3(3(1(0(x1)))))))))))
1022.76/289.08	   4(0(3(1(0(0(1(3(0(1(4(x1))))))))))) -> 1(5(5(0(2(2(5(2(5(1(x1))))))))))
1022.76/289.08	   4(0(3(2(2(4(0(5(2(0(5(x1))))))))))) -> 3(4(4(1(5(1(4(0(2(4(x1))))))))))
1022.76/289.08	   4(0(4(1(4(0(5(4(3(5(2(x1))))))))))) -> 4(1(3(1(0(3(3(0(0(3(x1))))))))))
1022.76/289.08	   4(3(4(3(3(4(5(2(4(4(1(x1))))))))))) -> 0(0(3(5(2(4(4(3(2(2(x1))))))))))
1022.76/289.08	   4(5(3(5(2(4(1(4(2(1(4(x1))))))))))) -> 4(1(0(2(5(2(4(0(1(4(x1))))))))))
1022.76/289.08	   4(5(5(2(4(3(4(3(4(2(1(x1))))))))))) -> 3(4(5(0(1(2(2(1(3(0(x1))))))))))
1022.76/289.08	   5(0(4(4(3(2(5(2(3(2(0(x1))))))))))) -> 2(3(0(1(0(3(5(2(0(2(x1))))))))))
1022.76/289.08	   5(2(1(4(0(3(2(4(0(0(3(x1))))))))))) -> 3(0(5(3(2(4(5(3(3(2(x1))))))))))
1022.76/289.08	   5(3(5(3(4(5(5(5(1(4(1(x1))))))))))) -> 3(0(3(2(0(2(5(3(4(1(x1))))))))))
1022.76/289.08	   5(5(4(1(2(0(5(2(4(0(0(x1))))))))))) -> 0(2(0(2(5(0(3(4(3(4(x1))))))))))
1022.76/289.08	   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))))))))))))
1022.76/289.08	   1(3(3(4(3(5(1(0(0(1(3(1(x1)))))))))))) -> 1(1(4(4(4(1(4(2(3(5(x1))))))))))
1022.76/289.08	   2(1(1(5(2(2(0(0(0(3(5(1(x1)))))))))))) -> 2(4(4(1(1(2(2(3(5(4(x1))))))))))
1022.76/289.08	   2(2(2(1(4(2(1(3(1(1(3(5(x1)))))))))))) -> 1(2(1(5(4(1(0(4(4(1(x1))))))))))
1022.76/289.08	   4(0(1(5(5(2(1(2(1(1(1(1(x1)))))))))))) -> 2(3(2(4(4(3(5(4(1(4(x1))))))))))
1022.76/289.08	   4(3(3(3(3(5(5(3(0(3(2(3(x1)))))))))))) -> 4(0(3(1(4(5(2(0(4(0(x1))))))))))
1022.76/289.08	   5(3(4(1(0(5(3(0(2(0(3(1(x1)))))))))))) -> 2(4(4(5(3(4(2(3(4(1(x1))))))))))
1022.76/289.08	   5(3(5(3(4(0(1(0(2(4(3(2(x1)))))))))))) -> 2(0(1(4(5(5(0(3(1(0(x1))))))))))
1022.76/289.08	   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))))))))))))
1022.76/289.08	   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)))))))))))))
1022.76/289.08	   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)))))))))))))
1022.76/289.08	   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)))))))))))))
1022.76/289.08	   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))))))))))))))
1022.76/289.08	   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)))))))))))))))
1022.76/289.08	   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)))))))))))))))
1022.76/289.08	   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)))))))))))))))
1022.76/289.08	   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))))))))))))))))
1022.76/289.08	   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))))))))))))))))))
1022.76/289.08	   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))))))))))))))))))
1022.76/289.08	   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))))))))))))))))))
1022.76/289.08	   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)))))))))))))))))))
1022.76/289.08	   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)))))))))))))))))))
1022.76/289.08	   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)))))))))))))))))))
1022.76/289.08	   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)))))))))))))))))))
1022.76/289.08	   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)))))))))))))))))))
1022.76/289.08	   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)))))))))))))))))))
1022.76/289.08	   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))))))))))))))))))))
1022.76/289.08	   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)))))))))))))))))))))
1022.76/289.08	   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)))))))))))))))))))))
1022.76/289.08	   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)))))))))))))))))))))
1022.76/289.08	   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))))))))))))))))))))))
1022.76/289.08	   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))))))))))))))))))))))
1022.76/289.08	   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))))))))))))))))))))))))
1022.76/289.08	   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))))))))))))))))))))))))
1022.76/289.08	   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)))))))))))))))))))))))))
1022.76/289.08	   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)))))))))))))))))))))))))
1022.76/289.08	   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))))))))))))))))))))))))))
1022.76/289.08	   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))))))))))))))))))))))))))
1022.76/289.08	   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))))))))))))))))))))))))))))
1022.76/289.08	   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)))))))))))))))))))))))))))))
1022.76/289.08	   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)))))))))))))))))))))))))))))
1022.76/289.08	   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))))))))))))))))))))))))))))))
1022.76/289.08	
1022.76/289.08	Q is empty.
1022.76/289.08	
1022.76/289.08	----------------------------------------
1022.76/289.08	
1022.76/289.08	(1) QTRS Reverse (EQUIVALENT)
1022.76/289.08	We applied the QTRS Reverse Processor [REVERSE].
1022.76/289.08	----------------------------------------
1022.76/289.08	
1022.76/289.08	(2)
1022.76/289.08	Obligation:
1022.76/289.08	Q restricted rewrite system:
1022.76/289.08	The TRS R consists of the following rules:
1022.76/289.08	
1022.76/289.08	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1022.76/289.08	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1022.76/289.08	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1022.76/289.08	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1022.76/289.08	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1022.76/289.08	   3(2(0(4(3(0(4(4(0(4(x1)))))))))) -> 3(2(1(0(3(5(0(3(0(0(x1))))))))))
1022.76/289.08	   4(1(0(2(1(0(0(4(4(0(0(x1))))))))))) -> 2(0(4(0(0(1(2(2(1(4(x1))))))))))
1022.76/289.08	   4(3(5(5(0(4(2(3(4(4(0(x1))))))))))) -> 4(4(2(1(1(1(3(1(4(1(x1))))))))))
1022.76/289.08	   3(5(5(0(3(4(2(3(0(0(1(x1))))))))))) -> 1(1(0(0(4(1(4(0(2(5(x1))))))))))
1022.76/289.08	   2(0(1(4(2(3(0(5(2(0(1(x1))))))))))) -> 2(4(5(1(0(2(5(2(2(4(x1))))))))))
1022.76/289.08	   3(5(0(3(3(3(0(1(0(2(1(x1))))))))))) -> 5(2(1(2(0(1(5(1(2(1(x1))))))))))
1022.76/289.08	   5(2(4(3(2(5(4(0(1(3(1(x1))))))))))) -> 5(4(5(4(5(0(0(2(4(5(x1))))))))))
1022.76/289.08	   3(1(5(2(2(0(2(2(1(3(1(x1))))))))))) -> 4(1(4(5(3(2(3(3(3(1(x1))))))))))
1022.76/289.08	   5(3(4(2(1(4(2(0(4(3(1(x1))))))))))) -> 5(2(3(0(3(3(2(4(2(0(x1))))))))))
1022.76/289.08	   0(0(4(4(3(5(1(0(2(4(1(x1))))))))))) -> 4(2(4(5(1(5(4(1(2(1(x1))))))))))
1022.76/289.08	   2(3(2(3(5(2(4(1(5(4(1(x1))))))))))) -> 2(0(2(3(1(0(4(2(4(2(x1))))))))))
1022.76/289.08	   3(4(3(5(5(1(3(2(5(4(1(x1))))))))))) -> 2(2(2(2(0(4(1(4(3(5(x1))))))))))
1022.76/289.08	   0(5(5(1(3(1(4(3(5(5(1(x1))))))))))) -> 3(4(3(3(0(2(1(0(3(5(x1))))))))))
1022.76/289.08	   3(3(5(4(2(1(5(5(2(0(2(x1))))))))))) -> 5(1(2(4(0(0(2(5(3(2(x1))))))))))
1022.76/289.08	   5(4(4(1(0(0(0(3(4(0(2(x1))))))))))) -> 2(2(3(5(1(0(5(1(0(0(x1))))))))))
1022.76/289.08	   3(5(0(2(5(1(1(0(3(1(2(x1))))))))))) -> 0(1(1(2(2(0(5(3(0(4(x1))))))))))
1022.76/289.08	   0(2(4(3(1(1(3(1(3(2(2(x1))))))))))) -> 5(0(3(1(4(5(0(5(1(4(x1))))))))))
1022.76/289.08	   3(4(1(1(2(0(4(1(2(3(2(x1))))))))))) -> 1(5(0(2(2(5(4(2(4(1(x1))))))))))
1022.76/289.08	   5(4(0(0(1(4(4(3(3(3(2(x1))))))))))) -> 0(0(1(0(1(3(5(3(4(5(x1))))))))))
1022.76/289.08	   4(4(4(4(3(5(0(1(5(3(2(x1))))))))))) -> 2(4(4(2(4(2(5(4(3(3(x1))))))))))
1022.76/289.08	   2(2(0(0(5(4(2(2(3(4(2(x1))))))))))) -> 4(0(5(4(5(3(0(1(2(0(x1))))))))))
1022.76/289.08	   2(0(5(2(3(1(2(2(0(5(2(x1))))))))))) -> 0(2(4(2(4(4(2(1(1(2(x1))))))))))
1022.76/289.08	   5(0(1(0(0(1(4(2(3(5(2(x1))))))))))) -> 5(2(5(4(0(1(4(2(0(0(x1))))))))))
1022.76/289.08	   3(2(2(0(1(1(4(1(4(5(2(x1))))))))))) -> 4(2(0(0(3(0(2(1(4(2(x1))))))))))
1022.76/289.08	   4(3(3(4(1(1(2(4(4(0(3(x1))))))))))) -> 0(2(4(0(5(2(3(5(1(0(x1))))))))))
1022.76/289.08	   5(0(2(4(4(1(1(2(2(1(3(x1))))))))))) -> 0(0(0(3(3(4(2(1(2(0(x1))))))))))
1022.76/289.08	   5(3(5(5(0(5(0(3(0(2(3(x1))))))))))) -> 0(4(3(5(5(5(4(5(5(3(x1))))))))))
1022.76/289.08	   4(2(1(4(2(5(4(3(2(2(3(x1))))))))))) -> 2(3(4(3(4(0(2(1(3(1(x1))))))))))
1022.76/289.08	   5(4(0(4(4(1(3(0(4(2(3(x1))))))))))) -> 1(5(1(1(0(4(1(5(3(3(x1))))))))))
1022.76/289.08	   2(2(1(3(0(0(3(4(4(2(3(x1))))))))))) -> 4(0(2(3(4(0(5(3(5(5(x1))))))))))
1022.76/289.08	   0(3(5(0(1(0(1(0(1(3(3(x1))))))))))) -> 0(1(5(3(3(1(5(2(1(1(x1))))))))))
1022.76/289.08	   4(4(1(1(4(4(1(5(5(4(3(x1))))))))))) -> 5(4(4(5(2(3(1(2(3(5(x1))))))))))
1022.76/289.08	   4(2(0(0(4(3(3(2(3(5(3(x1))))))))))) -> 1(5(5(1(0(4(1(1(0(3(x1))))))))))
1022.76/289.08	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1022.76/289.08	   4(1(0(3(1(0(0(1(3(0(4(x1))))))))))) -> 1(5(2(5(2(2(0(5(5(1(x1))))))))))
1022.76/289.08	   5(0(2(5(0(4(2(2(3(0(4(x1))))))))))) -> 4(2(0(4(1(5(1(4(4(3(x1))))))))))
1022.76/289.08	   2(5(3(4(5(0(4(1(4(0(4(x1))))))))))) -> 3(0(0(3(3(0(1(3(1(4(x1))))))))))
1022.76/289.08	   1(4(4(2(5(4(3(3(4(3(4(x1))))))))))) -> 2(2(3(4(4(2(5(3(0(0(x1))))))))))
1022.76/289.08	   4(1(2(4(1(4(2(5(3(5(4(x1))))))))))) -> 4(1(0(4(2(5(2(0(1(4(x1))))))))))
1022.76/289.08	   1(2(4(3(4(3(4(2(5(5(4(x1))))))))))) -> 0(3(1(2(2(1(0(5(4(3(x1))))))))))
1022.76/289.08	   0(2(3(2(5(2(3(4(4(0(5(x1))))))))))) -> 2(0(2(5(3(0(1(0(3(2(x1))))))))))
1022.76/289.08	   3(0(0(4(2(3(0(4(1(2(5(x1))))))))))) -> 2(3(3(5(4(2(3(5(0(3(x1))))))))))
1022.76/289.08	   1(4(1(5(5(5(4(3(5(3(5(x1))))))))))) -> 1(4(3(5(2(0(2(3(0(3(x1))))))))))
1022.76/289.08	   0(0(4(2(5(0(2(1(4(5(5(x1))))))))))) -> 4(3(4(3(0(5(2(0(2(0(x1))))))))))
1022.76/289.08	   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))))))))))))
1022.76/289.08	   1(3(1(0(0(1(5(3(4(3(3(1(x1)))))))))))) -> 5(3(2(4(1(4(4(4(1(1(x1))))))))))
1022.76/289.08	   1(5(3(0(0(0(2(2(5(1(1(2(x1)))))))))))) -> 4(5(3(2(2(1(1(4(4(2(x1))))))))))
1022.76/289.08	   5(3(1(1(3(1(2(4(1(2(2(2(x1)))))))))))) -> 1(4(4(0(1(4(5(1(2(1(x1))))))))))
1022.76/289.08	   1(1(1(1(2(1(2(5(5(1(0(4(x1)))))))))))) -> 4(1(4(5(3(4(4(2(3(2(x1))))))))))
1022.76/289.08	   3(2(3(0(3(5(5(3(3(3(3(4(x1)))))))))))) -> 0(4(0(2(5(4(1(3(0(4(x1))))))))))
1022.76/289.08	   1(3(0(2(0(3(5(0(1(4(3(5(x1)))))))))))) -> 1(4(3(2(4(3(5(4(4(2(x1))))))))))
1022.76/289.08	   2(3(4(2(0(1(0(4(3(5(3(5(x1)))))))))))) -> 0(1(3(0(5(5(4(1(0(2(x1))))))))))
1022.76/289.08	   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))))))))))))
1022.76/289.08	   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)))))))))))))
1022.76/289.08	   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)))))))))))))
1022.76/289.08	   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)))))))))))))
1022.76/289.08	   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))))))))))))))
1022.76/289.08	   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)))))))))))))))
1022.76/289.08	   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)))))))))))))))
1022.76/289.08	   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)))))))))))))))
1022.76/289.08	   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))))))))))))))))
1022.76/289.08	   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))))))))))))))))))
1022.76/289.08	   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))))))))))))))))))
1022.76/289.08	   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))))))))))))))))))
1022.76/289.08	   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)))))))))))))))))))
1022.76/289.08	   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)))))))))))))))))))
1022.76/289.08	   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)))))))))))))))))))
1022.76/289.08	   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)))))))))))))))))))
1022.76/289.08	   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)))))))))))))))))))
1022.76/289.08	   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)))))))))))))))))))
1022.76/289.08	   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))))))))))))))))))))
1022.76/289.08	   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)))))))))))))))))))))
1022.76/289.08	   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)))))))))))))))))))))
1022.76/289.08	   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)))))))))))))))))))))
1022.76/289.08	   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))))))))))))))))))))))
1022.76/289.08	   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))))))))))))))))))))))
1022.76/289.08	   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))))))))))))))))))))))))
1022.76/289.08	   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))))))))))))))))))))))))
1022.76/289.08	   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)))))))))))))))))))))))))
1022.76/289.08	   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)))))))))))))))))))))))))
1022.76/289.08	   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))))))))))))))))))))))))))
1022.76/289.08	   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))))))))))))))))))))))))))
1022.76/289.08	   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))))))))))))))))))))))))))))
1022.76/289.08	   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)))))))))))))))))))))))))))))
1022.76/289.08	   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)))))))))))))))))))))))))))))
1022.76/289.08	   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))))))))))))))))))))))))))))))
1022.76/289.08	
1022.76/289.08	Q is empty.
1022.76/289.08	
1022.76/289.08	----------------------------------------
1022.76/289.08	
1022.76/289.08	(3) QTRSRRRProof (EQUIVALENT)
1022.76/289.08	Used ordering:
1022.76/289.08	Polynomial interpretation [POLO]:
1022.76/289.08	
1022.76/289.08	   POL(0(x_1)) = 5 + x_1
1022.76/289.08	   POL(1(x_1)) = 8 + x_1
1022.76/289.08	   POL(2(x_1)) = 9 + x_1
1022.76/289.08	   POL(3(x_1)) = 9 + x_1
1022.76/289.08	   POL(4(x_1)) = 9 + x_1
1022.76/289.08	   POL(5(x_1)) = 7 + x_1
1022.76/289.08	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
1022.76/289.08	
1022.76/289.08	   3(2(0(4(3(0(4(4(0(4(x1)))))))))) -> 3(2(1(0(3(5(0(3(0(0(x1))))))))))
1022.76/289.08	   4(1(0(2(1(0(0(4(4(0(0(x1))))))))))) -> 2(0(4(0(0(1(2(2(1(4(x1))))))))))
1022.76/289.08	   4(3(5(5(0(4(2(3(4(4(0(x1))))))))))) -> 4(4(2(1(1(1(3(1(4(1(x1))))))))))
1022.76/289.08	   3(5(5(0(3(4(2(3(0(0(1(x1))))))))))) -> 1(1(0(0(4(1(4(0(2(5(x1))))))))))
1022.76/289.08	   2(0(1(4(2(3(0(5(2(0(1(x1))))))))))) -> 2(4(5(1(0(2(5(2(2(4(x1))))))))))
1022.76/289.08	   3(5(0(3(3(3(0(1(0(2(1(x1))))))))))) -> 5(2(1(2(0(1(5(1(2(1(x1))))))))))
1022.76/289.08	   5(2(4(3(2(5(4(0(1(3(1(x1))))))))))) -> 5(4(5(4(5(0(0(2(4(5(x1))))))))))
1022.76/289.08	   3(1(5(2(2(0(2(2(1(3(1(x1))))))))))) -> 4(1(4(5(3(2(3(3(3(1(x1))))))))))
1022.76/289.08	   5(3(4(2(1(4(2(0(4(3(1(x1))))))))))) -> 5(2(3(0(3(3(2(4(2(0(x1))))))))))
1022.76/289.08	   2(3(2(3(5(2(4(1(5(4(1(x1))))))))))) -> 2(0(2(3(1(0(4(2(4(2(x1))))))))))
1022.76/289.08	   3(4(3(5(5(1(3(2(5(4(1(x1))))))))))) -> 2(2(2(2(0(4(1(4(3(5(x1))))))))))
1022.76/289.08	   0(5(5(1(3(1(4(3(5(5(1(x1))))))))))) -> 3(4(3(3(0(2(1(0(3(5(x1))))))))))
1022.76/289.08	   3(3(5(4(2(1(5(5(2(0(2(x1))))))))))) -> 5(1(2(4(0(0(2(5(3(2(x1))))))))))
1022.76/289.08	   5(4(4(1(0(0(0(3(4(0(2(x1))))))))))) -> 2(2(3(5(1(0(5(1(0(0(x1))))))))))
1022.76/289.08	   3(5(0(2(5(1(1(0(3(1(2(x1))))))))))) -> 0(1(1(2(2(0(5(3(0(4(x1))))))))))
1022.76/289.08	   0(2(4(3(1(1(3(1(3(2(2(x1))))))))))) -> 5(0(3(1(4(5(0(5(1(4(x1))))))))))
1022.76/289.08	   3(4(1(1(2(0(4(1(2(3(2(x1))))))))))) -> 1(5(0(2(2(5(4(2(4(1(x1))))))))))
1022.76/289.08	   5(4(0(0(1(4(4(3(3(3(2(x1))))))))))) -> 0(0(1(0(1(3(5(3(4(5(x1))))))))))
1022.76/289.08	   4(4(4(4(3(5(0(1(5(3(2(x1))))))))))) -> 2(4(4(2(4(2(5(4(3(3(x1))))))))))
1022.76/289.08	   2(2(0(0(5(4(2(2(3(4(2(x1))))))))))) -> 4(0(5(4(5(3(0(1(2(0(x1))))))))))
1022.76/289.08	   2(0(5(2(3(1(2(2(0(5(2(x1))))))))))) -> 0(2(4(2(4(4(2(1(1(2(x1))))))))))
1022.76/289.08	   5(0(1(0(0(1(4(2(3(5(2(x1))))))))))) -> 5(2(5(4(0(1(4(2(0(0(x1))))))))))
1022.76/289.08	   3(2(2(0(1(1(4(1(4(5(2(x1))))))))))) -> 4(2(0(0(3(0(2(1(4(2(x1))))))))))
1022.76/289.08	   4(3(3(4(1(1(2(4(4(0(3(x1))))))))))) -> 0(2(4(0(5(2(3(5(1(0(x1))))))))))
1022.76/289.08	   5(0(2(4(4(1(1(2(2(1(3(x1))))))))))) -> 0(0(0(3(3(4(2(1(2(0(x1))))))))))
1022.76/289.08	   5(3(5(5(0(5(0(3(0(2(3(x1))))))))))) -> 0(4(3(5(5(5(4(5(5(3(x1))))))))))
1022.76/289.08	   4(2(1(4(2(5(4(3(2(2(3(x1))))))))))) -> 2(3(4(3(4(0(2(1(3(1(x1))))))))))
1022.76/289.08	   5(4(0(4(4(1(3(0(4(2(3(x1))))))))))) -> 1(5(1(1(0(4(1(5(3(3(x1))))))))))
1022.76/289.08	   2(2(1(3(0(0(3(4(4(2(3(x1))))))))))) -> 4(0(2(3(4(0(5(3(5(5(x1))))))))))
1022.76/289.08	   4(4(1(1(4(4(1(5(5(4(3(x1))))))))))) -> 5(4(4(5(2(3(1(2(3(5(x1))))))))))
1022.76/289.08	   4(2(0(0(4(3(3(2(3(5(3(x1))))))))))) -> 1(5(5(1(0(4(1(1(0(3(x1))))))))))
1022.76/289.08	   4(1(0(3(1(0(0(1(3(0(4(x1))))))))))) -> 1(5(2(5(2(2(0(5(5(1(x1))))))))))
1022.76/289.08	   5(0(2(5(0(4(2(2(3(0(4(x1))))))))))) -> 4(2(0(4(1(5(1(4(4(3(x1))))))))))
1022.76/289.08	   2(5(3(4(5(0(4(1(4(0(4(x1))))))))))) -> 3(0(0(3(3(0(1(3(1(4(x1))))))))))
1022.76/289.08	   1(4(4(2(5(4(3(3(4(3(4(x1))))))))))) -> 2(2(3(4(4(2(5(3(0(0(x1))))))))))
1022.76/289.08	   4(1(2(4(1(4(2(5(3(5(4(x1))))))))))) -> 4(1(0(4(2(5(2(0(1(4(x1))))))))))
1022.76/289.08	   1(2(4(3(4(3(4(2(5(5(4(x1))))))))))) -> 0(3(1(2(2(1(0(5(4(3(x1))))))))))
1022.76/289.08	   0(2(3(2(5(2(3(4(4(0(5(x1))))))))))) -> 2(0(2(5(3(0(1(0(3(2(x1))))))))))
1022.76/289.08	   3(0(0(4(2(3(0(4(1(2(5(x1))))))))))) -> 2(3(3(5(4(2(3(5(0(3(x1))))))))))
1022.76/289.08	   1(4(1(5(5(5(4(3(5(3(5(x1))))))))))) -> 1(4(3(5(2(0(2(3(0(3(x1))))))))))
1022.76/289.08	   0(0(4(2(5(0(2(1(4(5(5(x1))))))))))) -> 4(3(4(3(0(5(2(0(2(0(x1))))))))))
1022.76/289.08	   1(3(1(0(0(1(5(3(4(3(3(1(x1)))))))))))) -> 5(3(2(4(1(4(4(4(1(1(x1))))))))))
1022.76/289.08	   1(5(3(0(0(0(2(2(5(1(1(2(x1)))))))))))) -> 4(5(3(2(2(1(1(4(4(2(x1))))))))))
1022.76/289.08	   5(3(1(1(3(1(2(4(1(2(2(2(x1)))))))))))) -> 1(4(4(0(1(4(5(1(2(1(x1))))))))))
1022.76/289.08	   1(1(1(1(2(1(2(5(5(1(0(4(x1)))))))))))) -> 4(1(4(5(3(4(4(2(3(2(x1))))))))))
1022.76/289.08	   3(2(3(0(3(5(5(3(3(3(3(4(x1)))))))))))) -> 0(4(0(2(5(4(1(3(0(4(x1))))))))))
1022.76/289.08	   1(3(0(2(0(3(5(0(1(4(3(5(x1)))))))))))) -> 1(4(3(2(4(3(5(4(4(2(x1))))))))))
1022.76/289.08	   2(3(4(2(0(1(0(4(3(5(3(5(x1)))))))))))) -> 0(1(3(0(5(5(4(1(0(2(x1))))))))))
1022.76/289.08	
1022.76/289.08	
1022.76/289.08	
1022.76/289.08	
1022.76/289.08	----------------------------------------
1022.76/289.08	
1022.76/289.08	(4)
1022.76/289.08	Obligation:
1022.76/289.08	Q restricted rewrite system:
1022.76/289.08	The TRS R consists of the following rules:
1022.76/289.08	
1022.76/289.08	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1022.76/289.08	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1022.76/289.08	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1022.76/289.08	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1022.76/289.08	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1022.76/289.08	   0(0(4(4(3(5(1(0(2(4(1(x1))))))))))) -> 4(2(4(5(1(5(4(1(2(1(x1))))))))))
1022.76/289.08	   0(3(5(0(1(0(1(0(1(3(3(x1))))))))))) -> 0(1(5(3(3(1(5(2(1(1(x1))))))))))
1022.76/289.08	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1022.76/289.08	   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))))))))))))
1022.76/289.08	   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))))))))))))
1022.76/289.08	   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)))))))))))))
1022.76/289.08	   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)))))))))))))
1022.76/289.08	   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)))))))))))))
1022.76/289.08	   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))))))))))))))
1022.76/289.08	   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)))))))))))))))
1022.76/289.08	   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)))))))))))))))
1022.76/289.08	   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)))))))))))))))
1022.76/289.08	   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))))))))))))))))
1022.76/289.08	   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))))))))))))))))))
1022.76/289.08	   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))))))))))))))))))
1022.76/289.08	   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))))))))))))))))))
1022.76/289.08	   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)))))))))))))))))))
1022.76/289.08	   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)))))))))))))))))))
1022.76/289.08	   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)))))))))))))))))))
1022.76/289.08	   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)))))))))))))))))))
1022.76/289.08	   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)))))))))))))))))))
1022.76/289.08	   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)))))))))))))))))))
1022.76/289.08	   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))))))))))))))))))))
1022.76/289.08	   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)))))))))))))))))))))
1022.76/289.11	   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)))))))))))))))))))))
1022.76/289.11	   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)))))))))))))))))))))
1022.76/289.11	   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))))))))))))))))))))))
1022.76/289.11	   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))))))))))))))))))))))
1022.76/289.11	   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))))))))))))))))))))))))
1022.76/289.11	   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))))))))))))))))))))))))
1022.76/289.11	   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)))))))))))))))))))))))))
1022.76/289.11	   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)))))))))))))))))))))))))
1022.76/289.11	   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))))))))))))))))))))))))))
1022.76/289.11	   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))))))))))))))))))))))))))
1022.76/289.11	   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))))))))))))))))))))))))))))
1022.76/289.11	   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)))))))))))))))))))))))))))))
1022.76/289.11	   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)))))))))))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))))))))))))
1022.76/289.12	
1022.76/289.12	Q is empty.
1022.76/289.12	
1022.76/289.12	----------------------------------------
1022.76/289.12	
1022.76/289.12	(5) QTRSRRRProof (EQUIVALENT)
1022.76/289.12	Used ordering:
1022.76/289.12	Polynomial interpretation [POLO]:
1022.76/289.12	
1022.76/289.12	   POL(0(x_1)) = x_1
1022.76/289.12	   POL(1(x_1)) = x_1
1022.76/289.12	   POL(2(x_1)) = x_1
1022.76/289.12	   POL(3(x_1)) = 1 + x_1
1022.76/289.12	   POL(4(x_1)) = x_1
1022.76/289.12	   POL(5(x_1)) = x_1
1022.76/289.12	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
1022.76/289.12	
1022.76/289.12	   0(0(4(4(3(5(1(0(2(4(1(x1))))))))))) -> 4(2(4(5(1(5(4(1(2(1(x1))))))))))
1022.76/289.12	   0(3(5(0(1(0(1(0(1(3(3(x1))))))))))) -> 0(1(5(3(3(1(5(2(1(1(x1))))))))))
1022.76/289.12	
1022.76/289.12	
1022.76/289.12	
1022.76/289.12	
1022.76/289.12	----------------------------------------
1022.76/289.12	
1022.76/289.12	(6)
1022.76/289.12	Obligation:
1022.76/289.12	Q restricted rewrite system:
1022.76/289.12	The TRS R consists of the following rules:
1022.76/289.12	
1022.76/289.12	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1022.76/289.12	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1022.76/289.12	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1022.76/289.12	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1022.76/289.12	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1022.76/289.12	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1022.76/289.12	   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))))))))))))
1022.76/289.12	   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))))))))))))
1022.76/289.12	   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)))))))))))))
1022.76/289.12	   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)))))))))))))
1022.76/289.12	   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)))))))))))))
1022.76/289.12	   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))))))))))))))
1022.76/289.12	   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)))))))))))))))
1022.76/289.12	   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)))))))))))))))
1022.76/289.12	   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)))))))))))))))
1022.76/289.12	   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))))))))))))))))
1022.76/289.12	   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))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))))))))))))
1022.76/289.12	
1022.76/289.12	Q is empty.
1022.76/289.12	
1022.76/289.12	----------------------------------------
1022.76/289.12	
1022.76/289.12	(7) DependencyPairsProof (EQUIVALENT)
1022.76/289.12	Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
1022.76/289.12	----------------------------------------
1022.76/289.12	
1022.76/289.12	(8)
1022.76/289.12	Obligation:
1022.76/289.12	Q DP problem:
1022.76/289.12	The TRS P consists of the following rules:
1022.76/289.12	
1022.76/289.12	   5^1(4(3(1(2(1(1(0(x1)))))))) -> 5^1(4(3(2(1(1(1(0(x1))))))))
1022.76/289.12	   5^1(4(3(1(2(1(1(0(x1)))))))) -> 4^1(3(2(1(1(1(0(x1)))))))
1022.76/289.12	   5^1(4(3(1(2(1(1(0(x1)))))))) -> 3^1(2(1(1(1(0(x1))))))
1022.76/289.12	   5^1(4(3(1(2(1(1(0(x1)))))))) -> 2^1(1(1(1(0(x1)))))
1022.76/289.12	   5^1(4(3(1(2(1(1(0(x1)))))))) -> 1^1(1(1(0(x1))))
1022.76/289.12	   1^1(3(3(5(2(2(5(1(x1)))))))) -> 1^1(3(5(3(2(2(5(1(x1))))))))
1022.76/289.12	   1^1(3(3(5(2(2(5(1(x1)))))))) -> 3^1(5(3(2(2(5(1(x1)))))))
1022.76/289.12	   1^1(3(3(5(2(2(5(1(x1)))))))) -> 5^1(3(2(2(5(1(x1))))))
1022.76/289.12	   1^1(3(3(5(2(2(5(1(x1)))))))) -> 3^1(2(2(5(1(x1)))))
1022.76/289.12	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2^1(1(3(2(2(0(0(5(1(1(x1))))))))))
1022.76/289.12	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 1^1(3(2(2(0(0(5(1(1(x1)))))))))
1022.76/289.12	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 3^1(2(2(0(0(5(1(1(x1))))))))
1022.76/289.12	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2^1(2(0(0(5(1(1(x1)))))))
1022.76/289.12	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2^1(0(0(5(1(1(x1))))))
1022.76/289.12	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 0^1(0(5(1(1(x1)))))
1022.76/289.12	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 0^1(5(1(1(x1))))
1022.76/289.12	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 5^1(1(1(x1)))
1022.76/289.12	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 1^1(1(x1))
1022.76/289.12	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2^1(0(2(3(1(1(3(0(5(2(x1))))))))))
1022.76/289.12	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 0^1(2(3(1(1(3(0(5(2(x1)))))))))
1022.76/289.12	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2^1(3(1(1(3(0(5(2(x1))))))))
1022.76/289.12	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 3^1(1(1(3(0(5(2(x1)))))))
1022.76/289.12	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 1^1(1(3(0(5(2(x1))))))
1022.76/289.12	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 1^1(3(0(5(2(x1)))))
1022.76/289.12	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 3^1(0(5(2(x1))))
1022.76/289.12	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 0^1(5(2(x1)))
1022.76/289.12	   5^1(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5^1(1(3(2(1(3(2(0(0(3(x1))))))))))
1022.76/289.12	   5^1(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 1^1(3(2(1(3(2(0(0(3(x1)))))))))
1022.76/289.12	   5^1(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 3^1(2(1(3(2(0(0(3(x1))))))))
1022.76/289.12	   5^1(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 2^1(1(3(2(0(0(3(x1)))))))
1022.76/289.12	   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)))))))))))
1022.76/289.12	   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))))))))))
1022.76/289.12	   0^1(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 3^1(3(2(3(2(0(0(0(4(x1)))))))))
1022.76/289.12	   0^1(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 3^1(2(3(2(0(0(0(4(x1))))))))
1022.76/289.12	   0^1(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 2^1(3(2(0(0(0(4(x1)))))))
1022.76/289.12	   0^1(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 3^1(2(0(0(0(4(x1))))))
1022.76/289.12	   0^1(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 2^1(0(0(0(4(x1)))))
1022.76/289.12	   0^1(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0^1(0(0(4(x1))))
1022.76/289.12	   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))))))))))))
1022.76/289.12	   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)))))))))))
1022.76/289.12	   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))))))))))
1022.76/289.12	   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)))))))))
1022.76/289.12	   2^1(4(2(2(5(2(3(3(2(0(1(0(x1)))))))))))) -> 2^1(2(3(3(2(0(1(0(x1))))))))
1022.76/289.12	   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))))))))))))
1022.76/289.12	   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)))))))))))
1022.76/289.12	   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))))))))))
1022.76/289.12	   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)))))))))
1022.76/289.12	   1^1(0(4(1(3(1(5(0(2(4(4(5(x1)))))))))))) -> 1^1(3(5(0(2(4(4(5(x1))))))))
1022.76/289.12	   1^1(0(4(1(3(1(5(0(2(4(4(5(x1)))))))))))) -> 3^1(5(0(2(4(4(5(x1)))))))
1022.76/289.12	   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)))))))))))))
1022.76/289.12	   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))))))))))))
1022.76/289.12	   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)))))))))))
1022.76/289.12	   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))))))))))
1022.76/289.12	   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)))))))))
1022.76/289.12	   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))))))))
1022.76/289.12	   1^1(1(2(5(4(1(4(1(1(2(1(1(2(x1))))))))))))) -> 1^1(1(1(2(1(1(2(x1)))))))
1022.76/289.12	   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)))))))))))))
1022.76/289.12	   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))))))))))))
1022.76/289.12	   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)))))))))))
1022.76/289.12	   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))))))))))
1022.76/289.12	   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)))))))))
1022.76/289.12	   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))))))))
1022.76/289.12	   1^1(1(3(5(2(1(1(3(5(0(5(0(3(x1))))))))))))) -> 2^1(5(3(0(0(5(3(x1)))))))
1022.76/289.12	   1^1(1(3(5(2(1(1(3(5(0(5(0(3(x1))))))))))))) -> 5^1(3(0(0(5(3(x1))))))
1022.76/289.12	   1^1(1(3(5(2(1(1(3(5(0(5(0(3(x1))))))))))))) -> 3^1(0(0(5(3(x1)))))
1022.76/289.12	   1^1(1(3(5(2(1(1(3(5(0(5(0(3(x1))))))))))))) -> 0^1(0(5(3(x1))))
1022.76/289.12	   1^1(1(3(5(2(1(1(3(5(0(5(0(3(x1))))))))))))) -> 0^1(5(3(x1)))
1022.76/289.12	   1^1(1(3(5(2(1(1(3(5(0(5(0(3(x1))))))))))))) -> 5^1(3(x1))
1022.76/289.12	   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)))))))))))))
1022.76/289.12	   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))))))))))))
1022.76/289.12	   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)))))))))))
1022.76/289.12	   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))))))))))
1022.76/289.12	   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)))))))))
1022.76/289.12	   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))))))))))))))
1022.76/289.12	   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)))))))))))))
1022.76/289.12	   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))))))))))))
1022.76/289.12	   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)))))))))))
1022.76/289.12	   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))))))))))
1022.76/289.12	   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)))))))))
1022.76/289.12	   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))))))))
1022.76/289.12	   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)))))))
1022.76/289.12	   4^1(1(2(0(3(1(0(5(3(0(2(2(5(1(x1)))))))))))))) -> 3^1(2(0(2(5(1(x1))))))
1022.76/289.12	   4^1(1(2(0(3(1(0(5(3(0(2(2(5(1(x1)))))))))))))) -> 2^1(0(2(5(1(x1)))))
1022.76/289.12	   4^1(1(2(0(3(1(0(5(3(0(2(2(5(1(x1)))))))))))))) -> 0^1(2(5(1(x1))))
1022.76/289.12	   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)))))))))))))))
1022.76/289.12	   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))))))))))))))
1022.76/289.12	   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)))))))))))))
1022.76/289.12	   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))))))))))))
1022.76/289.12	   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)))))))))))
1022.76/289.12	   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))))))))))
1022.76/289.12	   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)))))))))))))))
1022.76/289.12	   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))))))))))))))
1022.76/289.12	   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)))))))))))))
1022.76/289.12	   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))))))))))))
1022.76/289.12	   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)))))))))))
1022.76/289.12	   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))))))))))
1022.76/289.12	   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)))))))))
1022.76/289.12	   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))))))))
1022.76/289.12	   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)))))))
1022.76/289.12	   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))))))
1022.76/289.12	   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)))))))))))))))
1022.76/289.12	   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))))))))))))))
1022.76/289.12	   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)))))))))))))
1022.76/289.12	   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))))))))))))
1022.76/289.12	   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)))))))))))
1022.76/289.12	   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))))))))))
1022.76/289.12	   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)))))))))
1022.76/289.12	   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))))))))
1022.76/289.12	   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)))))))
1022.76/289.12	   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))))))
1022.76/289.12	   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))))))))))))))))
1022.76/289.12	   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)))))))))))))))
1022.76/289.12	   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))))))))))))))
1022.76/289.12	   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)))))))))))))
1022.76/289.12	   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))))))))))))
1022.76/289.12	   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)))))))))))
1022.76/289.12	   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))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))
1022.76/289.12	   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))))))))))))))))
1022.76/289.12	   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)))))))))))))))
1022.76/289.12	   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))))))))))))))
1022.76/289.12	   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)))))))))))))
1022.76/289.12	   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))))))))))))
1022.76/289.12	   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)))))))))))
1022.76/289.12	   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))))))))))
1022.76/289.12	   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)))))))))
1022.76/289.12	   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))))))))
1022.76/289.12	   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)))))))
1022.76/289.12	   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))))))
1022.76/289.12	   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)))))
1022.76/289.12	   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))))
1022.76/289.12	   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)))
1022.76/289.12	   0^1(2(4(4(0(1(1(3(2(3(0(2(3(2(3(0(2(0(x1)))))))))))))))))) -> 0^1(0(x1))
1022.76/289.12	   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))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))
1022.76/289.12	   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))))))))))))))))
1022.76/289.12	   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)))))))))))))))
1022.76/289.12	   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))))))))))))))
1022.76/289.12	   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)))))))))))))
1022.76/289.12	   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))))))))))))
1022.76/289.12	   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)))))))))))
1022.76/289.12	   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))))))))))
1022.76/289.12	   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)))))))))
1022.76/289.12	   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))))))))
1022.76/289.12	   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))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))
1022.76/289.12	   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))))))))))))))))
1022.76/289.12	   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)))))))))))))))
1022.76/289.12	   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))))))))))))))
1022.76/289.12	   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)))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))
1022.76/289.12	   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))))))))))))))))
1022.76/289.12	   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)))))))))))))))
1022.76/289.12	   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))))))))))))))
1022.76/289.12	   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)))))))))))))
1022.76/289.12	   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))))))))))))
1022.76/289.12	   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)))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))
1022.76/289.12	   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))))))))))))))))
1022.76/289.12	   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)))))))))))))))
1022.76/289.12	   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))))))))))))))
1022.76/289.12	   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)))))))))))))
1022.76/289.12	   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))))))))))))
1022.76/289.12	   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)))))))))))
1022.76/289.12	   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))))))))))
1022.76/289.12	   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)))))))))
1022.76/289.12	   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))))))))
1022.76/289.12	   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)))))))
1022.76/289.12	   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))))))
1022.76/289.12	   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)))))
1022.76/289.12	   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))))
1022.76/289.12	   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)))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))
1022.76/289.12	   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))))))))))))))))
1022.76/289.12	   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)))))))))))))))
1022.76/289.12	   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))))))))))))))
1022.76/289.12	   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)))))))))))))
1022.76/289.12	   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))))))))))))
1022.76/289.12	   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)))))))))))
1022.76/289.12	   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))))))))))
1022.76/289.12	   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)))))))))
1022.76/289.12	   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))))))))
1022.76/289.12	   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)))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))
1022.76/289.12	   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))))))))))))))))
1022.76/289.12	   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)))))))))))))))
1022.76/289.12	   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))))))))))))))
1022.76/289.12	   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)))))))))))))
1022.76/289.12	   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))))))))))))
1022.76/289.12	   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)))))))))))
1022.76/289.12	   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))))))))))
1022.76/289.12	   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)))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))
1022.76/289.12	   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))))))))))))))))
1022.76/289.12	   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)))))))))))))))
1022.76/289.12	   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)))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))
1022.76/289.12	   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))))))))))))))))
1022.76/289.12	   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)))))))))))))))
1022.76/289.12	   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))))))))))))))
1022.76/289.12	   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)))))))))))))
1022.76/289.12	   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))))))))))))
1022.76/289.12	   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)))))))))))
1022.76/289.12	   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))))))))))
1022.76/289.12	   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)))))))))
1022.76/289.12	   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))))))))
1022.76/289.12	   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)))))))
1022.76/289.12	   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))))))
1022.76/289.12	   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)))))
1022.76/289.12	   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))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))
1022.76/289.12	   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))))))))))))))))
1022.76/289.12	   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)))))))))))))))
1022.76/289.12	   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))))))))))))))
1022.76/289.12	   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)))))))))))))
1022.76/289.12	   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))))))))))))
1022.76/289.12	   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)))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))
1022.76/289.12	   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))))))))))))))))
1022.76/289.12	   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)))))))))))))))
1022.76/289.12	   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))))))))))))))
1022.76/289.12	   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)))))))))))))
1022.76/289.12	   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))))))))))))
1022.76/289.12	   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)))))))))))
1022.76/289.12	   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))))))))))
1022.76/289.12	   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)))))))))
1022.76/289.12	   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))))))))
1022.76/289.12	   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)))))))
1022.76/289.12	   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))))))
1022.76/289.12	   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)))))
1022.76/289.12	   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))))
1022.76/289.12	   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)))
1022.76/289.12	   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))
1022.76/289.12	   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)
1022.76/289.12	   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)))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))
1022.76/289.12	   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))))))))))))))))
1022.76/289.12	   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)))))))))))))))
1022.76/289.12	   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))))))))))))))
1022.76/289.12	   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)))))))))))))
1022.76/289.12	   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))))))))))))
1022.76/289.12	   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)))))))))))
1022.76/289.12	   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))))))))))
1022.76/289.12	   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)))))))))
1022.76/289.12	   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))))))))
1022.76/289.12	   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)))))))
1022.76/289.12	   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))))))
1022.76/289.12	   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)))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))
1022.76/289.12	   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))))))))))))))))
1022.76/289.12	   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)))))))))))))))
1022.76/289.12	   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))))))))))))))
1022.76/289.12	   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)))))))))))))
1022.76/289.12	   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))))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))
1022.76/289.12	   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))))))))))))))))
1022.76/289.12	   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)))))))))))))))
1022.76/289.12	   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))))))))))))))
1022.76/289.12	   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)))))))))))))
1022.76/289.12	   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))))))))))))
1022.76/289.12	   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)))))))))))
1022.76/289.12	   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))))))))))
1022.76/289.12	   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)))))))))
1022.76/289.12	   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))))))))
1022.76/289.12	   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)))))))
1022.76/289.12	   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))))))
1022.76/289.12	   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)))))
1022.76/289.12	   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))))
1022.76/289.12	   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)))
1022.76/289.12	   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))))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))
1022.76/289.12	   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))))))))))))))))
1022.76/289.12	   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)))))))))))))))
1022.76/289.12	   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))))))))))))))
1022.76/289.12	   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)))))))))))))
1022.76/289.12	   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))))))))))))
1022.76/289.12	   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)))))))))))
1022.76/289.12	   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))))))))))
1022.76/289.12	   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)))))))))
1022.76/289.12	   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))))))))
1022.76/289.12	   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)))))))
1022.76/289.12	   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))))))
1022.76/289.12	   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)))))
1022.76/289.12	   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))))
1022.76/289.12	   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))))))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))
1022.76/289.12	   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))))))))))))))))
1022.76/289.12	   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)))))))))))))))
1022.76/289.12	   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))))))))))))))
1022.76/289.12	   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)))))))))))))
1022.76/289.12	   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))))))))))))
1022.76/289.12	   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)))))))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))
1022.76/289.12	   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))))))))))))))))
1022.76/289.12	   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)))))))))))))))
1022.76/289.12	   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))))))))))))))
1022.76/289.12	   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)))))))))))))
1022.76/289.12	   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))))))))))))
1022.76/289.12	   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)))))))))))
1022.76/289.12	   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)))))))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))
1022.76/289.12	   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))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))
1022.76/289.12	   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))))))))))))))))
1022.76/289.12	   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)))))))))))))))
1022.76/289.12	   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))))))))))))))
1022.76/289.12	   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)))))))))))))
1022.76/289.12	   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))))))))))))
1022.76/289.12	   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)))))))))))
1022.76/289.12	   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))))))))))
1022.76/289.12	   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)))))))))
1022.76/289.12	   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))))))))
1022.76/289.12	   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)))))))
1022.76/289.12	   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))))))
1022.76/289.12	   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)))))
1022.76/289.12	   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))))
1022.76/289.12	   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))))))))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))
1022.76/289.12	   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))))))))))))))))
1022.76/289.12	   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)))))))))))))))
1022.76/289.12	   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))))))))))))))
1022.76/289.12	   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)))))))))))))
1022.76/289.12	   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)))))))))))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))))))))))
1022.76/289.12	   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)))))))))))))))))))))))))))
1022.76/289.12	   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))))))))))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))
1022.76/289.13	   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))))))))))))))))
1022.76/289.13	   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)))))))))))))))
1022.76/289.13	   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))))))))))))))
1022.76/289.13	   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)))))))))))))
1022.76/289.13	   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))))))))))))
1022.76/289.13	   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)))))))))))
1022.76/289.13	   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))))))))))
1022.76/289.13	   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)))))))))
1022.76/289.13	   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))))))))
1022.76/289.13	   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)))))))
1022.76/289.13	   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))))))
1022.76/289.13	   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)))))
1022.76/289.13	   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))))
1022.76/289.13	   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)))
1022.76/289.13	   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))
1022.76/289.13	   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)
1022.76/289.13	
1022.76/289.13	The TRS R consists of the following rules:
1022.76/289.13	
1022.76/289.13	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1022.76/289.13	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1022.76/289.13	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1022.76/289.13	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1022.76/289.13	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1022.76/289.13	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1022.76/289.13	   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))))))))))))
1022.76/289.13	   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))))))))))))
1022.76/289.13	   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)))))))))))))
1022.76/289.13	   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)))))))))))))
1022.76/289.13	   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)))))))))))))
1022.76/289.13	   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))))))))))))))
1022.76/289.13	   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)))))))))))))))
1022.76/289.13	   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)))))))))))))))
1022.76/289.13	   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)))))))))))))))
1022.76/289.13	   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))))))))))))))))
1022.76/289.13	   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))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))))))))))))))
1022.76/289.13	
1022.76/289.13	Q is empty.
1022.76/289.13	We have to consider all minimal (P,Q,R)-chains.
1022.76/289.13	----------------------------------------
1022.76/289.13	
1022.76/289.13	(9) QDPOrderProof (EQUIVALENT)
1022.76/289.13	We use the reduction pair processor [LPAR04,JAR06].
1022.76/289.13	
1022.76/289.13	
1022.76/289.13	The following pairs can be oriented strictly and are deleted.
1022.76/289.13	
1022.76/289.13	   5^1(4(3(1(2(1(1(0(x1)))))))) -> 4^1(3(2(1(1(1(0(x1)))))))
1022.76/289.13	   5^1(4(3(1(2(1(1(0(x1)))))))) -> 3^1(2(1(1(1(0(x1))))))
1022.76/289.13	   5^1(4(3(1(2(1(1(0(x1)))))))) -> 2^1(1(1(1(0(x1)))))
1022.76/289.13	   5^1(4(3(1(2(1(1(0(x1)))))))) -> 1^1(1(1(0(x1))))
1022.76/289.13	   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)))))))))))
1022.76/289.13	   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))))))))))
1022.76/289.13	   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)))))))))
1022.76/289.13	   2^1(4(2(2(5(2(3(3(2(0(1(0(x1)))))))))))) -> 2^1(2(3(3(2(0(1(0(x1))))))))
1022.76/289.13	   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))))))))))
1022.76/289.13	   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)))))))))
1022.76/289.13	   1^1(0(4(1(3(1(5(0(2(4(4(5(x1)))))))))))) -> 1^1(3(5(0(2(4(4(5(x1))))))))
1022.76/289.13	   1^1(0(4(1(3(1(5(0(2(4(4(5(x1)))))))))))) -> 3^1(5(0(2(4(4(5(x1)))))))
1022.76/289.13	   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)))))))))
1022.76/289.13	   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))))))))
1022.76/289.13	   1^1(1(2(5(4(1(4(1(1(2(1(1(2(x1))))))))))))) -> 1^1(1(1(2(1(1(2(x1)))))))
1022.76/289.13	   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)))))))))))))
1022.76/289.13	   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))))))))))))
1022.76/289.13	   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)))))))))))
1022.76/289.13	   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))))))))))
1022.76/289.13	   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)))))))))
1022.76/289.13	   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))))))))
1022.76/289.13	   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)))))))
1022.76/289.13	   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))))))
1022.76/289.13	   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)))))))))))))
1022.76/289.13	   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))))))))))))
1022.76/289.13	   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)))))))))))
1022.76/289.13	   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))))))))))
1022.76/289.13	   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)))))))))
1022.76/289.13	   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))))))))
1022.76/289.13	   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)))))))
1022.76/289.13	   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))))))
1022.76/289.13	   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))))))))))))))))
1022.76/289.13	   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)))))))))))))))
1022.76/289.13	   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))))))))))))))
1022.76/289.13	   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)))))))))))))
1022.76/289.13	   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))))))))))))
1022.76/289.13	   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)))))))))))
1022.76/289.13	   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))))))))))
1022.76/289.13	   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)))))))))
1022.76/289.13	   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))))))))
1022.76/289.13	   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)))))))
1022.76/289.13	   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))))))
1022.76/289.13	   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)))))
1022.76/289.13	   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))))
1022.76/289.13	   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)))
1022.76/289.13	   0^1(2(4(4(0(1(1(3(2(3(0(2(3(2(3(0(2(0(x1)))))))))))))))))) -> 0^1(0(x1))
1022.76/289.13	   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)))))))))))))))))
1022.76/289.13	   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))))))))))))))))
1022.76/289.13	   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)))))))))))))))
1022.76/289.13	   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))))))))))))))
1022.76/289.13	   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)))))))))))))
1022.76/289.13	   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))))))))))))
1022.76/289.13	   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))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))
1022.76/289.13	   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))))))))))))))))
1022.76/289.13	   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)))))))))))))))
1022.76/289.13	   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))))))))))))))
1022.76/289.13	   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)))))))))))))
1022.76/289.13	   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))))))))))))
1022.76/289.13	   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)))))))))))
1022.76/289.13	   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))))))))))
1022.76/289.13	   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)))))))))
1022.76/289.13	   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))))))))
1022.76/289.13	   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)))))))
1022.76/289.13	   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))))))
1022.76/289.13	   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)))))
1022.76/289.13	   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))))
1022.76/289.13	   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)))))))))))))
1022.76/289.13	   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))))))))))))
1022.76/289.13	   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)))))))))))
1022.76/289.13	   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))))))))))
1022.76/289.13	   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)))))))))
1022.76/289.13	   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))))))))
1022.76/289.13	   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))))))))))))
1022.76/289.13	   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)))))))))))
1022.76/289.13	   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))))))))))
1022.76/289.13	   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)))))))))))))))
1022.76/289.13	   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)))))))))))
1022.76/289.13	   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))))))))))
1022.76/289.13	   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)))))))))
1022.76/289.13	   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))))))))
1022.76/289.13	   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)))))))
1022.76/289.13	   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))))))
1022.76/289.13	   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)))))
1022.76/289.13	   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)))))))))))))))))
1022.76/289.13	   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))))))))))))))))
1022.76/289.13	   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)))))))))))))))
1022.76/289.13	   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))))))))))))))
1022.76/289.13	   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)))))))))))))
1022.76/289.13	   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))))))))))))
1022.76/289.13	   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))))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))
1022.76/289.13	   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))))))))))))))))
1022.76/289.13	   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)))))))))))))))
1022.76/289.13	   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))))))))))))))
1022.76/289.13	   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)))))))))))))
1022.76/289.13	   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))))))))))))
1022.76/289.13	   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)))))))))))
1022.76/289.13	   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))))))))))
1022.76/289.13	   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)))))))))
1022.76/289.13	   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))))))))
1022.76/289.13	   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)))))))
1022.76/289.13	   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))))))
1022.76/289.13	   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)))))))))))))
1022.76/289.13	   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))))))))))))))))
1022.76/289.13	   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)))))))))))))))
1022.76/289.13	   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))))))))))))))
1022.76/289.13	   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)))))))))))))
1022.76/289.13	   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))))))))))))
1022.76/289.13	   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)))))))))))
1022.76/289.13	   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))))))))))
1022.76/289.13	   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)))))))))
1022.76/289.13	   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))))))))
1022.76/289.13	   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)))))))
1022.76/289.13	   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))))))
1022.76/289.13	   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)))))
1022.76/289.13	   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))))
1022.76/289.13	   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)))
1022.76/289.13	   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)))))))))
1022.76/289.13	   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))))))))
1022.76/289.13	   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)))))))
1022.76/289.13	   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))))))
1022.76/289.13	   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)))))
1022.76/289.13	   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))))
1022.76/289.13	   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)))))))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))
1022.76/289.13	   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))))))))))))))))
1022.76/289.13	   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)))))))))))))))
1022.76/289.13	   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))))))))))))))
1022.76/289.13	   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)))))))))))))
1022.76/289.13	   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))))))))))))
1022.76/289.13	   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))))))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))
1022.76/289.13	   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))))))))))))))))
1022.76/289.13	   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)))))))))))))))
1022.76/289.13	   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))))))))))))))
1022.76/289.13	   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)))))))))))))
1022.76/289.13	   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))))))))))))
1022.76/289.13	   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)))))))))))
1022.76/289.13	   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)))))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))
1022.76/289.13	   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))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))
1022.76/289.13	   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))))))))))))))))
1022.76/289.13	   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)))))))))))))))
1022.76/289.13	   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))))))))))))))
1022.76/289.13	   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)))))))))))))
1022.76/289.13	   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))))))))))))
1022.76/289.13	   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)))))))))))
1022.76/289.13	   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))))))))))
1022.76/289.13	   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)))))))))
1022.76/289.13	   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))))))))
1022.76/289.13	   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)))))))
1022.76/289.13	   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))))))
1022.76/289.13	   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)))))
1022.76/289.13	   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))))
1022.76/289.13	   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))))))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))
1022.76/289.13	   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))))))))))))))))
1022.76/289.13	   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)))))))))))))))
1022.76/289.13	   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))))))))))))))
1022.76/289.13	   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)))))))))))))
1022.76/289.13	   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))))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))
1022.76/289.13	   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))))))))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))
1022.76/289.13	   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))))))))))))))))
1022.76/289.13	   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)))))))))))))))
1022.76/289.13	   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))))))))))))))
1022.76/289.13	   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)))))))))))))
1022.76/289.13	   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))))))))))))
1022.76/289.13	   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)))))))))))
1022.76/289.13	   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))))))))))
1022.76/289.13	   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)))))))))
1022.76/289.13	   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))))))))
1022.76/289.13	   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)))))))
1022.76/289.13	   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))))))
1022.76/289.13	   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)))))
1022.76/289.13	   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))))
1022.76/289.13	   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)))
1022.76/289.13	   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))
1022.76/289.13	   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)
1022.76/289.13	The remaining pairs can at least be oriented weakly.
1022.76/289.13	Used ordering:  Polynomial interpretation [POLO]:
1022.76/289.13	
1022.76/289.13	   POL(0(x_1)) = x_1
1022.76/289.13	   POL(0^1(x_1)) = x_1
1022.76/289.13	   POL(1(x_1)) = x_1
1022.76/289.13	   POL(1^1(x_1)) = x_1
1022.76/289.13	   POL(2(x_1)) = x_1
1022.76/289.13	   POL(2^1(x_1)) = x_1
1022.76/289.13	   POL(3(x_1)) = x_1
1022.76/289.13	   POL(3^1(x_1)) = x_1
1022.76/289.13	   POL(4(x_1)) = 1 + x_1
1022.76/289.13	   POL(4^1(x_1)) = x_1
1022.76/289.13	   POL(5(x_1)) = x_1
1022.76/289.13	   POL(5^1(x_1)) = x_1
1022.76/289.13	
1022.76/289.13	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
1022.76/289.13	
1022.76/289.13	   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)))))))))))))))
1022.76/289.13	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1022.76/289.13	   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))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))))))))))))
1022.76/289.13	   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))))))))))))
1022.76/289.13	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1022.76/289.13	   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)))))))))))))
1022.76/289.13	   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)))))))))))))
1022.76/289.13	   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)))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))))))))))))))
1022.76/289.13	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1022.76/289.13	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1022.76/289.13	   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))))))))))))
1022.76/289.13	   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)))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))
1022.76/289.13	   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)))))))))))))))
1022.76/289.13	   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))))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))))))))))))
1022.76/289.13	   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))))))))))))))
1022.76/289.13	   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)))))))))))))
1022.76/289.13	   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))))))))))))))))
1022.76/289.13	   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))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))))))))))))
1022.76/289.13	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1022.76/289.13	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1022.76/289.13	   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)))))))))))))))
1022.76/289.13	   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)))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))))))))))
1022.76/289.13	
1022.76/289.13	
1022.76/289.13	----------------------------------------
1022.76/289.13	
1022.76/289.13	(10)
1022.76/289.13	Obligation:
1022.76/289.13	Q DP problem:
1022.76/289.13	The TRS P consists of the following rules:
1022.76/289.13	
1022.76/289.13	   5^1(4(3(1(2(1(1(0(x1)))))))) -> 5^1(4(3(2(1(1(1(0(x1))))))))
1022.76/289.13	   1^1(3(3(5(2(2(5(1(x1)))))))) -> 1^1(3(5(3(2(2(5(1(x1))))))))
1022.76/289.13	   1^1(3(3(5(2(2(5(1(x1)))))))) -> 3^1(5(3(2(2(5(1(x1)))))))
1022.76/289.13	   1^1(3(3(5(2(2(5(1(x1)))))))) -> 5^1(3(2(2(5(1(x1))))))
1022.76/289.13	   1^1(3(3(5(2(2(5(1(x1)))))))) -> 3^1(2(2(5(1(x1)))))
1022.76/289.13	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2^1(1(3(2(2(0(0(5(1(1(x1))))))))))
1022.76/289.13	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 1^1(3(2(2(0(0(5(1(1(x1)))))))))
1022.76/289.13	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 3^1(2(2(0(0(5(1(1(x1))))))))
1022.76/289.13	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2^1(2(0(0(5(1(1(x1)))))))
1022.76/289.13	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2^1(0(0(5(1(1(x1))))))
1022.76/289.13	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 0^1(0(5(1(1(x1)))))
1022.76/289.13	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 0^1(5(1(1(x1))))
1022.76/289.13	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 5^1(1(1(x1)))
1022.76/289.13	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 1^1(1(x1))
1022.76/289.13	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2^1(0(2(3(1(1(3(0(5(2(x1))))))))))
1022.76/289.13	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 0^1(2(3(1(1(3(0(5(2(x1)))))))))
1022.76/289.13	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2^1(3(1(1(3(0(5(2(x1))))))))
1022.76/289.13	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 3^1(1(1(3(0(5(2(x1)))))))
1022.76/289.13	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 1^1(1(3(0(5(2(x1))))))
1022.76/289.13	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 1^1(3(0(5(2(x1)))))
1022.76/289.13	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 3^1(0(5(2(x1))))
1022.76/289.13	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 0^1(5(2(x1)))
1022.76/289.13	   5^1(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5^1(1(3(2(1(3(2(0(0(3(x1))))))))))
1022.76/289.13	   5^1(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 1^1(3(2(1(3(2(0(0(3(x1)))))))))
1022.76/289.13	   5^1(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 3^1(2(1(3(2(0(0(3(x1))))))))
1022.76/289.13	   5^1(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 2^1(1(3(2(0(0(3(x1)))))))
1022.76/289.13	   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)))))))))))
1022.76/289.13	   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))))))))))
1022.76/289.13	   0^1(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 3^1(3(2(3(2(0(0(0(4(x1)))))))))
1022.76/289.13	   0^1(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 3^1(2(3(2(0(0(0(4(x1))))))))
1022.76/289.13	   0^1(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 2^1(3(2(0(0(0(4(x1)))))))
1022.76/289.13	   0^1(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 3^1(2(0(0(0(4(x1))))))
1022.76/289.13	   0^1(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 2^1(0(0(0(4(x1)))))
1022.76/289.13	   0^1(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0^1(0(0(4(x1))))
1022.76/289.13	   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))))))))))))
1022.76/289.13	   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))))))))))))
1022.76/289.13	   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)))))))))))
1022.76/289.13	   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)))))))))))))
1022.76/289.13	   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))))))))))))
1022.76/289.13	   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)))))))))))
1022.76/289.13	   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))))))))))
1022.76/289.13	   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)))))))))))))
1022.76/289.13	   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))))))))))))
1022.76/289.13	   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)))))))))))
1022.76/289.13	   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))))))))))
1022.76/289.13	   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)))))))))
1022.76/289.13	   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))))))))
1022.76/289.13	   1^1(1(3(5(2(1(1(3(5(0(5(0(3(x1))))))))))))) -> 2^1(5(3(0(0(5(3(x1)))))))
1022.76/289.13	   1^1(1(3(5(2(1(1(3(5(0(5(0(3(x1))))))))))))) -> 5^1(3(0(0(5(3(x1))))))
1022.76/289.13	   1^1(1(3(5(2(1(1(3(5(0(5(0(3(x1))))))))))))) -> 3^1(0(0(5(3(x1)))))
1022.76/289.13	   1^1(1(3(5(2(1(1(3(5(0(5(0(3(x1))))))))))))) -> 0^1(0(5(3(x1))))
1022.76/289.13	   1^1(1(3(5(2(1(1(3(5(0(5(0(3(x1))))))))))))) -> 0^1(5(3(x1)))
1022.76/289.13	   1^1(1(3(5(2(1(1(3(5(0(5(0(3(x1))))))))))))) -> 5^1(3(x1))
1022.76/289.13	   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)))))))))))))
1022.76/289.13	   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))))))))))))
1022.76/289.13	   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)))))))))))
1022.76/289.13	   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))))))))))
1022.76/289.13	   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)))))))))
1022.76/289.13	   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))))))))))))))
1022.76/289.13	   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)))))))))))))
1022.76/289.13	   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))))))))))))
1022.76/289.13	   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)))))))))))
1022.76/289.13	   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))))))))))
1022.76/289.13	   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)))))))))
1022.76/289.13	   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))))))))
1022.76/289.13	   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)))))))
1022.76/289.13	   4^1(1(2(0(3(1(0(5(3(0(2(2(5(1(x1)))))))))))))) -> 3^1(2(0(2(5(1(x1))))))
1022.76/289.13	   4^1(1(2(0(3(1(0(5(3(0(2(2(5(1(x1)))))))))))))) -> 2^1(0(2(5(1(x1)))))
1022.76/289.13	   4^1(1(2(0(3(1(0(5(3(0(2(2(5(1(x1)))))))))))))) -> 0^1(2(5(1(x1))))
1022.76/289.13	   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)))))))))))))))
1022.76/289.13	   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))))))))))))))
1022.76/289.13	   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)))))))))))))
1022.76/289.13	   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))))))))))))
1022.76/289.13	   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)))))))))))
1022.76/289.13	   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))))))))))
1022.76/289.13	   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)))))))))))))))
1022.76/289.13	   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))))))))))))))
1022.76/289.13	   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)))))))))))))))
1022.76/289.13	   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))))))))))))))
1022.76/289.13	   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))))))))))))))))
1022.76/289.13	   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)))))))))))))))
1022.76/289.13	   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))))))))))))))
1022.76/289.13	   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)))))))))))))
1022.76/289.13	   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))))))))))))
1022.76/289.13	   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)))))))))))
1022.76/289.13	   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))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))
1022.76/289.13	   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))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))
1022.76/289.13	   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))))))))))))))))
1022.76/289.13	   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)))))))))))))))
1022.76/289.13	   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))))))))))))))
1022.76/289.13	   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)))))))))))))
1022.76/289.13	   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))))))))))))
1022.76/289.13	   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)))))))))))
1022.76/289.13	   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))))))))))
1022.76/289.13	   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)))))))))
1022.76/289.13	   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))))))))
1022.76/289.13	   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))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))
1022.76/289.13	   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))))))))))))))))
1022.76/289.13	   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)))))))))))))))
1022.76/289.13	   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))))))))))))))
1022.76/289.13	   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)))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))
1022.76/289.13	   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))))))))))))))))
1022.76/289.13	   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)))))))))))))))
1022.76/289.13	   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))))))))))))))
1022.76/289.13	   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)))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))
1022.76/289.13	   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))))))))))))))))
1022.76/289.13	   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)))))))))))))))
1022.76/289.13	   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))))))))))))))
1022.76/289.13	   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)))))))))))))
1022.76/289.13	   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)))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))
1022.76/289.13	   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))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))
1022.76/289.13	   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))))))))))))))))
1022.76/289.13	   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)))))))))))))))
1022.76/289.13	   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))))))))))))))
1022.76/289.13	   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)))))))))))))
1022.76/289.13	   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))))))))))))
1022.76/289.13	   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))))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))
1022.76/289.13	   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))))))))))))))))
1022.76/289.13	   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)))))))))))))))
1022.76/289.13	   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))))))))))))))
1022.76/289.13	   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)))))))))))))
1022.76/289.13	   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))))))))))))
1022.76/289.13	   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)))))))))))
1022.76/289.13	   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))))))))))
1022.76/289.13	   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)))))))))
1022.76/289.13	   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))))))))
1022.76/289.13	   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)))))))
1022.76/289.13	   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))))))
1022.76/289.13	   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)))))
1022.76/289.13	   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))))
1022.76/289.13	   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)))
1022.76/289.13	   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))
1022.76/289.13	   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)
1022.76/289.13	   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)))))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))
1022.76/289.13	   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))))))))))))))))
1022.76/289.13	   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)))))))))))))))
1022.76/289.13	   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))))))))))))))
1022.76/289.13	   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))))))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))))
1022.76/289.13	   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))))))))))))))))))
1022.76/289.13	   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)))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))
1022.76/289.14	   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))))))))))))))))
1022.76/289.14	   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)))))))))))))))
1022.76/289.14	   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))))))))))))))
1022.76/289.14	   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)))))))))))))
1022.76/289.14	   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))))))))))))
1022.76/289.14	   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)))))))))))
1022.76/289.14	   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))))))))))
1022.76/289.14	   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))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))
1022.76/289.14	
1022.76/289.14	The TRS R consists of the following rules:
1022.76/289.14	
1022.76/289.14	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1022.76/289.14	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1022.76/289.14	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1022.76/289.14	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1022.76/289.14	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1022.76/289.14	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1022.76/289.14	   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))))))))))))
1022.76/289.14	   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))))))))))))
1022.76/289.14	   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)))))))))))))
1022.76/289.14	   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)))))))))))))
1022.76/289.14	   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)))))))))))))
1022.76/289.14	   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))))))))))))))
1022.76/289.14	   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)))))))))))))))
1022.76/289.14	   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)))))))))))))))
1022.76/289.14	   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)))))))))))))))
1022.76/289.14	   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))))))))))))))))
1022.76/289.14	   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))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))))))))
1022.76/289.14	
1022.76/289.14	Q is empty.
1022.76/289.14	We have to consider all minimal (P,Q,R)-chains.
1022.76/289.14	----------------------------------------
1022.76/289.14	
1022.76/289.14	(11) DependencyGraphProof (EQUIVALENT)
1022.76/289.14	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 54 less nodes.
1022.76/289.14	----------------------------------------
1022.76/289.14	
1022.76/289.14	(12)
1022.76/289.14	Complex Obligation (AND)
1022.76/289.14	
1022.76/289.14	----------------------------------------
1022.76/289.14	
1022.76/289.14	(13)
1022.76/289.14	Obligation:
1022.76/289.14	Q DP problem:
1022.76/289.14	The TRS P consists of the following rules:
1022.76/289.14	
1022.76/289.14	   5^1(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5^1(1(3(2(1(3(2(0(0(3(x1))))))))))
1022.76/289.14	   5^1(4(3(1(2(1(1(0(x1)))))))) -> 5^1(4(3(2(1(1(1(0(x1))))))))
1022.76/289.14	   5^1(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 1^1(3(2(1(3(2(0(0(3(x1)))))))))
1022.76/289.14	   1^1(3(3(5(2(2(5(1(x1)))))))) -> 1^1(3(5(3(2(2(5(1(x1))))))))
1022.76/289.14	   1^1(3(3(5(2(2(5(1(x1)))))))) -> 3^1(5(3(2(2(5(1(x1)))))))
1022.76/289.14	   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)))))))))))))))
1022.76/289.14	   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))))))))))))))
1022.76/289.14	   5^1(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 3^1(2(1(3(2(0(0(3(x1))))))))
1022.76/289.14	   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))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))
1022.76/289.14	   5^1(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 2^1(1(3(2(0(0(3(x1)))))))
1022.76/289.14	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2^1(1(3(2(2(0(0(5(1(1(x1))))))))))
1022.76/289.14	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 1^1(3(2(2(0(0(5(1(1(x1)))))))))
1022.76/289.14	   1^1(3(3(5(2(2(5(1(x1)))))))) -> 5^1(3(2(2(5(1(x1))))))
1022.76/289.14	   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)))))))))))))))
1022.76/289.14	   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))))))))))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))
1022.76/289.14	   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)))))))))))
1022.76/289.14	   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))))))))))
1022.76/289.14	   1^1(3(3(5(2(2(5(1(x1)))))))) -> 3^1(2(2(5(1(x1)))))
1022.76/289.14	   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))))))))))))))))
1022.76/289.14	   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))))))))))))
1022.76/289.14	   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)))))))))))
1022.76/289.14	   0^1(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 3^1(3(2(3(2(0(0(0(4(x1)))))))))
1022.76/289.14	   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)))))))))))))))
1022.76/289.14	   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)))))))))))))
1022.76/289.14	   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))))))))))))
1022.76/289.14	   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)))))))))))
1022.76/289.14	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 3^1(2(2(0(0(5(1(1(x1))))))))
1022.76/289.14	   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))))))))))))))
1022.76/289.14	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2^1(2(0(0(5(1(1(x1)))))))
1022.76/289.14	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2^1(0(0(5(1(1(x1))))))
1022.76/289.14	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 0^1(0(5(1(1(x1)))))
1022.76/289.14	   0^1(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 3^1(2(3(2(0(0(0(4(x1))))))))
1022.76/289.14	   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))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   0^1(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 2^1(3(2(0(0(0(4(x1)))))))
1022.76/289.14	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 0^1(5(1(1(x1))))
1022.76/289.14	   0^1(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 3^1(2(0(0(0(4(x1))))))
1022.76/289.14	   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))))))))))))))))))
1022.76/289.14	   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))))))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))
1022.76/289.14	   0^1(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 2^1(0(0(0(4(x1)))))
1022.76/289.14	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 5^1(1(1(x1)))
1022.76/289.14	   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)))))))))))))))))
1022.76/289.14	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 1^1(1(x1))
1022.76/289.14	   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)))))))))))))
1022.76/289.14	   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))))))))))))
1022.76/289.14	   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)))))))))))
1022.76/289.14	   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))))))))))
1022.76/289.14	   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)))))))))
1022.76/289.14	   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))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))
1022.76/289.14	   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))))))))
1022.76/289.14	   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))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))
1022.76/289.14	   1^1(1(3(5(2(1(1(3(5(0(5(0(3(x1))))))))))))) -> 2^1(5(3(0(0(5(3(x1)))))))
1022.76/289.14	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2^1(0(2(3(1(1(3(0(5(2(x1))))))))))
1022.76/289.14	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 0^1(2(3(1(1(3(0(5(2(x1)))))))))
1022.76/289.14	   0^1(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0^1(0(0(4(x1))))
1022.76/289.14	   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)))))))))))))))
1022.76/289.14	   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))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))
1022.76/289.14	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2^1(3(1(1(3(0(5(2(x1))))))))
1022.76/289.14	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 3^1(1(1(3(0(5(2(x1)))))))
1022.76/289.14	   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))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))
1022.76/289.14	   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)))))))))))))
1022.76/289.14	   1^1(1(3(5(2(1(1(3(5(0(5(0(3(x1))))))))))))) -> 5^1(3(0(0(5(3(x1))))))
1022.76/289.14	   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))))))))))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 1^1(1(3(0(5(2(x1))))))
1022.76/289.14	   1^1(1(3(5(2(1(1(3(5(0(5(0(3(x1))))))))))))) -> 3^1(0(0(5(3(x1)))))
1022.76/289.14	   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))))))))))))))))))
1022.76/289.14	   1^1(1(3(5(2(1(1(3(5(0(5(0(3(x1))))))))))))) -> 0^1(0(5(3(x1))))
1022.76/289.14	   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))))))))))))
1022.76/289.14	   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)))))))))))))))))
1022.76/289.14	   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)))))))))))
1022.76/289.14	   1^1(1(3(5(2(1(1(3(5(0(5(0(3(x1))))))))))))) -> 0^1(5(3(x1)))
1022.76/289.14	   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))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))
1022.76/289.14	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 1^1(3(0(5(2(x1)))))
1022.76/289.14	   1^1(1(3(5(2(1(1(3(5(0(5(0(3(x1))))))))))))) -> 5^1(3(x1))
1022.76/289.14	   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)))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))
1022.76/289.14	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 3^1(0(5(2(x1))))
1022.76/289.14	   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))))))))))))))))))))))))))
1022.76/289.14	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 0^1(5(2(x1)))
1022.76/289.14	   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)))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))
1022.76/289.14	   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))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))
1022.76/289.14	   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)))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))
1022.76/289.14	   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))))))))))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   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)))))))))))))
1022.76/289.14	   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))))))))))))
1022.76/289.14	   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)))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))
1022.76/289.14	   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))))))))))))))))
1022.76/289.14	   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)))))))))))))))
1022.76/289.14	   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))))))))))))))
1022.76/289.14	   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)))))))))))))
1022.76/289.14	   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))))))))))))
1022.76/289.14	   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)))))))))))
1022.76/289.14	   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))))))))))
1022.76/289.14	   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)))))))))
1022.76/289.14	   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))))))))
1022.76/289.14	   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)))))))
1022.76/289.14	   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))))))
1022.76/289.14	   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)))))
1022.76/289.14	   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))))
1022.76/289.14	   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)))
1022.76/289.14	   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))
1022.76/289.14	   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)
1022.76/289.14	   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)))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))
1022.76/289.14	   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))))))))))))))))
1022.76/289.14	   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)))))))))))))))
1022.76/289.14	   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))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))
1022.76/289.14	
1022.76/289.14	The TRS R consists of the following rules:
1022.76/289.14	
1022.76/289.14	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1022.76/289.14	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1022.76/289.14	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1022.76/289.14	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1022.76/289.14	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1022.76/289.14	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1022.76/289.14	   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))))))))))))
1022.76/289.14	   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))))))))))))
1022.76/289.14	   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)))))))))))))
1022.76/289.14	   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)))))))))))))
1022.76/289.14	   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)))))))))))))
1022.76/289.14	   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))))))))))))))
1022.76/289.14	   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)))))))))))))))
1022.76/289.14	   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)))))))))))))))
1022.76/289.14	   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)))))))))))))))
1022.76/289.14	   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))))))))))))))))
1022.76/289.14	   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))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))))))))
1022.76/289.14	
1022.76/289.14	Q is empty.
1022.76/289.14	We have to consider all minimal (P,Q,R)-chains.
1022.76/289.14	----------------------------------------
1022.76/289.14	
1022.76/289.14	(14) QDPOrderProof (EQUIVALENT)
1022.76/289.14	We use the reduction pair processor [LPAR04,JAR06].
1022.76/289.14	
1022.76/289.14	
1022.76/289.14	The following pairs can be oriented strictly and are deleted.
1022.76/289.14	
1022.76/289.14	   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))))))))))))))
1022.76/289.14	   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)))))))))))))))))
1022.76/289.14	   1^1(3(3(5(2(2(5(1(x1)))))))) -> 5^1(3(2(2(5(1(x1))))))
1022.76/289.14	   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))))))))))))))
1022.76/289.14	   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))))))))))))))))))
1022.76/289.14	   1^1(3(3(5(2(2(5(1(x1)))))))) -> 3^1(2(2(5(1(x1)))))
1022.76/289.14	   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))))))))))))))))
1022.76/289.14	   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)))))))))))
1022.76/289.14	   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)))))))))))))))
1022.76/289.14	   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))))))))))))))
1022.76/289.14	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 0^1(0(5(1(1(x1)))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 0^1(5(1(1(x1))))
1022.76/289.14	   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))))))))))))))))))
1022.76/289.14	   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))))))))))
1022.76/289.14	   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))))))))))))))))))
1022.76/289.14	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 5^1(1(1(x1)))
1022.76/289.14	   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)))))))))))))))))
1022.76/289.14	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 1^1(1(x1))
1022.76/289.14	   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))))))))
1022.76/289.14	   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))))))))))))))))
1022.76/289.14	   1^1(1(3(5(2(1(1(3(5(0(5(0(3(x1))))))))))))) -> 2^1(5(3(0(0(5(3(x1)))))))
1022.76/289.14	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 0^1(2(3(1(1(3(0(5(2(x1)))))))))
1022.76/289.14	   0^1(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0^1(0(0(4(x1))))
1022.76/289.14	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2^1(3(1(1(3(0(5(2(x1))))))))
1022.76/289.14	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 3^1(1(1(3(0(5(2(x1)))))))
1022.76/289.14	   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))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))
1022.76/289.14	   1^1(1(3(5(2(1(1(3(5(0(5(0(3(x1))))))))))))) -> 5^1(3(0(0(5(3(x1))))))
1022.76/289.14	   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))))))))))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 1^1(1(3(0(5(2(x1))))))
1022.76/289.14	   1^1(1(3(5(2(1(1(3(5(0(5(0(3(x1))))))))))))) -> 3^1(0(0(5(3(x1)))))
1022.76/289.14	   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))))))))))))))))))
1022.76/289.14	   1^1(1(3(5(2(1(1(3(5(0(5(0(3(x1))))))))))))) -> 0^1(0(5(3(x1))))
1022.76/289.14	   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)))))))))))))))))
1022.76/289.14	   1^1(1(3(5(2(1(1(3(5(0(5(0(3(x1))))))))))))) -> 0^1(5(3(x1)))
1022.76/289.14	   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))))))))))))))))))))))))))))
1022.76/289.14	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 1^1(3(0(5(2(x1)))))
1022.76/289.14	   1^1(1(3(5(2(1(1(3(5(0(5(0(3(x1))))))))))))) -> 5^1(3(x1))
1022.76/289.14	   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)))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))))
1022.76/289.14	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 3^1(0(5(2(x1))))
1022.76/289.14	   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))))))))))))))))))))))))))
1022.76/289.14	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 0^1(5(2(x1)))
1022.76/289.14	   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)))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))
1022.76/289.14	   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)))))))))))))))))
1022.76/289.14	   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))))))))))))))))
1022.76/289.14	   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)))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))
1022.76/289.14	   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)))))))))))))))
1022.76/289.14	   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))))))))))))))
1022.76/289.14	   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)))))))))))))
1022.76/289.14	   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))))))))))))
1022.76/289.14	   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)))))))))))))))
1022.76/289.14	   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))))))))))))))
1022.76/289.14	   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)))))))))))))
1022.76/289.14	   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))))))))))))
1022.76/289.14	   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)))))))))))
1022.76/289.14	   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))))))))))
1022.76/289.14	   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)))))))))
1022.76/289.14	   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))))))))
1022.76/289.14	   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)))))))
1022.76/289.14	   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))))))
1022.76/289.14	   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)))))
1022.76/289.14	   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))))
1022.76/289.14	   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)))
1022.76/289.14	   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))
1022.76/289.14	   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)
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))
1022.76/289.14	   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))))))))))))))))
1022.76/289.14	   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)))))))))))))))
1022.76/289.14	   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))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))
1022.76/289.14	The remaining pairs can at least be oriented weakly.
1022.76/289.14	Used ordering:  Polynomial interpretation [POLO]:
1022.76/289.14	
1022.76/289.14	   POL(0(x_1)) = 1 + x_1
1022.76/289.14	   POL(0^1(x_1)) = 1 + x_1
1022.76/289.14	   POL(1(x_1)) = x_1
1022.76/289.14	   POL(1^1(x_1)) = 1 + x_1
1022.76/289.14	   POL(2(x_1)) = x_1
1022.76/289.14	   POL(2^1(x_1)) = 1 + x_1
1022.76/289.14	   POL(3(x_1)) = x_1
1022.76/289.14	   POL(3^1(x_1)) = 1 + x_1
1022.76/289.14	   POL(4(x_1)) = x_1
1022.76/289.14	   POL(5(x_1)) = 1 + x_1
1022.76/289.14	   POL(5^1(x_1)) = 1 + x_1
1022.76/289.14	
1022.76/289.14	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
1022.76/289.14	
1022.76/289.14	   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))))))))))))))))))
1022.76/289.14	   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)))))))))))))))
1022.76/289.14	   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))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))
1022.76/289.14	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1022.76/289.14	   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))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))))))
1022.76/289.14	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1022.76/289.14	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1022.76/289.14	   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))))))))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))
1022.76/289.14	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1022.76/289.14	   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)))))))))))))
1022.76/289.14	   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)))))))))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))
1022.76/289.14	   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)))))))))))))
1022.76/289.14	   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))))))))))))))))
1022.76/289.14	   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))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))))))
1022.76/289.14	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1022.76/289.14	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1022.76/289.14	   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)))))))))))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))))
1022.76/289.14	
1022.76/289.14	
1022.76/289.14	----------------------------------------
1022.76/289.14	
1022.76/289.14	(15)
1022.76/289.14	Obligation:
1022.76/289.14	Q DP problem:
1022.76/289.14	The TRS P consists of the following rules:
1022.76/289.14	
1022.76/289.14	   5^1(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5^1(1(3(2(1(3(2(0(0(3(x1))))))))))
1022.76/289.14	   5^1(4(3(1(2(1(1(0(x1)))))))) -> 5^1(4(3(2(1(1(1(0(x1))))))))
1022.76/289.14	   5^1(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 1^1(3(2(1(3(2(0(0(3(x1)))))))))
1022.76/289.14	   1^1(3(3(5(2(2(5(1(x1)))))))) -> 1^1(3(5(3(2(2(5(1(x1))))))))
1022.76/289.14	   1^1(3(3(5(2(2(5(1(x1)))))))) -> 3^1(5(3(2(2(5(1(x1)))))))
1022.76/289.14	   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)))))))))))))))
1022.76/289.14	   5^1(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 3^1(2(1(3(2(0(0(3(x1))))))))
1022.76/289.14	   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))))))))))))))))))
1022.76/289.14	   5^1(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 2^1(1(3(2(0(0(3(x1)))))))
1022.76/289.14	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2^1(1(3(2(2(0(0(5(1(1(x1))))))))))
1022.76/289.14	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 1^1(3(2(2(0(0(5(1(1(x1)))))))))
1022.76/289.14	   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)))))))))))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   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)))))))))))
1022.76/289.14	   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))))))))))
1022.76/289.14	   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))))))))))))
1022.76/289.14	   0^1(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 3^1(3(2(3(2(0(0(0(4(x1)))))))))
1022.76/289.14	   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)))))))))))))
1022.76/289.14	   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))))))))))))
1022.76/289.14	   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)))))))))))
1022.76/289.14	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 3^1(2(2(0(0(5(1(1(x1))))))))
1022.76/289.14	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2^1(2(0(0(5(1(1(x1)))))))
1022.76/289.14	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2^1(0(0(5(1(1(x1))))))
1022.76/289.14	   0^1(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 3^1(2(3(2(0(0(0(4(x1))))))))
1022.76/289.14	   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))))))))))))))))))))
1022.76/289.14	   0^1(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 2^1(3(2(0(0(0(4(x1)))))))
1022.76/289.14	   0^1(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 3^1(2(0(0(0(4(x1))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   0^1(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 2^1(0(0(0(4(x1)))))
1022.76/289.14	   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)))))))))))))
1022.76/289.14	   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))))))))))))
1022.76/289.14	   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)))))))))))
1022.76/289.14	   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))))))))))
1022.76/289.14	   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)))))))))
1022.76/289.14	   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))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))
1022.76/289.14	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2^1(0(2(3(1(1(3(0(5(2(x1))))))))))
1022.76/289.14	   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)))))))))))))))
1022.76/289.14	   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))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))
1022.76/289.14	   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)))))))))))))
1022.76/289.14	   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))))))))))))
1022.76/289.14	   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)))))))))))
1022.76/289.14	   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))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))
1022.76/289.14	   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))))))))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))
1022.76/289.14	   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)))))))))))))))))
1022.76/289.14	   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))))))))))))))))
1022.76/289.14	   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)))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))
1022.76/289.14	   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))))))))))))))))))))))))))))))
1022.76/289.14	
1022.76/289.14	The TRS R consists of the following rules:
1022.76/289.14	
1022.76/289.14	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1022.76/289.14	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.03/289.15	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.03/289.15	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.03/289.15	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.03/289.15	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.03/289.15	   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))))))))))))
1023.03/289.15	   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))))))))))))
1023.03/289.15	   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)))))))))))))
1023.03/289.15	   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)))))))))))))
1023.03/289.15	   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)))))))))))))
1023.03/289.15	   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))))))))))))))
1023.03/289.15	   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)))))))))))))))
1023.03/289.15	   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)))))))))))))))
1023.03/289.15	   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)))))))))))))))
1023.03/289.15	   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))))))))))))))))
1023.03/289.15	   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))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))))))))))
1023.03/289.15	
1023.03/289.15	Q is empty.
1023.03/289.15	We have to consider all minimal (P,Q,R)-chains.
1023.03/289.15	----------------------------------------
1023.03/289.15	
1023.03/289.15	(16) DependencyGraphProof (EQUIVALENT)
1023.03/289.15	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 3 SCCs with 22 less nodes.
1023.03/289.15	----------------------------------------
1023.03/289.15	
1023.03/289.15	(17)
1023.03/289.15	Complex Obligation (AND)
1023.03/289.15	
1023.03/289.15	----------------------------------------
1023.03/289.15	
1023.03/289.15	(18)
1023.03/289.15	Obligation:
1023.03/289.15	Q DP problem:
1023.03/289.15	The TRS P consists of the following rules:
1023.03/289.15	
1023.03/289.15	   1^1(3(3(5(2(2(5(1(x1)))))))) -> 3^1(5(3(2(2(5(1(x1)))))))
1023.03/289.15	   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)))))))))))))))
1023.03/289.15	   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))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))))
1023.03/289.15	   1^1(3(3(5(2(2(5(1(x1)))))))) -> 1^1(3(5(3(2(2(5(1(x1))))))))
1023.03/289.15	   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))))))))))))
1023.03/289.15	   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)))))))))))))
1023.03/289.15	   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))))))))))))
1023.03/289.15	   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)))))))))))
1023.03/289.15	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2^1(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.03/289.15	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 1^1(3(2(2(0(0(5(1(1(x1)))))))))
1023.03/289.15	   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)))))))))))))
1023.03/289.15	   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))))))))))))
1023.03/289.15	   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)))))))))))
1023.03/289.15	   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))))))))))
1023.03/289.15	   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)))))))))
1023.03/289.15	   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))))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))
1023.03/289.15	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 3^1(2(2(0(0(5(1(1(x1))))))))
1023.03/289.15	   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)))))))))))))))))))))
1023.03/289.15	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2^1(2(0(0(5(1(1(x1)))))))
1023.03/289.15	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2^1(0(0(5(1(1(x1))))))
1023.03/289.15	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2^1(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.03/289.15	   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))))))))))))
1023.03/289.15	   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)))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))
1023.03/289.15	   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))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))))))))))
1023.03/289.15	
1023.03/289.15	The TRS R consists of the following rules:
1023.03/289.15	
1023.03/289.15	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.03/289.15	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.03/289.15	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.03/289.15	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.03/289.15	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.03/289.15	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.03/289.15	   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))))))))))))
1023.03/289.15	   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))))))))))))
1023.03/289.15	   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)))))))))))))
1023.03/289.15	   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)))))))))))))
1023.03/289.15	   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)))))))))))))
1023.03/289.15	   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))))))))))))))
1023.03/289.15	   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)))))))))))))))
1023.03/289.15	   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)))))))))))))))
1023.03/289.15	   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)))))))))))))))
1023.03/289.15	   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))))))))))))))))
1023.03/289.15	   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))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))))))))))
1023.03/289.15	
1023.03/289.15	Q is empty.
1023.03/289.15	We have to consider all minimal (P,Q,R)-chains.
1023.03/289.15	----------------------------------------
1023.03/289.15	
1023.03/289.15	(19) QDPOrderProof (EQUIVALENT)
1023.03/289.15	We use the reduction pair processor [LPAR04,JAR06].
1023.03/289.15	
1023.03/289.15	
1023.03/289.15	The following pairs can be oriented strictly and are deleted.
1023.03/289.15	
1023.03/289.15	   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)))))))))))))))))))))
1023.03/289.15	The remaining pairs can at least be oriented weakly.
1023.03/289.15	Used ordering:  Polynomial interpretation [POLO]:
1023.03/289.15	
1023.03/289.15	   POL(0(x_1)) = x_1
1023.03/289.15	   POL(1(x_1)) = x_1
1023.03/289.15	   POL(1^1(x_1)) = 0
1023.03/289.15	   POL(2(x_1)) = 0
1023.03/289.15	   POL(2^1(x_1)) = x_1
1023.03/289.15	   POL(3(x_1)) = 0
1023.03/289.15	   POL(3^1(x_1)) = 0
1023.03/289.15	   POL(4(x_1)) = 1 + x_1
1023.03/289.15	   POL(5(x_1)) = 0
1023.03/289.15	
1023.03/289.15	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
1023.03/289.15	
1023.03/289.15	   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))))))))))))
1023.03/289.15	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.03/289.15	   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)))))))))))))
1023.03/289.15	   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)))))))))))))
1023.03/289.15	   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)))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))))))))))
1023.03/289.15	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.03/289.15	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.03/289.15	   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)))))))))))))))
1023.03/289.15	   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)))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))))))
1023.03/289.15	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.03/289.15	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.03/289.15	   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))))))))))))
1023.03/289.15	   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)))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))
1023.03/289.15	   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)))))))))))))))
1023.03/289.15	   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))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))
1023.03/289.15	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.03/289.15	   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))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))))))))
1023.03/289.15	   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))))))))))))))
1023.03/289.15	   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)))))))))))))
1023.03/289.15	   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))))))))))))))))
1023.03/289.15	   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))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))))))))))
1023.03/289.15	
1023.03/289.15	
1023.03/289.15	----------------------------------------
1023.03/289.15	
1023.03/289.15	(20)
1023.03/289.15	Obligation:
1023.03/289.15	Q DP problem:
1023.03/289.15	The TRS P consists of the following rules:
1023.03/289.15	
1023.03/289.15	   1^1(3(3(5(2(2(5(1(x1)))))))) -> 3^1(5(3(2(2(5(1(x1)))))))
1023.03/289.15	   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)))))))))))))))
1023.03/289.15	   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))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))))
1023.03/289.15	   1^1(3(3(5(2(2(5(1(x1)))))))) -> 1^1(3(5(3(2(2(5(1(x1))))))))
1023.03/289.15	   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))))))))))))
1023.03/289.15	   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)))))))))))))
1023.03/289.15	   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))))))))))))
1023.03/289.15	   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)))))))))))
1023.03/289.15	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2^1(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.03/289.15	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 1^1(3(2(2(0(0(5(1(1(x1)))))))))
1023.03/289.15	   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)))))))))))))
1023.03/289.15	   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))))))))))))
1023.03/289.15	   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)))))))))))
1023.03/289.15	   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))))))))))
1023.03/289.15	   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)))))))))
1023.03/289.15	   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))))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))
1023.03/289.15	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 3^1(2(2(0(0(5(1(1(x1))))))))
1023.03/289.15	   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)))))))))))))))))))))
1023.03/289.15	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2^1(2(0(0(5(1(1(x1)))))))
1023.03/289.15	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2^1(0(0(5(1(1(x1))))))
1023.03/289.15	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2^1(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.03/289.15	   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))))))))))))
1023.03/289.15	   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)))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))
1023.03/289.15	   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))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))))))))))
1023.03/289.15	
1023.03/289.15	The TRS R consists of the following rules:
1023.03/289.15	
1023.03/289.15	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.03/289.15	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.03/289.15	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.03/289.15	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.03/289.15	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.03/289.15	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.03/289.15	   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))))))))))))
1023.03/289.15	   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))))))))))))
1023.03/289.15	   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)))))))))))))
1023.03/289.15	   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)))))))))))))
1023.03/289.15	   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)))))))))))))
1023.03/289.15	   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))))))))))))))
1023.03/289.15	   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)))))))))))))))
1023.03/289.15	   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)))))))))))))))
1023.03/289.15	   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)))))))))))))))
1023.03/289.15	   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))))))))))))))))
1023.03/289.15	   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))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))))))))))
1023.03/289.15	
1023.03/289.15	Q is empty.
1023.03/289.15	We have to consider all minimal (P,Q,R)-chains.
1023.03/289.15	----------------------------------------
1023.03/289.15	
1023.03/289.15	(21) QDPOrderProof (EQUIVALENT)
1023.03/289.15	We use the reduction pair processor [LPAR04,JAR06].
1023.03/289.15	
1023.03/289.15	
1023.03/289.15	The following pairs can be oriented strictly and are deleted.
1023.03/289.15	
1023.03/289.15	   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)))))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))
1023.03/289.15	The remaining pairs can at least be oriented weakly.
1023.03/289.15	Used ordering:  Polynomial interpretation [POLO]:
1023.03/289.15	
1023.03/289.15	   POL(0(x_1)) = 0
1023.03/289.15	   POL(1(x_1)) = 1
1023.03/289.15	   POL(1^1(x_1)) = 0
1023.03/289.15	   POL(2(x_1)) = 0
1023.03/289.15	   POL(2^1(x_1)) = 0
1023.03/289.15	   POL(3(x_1)) = 0
1023.03/289.15	   POL(3^1(x_1)) = x_1
1023.03/289.15	   POL(4(x_1)) = x_1
1023.03/289.15	   POL(5(x_1)) = 0
1023.03/289.15	
1023.03/289.15	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
1023.03/289.15	
1023.03/289.15	   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))))))))))))
1023.03/289.15	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.03/289.15	   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)))))))))))))
1023.03/289.15	   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)))))))))))))
1023.03/289.15	   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)))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))))))))))
1023.03/289.15	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.03/289.15	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.03/289.15	   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)))))))))))))))
1023.03/289.15	   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)))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))))))
1023.03/289.15	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.03/289.15	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.03/289.15	   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))))))))))))
1023.03/289.15	   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)))))))))))))))))))
1023.03/289.15	   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)))))))))))))))))))))
1023.03/289.15	   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))))))))))))))))))))))))))
1023.03/289.15	   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)))))))))))))))
1023.03/289.15	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.03/289.16	   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))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))))))))
1023.03/289.16	
1023.03/289.16	
1023.03/289.16	----------------------------------------
1023.03/289.16	
1023.03/289.16	(22)
1023.03/289.16	Obligation:
1023.03/289.16	Q DP problem:
1023.03/289.16	The TRS P consists of the following rules:
1023.03/289.16	
1023.03/289.16	   1^1(3(3(5(2(2(5(1(x1)))))))) -> 3^1(5(3(2(2(5(1(x1)))))))
1023.03/289.16	   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)))))))))))))))
1023.03/289.16	   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))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))))
1023.03/289.16	   1^1(3(3(5(2(2(5(1(x1)))))))) -> 1^1(3(5(3(2(2(5(1(x1))))))))
1023.03/289.16	   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))))))))))))
1023.03/289.16	   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)))))))))))))
1023.03/289.16	   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))))))))))))
1023.03/289.16	   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)))))))))))
1023.03/289.16	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2^1(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.03/289.16	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 1^1(3(2(2(0(0(5(1(1(x1)))))))))
1023.03/289.16	   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)))))))))))))
1023.03/289.16	   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))))))))))))
1023.03/289.16	   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)))))))))))
1023.03/289.16	   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))))))))))
1023.03/289.16	   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)))))))))
1023.03/289.16	   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)))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))
1023.03/289.16	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 3^1(2(2(0(0(5(1(1(x1))))))))
1023.03/289.16	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2^1(2(0(0(5(1(1(x1)))))))
1023.03/289.16	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2^1(0(0(5(1(1(x1))))))
1023.03/289.16	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2^1(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.03/289.16	   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))))))))))))
1023.03/289.16	   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)))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))
1023.03/289.16	   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))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))))))))))
1023.03/289.16	
1023.03/289.16	The TRS R consists of the following rules:
1023.03/289.16	
1023.03/289.16	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.03/289.16	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.03/289.16	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.03/289.16	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.03/289.16	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.03/289.16	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.03/289.16	   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))))))))))))
1023.03/289.16	   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))))))))))))
1023.03/289.16	   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)))))))))))))
1023.03/289.16	   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)))))))))))))
1023.03/289.16	   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)))))))))))))
1023.03/289.16	   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))))))))))))))
1023.03/289.16	   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)))))))))))))))
1023.03/289.16	   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)))))))))))))))
1023.03/289.16	   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)))))))))))))))
1023.03/289.16	   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))))))))))))))))
1023.03/289.16	   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))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))))))))))
1023.03/289.16	
1023.03/289.16	Q is empty.
1023.03/289.16	We have to consider all minimal (P,Q,R)-chains.
1023.03/289.16	----------------------------------------
1023.03/289.16	
1023.03/289.16	(23) DependencyGraphProof (EQUIVALENT)
1023.03/289.16	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 3 less nodes.
1023.03/289.16	----------------------------------------
1023.03/289.16	
1023.03/289.16	(24)
1023.03/289.16	Complex Obligation (AND)
1023.03/289.16	
1023.03/289.16	----------------------------------------
1023.03/289.16	
1023.03/289.16	(25)
1023.03/289.16	Obligation:
1023.03/289.16	Q DP problem:
1023.03/289.16	The TRS P consists of the following rules:
1023.03/289.16	
1023.03/289.16	   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))))))))))))))))))
1023.03/289.16	   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)))))))))))))))
1023.03/289.16	   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))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))))))))))))
1023.03/289.16	
1023.03/289.16	The TRS R consists of the following rules:
1023.03/289.16	
1023.03/289.16	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.03/289.16	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.03/289.16	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.03/289.16	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.03/289.16	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.03/289.16	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.03/289.16	   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))))))))))))
1023.03/289.16	   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))))))))))))
1023.03/289.16	   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)))))))))))))
1023.03/289.16	   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)))))))))))))
1023.03/289.16	   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)))))))))))))
1023.03/289.16	   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))))))))))))))
1023.03/289.16	   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)))))))))))))))
1023.03/289.16	   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)))))))))))))))
1023.03/289.16	   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)))))))))))))))
1023.03/289.16	   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))))))))))))))))
1023.03/289.16	   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))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))))))))))
1023.03/289.16	
1023.03/289.16	Q is empty.
1023.03/289.16	We have to consider all minimal (P,Q,R)-chains.
1023.03/289.16	----------------------------------------
1023.03/289.16	
1023.03/289.16	(26) QDPOrderProof (EQUIVALENT)
1023.03/289.16	We use the reduction pair processor [LPAR04,JAR06].
1023.03/289.16	
1023.03/289.16	
1023.03/289.16	The following pairs can be oriented strictly and are deleted.
1023.03/289.16	
1023.03/289.16	   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)))))))))))))))
1023.03/289.16	The remaining pairs can at least be oriented weakly.
1023.03/289.16	Used ordering:  Polynomial interpretation [POLO]:
1023.03/289.16	
1023.03/289.16	   POL(0(x_1)) = 1
1023.03/289.16	   POL(1(x_1)) = x_1
1023.03/289.16	   POL(2(x_1)) = x_1
1023.03/289.16	   POL(3(x_1)) = 0
1023.03/289.16	   POL(3^1(x_1)) = x_1
1023.03/289.16	   POL(4(x_1)) = x_1
1023.03/289.16	   POL(5(x_1)) = 1 + x_1
1023.03/289.16	
1023.03/289.16	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
1023.03/289.16	
1023.03/289.16	   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))))))))))))))))))
1023.03/289.16	   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)))))))))))))))
1023.03/289.16	   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))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))))))))))))
1023.03/289.16	   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))))))))))))
1023.03/289.16	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.03/289.16	   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)))))))))))))
1023.03/289.16	   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)))))))))))))
1023.03/289.16	   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)))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))))))))))
1023.03/289.16	   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))))))))))))))
1023.03/289.16	   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)))))))))))))
1023.03/289.16	   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))))))))))))))))
1023.03/289.16	   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))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))))))))))))
1023.03/289.16	   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)))))))))))))))
1023.03/289.16	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.03/289.16	   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))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))))))))
1023.03/289.16	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.03/289.16	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.03/289.16	   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))))))))))))
1023.03/289.16	   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)))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))))))
1023.03/289.16	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.03/289.16	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.03/289.16	   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)))))))))))))))
1023.03/289.16	   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)))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))))))
1023.03/289.16	
1023.03/289.16	
1023.03/289.16	----------------------------------------
1023.03/289.16	
1023.03/289.16	(27)
1023.03/289.16	Obligation:
1023.03/289.16	Q DP problem:
1023.03/289.16	The TRS P consists of the following rules:
1023.03/289.16	
1023.03/289.16	   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))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))))))))))))
1023.03/289.16	
1023.03/289.16	The TRS R consists of the following rules:
1023.03/289.16	
1023.03/289.16	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.03/289.16	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.03/289.16	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.03/289.16	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.03/289.16	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.03/289.16	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.03/289.16	   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))))))))))))
1023.03/289.16	   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))))))))))))
1023.03/289.16	   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)))))))))))))
1023.03/289.16	   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)))))))))))))
1023.03/289.16	   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)))))))))))))
1023.03/289.16	   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))))))))))))))
1023.03/289.16	   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)))))))))))))))
1023.03/289.16	   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)))))))))))))))
1023.03/289.16	   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)))))))))))))))
1023.03/289.16	   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))))))))))))))))
1023.03/289.16	   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))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))))))))))
1023.03/289.16	
1023.03/289.16	Q is empty.
1023.03/289.16	We have to consider all minimal (P,Q,R)-chains.
1023.03/289.16	----------------------------------------
1023.03/289.16	
1023.03/289.16	(28) MRRProof (EQUIVALENT)
1023.03/289.16	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.
1023.03/289.16	
1023.03/289.16	Strictly oriented dependency pairs:
1023.03/289.16	
1023.03/289.16	   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)))))))))))))))))))))))))))))
1023.03/289.16	
1023.03/289.16	Strictly oriented rules of the TRS R:
1023.03/289.16	
1023.03/289.16	   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)))))))))))))))
1023.03/289.16	   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)))))))))))))))))))))
1023.03/289.16	   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)))))))))))))))))))))))))))))
1023.03/289.16	
1023.03/289.16	Used ordering: Polynomial interpretation [POLO]:
1023.03/289.16	
1023.03/289.16	   POL(0(x_1)) = x_1
1023.03/289.16	   POL(1(x_1)) = x_1
1023.03/289.16	   POL(2(x_1)) = 2 + x_1
1023.03/289.16	   POL(3(x_1)) = x_1
1023.03/289.16	   POL(3^1(x_1)) = 3*x_1
1023.03/289.16	   POL(4(x_1)) = 2*x_1
1023.03/289.16	   POL(5(x_1)) = x_1
1023.03/289.16	
1023.03/289.16	
1023.03/289.16	----------------------------------------
1023.03/289.16	
1023.03/289.16	(29)
1023.03/289.16	Obligation:
1023.03/289.16	Q DP problem:
1023.03/289.16	The TRS P consists of the following rules:
1023.03/289.16	
1023.03/289.16	   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))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))
1023.03/289.16	   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))))))))))))))))))))))))
1023.03/289.16	
1023.03/289.16	The TRS R consists of the following rules:
1023.03/289.16	
1023.03/289.16	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.03/289.16	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.03/289.16	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.03/289.16	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.03/289.16	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.03/289.16	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.03/289.16	   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))))))))))))
1023.03/289.16	   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))))))))))))
1023.03/289.16	   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)))))))))))))
1023.03/289.16	   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)))))))))))))
1023.03/289.16	   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)))))))))))))
1023.03/289.16	   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))))))))))))))
1023.03/289.16	   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)))))))))))))))
1023.03/289.16	   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)))))))))))))))
1023.03/289.17	   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))))))))))))))))
1023.03/289.17	   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))))))))))))))))))
1023.03/289.17	   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))))))))))))))))))
1023.03/289.17	   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))))))))))))))))))
1023.03/289.17	   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)))))))))))))))))))
1023.03/289.17	   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)))))))))))))))))))
1023.03/289.17	   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)))))))))))))))))))
1023.03/289.17	   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)))))))))))))))))))
1023.03/289.17	   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)))))))))))))))))))
1023.03/289.17	   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)))))))))))))))))))
1023.03/289.17	   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))))))))))))))))))))
1023.03/289.17	   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)))))))))))))))))))))
1023.03/289.17	   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)))))))))))))))))))))
1023.03/289.17	   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))))))))))))))))))))))
1023.03/289.17	   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))))))))))))))))))))))
1023.03/289.17	   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))))))))))))))))))))))))
1023.03/289.17	   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))))))))))))))))))))))))
1023.03/289.17	   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)))))))))))))))))))))))))
1023.03/289.17	   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)))))))))))))))))))))))))
1023.03/289.17	   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))))))))))))))))))))))))))
1023.03/289.17	   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))))))))))))))))))))))))))
1023.03/289.17	   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))))))))))))))))))))))))))))
1023.03/289.17	   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)))))))))))))))))))))))))))))
1023.03/289.17	   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))))))))))))))))))))))))))))))
1023.03/289.17	
1023.03/289.17	Q is empty.
1023.03/289.17	We have to consider all minimal (P,Q,R)-chains.
1023.03/289.17	----------------------------------------
1023.03/289.17	
1023.03/289.17	(30) MRRProof (EQUIVALENT)
1023.03/289.17	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.
1023.03/289.17	
1023.03/289.17	
1023.03/289.17	Strictly oriented rules of the TRS R:
1023.03/289.17	
1023.03/289.17	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.03/289.17	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.03/289.17	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.03/289.17	   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))))))))))))))))))
1023.03/289.17	   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)))))))))))))))))))
1023.03/289.17	   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)))))))))))))))))))))
1023.03/289.17	   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))))))))))))))))))))))
1023.03/289.17	
1023.03/289.17	Used ordering: Polynomial interpretation [POLO]:
1023.03/289.17	
1023.03/289.17	   POL(0(x_1)) = 2*x_1
1023.03/289.17	   POL(1(x_1)) = x_1
1023.03/289.17	   POL(2(x_1)) = 2*x_1
1023.03/289.17	   POL(3(x_1)) = 1 + x_1
1023.03/289.17	   POL(3^1(x_1)) = x_1
1023.03/289.17	   POL(4(x_1)) = x_1
1023.03/289.17	   POL(5(x_1)) = x_1
1023.03/289.17	
1023.03/289.17	
1023.03/289.17	----------------------------------------
1023.03/289.17	
1023.03/289.17	(31)
1023.03/289.17	Obligation:
1023.03/289.17	Q DP problem:
1023.03/289.17	The TRS P consists of the following rules:
1023.03/289.17	
1023.03/289.17	   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))))))))))))))))))
1023.03/289.17	   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))))))))))))))))))))
1023.03/289.17	   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))))))))))))))))))))))))
1023.03/289.17	
1023.03/289.17	The TRS R consists of the following rules:
1023.03/289.17	
1023.03/289.17	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.03/289.17	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.03/289.17	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.03/289.17	   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))))))))))))
1023.03/289.17	   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))))))))))))
1023.03/289.17	   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)))))))))))))
1023.03/289.17	   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)))))))))))))
1023.03/289.17	   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)))))))))))))
1023.03/289.17	   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))))))))))))))
1023.03/289.17	   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)))))))))))))))
1023.03/289.17	   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)))))))))))))))
1023.03/289.17	   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))))))))))))))))
1023.03/289.17	   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))))))))))))))))))
1023.03/289.17	   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))))))))))))))))))
1023.03/289.17	   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)))))))))))))))))))
1023.03/289.17	   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)))))))))))))))))))
1023.03/289.17	   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)))))))))))))))))))
1023.03/289.17	   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)))))))))))))))))))
1023.03/289.17	   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)))))))))))))))))))
1023.03/289.17	   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))))))))))))))))))))
1023.03/289.17	   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)))))))))))))))))))))
1023.03/289.17	   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))))))))))))))))))))))
1023.03/289.17	   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))))))))))))))))))))))))
1023.03/289.17	   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))))))))))))))))))))))))
1023.03/289.17	   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)))))))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))))))
1023.14/289.18	
1023.14/289.18	Q is empty.
1023.14/289.18	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.18	----------------------------------------
1023.14/289.18	
1023.14/289.18	(32) MRRProof (EQUIVALENT)
1023.14/289.18	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.
1023.14/289.18	
1023.14/289.18	
1023.14/289.18	Strictly oriented rules of the TRS R:
1023.14/289.18	
1023.14/289.18	   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))))))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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)))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))))))))))
1023.14/289.18	
1023.14/289.18	Used ordering: Polynomial interpretation [POLO]:
1023.14/289.18	
1023.14/289.18	   POL(0(x_1)) = 2 + 2*x_1
1023.14/289.18	   POL(1(x_1)) = 2 + 2*x_1
1023.14/289.18	   POL(2(x_1)) = 2 + 2*x_1
1023.14/289.18	   POL(3(x_1)) = 2*x_1
1023.14/289.18	   POL(3^1(x_1)) = 2*x_1
1023.14/289.18	   POL(4(x_1)) = 2 + 2*x_1
1023.14/289.18	   POL(5(x_1)) = x_1
1023.14/289.18	
1023.14/289.18	
1023.14/289.18	----------------------------------------
1023.14/289.18	
1023.14/289.18	(33)
1023.14/289.18	Obligation:
1023.14/289.18	Q DP problem:
1023.14/289.18	The TRS P consists of the following rules:
1023.14/289.18	
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))
1023.14/289.18	
1023.14/289.18	The TRS R consists of the following rules:
1023.14/289.18	
1023.14/289.18	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.18	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.18	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.18	   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))))))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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))))))))))))))
1023.14/289.18	   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)))))))))))))))
1023.14/289.18	   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))))))))))))))))
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))))))
1023.14/289.18	
1023.14/289.18	Q is empty.
1023.14/289.18	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.18	----------------------------------------
1023.14/289.18	
1023.14/289.18	(34) MRRProof (EQUIVALENT)
1023.14/289.18	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.
1023.14/289.18	
1023.14/289.18	
1023.14/289.18	Strictly oriented rules of the TRS R:
1023.14/289.18	
1023.14/289.18	   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))))))))))))
1023.14/289.18	
1023.14/289.18	Used ordering: Polynomial interpretation [POLO]:
1023.14/289.18	
1023.14/289.18	   POL(0(x_1)) = x_1
1023.14/289.18	   POL(1(x_1)) = 2 + 2*x_1
1023.14/289.18	   POL(2(x_1)) = 2 + 2*x_1
1023.14/289.18	   POL(3(x_1)) = x_1
1023.14/289.18	   POL(3^1(x_1)) = x_1
1023.14/289.18	   POL(4(x_1)) = x_1
1023.14/289.18	   POL(5(x_1)) = 1 + x_1
1023.14/289.18	
1023.14/289.18	
1023.14/289.18	----------------------------------------
1023.14/289.18	
1023.14/289.18	(35)
1023.14/289.18	Obligation:
1023.14/289.18	Q DP problem:
1023.14/289.18	The TRS P consists of the following rules:
1023.14/289.18	
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))
1023.14/289.18	
1023.14/289.18	The TRS R consists of the following rules:
1023.14/289.18	
1023.14/289.18	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.18	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.18	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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))))))))))))))
1023.14/289.18	   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)))))))))))))))
1023.14/289.18	   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))))))))))))))))
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))))))
1023.14/289.18	
1023.14/289.18	Q is empty.
1023.14/289.18	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.18	----------------------------------------
1023.14/289.18	
1023.14/289.18	(36) MRRProof (EQUIVALENT)
1023.14/289.18	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.
1023.14/289.18	
1023.14/289.18	
1023.14/289.18	Strictly oriented rules of the TRS R:
1023.14/289.18	
1023.14/289.18	   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)))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))))))
1023.14/289.18	
1023.14/289.18	Used ordering: Polynomial interpretation [POLO]:
1023.14/289.18	
1023.14/289.18	   POL(0(x_1)) = 2 + 2*x_1
1023.14/289.18	   POL(1(x_1)) = 2 + 2*x_1
1023.14/289.18	   POL(2(x_1)) = 2 + 2*x_1
1023.14/289.18	   POL(3(x_1)) = 2*x_1
1023.14/289.18	   POL(3^1(x_1)) = x_1
1023.14/289.18	   POL(4(x_1)) = x_1
1023.14/289.18	   POL(5(x_1)) = 2*x_1
1023.14/289.18	
1023.14/289.18	
1023.14/289.18	----------------------------------------
1023.14/289.18	
1023.14/289.18	(37)
1023.14/289.18	Obligation:
1023.14/289.18	Q DP problem:
1023.14/289.18	The TRS P consists of the following rules:
1023.14/289.18	
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))
1023.14/289.18	
1023.14/289.18	The TRS R consists of the following rules:
1023.14/289.18	
1023.14/289.18	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.18	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.18	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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))))))))))))))
1023.14/289.18	   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))))))))))))))))
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))))
1023.14/289.18	
1023.14/289.18	Q is empty.
1023.14/289.18	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.18	----------------------------------------
1023.14/289.18	
1023.14/289.18	(38) MRRProof (EQUIVALENT)
1023.14/289.18	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.
1023.14/289.18	
1023.14/289.18	
1023.14/289.18	Strictly oriented rules of the TRS R:
1023.14/289.18	
1023.14/289.18	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.18	   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))))))))))))))
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	
1023.14/289.18	Used ordering: Polynomial interpretation [POLO]:
1023.14/289.18	
1023.14/289.18	   POL(0(x_1)) = 2*x_1
1023.14/289.18	   POL(1(x_1)) = x_1
1023.14/289.18	   POL(2(x_1)) = 1 + 2*x_1
1023.14/289.18	   POL(3(x_1)) = x_1
1023.14/289.18	   POL(3^1(x_1)) = x_1
1023.14/289.18	   POL(4(x_1)) = x_1
1023.14/289.18	   POL(5(x_1)) = 2*x_1
1023.14/289.18	
1023.14/289.18	
1023.14/289.18	----------------------------------------
1023.14/289.18	
1023.14/289.18	(39)
1023.14/289.18	Obligation:
1023.14/289.18	Q DP problem:
1023.14/289.18	The TRS P consists of the following rules:
1023.14/289.18	
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))
1023.14/289.18	
1023.14/289.18	The TRS R consists of the following rules:
1023.14/289.18	
1023.14/289.18	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.18	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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))))))))))))))))
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))))
1023.14/289.18	
1023.14/289.18	Q is empty.
1023.14/289.18	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.18	----------------------------------------
1023.14/289.18	
1023.14/289.18	(40) MRRProof (EQUIVALENT)
1023.14/289.18	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.
1023.14/289.18	
1023.14/289.18	Strictly oriented dependency pairs:
1023.14/289.18	
1023.14/289.18	   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))))))))))))))))))))
1023.14/289.18	
1023.14/289.18	Strictly oriented rules of the TRS R:
1023.14/289.18	
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))))
1023.14/289.18	
1023.14/289.18	Used ordering: Polynomial interpretation [POLO]:
1023.14/289.18	
1023.14/289.18	   POL(0(x_1)) = 3 + 2*x_1
1023.14/289.18	   POL(1(x_1)) = 2 + 2*x_1
1023.14/289.18	   POL(2(x_1)) = 2 + 2*x_1
1023.14/289.18	   POL(3(x_1)) = 2*x_1
1023.14/289.18	   POL(3^1(x_1)) = 2*x_1
1023.14/289.18	   POL(4(x_1)) = 2 + 2*x_1
1023.14/289.18	   POL(5(x_1)) = x_1
1023.14/289.18	
1023.14/289.18	
1023.14/289.18	----------------------------------------
1023.14/289.18	
1023.14/289.18	(41)
1023.14/289.18	Obligation:
1023.14/289.18	Q DP problem:
1023.14/289.18	The TRS P consists of the following rules:
1023.14/289.18	
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))
1023.14/289.18	
1023.14/289.18	The TRS R consists of the following rules:
1023.14/289.18	
1023.14/289.18	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.18	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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))))))))))))))))
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))
1023.14/289.18	
1023.14/289.18	Q is empty.
1023.14/289.18	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.18	----------------------------------------
1023.14/289.18	
1023.14/289.18	(42) DependencyGraphProof (EQUIVALENT)
1023.14/289.18	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 2 less nodes.
1023.14/289.18	----------------------------------------
1023.14/289.18	
1023.14/289.18	(43)
1023.14/289.18	TRUE
1023.14/289.18	
1023.14/289.18	----------------------------------------
1023.14/289.18	
1023.14/289.18	(44)
1023.14/289.18	Obligation:
1023.14/289.18	Q DP problem:
1023.14/289.18	The TRS P consists of the following rules:
1023.14/289.18	
1023.14/289.18	   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))))))))))))
1023.14/289.18	   1^1(3(3(5(2(2(5(1(x1)))))))) -> 1^1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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))))))))))))
1023.14/289.18	   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)))))))))))
1023.14/289.18	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2^1(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.18	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 1^1(3(2(2(0(0(5(1(1(x1)))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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))))))))))))
1023.14/289.18	   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)))))))))))
1023.14/289.18	   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))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2^1(2(0(0(5(1(1(x1)))))))
1023.14/289.18	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2^1(0(0(5(1(1(x1))))))
1023.14/289.18	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2^1(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.18	   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))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))
1023.14/289.18	   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))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))))))
1023.14/289.18	
1023.14/289.18	The TRS R consists of the following rules:
1023.14/289.18	
1023.14/289.18	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.18	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.18	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.18	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.18	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.14/289.18	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.18	   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))))))))))))
1023.14/289.18	   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))))))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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))))))))))))))
1023.14/289.18	   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)))))))))))))))
1023.14/289.18	   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)))))))))))))))
1023.14/289.18	   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)))))))))))))))
1023.14/289.18	   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))))))))))))))))
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))))))
1023.14/289.18	
1023.14/289.18	Q is empty.
1023.14/289.18	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.18	----------------------------------------
1023.14/289.18	
1023.14/289.18	(45) QDPOrderProof (EQUIVALENT)
1023.14/289.18	We use the reduction pair processor [LPAR04,JAR06].
1023.14/289.18	
1023.14/289.18	
1023.14/289.18	The following pairs can be oriented strictly and are deleted.
1023.14/289.18	
1023.14/289.18	   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)))))))))))
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))
1023.14/289.18	   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))))))))))))))))
1023.14/289.18	The remaining pairs can at least be oriented weakly.
1023.14/289.18	Used ordering:  Polynomial interpretation [POLO]:
1023.14/289.18	
1023.14/289.18	   POL(0(x_1)) = 0
1023.14/289.18	   POL(1(x_1)) = x_1
1023.14/289.18	   POL(1^1(x_1)) = x_1
1023.14/289.18	   POL(2(x_1)) = 1
1023.14/289.18	   POL(2^1(x_1)) = 0
1023.14/289.18	   POL(3(x_1)) = 0
1023.14/289.18	   POL(4(x_1)) = 0
1023.14/289.18	   POL(5(x_1)) = 0
1023.14/289.18	
1023.14/289.18	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
1023.14/289.18	
1023.14/289.18	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.18	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.18	   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))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))
1023.14/289.18	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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)))))))))))))))
1023.14/289.18	   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))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))
1023.14/289.18	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))))))
1023.14/289.18	
1023.14/289.18	
1023.14/289.18	----------------------------------------
1023.14/289.18	
1023.14/289.18	(46)
1023.14/289.18	Obligation:
1023.14/289.18	Q DP problem:
1023.14/289.18	The TRS P consists of the following rules:
1023.14/289.18	
1023.14/289.18	   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))))))))))))
1023.14/289.18	   1^1(3(3(5(2(2(5(1(x1)))))))) -> 1^1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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))))))))))))
1023.14/289.18	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2^1(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.18	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 1^1(3(2(2(0(0(5(1(1(x1)))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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))))))))))))
1023.14/289.18	   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)))))))))))
1023.14/289.18	   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))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2^1(2(0(0(5(1(1(x1)))))))
1023.14/289.18	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2^1(0(0(5(1(1(x1))))))
1023.14/289.18	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2^1(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.18	   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))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))))))
1023.14/289.18	
1023.14/289.18	The TRS R consists of the following rules:
1023.14/289.18	
1023.14/289.18	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.18	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.18	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.18	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.18	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.14/289.18	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.18	   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))))))))))))
1023.14/289.18	   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))))))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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))))))))))))))
1023.14/289.18	   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)))))))))))))))
1023.14/289.18	   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)))))))))))))))
1023.14/289.18	   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)))))))))))))))
1023.14/289.18	   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))))))))))))))))
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))))))
1023.14/289.18	
1023.14/289.18	Q is empty.
1023.14/289.18	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.18	----------------------------------------
1023.14/289.18	
1023.14/289.18	(47) DependencyGraphProof (EQUIVALENT)
1023.14/289.18	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 1 less node.
1023.14/289.18	----------------------------------------
1023.14/289.18	
1023.14/289.18	(48)
1023.14/289.18	Complex Obligation (AND)
1023.14/289.18	
1023.14/289.18	----------------------------------------
1023.14/289.18	
1023.14/289.18	(49)
1023.14/289.18	Obligation:
1023.14/289.18	Q DP problem:
1023.14/289.18	The TRS P consists of the following rules:
1023.14/289.18	
1023.14/289.18	   1^1(3(3(5(2(2(5(1(x1)))))))) -> 1^1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.18	   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))))))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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))))))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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))))))))))))
1023.14/289.18	   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)))))))))))
1023.14/289.18	   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))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))))))
1023.14/289.18	
1023.14/289.18	The TRS R consists of the following rules:
1023.14/289.18	
1023.14/289.18	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.18	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.18	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.18	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.18	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.14/289.18	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.18	   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))))))))))))
1023.14/289.18	   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))))))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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))))))))))))))
1023.14/289.18	   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)))))))))))))))
1023.14/289.18	   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)))))))))))))))
1023.14/289.18	   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)))))))))))))))
1023.14/289.18	   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))))))))))))))))
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))))))
1023.14/289.18	
1023.14/289.18	Q is empty.
1023.14/289.18	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.18	----------------------------------------
1023.14/289.18	
1023.14/289.18	(50) QDPOrderProof (EQUIVALENT)
1023.14/289.18	We use the reduction pair processor [LPAR04,JAR06].
1023.14/289.18	
1023.14/289.18	
1023.14/289.18	The following pairs can be oriented strictly and are deleted.
1023.14/289.18	
1023.14/289.18	   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))))))))))))
1023.14/289.18	   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))))))))))
1023.14/289.18	   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))))))))))))))))))))
1023.14/289.18	The remaining pairs can at least be oriented weakly.
1023.14/289.18	Used ordering:  Polynomial interpretation [POLO]:
1023.14/289.18	
1023.14/289.18	   POL(0(x_1)) = 0
1023.14/289.18	   POL(1(x_1)) = 1
1023.14/289.18	   POL(1^1(x_1)) = x_1
1023.14/289.18	   POL(2(x_1)) = 0
1023.14/289.18	   POL(3(x_1)) = 0
1023.14/289.18	   POL(4(x_1)) = 0
1023.14/289.18	   POL(5(x_1)) = 0
1023.14/289.18	
1023.14/289.18	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
1023.14/289.18	
1023.14/289.18	   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))))))))))))
1023.14/289.18	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))))))
1023.14/289.18	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.18	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.18	   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))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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)))))))))))))))
1023.14/289.18	   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))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))
1023.14/289.18	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))))
1023.14/289.18	
1023.14/289.18	
1023.14/289.18	----------------------------------------
1023.14/289.18	
1023.14/289.18	(51)
1023.14/289.18	Obligation:
1023.14/289.18	Q DP problem:
1023.14/289.18	The TRS P consists of the following rules:
1023.14/289.18	
1023.14/289.18	   1^1(3(3(5(2(2(5(1(x1)))))))) -> 1^1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.18	   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))))))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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))))))))))))
1023.14/289.18	   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)))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))))))
1023.14/289.18	
1023.14/289.18	The TRS R consists of the following rules:
1023.14/289.18	
1023.14/289.18	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.18	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.18	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.18	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.18	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.14/289.18	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.18	   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))))))))))))
1023.14/289.18	   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))))))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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))))))))))))))
1023.14/289.18	   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)))))))))))))))
1023.14/289.18	   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)))))))))))))))
1023.14/289.18	   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)))))))))))))))
1023.14/289.18	   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))))))))))))))))
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))))))
1023.14/289.18	
1023.14/289.18	Q is empty.
1023.14/289.18	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.18	----------------------------------------
1023.14/289.18	
1023.14/289.18	(52) QDPOrderProof (EQUIVALENT)
1023.14/289.18	We use the reduction pair processor [LPAR04,JAR06].
1023.14/289.18	
1023.14/289.18	
1023.14/289.18	The following pairs can be oriented strictly and are deleted.
1023.14/289.18	
1023.14/289.18	   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))))))))))))
1023.14/289.18	   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)))))))))))
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	The remaining pairs can at least be oriented weakly.
1023.14/289.18	Used ordering:  Polynomial interpretation [POLO]:
1023.14/289.18	
1023.14/289.18	   POL(0(x_1)) = 1 + x_1
1023.14/289.18	   POL(1(x_1)) = 1 + x_1
1023.14/289.18	   POL(1^1(x_1)) = x_1
1023.14/289.18	   POL(2(x_1)) = 1 + x_1
1023.14/289.18	   POL(3(x_1)) = 1 + x_1
1023.14/289.18	   POL(4(x_1)) = x_1
1023.14/289.18	   POL(5(x_1)) = x_1
1023.14/289.18	
1023.14/289.18	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
1023.14/289.18	
1023.14/289.18	   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))))))))))))
1023.14/289.18	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))))))
1023.14/289.18	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.14/289.18	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.18	   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)))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))
1023.14/289.18	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.18	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.18	   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))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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)))))))))))))))
1023.14/289.18	   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))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))
1023.14/289.18	   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)))))))))))))
1023.14/289.18	   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))))))))))))))))
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))))))))))
1023.14/289.18	   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)))))))))))))))
1023.14/289.18	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.18	   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))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))
1023.14/289.18	   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)))))))))))))))))))))))))
1023.14/289.18	   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))))))))))))))))))))))))))))
1023.14/289.18	
1023.14/289.18	
1023.14/289.18	----------------------------------------
1023.14/289.18	
1023.14/289.18	(53)
1023.14/289.18	Obligation:
1023.14/289.18	Q DP problem:
1023.14/289.18	The TRS P consists of the following rules:
1023.14/289.18	
1023.14/289.18	   1^1(3(3(5(2(2(5(1(x1)))))))) -> 1^1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.19	   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))))))))))))
1023.14/289.19	   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)))))))))))))
1023.14/289.19	   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)))))))))))))
1023.14/289.19	   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)))))))))))))))))))
1023.14/289.19	   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)))))))))))))))))))))
1023.14/289.19	   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)))))))))))))))))))))
1023.14/289.19	   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))))))))))))))))))))))))))))))
1023.14/289.19	
1023.14/289.19	The TRS R consists of the following rules:
1023.14/289.19	
1023.14/289.19	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.19	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.19	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.19	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.19	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.14/289.19	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.19	   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))))))))))))
1023.14/289.19	   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))))))))))))
1023.14/289.19	   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)))))))))))))
1023.14/289.19	   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)))))))))))))
1023.14/289.19	   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)))))))))))))
1023.14/289.19	   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))))))))))))))
1023.14/289.19	   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)))))))))))))))
1023.14/289.19	   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)))))))))))))))
1023.14/289.19	   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)))))))))))))))
1023.14/289.19	   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))))))))))))))))
1023.14/289.19	   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))))))))))))))))))
1023.14/289.19	   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))))))))))))))))))
1023.14/289.19	   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))))))))))))))))))
1023.14/289.19	   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)))))))))))))))))))
1023.14/289.19	   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)))))))))))))))))))
1023.14/289.19	   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)))))))))))))))))))
1023.14/289.19	   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)))))))))))))))))))
1023.14/289.19	   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)))))))))))))))))))
1023.14/289.19	   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)))))))))))))))))))
1023.14/289.19	   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))))))))))))))))))))
1023.14/289.19	   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)))))))))))))))))))))
1023.14/289.19	   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)))))))))))))))))))))
1023.14/289.19	   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)))))))))))))))))))))
1023.14/289.19	   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))))))))))))))))))))))
1023.14/289.19	   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))))))))))))))))))))))
1023.14/289.19	   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))))))))))))))))))))))))
1023.14/289.19	   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))))))))))))))))))))))))
1023.14/289.19	   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)))))))))))))))))))))))))
1023.14/289.19	   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)))))))))))))))))))))))))
1023.14/289.19	   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))))))))))))))))))))))))))
1023.14/289.19	   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))))))))))))))))))))))))))
1023.14/289.19	   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))))))))))))))))))))))))))))
1023.14/289.19	   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)))))))))))))))))))))))))))))
1023.14/289.19	   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)))))))))))))))))))))))))))))
1023.14/289.19	   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))))))))))))))))))))))))))))))
1023.14/289.19	
1023.14/289.19	Q is empty.
1023.14/289.19	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.19	----------------------------------------
1023.14/289.19	
1023.14/289.19	(54) QDPOrderProof (EQUIVALENT)
1023.14/289.19	We use the reduction pair processor [LPAR04,JAR06].
1023.14/289.19	
1023.14/289.19	
1023.14/289.19	The following pairs can be oriented strictly and are deleted.
1023.14/289.19	
1023.14/289.19	   1^1(3(3(5(2(2(5(1(x1)))))))) -> 1^1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.19	The remaining pairs can at least be oriented weakly.
1023.14/289.19	Used ordering:  Polynomial interpretation [POLO]:
1023.14/289.19	
1023.14/289.19	   POL(0(x_1)) = 0
1023.14/289.19	   POL(1(x_1)) = 0
1023.14/289.19	   POL(1^1(x_1)) = x_1
1023.14/289.19	   POL(2(x_1)) = 0
1023.14/289.19	   POL(3(x_1)) = 1 + x_1
1023.14/289.19	   POL(4(x_1)) = 0
1023.14/289.19	   POL(5(x_1)) = 0
1023.14/289.19	
1023.14/289.19	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
1023.14/289.19	
1023.14/289.19	   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))))))))))))
1023.14/289.19	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.19	   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)))))))))))))
1023.14/289.19	   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)))))))))))))
1023.14/289.19	   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)))))))))))))))))))
1023.14/289.19	   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)))))))))))))))))))))
1023.14/289.19	   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)))))))))))))))))))))
1023.14/289.19	   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))))))))))))))))))))))))))))))
1023.14/289.19	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.14/289.19	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.19	   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)))))))))))))))
1023.14/289.19	   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)))))))))))))))))))
1023.14/289.19	   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)))))))))))))))))))
1023.14/289.19	   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)))))))))))))))))))
1023.14/289.19	   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)))))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))))
1023.14/289.20	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.20	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.20	   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))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))
1023.14/289.20	   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)))))))))))))))
1023.14/289.20	   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))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))
1023.14/289.20	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.20	   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))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))))))
1023.14/289.20	
1023.14/289.20	
1023.14/289.20	----------------------------------------
1023.14/289.20	
1023.14/289.20	(55)
1023.14/289.20	Obligation:
1023.14/289.20	Q DP problem:
1023.14/289.20	The TRS P consists of the following rules:
1023.14/289.20	
1023.14/289.20	   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))))))))))))
1023.14/289.20	   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)))))))))))))
1023.14/289.20	   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)))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))))))))
1023.14/289.20	
1023.14/289.20	The TRS R consists of the following rules:
1023.14/289.20	
1023.14/289.20	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.20	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.20	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.20	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.20	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.14/289.20	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.20	   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))))))))))))
1023.14/289.20	   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))))))))))))
1023.14/289.20	   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)))))))))))))
1023.14/289.20	   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)))))))))))))
1023.14/289.20	   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)))))))))))))
1023.14/289.20	   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))))))))))))))
1023.14/289.20	   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)))))))))))))))
1023.14/289.20	   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)))))))))))))))
1023.14/289.20	   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)))))))))))))))
1023.14/289.20	   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))))))))))))))))
1023.14/289.20	   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))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))))))))
1023.14/289.20	
1023.14/289.20	Q is empty.
1023.14/289.20	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.20	----------------------------------------
1023.14/289.20	
1023.14/289.20	(56) QDPOrderProof (EQUIVALENT)
1023.14/289.20	We use the reduction pair processor [LPAR04,JAR06].
1023.14/289.20	
1023.14/289.20	
1023.14/289.20	The following pairs can be oriented strictly and are deleted.
1023.14/289.20	
1023.14/289.20	   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)))))))))))))))))))))
1023.14/289.20	The remaining pairs can at least be oriented weakly.
1023.14/289.20	Used ordering:  Polynomial interpretation [POLO]:
1023.14/289.20	
1023.14/289.20	   POL(0(x_1)) = 1 + x_1
1023.14/289.20	   POL(1(x_1)) = x_1
1023.14/289.20	   POL(1^1(x_1)) = x_1
1023.14/289.20	   POL(2(x_1)) = x_1
1023.14/289.20	   POL(3(x_1)) = 1
1023.14/289.20	   POL(4(x_1)) = 0
1023.14/289.20	   POL(5(x_1)) = 0
1023.14/289.20	
1023.14/289.20	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
1023.14/289.20	
1023.14/289.20	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.14/289.20	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.20	   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)))))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))
1023.14/289.20	   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)))))))))))))
1023.14/289.20	   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))))))))))))))))
1023.14/289.20	   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))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))))))))))
1023.14/289.20	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.20	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.20	   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))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))
1023.14/289.20	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.20	   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))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))
1023.14/289.20	   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)))))))))))))))
1023.14/289.20	   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))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))))))))))
1023.14/289.20	   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))))))))))))
1023.14/289.20	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.20	   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)))))))))))))
1023.14/289.20	   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)))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))))))))
1023.14/289.20	
1023.14/289.20	
1023.14/289.20	----------------------------------------
1023.14/289.20	
1023.14/289.20	(57)
1023.14/289.20	Obligation:
1023.14/289.20	Q DP problem:
1023.14/289.20	The TRS P consists of the following rules:
1023.14/289.20	
1023.14/289.20	   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))))))))))))
1023.14/289.20	   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)))))))))))))
1023.14/289.20	   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)))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))))))))
1023.14/289.20	
1023.14/289.20	The TRS R consists of the following rules:
1023.14/289.20	
1023.14/289.20	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.20	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.20	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.20	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.20	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.14/289.20	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.20	   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))))))))))))
1023.14/289.20	   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))))))))))))
1023.14/289.20	   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)))))))))))))
1023.14/289.20	   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)))))))))))))
1023.14/289.20	   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)))))))))))))
1023.14/289.20	   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))))))))))))))
1023.14/289.20	   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)))))))))))))))
1023.14/289.20	   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)))))))))))))))
1023.14/289.20	   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)))))))))))))))
1023.14/289.20	   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))))))))))))))))
1023.14/289.20	   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))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))))))))
1023.14/289.20	
1023.14/289.20	Q is empty.
1023.14/289.20	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.20	----------------------------------------
1023.14/289.20	
1023.14/289.20	(58) MRRProof (EQUIVALENT)
1023.14/289.20	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.
1023.14/289.20	
1023.14/289.20	
1023.14/289.20	Strictly oriented rules of the TRS R:
1023.14/289.20	
1023.14/289.20	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.20	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.20	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.14/289.20	   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))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))
1023.14/289.20	
1023.14/289.20	Used ordering: Polynomial interpretation [POLO]:
1023.14/289.20	
1023.14/289.20	   POL(0(x_1)) = 2*x_1
1023.14/289.20	   POL(1(x_1)) = x_1
1023.14/289.20	   POL(1^1(x_1)) = x_1
1023.14/289.20	   POL(2(x_1)) = 2*x_1
1023.14/289.20	   POL(3(x_1)) = 1 + 2*x_1
1023.14/289.20	   POL(4(x_1)) = x_1
1023.14/289.20	   POL(5(x_1)) = x_1
1023.14/289.20	
1023.14/289.20	
1023.14/289.20	----------------------------------------
1023.14/289.20	
1023.14/289.20	(59)
1023.14/289.20	Obligation:
1023.14/289.20	Q DP problem:
1023.14/289.20	The TRS P consists of the following rules:
1023.14/289.20	
1023.14/289.20	   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))))))))))))
1023.14/289.20	   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)))))))))))))
1023.14/289.20	   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)))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))))))))
1023.14/289.20	
1023.14/289.20	The TRS R consists of the following rules:
1023.14/289.20	
1023.14/289.20	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.20	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.20	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.20	   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))))))))))))
1023.14/289.20	   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))))))))))))
1023.14/289.20	   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)))))))))))))
1023.14/289.20	   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)))))))))))))
1023.14/289.20	   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)))))))))))))
1023.14/289.20	   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))))))))))))))
1023.14/289.20	   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)))))))))))))))
1023.14/289.20	   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)))))))))))))))
1023.14/289.20	   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)))))))))))))))
1023.14/289.20	   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))))))))))))))))
1023.14/289.20	   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))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))))))))
1023.14/289.20	
1023.14/289.20	Q is empty.
1023.14/289.20	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.20	----------------------------------------
1023.14/289.20	
1023.14/289.20	(60) MRRProof (EQUIVALENT)
1023.14/289.20	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.
1023.14/289.20	
1023.14/289.20	Strictly oriented dependency pairs:
1023.14/289.20	
1023.14/289.20	   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))))))))))))
1023.14/289.20	   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)))))))))))))
1023.14/289.20	
1023.14/289.20	Strictly oriented rules of the TRS R:
1023.14/289.20	
1023.14/289.20	   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))))))))))))
1023.14/289.20	   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)))))))))))))
1023.14/289.20	   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)))))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))))))))))
1023.14/289.20	
1023.14/289.20	Used ordering: Polynomial interpretation [POLO]:
1023.14/289.20	
1023.14/289.20	   POL(0(x_1)) = x_1
1023.14/289.20	   POL(1(x_1)) = 1 + x_1
1023.14/289.20	   POL(1^1(x_1)) = 2*x_1
1023.14/289.20	   POL(2(x_1)) = x_1
1023.14/289.20	   POL(3(x_1)) = 2*x_1
1023.14/289.20	   POL(4(x_1)) = x_1
1023.14/289.20	   POL(5(x_1)) = 2*x_1
1023.14/289.20	
1023.14/289.20	
1023.14/289.20	----------------------------------------
1023.14/289.20	
1023.14/289.20	(61)
1023.14/289.20	Obligation:
1023.14/289.20	Q DP problem:
1023.14/289.20	The TRS P consists of the following rules:
1023.14/289.20	
1023.14/289.20	   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)))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))))))))
1023.14/289.20	
1023.14/289.20	The TRS R consists of the following rules:
1023.14/289.20	
1023.14/289.20	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.20	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.20	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.20	   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))))))))))))
1023.14/289.20	   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)))))))))))))
1023.14/289.20	   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)))))))))))))
1023.14/289.20	   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))))))))))))))
1023.14/289.20	   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)))))))))))))))
1023.14/289.20	   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)))))))))))))))
1023.14/289.20	   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))))))))))))))))
1023.14/289.20	   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))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))))))))
1023.14/289.20	
1023.14/289.20	Q is empty.
1023.14/289.20	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.20	----------------------------------------
1023.14/289.20	
1023.14/289.20	(62) MRRProof (EQUIVALENT)
1023.14/289.20	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.
1023.14/289.20	
1023.14/289.20	Strictly oriented dependency pairs:
1023.14/289.20	
1023.14/289.20	   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))))))))))))))))))))))))))))))
1023.14/289.20	
1023.14/289.20	Strictly oriented rules of the TRS R:
1023.14/289.20	
1023.14/289.20	   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))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))))))))
1023.14/289.20	
1023.14/289.20	Used ordering: Polynomial interpretation [POLO]:
1023.14/289.20	
1023.14/289.20	   POL(0(x_1)) = x_1
1023.14/289.20	   POL(1(x_1)) = x_1
1023.14/289.20	   POL(1^1(x_1)) = 2*x_1
1023.14/289.20	   POL(2(x_1)) = x_1
1023.14/289.20	   POL(3(x_1)) = 2*x_1
1023.14/289.20	   POL(4(x_1)) = 2 + x_1
1023.14/289.20	   POL(5(x_1)) = 2*x_1
1023.14/289.20	
1023.14/289.20	
1023.14/289.20	----------------------------------------
1023.14/289.20	
1023.14/289.20	(63)
1023.14/289.20	Obligation:
1023.14/289.20	Q DP problem:
1023.14/289.20	The TRS P consists of the following rules:
1023.14/289.20	
1023.14/289.20	   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)))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))
1023.14/289.20	
1023.14/289.20	The TRS R consists of the following rules:
1023.14/289.20	
1023.14/289.20	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.20	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.20	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.20	   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))))))))))))
1023.14/289.20	   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)))))))))))))
1023.14/289.20	   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)))))))))))))
1023.14/289.20	   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))))))))))))))
1023.14/289.20	   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)))))))))))))))
1023.14/289.20	   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)))))))))))))))
1023.14/289.20	   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))))))))))))))))
1023.14/289.20	   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))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))))))))))
1023.14/289.20	
1023.14/289.20	Q is empty.
1023.14/289.20	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.20	----------------------------------------
1023.14/289.20	
1023.14/289.20	(64) MRRProof (EQUIVALENT)
1023.14/289.20	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.
1023.14/289.20	
1023.14/289.20	Strictly oriented dependency pairs:
1023.14/289.20	
1023.14/289.20	   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)))))))))))))))))))))
1023.14/289.20	
1023.14/289.20	Strictly oriented rules of the TRS R:
1023.14/289.20	
1023.14/289.20	   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)))))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))))))))))))
1023.14/289.20	
1023.14/289.20	Used ordering: Polynomial interpretation [POLO]:
1023.14/289.20	
1023.14/289.20	   POL(0(x_1)) = 1 + x_1
1023.14/289.20	   POL(1(x_1)) = x_1
1023.14/289.20	   POL(1^1(x_1)) = x_1
1023.14/289.20	   POL(2(x_1)) = 3 + x_1
1023.14/289.20	   POL(3(x_1)) = x_1
1023.14/289.20	   POL(4(x_1)) = 1 + 2*x_1
1023.14/289.20	   POL(5(x_1)) = x_1
1023.14/289.20	
1023.14/289.20	
1023.14/289.20	----------------------------------------
1023.14/289.20	
1023.14/289.20	(65)
1023.14/289.20	Obligation:
1023.14/289.20	Q DP problem:
1023.14/289.20	The TRS P consists of the following rules:
1023.14/289.20	
1023.14/289.20	   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)))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	
1023.14/289.20	The TRS R consists of the following rules:
1023.14/289.20	
1023.14/289.20	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.20	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.20	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.20	   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))))))))))))
1023.14/289.20	   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)))))))))))))
1023.14/289.20	   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)))))))))))))
1023.14/289.20	   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))))))))))))))
1023.14/289.20	   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)))))))))))))))
1023.14/289.20	   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))))))))))))))))
1023.14/289.20	   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))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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)))))))))))))))))))
1023.14/289.20	   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))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))
1023.14/289.21	
1023.14/289.21	Q is empty.
1023.14/289.21	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.21	----------------------------------------
1023.14/289.21	
1023.14/289.21	(66) MRRProof (EQUIVALENT)
1023.14/289.21	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.
1023.14/289.21	
1023.14/289.21	
1023.14/289.21	Strictly oriented rules of the TRS R:
1023.14/289.21	
1023.14/289.21	   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)))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))
1023.14/289.21	
1023.14/289.21	Used ordering: Polynomial interpretation [POLO]:
1023.14/289.21	
1023.14/289.21	   POL(0(x_1)) = 2 + x_1
1023.14/289.21	   POL(1(x_1)) = 2*x_1
1023.14/289.21	   POL(1^1(x_1)) = x_1
1023.14/289.21	   POL(2(x_1)) = x_1
1023.14/289.21	   POL(3(x_1)) = 2*x_1
1023.14/289.21	   POL(4(x_1)) = x_1
1023.14/289.21	   POL(5(x_1)) = 2*x_1
1023.14/289.21	
1023.14/289.21	
1023.14/289.21	----------------------------------------
1023.14/289.21	
1023.14/289.21	(67)
1023.14/289.21	Obligation:
1023.14/289.21	Q DP problem:
1023.14/289.21	The TRS P consists of the following rules:
1023.14/289.21	
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	
1023.14/289.21	The TRS R consists of the following rules:
1023.14/289.21	
1023.14/289.21	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.21	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.21	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.21	   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))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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))))))))))))))
1023.14/289.21	   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))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))
1023.14/289.21	
1023.14/289.21	Q is empty.
1023.14/289.21	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.21	----------------------------------------
1023.14/289.21	
1023.14/289.21	(68) MRRProof (EQUIVALENT)
1023.14/289.21	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.
1023.14/289.21	
1023.14/289.21	
1023.14/289.21	Strictly oriented rules of the TRS R:
1023.14/289.21	
1023.14/289.21	   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))))))))))))
1023.14/289.21	
1023.14/289.21	Used ordering: Polynomial interpretation [POLO]:
1023.14/289.21	
1023.14/289.21	   POL(0(x_1)) = 2*x_1
1023.14/289.21	   POL(1(x_1)) = x_1
1023.14/289.21	   POL(1^1(x_1)) = 2*x_1
1023.14/289.21	   POL(2(x_1)) = 2*x_1
1023.14/289.21	   POL(3(x_1)) = 3 + 2*x_1
1023.14/289.21	   POL(4(x_1)) = 2*x_1
1023.14/289.21	   POL(5(x_1)) = 3 + 2*x_1
1023.14/289.21	
1023.14/289.21	
1023.14/289.21	----------------------------------------
1023.14/289.21	
1023.14/289.21	(69)
1023.14/289.21	Obligation:
1023.14/289.21	Q DP problem:
1023.14/289.21	The TRS P consists of the following rules:
1023.14/289.21	
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	
1023.14/289.21	The TRS R consists of the following rules:
1023.14/289.21	
1023.14/289.21	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.21	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.21	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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))))))))))))))
1023.14/289.21	   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))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))
1023.14/289.21	
1023.14/289.21	Q is empty.
1023.14/289.21	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.21	----------------------------------------
1023.14/289.21	
1023.14/289.21	(70) QDPOrderProof (EQUIVALENT)
1023.14/289.21	We use the reduction pair processor [LPAR04,JAR06].
1023.14/289.21	
1023.14/289.21	
1023.14/289.21	The following pairs can be oriented strictly and are deleted.
1023.14/289.21	
1023.14/289.21	   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)))))))))))))
1023.14/289.21	The remaining pairs can at least be oriented weakly.
1023.14/289.21	Used ordering:  Polynomial interpretation [POLO]:
1023.14/289.21	
1023.14/289.21	   POL(0(x_1)) = 0
1023.14/289.21	   POL(1(x_1)) = 2*x_1
1023.14/289.21	   POL(1^1(x_1)) = x_1
1023.14/289.21	   POL(2(x_1)) = x_1
1023.14/289.21	   POL(3(x_1)) = 4
1023.14/289.21	   POL(4(x_1)) = 2 + x_1
1023.14/289.21	   POL(5(x_1)) = 2 + 4*x_1
1023.14/289.21	
1023.14/289.21	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
1023.14/289.21	
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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))))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))
1023.14/289.21	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.21	   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))))))))))))))))))))))))))
1023.14/289.21	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.21	   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))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	
1023.14/289.21	
1023.14/289.21	----------------------------------------
1023.14/289.21	
1023.14/289.21	(71)
1023.14/289.21	Obligation:
1023.14/289.21	Q DP problem:
1023.14/289.21	The TRS P consists of the following rules:
1023.14/289.21	
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	
1023.14/289.21	The TRS R consists of the following rules:
1023.14/289.21	
1023.14/289.21	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.21	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.21	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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))))))))))))))
1023.14/289.21	   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))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))
1023.14/289.21	
1023.14/289.21	Q is empty.
1023.14/289.21	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.21	----------------------------------------
1023.14/289.21	
1023.14/289.21	(72) MRRProof (EQUIVALENT)
1023.14/289.21	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.
1023.14/289.21	
1023.14/289.21	
1023.14/289.21	Strictly oriented rules of the TRS R:
1023.14/289.21	
1023.14/289.21	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.21	   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))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	
1023.14/289.21	Used ordering: Polynomial interpretation [POLO]:
1023.14/289.21	
1023.14/289.21	   POL(0(x_1)) = 2*x_1
1023.14/289.21	   POL(1(x_1)) = x_1
1023.14/289.21	   POL(1^1(x_1)) = 2*x_1
1023.14/289.21	   POL(2(x_1)) = 1 + 2*x_1
1023.14/289.21	   POL(3(x_1)) = x_1
1023.14/289.21	   POL(4(x_1)) = 2*x_1
1023.14/289.21	   POL(5(x_1)) = 2*x_1
1023.14/289.21	
1023.14/289.21	
1023.14/289.21	----------------------------------------
1023.14/289.21	
1023.14/289.21	(73)
1023.14/289.21	Obligation:
1023.14/289.21	Q DP problem:
1023.14/289.21	The TRS P consists of the following rules:
1023.14/289.21	
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	
1023.14/289.21	The TRS R consists of the following rules:
1023.14/289.21	
1023.14/289.21	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.21	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))
1023.14/289.21	
1023.14/289.21	Q is empty.
1023.14/289.21	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.21	----------------------------------------
1023.14/289.21	
1023.14/289.21	(74) DependencyGraphProof (EQUIVALENT)
1023.14/289.21	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node.
1023.14/289.21	----------------------------------------
1023.14/289.21	
1023.14/289.21	(75)
1023.14/289.21	TRUE
1023.14/289.21	
1023.14/289.21	----------------------------------------
1023.14/289.21	
1023.14/289.21	(76)
1023.14/289.21	Obligation:
1023.14/289.21	Q DP problem:
1023.14/289.21	The TRS P consists of the following rules:
1023.14/289.21	
1023.14/289.21	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2^1(2(0(0(5(1(1(x1)))))))
1023.14/289.21	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2^1(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.21	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2^1(0(0(5(1(1(x1))))))
1023.14/289.21	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2^1(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.21	   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))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))
1023.14/289.21	
1023.14/289.21	The TRS R consists of the following rules:
1023.14/289.21	
1023.14/289.21	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.21	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.21	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.21	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.21	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.14/289.21	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.21	   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))))))))))))
1023.14/289.21	   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))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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))))))))))))))
1023.14/289.21	   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)))))))))))))))
1023.14/289.21	   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)))))))))))))))
1023.14/289.21	   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)))))))))))))))
1023.14/289.21	   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))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))))))
1023.14/289.21	
1023.14/289.21	Q is empty.
1023.14/289.21	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.21	----------------------------------------
1023.14/289.21	
1023.14/289.21	(77) QDPOrderProof (EQUIVALENT)
1023.14/289.21	We use the reduction pair processor [LPAR04,JAR06].
1023.14/289.21	
1023.14/289.21	
1023.14/289.21	The following pairs can be oriented strictly and are deleted.
1023.14/289.21	
1023.14/289.21	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2^1(2(0(0(5(1(1(x1)))))))
1023.14/289.21	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2^1(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.21	The remaining pairs can at least be oriented weakly.
1023.14/289.21	Used ordering:  Polynomial interpretation [POLO]:
1023.14/289.21	
1023.14/289.21	   POL(0(x_1)) = 1
1023.14/289.21	   POL(1(x_1)) = 0
1023.14/289.21	   POL(2(x_1)) = 0
1023.14/289.21	   POL(2^1(x_1)) = x_1
1023.14/289.21	   POL(3(x_1)) = 0
1023.14/289.21	   POL(4(x_1)) = 0
1023.14/289.21	   POL(5(x_1)) = 0
1023.14/289.21	
1023.14/289.21	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
1023.14/289.21	
1023.14/289.21	   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))))))))))))
1023.14/289.21	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))))))
1023.14/289.21	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.14/289.21	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.21	   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)))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))
1023.14/289.21	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))))
1023.14/289.21	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.21	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.21	   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))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))))))
1023.14/289.21	
1023.14/289.21	
1023.14/289.21	----------------------------------------
1023.14/289.21	
1023.14/289.21	(78)
1023.14/289.21	Obligation:
1023.14/289.21	Q DP problem:
1023.14/289.21	The TRS P consists of the following rules:
1023.14/289.21	
1023.14/289.21	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2^1(0(0(5(1(1(x1))))))
1023.14/289.21	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2^1(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.21	   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))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))
1023.14/289.21	
1023.14/289.21	The TRS R consists of the following rules:
1023.14/289.21	
1023.14/289.21	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.21	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.21	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.21	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.21	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.14/289.21	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.21	   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))))))))))))
1023.14/289.21	   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))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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))))))))))))))
1023.14/289.21	   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)))))))))))))))
1023.14/289.21	   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)))))))))))))))
1023.14/289.21	   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)))))))))))))))
1023.14/289.21	   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))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))))))
1023.14/289.21	
1023.14/289.21	Q is empty.
1023.14/289.21	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.21	----------------------------------------
1023.14/289.21	
1023.14/289.21	(79) QDPOrderProof (EQUIVALENT)
1023.14/289.21	We use the reduction pair processor [LPAR04,JAR06].
1023.14/289.21	
1023.14/289.21	
1023.14/289.21	The following pairs can be oriented strictly and are deleted.
1023.14/289.21	
1023.14/289.21	   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)))))))))))))))))
1023.14/289.21	The remaining pairs can at least be oriented weakly.
1023.14/289.21	Used ordering:  Polynomial interpretation [POLO]:
1023.14/289.21	
1023.14/289.21	   POL(0(x_1)) = 0
1023.14/289.21	   POL(1(x_1)) = 0
1023.14/289.21	   POL(2(x_1)) = 1
1023.14/289.21	   POL(2^1(x_1)) = x_1
1023.14/289.21	   POL(3(x_1)) = 0
1023.14/289.21	   POL(4(x_1)) = 0
1023.14/289.21	   POL(5(x_1)) = 0
1023.14/289.21	
1023.14/289.21	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
1023.14/289.21	
1023.14/289.21	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.14/289.21	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.21	   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)))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))
1023.14/289.21	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))))
1023.14/289.21	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.21	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.21	   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))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))))))
1023.14/289.21	
1023.14/289.21	
1023.14/289.21	----------------------------------------
1023.14/289.21	
1023.14/289.21	(80)
1023.14/289.21	Obligation:
1023.14/289.21	Q DP problem:
1023.14/289.21	The TRS P consists of the following rules:
1023.14/289.21	
1023.14/289.21	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2^1(0(0(5(1(1(x1))))))
1023.14/289.21	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2^1(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.21	   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))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))
1023.14/289.21	
1023.14/289.21	The TRS R consists of the following rules:
1023.14/289.21	
1023.14/289.21	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.21	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.21	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.21	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.21	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.14/289.21	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.21	   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))))))))))))
1023.14/289.21	   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))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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))))))))))))))
1023.14/289.21	   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)))))))))))))))
1023.14/289.21	   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)))))))))))))))
1023.14/289.21	   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)))))))))))))))
1023.14/289.21	   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))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))))))
1023.14/289.21	
1023.14/289.21	Q is empty.
1023.14/289.21	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.21	----------------------------------------
1023.14/289.21	
1023.14/289.21	(81) QDPOrderProof (EQUIVALENT)
1023.14/289.21	We use the reduction pair processor [LPAR04,JAR06].
1023.14/289.21	
1023.14/289.21	
1023.14/289.21	The following pairs can be oriented strictly and are deleted.
1023.14/289.21	
1023.14/289.21	   2^1(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2^1(0(0(5(1(1(x1))))))
1023.14/289.21	The remaining pairs can at least be oriented weakly.
1023.14/289.21	Used ordering:  Polynomial interpretation [POLO]:
1023.14/289.21	
1023.14/289.21	   POL(0(x_1)) = x_1
1023.14/289.21	   POL(1(x_1)) = 1
1023.14/289.21	   POL(2(x_1)) = 0
1023.14/289.21	   POL(2^1(x_1)) = x_1
1023.14/289.21	   POL(3(x_1)) = 0
1023.14/289.21	   POL(4(x_1)) = 0
1023.14/289.21	   POL(5(x_1)) = 0
1023.14/289.21	
1023.14/289.21	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
1023.14/289.21	
1023.14/289.21	   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))))))))))))
1023.14/289.21	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))))))
1023.14/289.21	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.14/289.21	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.21	   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)))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))
1023.14/289.21	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))))
1023.14/289.21	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.21	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.21	   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))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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)))))))))))))))
1023.14/289.21	   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))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))))))
1023.14/289.21	
1023.14/289.21	
1023.14/289.21	----------------------------------------
1023.14/289.21	
1023.14/289.21	(82)
1023.14/289.21	Obligation:
1023.14/289.21	Q DP problem:
1023.14/289.21	The TRS P consists of the following rules:
1023.14/289.21	
1023.14/289.21	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2^1(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.21	   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))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))
1023.14/289.21	
1023.14/289.21	The TRS R consists of the following rules:
1023.14/289.21	
1023.14/289.21	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.21	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.21	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.21	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.21	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.14/289.21	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.21	   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))))))))))))
1023.14/289.21	   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))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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))))))))))))))
1023.14/289.21	   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)))))))))))))))
1023.14/289.21	   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)))))))))))))))
1023.14/289.21	   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)))))))))))))))
1023.14/289.21	   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))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))))))
1023.14/289.21	
1023.14/289.21	Q is empty.
1023.14/289.21	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.21	----------------------------------------
1023.14/289.21	
1023.14/289.21	(83) QDPOrderProof (EQUIVALENT)
1023.14/289.21	We use the reduction pair processor [LPAR04,JAR06].
1023.14/289.21	
1023.14/289.21	
1023.14/289.21	The following pairs can be oriented strictly and are deleted.
1023.14/289.21	
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	The remaining pairs can at least be oriented weakly.
1023.14/289.21	Used ordering:  Polynomial interpretation [POLO]:
1023.14/289.21	
1023.14/289.21	   POL(0(x_1)) = 0
1023.14/289.21	   POL(1(x_1)) = 0
1023.14/289.21	   POL(2(x_1)) = 1 + x_1
1023.14/289.21	   POL(2^1(x_1)) = x_1
1023.14/289.21	   POL(3(x_1)) = 0
1023.14/289.21	   POL(4(x_1)) = 0
1023.14/289.21	   POL(5(x_1)) = 0
1023.14/289.21	
1023.14/289.21	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
1023.14/289.21	
1023.14/289.21	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.21	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.21	   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))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))
1023.14/289.21	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.14/289.21	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.21	   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)))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))
1023.14/289.21	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))
1023.14/289.21	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))))))
1023.14/289.21	
1023.14/289.21	
1023.14/289.21	----------------------------------------
1023.14/289.21	
1023.14/289.21	(84)
1023.14/289.21	Obligation:
1023.14/289.21	Q DP problem:
1023.14/289.21	The TRS P consists of the following rules:
1023.14/289.21	
1023.14/289.21	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2^1(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.21	   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))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))
1023.14/289.21	
1023.14/289.21	The TRS R consists of the following rules:
1023.14/289.21	
1023.14/289.21	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.21	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.21	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.21	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.21	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.14/289.21	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.21	   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))))))))))))
1023.14/289.21	   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))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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))))))))))))))
1023.14/289.21	   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)))))))))))))))
1023.14/289.21	   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)))))))))))))))
1023.14/289.21	   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)))))))))))))))
1023.14/289.21	   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))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))))))
1023.14/289.21	
1023.14/289.21	Q is empty.
1023.14/289.21	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.21	----------------------------------------
1023.14/289.21	
1023.14/289.21	(85) QDPOrderProof (EQUIVALENT)
1023.14/289.21	We use the reduction pair processor [LPAR04,JAR06].
1023.14/289.21	
1023.14/289.21	
1023.14/289.21	The following pairs can be oriented strictly and are deleted.
1023.14/289.21	
1023.14/289.21	   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))))))))))))))))))))))))))
1023.14/289.21	The remaining pairs can at least be oriented weakly.
1023.14/289.21	Used ordering:  Polynomial interpretation [POLO]:
1023.14/289.21	
1023.14/289.21	   POL(0(x_1)) = x_1
1023.14/289.21	   POL(1(x_1)) = x_1
1023.14/289.21	   POL(2(x_1)) = 1
1023.14/289.21	   POL(2^1(x_1)) = x_1
1023.14/289.21	   POL(3(x_1)) = x_1
1023.14/289.21	   POL(4(x_1)) = 1 + x_1
1023.14/289.21	   POL(5(x_1)) = 1 + x_1
1023.14/289.21	
1023.14/289.21	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
1023.14/289.21	
1023.14/289.21	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.21	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.21	   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))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))
1023.14/289.21	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.14/289.21	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.21	   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)))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))
1023.14/289.21	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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)))))))))))))))
1023.14/289.21	   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))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))
1023.14/289.21	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))))))
1023.14/289.21	
1023.14/289.21	
1023.14/289.21	----------------------------------------
1023.14/289.21	
1023.14/289.21	(86)
1023.14/289.21	Obligation:
1023.14/289.21	Q DP problem:
1023.14/289.21	The TRS P consists of the following rules:
1023.14/289.21	
1023.14/289.21	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2^1(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.21	   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))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	
1023.14/289.21	The TRS R consists of the following rules:
1023.14/289.21	
1023.14/289.21	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.21	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.21	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.21	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.21	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.14/289.21	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.21	   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))))))))))))
1023.14/289.21	   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))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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))))))))))))))
1023.14/289.21	   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)))))))))))))))
1023.14/289.21	   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)))))))))))))))
1023.14/289.21	   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)))))))))))))))
1023.14/289.21	   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))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))))))
1023.14/289.21	
1023.14/289.21	Q is empty.
1023.14/289.21	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.21	----------------------------------------
1023.14/289.21	
1023.14/289.21	(87) MRRProof (EQUIVALENT)
1023.14/289.21	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.
1023.14/289.21	
1023.14/289.21	Strictly oriented dependency pairs:
1023.14/289.21	
1023.14/289.21	   2^1(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2^1(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.21	
1023.14/289.21	Strictly oriented rules of the TRS R:
1023.14/289.21	
1023.14/289.21	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.21	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.21	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))
1023.14/289.21	
1023.14/289.21	Used ordering: Polynomial interpretation [POLO]:
1023.14/289.21	
1023.14/289.21	   POL(0(x_1)) = 2*x_1
1023.14/289.21	   POL(1(x_1)) = x_1
1023.14/289.21	   POL(2(x_1)) = 2*x_1
1023.14/289.21	   POL(2^1(x_1)) = 2*x_1
1023.14/289.21	   POL(3(x_1)) = 2 + x_1
1023.14/289.21	   POL(4(x_1)) = x_1
1023.14/289.21	   POL(5(x_1)) = x_1
1023.14/289.21	
1023.14/289.21	
1023.14/289.21	----------------------------------------
1023.14/289.21	
1023.14/289.21	(88)
1023.14/289.21	Obligation:
1023.14/289.21	Q DP problem:
1023.14/289.21	The TRS P consists of the following rules:
1023.14/289.21	
1023.14/289.21	   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))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	
1023.14/289.21	The TRS R consists of the following rules:
1023.14/289.21	
1023.14/289.21	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.21	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.21	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.21	   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))))))))))))
1023.14/289.21	   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))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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))))))))))))))
1023.14/289.21	   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)))))))))))))))
1023.14/289.21	   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)))))))))))))))
1023.14/289.21	   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)))))))))))))))
1023.14/289.21	   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))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))))))
1023.14/289.21	
1023.14/289.21	Q is empty.
1023.14/289.21	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.21	----------------------------------------
1023.14/289.21	
1023.14/289.21	(89) QDPOrderProof (EQUIVALENT)
1023.14/289.21	We use the reduction pair processor [LPAR04,JAR06].
1023.14/289.21	
1023.14/289.21	
1023.14/289.21	The following pairs can be oriented strictly and are deleted.
1023.14/289.21	
1023.14/289.21	   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))))))))))))
1023.14/289.21	The remaining pairs can at least be oriented weakly.
1023.14/289.21	Used ordering:  Polynomial interpretation [POLO]:
1023.14/289.21	
1023.14/289.21	   POL(0(x_1)) = 0
1023.14/289.21	   POL(1(x_1)) = 0
1023.14/289.21	   POL(2(x_1)) = 1 + x_1
1023.14/289.21	   POL(2^1(x_1)) = x_1
1023.14/289.21	   POL(3(x_1)) = 0
1023.14/289.21	   POL(4(x_1)) = x_1
1023.14/289.21	   POL(5(x_1)) = 0
1023.14/289.21	
1023.14/289.21	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
1023.14/289.21	
1023.14/289.21	   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)))))))))))))))
1023.14/289.21	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))))
1023.14/289.21	   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))))))))))))
1023.14/289.21	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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)))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))))))
1023.14/289.21	   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)))))))))))))))))))
1023.14/289.21	   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))))))))))))
1023.14/289.21	   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)))))))))))))))))))))
1023.14/289.21	   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))))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	
1023.14/289.22	----------------------------------------
1023.14/289.22	
1023.14/289.22	(90)
1023.14/289.22	Obligation:
1023.14/289.22	Q DP problem:
1023.14/289.22	The TRS P consists of the following rules:
1023.14/289.22	
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	
1023.14/289.22	The TRS R consists of the following rules:
1023.14/289.22	
1023.14/289.22	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.22	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.22	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.22	   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))))))))))))
1023.14/289.22	   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))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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))))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	Q is empty.
1023.14/289.22	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.22	----------------------------------------
1023.14/289.22	
1023.14/289.22	(91) MRRProof (EQUIVALENT)
1023.14/289.22	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.
1023.14/289.22	
1023.14/289.22	
1023.14/289.22	Strictly oriented rules of the TRS R:
1023.14/289.22	
1023.14/289.22	   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))))))))))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	Used ordering: Polynomial interpretation [POLO]:
1023.14/289.22	
1023.14/289.22	   POL(0(x_1)) = x_1
1023.14/289.22	   POL(1(x_1)) = x_1
1023.14/289.22	   POL(2(x_1)) = x_1
1023.14/289.22	   POL(2^1(x_1)) = x_1
1023.14/289.22	   POL(3(x_1)) = x_1
1023.14/289.22	   POL(4(x_1)) = 1 + x_1
1023.14/289.22	   POL(5(x_1)) = 2*x_1
1023.14/289.22	
1023.14/289.22	
1023.14/289.22	----------------------------------------
1023.14/289.22	
1023.14/289.22	(92)
1023.14/289.22	Obligation:
1023.14/289.22	Q DP problem:
1023.14/289.22	The TRS P consists of the following rules:
1023.14/289.22	
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	
1023.14/289.22	The TRS R consists of the following rules:
1023.14/289.22	
1023.14/289.22	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.22	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.22	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.22	   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))))))))))))
1023.14/289.22	   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))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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))))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	Q is empty.
1023.14/289.22	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.22	----------------------------------------
1023.14/289.22	
1023.14/289.22	(93) MRRProof (EQUIVALENT)
1023.14/289.22	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.
1023.14/289.22	
1023.14/289.22	
1023.14/289.22	Strictly oriented rules of the TRS R:
1023.14/289.22	
1023.14/289.22	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.22	   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))))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	Used ordering: Polynomial interpretation [POLO]:
1023.14/289.22	
1023.14/289.22	   POL(0(x_1)) = 2 + 2*x_1
1023.14/289.22	   POL(1(x_1)) = x_1
1023.14/289.22	   POL(2(x_1)) = 3 + 2*x_1
1023.14/289.22	   POL(2^1(x_1)) = x_1
1023.14/289.22	   POL(3(x_1)) = 2 + 2*x_1
1023.14/289.22	   POL(4(x_1)) = 2 + 2*x_1
1023.14/289.22	   POL(5(x_1)) = x_1
1023.14/289.22	
1023.14/289.22	
1023.14/289.22	----------------------------------------
1023.14/289.22	
1023.14/289.22	(94)
1023.14/289.22	Obligation:
1023.14/289.22	Q DP problem:
1023.14/289.22	The TRS P consists of the following rules:
1023.14/289.22	
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	
1023.14/289.22	The TRS R consists of the following rules:
1023.14/289.22	
1023.14/289.22	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.22	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.22	   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))))))))))))
1023.14/289.22	   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))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	Q is empty.
1023.14/289.22	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.22	----------------------------------------
1023.14/289.22	
1023.14/289.22	(95) MRRProof (EQUIVALENT)
1023.14/289.22	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.
1023.14/289.22	
1023.14/289.22	
1023.14/289.22	Strictly oriented rules of the TRS R:
1023.14/289.22	
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	Used ordering: Polynomial interpretation [POLO]:
1023.14/289.22	
1023.14/289.22	   POL(0(x_1)) = 1 + 2*x_1
1023.14/289.22	   POL(1(x_1)) = 2*x_1
1023.14/289.22	   POL(2(x_1)) = 2*x_1
1023.14/289.22	   POL(2^1(x_1)) = 2*x_1
1023.14/289.22	   POL(3(x_1)) = x_1
1023.14/289.22	   POL(4(x_1)) = 2*x_1
1023.14/289.22	   POL(5(x_1)) = x_1
1023.14/289.22	
1023.14/289.22	
1023.14/289.22	----------------------------------------
1023.14/289.22	
1023.14/289.22	(96)
1023.14/289.22	Obligation:
1023.14/289.22	Q DP problem:
1023.14/289.22	The TRS P consists of the following rules:
1023.14/289.22	
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	
1023.14/289.22	The TRS R consists of the following rules:
1023.14/289.22	
1023.14/289.22	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.22	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.22	   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))))))))))))
1023.14/289.22	   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))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	Q is empty.
1023.14/289.22	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.22	----------------------------------------
1023.14/289.22	
1023.14/289.22	(97) MRRProof (EQUIVALENT)
1023.14/289.22	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.
1023.14/289.22	
1023.14/289.22	
1023.14/289.22	Strictly oriented rules of the TRS R:
1023.14/289.22	
1023.14/289.22	   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))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	Used ordering: Polynomial interpretation [POLO]:
1023.14/289.22	
1023.14/289.22	   POL(0(x_1)) = 2*x_1
1023.14/289.22	   POL(1(x_1)) = x_1
1023.14/289.22	   POL(2(x_1)) = 2*x_1
1023.14/289.22	   POL(2^1(x_1)) = 2*x_1
1023.14/289.22	   POL(3(x_1)) = 2*x_1
1023.14/289.22	   POL(4(x_1)) = 3 + x_1
1023.14/289.22	   POL(5(x_1)) = 2*x_1
1023.14/289.22	
1023.14/289.22	
1023.14/289.22	----------------------------------------
1023.14/289.22	
1023.14/289.22	(98)
1023.14/289.22	Obligation:
1023.14/289.22	Q DP problem:
1023.14/289.22	The TRS P consists of the following rules:
1023.14/289.22	
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	
1023.14/289.22	The TRS R consists of the following rules:
1023.14/289.22	
1023.14/289.22	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.22	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.22	   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))))))))))))
1023.14/289.22	   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))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	Q is empty.
1023.14/289.22	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.22	----------------------------------------
1023.14/289.22	
1023.14/289.22	(99) MRRProof (EQUIVALENT)
1023.14/289.22	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.
1023.14/289.22	
1023.14/289.22	
1023.14/289.22	Strictly oriented rules of the TRS R:
1023.14/289.22	
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	Used ordering: Polynomial interpretation [POLO]:
1023.14/289.22	
1023.14/289.22	   POL(0(x_1)) = 1 + 2*x_1
1023.14/289.22	   POL(1(x_1)) = x_1
1023.14/289.22	   POL(2(x_1)) = x_1
1023.14/289.22	   POL(2^1(x_1)) = x_1
1023.14/289.22	   POL(3(x_1)) = 2*x_1
1023.14/289.22	   POL(4(x_1)) = x_1
1023.14/289.22	   POL(5(x_1)) = 2*x_1
1023.14/289.22	
1023.14/289.22	
1023.14/289.22	----------------------------------------
1023.14/289.22	
1023.14/289.22	(100)
1023.14/289.22	Obligation:
1023.14/289.22	Q DP problem:
1023.14/289.22	The TRS P consists of the following rules:
1023.14/289.22	
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	
1023.14/289.22	The TRS R consists of the following rules:
1023.14/289.22	
1023.14/289.22	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.22	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.22	   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))))))))))))
1023.14/289.22	   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))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	Q is empty.
1023.14/289.22	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.22	----------------------------------------
1023.14/289.22	
1023.14/289.22	(101) MRRProof (EQUIVALENT)
1023.14/289.22	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.
1023.14/289.22	
1023.14/289.22	
1023.14/289.22	Strictly oriented rules of the TRS R:
1023.14/289.22	
1023.14/289.22	   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))))))))))))
1023.14/289.22	
1023.14/289.22	Used ordering: Polynomial interpretation [POLO]:
1023.14/289.22	
1023.14/289.22	   POL(0(x_1)) = 2*x_1
1023.14/289.22	   POL(1(x_1)) = 2*x_1
1023.14/289.22	   POL(2(x_1)) = 2*x_1
1023.14/289.22	   POL(2^1(x_1)) = 2*x_1
1023.14/289.22	   POL(3(x_1)) = x_1
1023.14/289.22	   POL(4(x_1)) = 2*x_1
1023.14/289.22	   POL(5(x_1)) = 2 + x_1
1023.14/289.22	
1023.14/289.22	
1023.14/289.22	----------------------------------------
1023.14/289.22	
1023.14/289.22	(102)
1023.14/289.22	Obligation:
1023.14/289.22	Q DP problem:
1023.14/289.22	The TRS P consists of the following rules:
1023.14/289.22	
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	
1023.14/289.22	The TRS R consists of the following rules:
1023.14/289.22	
1023.14/289.22	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.22	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.22	   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))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	Q is empty.
1023.14/289.22	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.22	----------------------------------------
1023.14/289.22	
1023.14/289.22	(103) MRRProof (EQUIVALENT)
1023.14/289.22	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.
1023.14/289.22	
1023.14/289.22	
1023.14/289.22	Strictly oriented rules of the TRS R:
1023.14/289.22	
1023.14/289.22	   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))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	Used ordering: Polynomial interpretation [POLO]:
1023.14/289.22	
1023.14/289.22	   POL(0(x_1)) = x_1
1023.14/289.22	   POL(1(x_1)) = 2 + 2*x_1
1023.14/289.22	   POL(2(x_1)) = 2 + 2*x_1
1023.14/289.22	   POL(2^1(x_1)) = x_1
1023.14/289.22	   POL(3(x_1)) = 2*x_1
1023.14/289.22	   POL(4(x_1)) = 2 + 2*x_1
1023.14/289.22	   POL(5(x_1)) = 2*x_1
1023.14/289.22	
1023.14/289.22	
1023.14/289.22	----------------------------------------
1023.14/289.22	
1023.14/289.22	(104)
1023.14/289.22	Obligation:
1023.14/289.22	Q DP problem:
1023.14/289.22	The TRS P consists of the following rules:
1023.14/289.22	
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	
1023.14/289.22	The TRS R consists of the following rules:
1023.14/289.22	
1023.14/289.22	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.22	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	Q is empty.
1023.14/289.22	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.22	----------------------------------------
1023.14/289.22	
1023.14/289.22	(105) DependencyGraphProof (EQUIVALENT)
1023.14/289.22	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node.
1023.14/289.22	----------------------------------------
1023.14/289.22	
1023.14/289.22	(106)
1023.14/289.22	TRUE
1023.14/289.22	
1023.14/289.22	----------------------------------------
1023.14/289.22	
1023.14/289.22	(107)
1023.14/289.22	Obligation:
1023.14/289.22	Q DP problem:
1023.14/289.22	The TRS P consists of the following rules:
1023.14/289.22	
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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)))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	The TRS R consists of the following rules:
1023.14/289.22	
1023.14/289.22	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.22	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.22	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.22	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.22	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.14/289.22	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.22	   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))))))))))))
1023.14/289.22	   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))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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))))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	Q is empty.
1023.14/289.22	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.22	----------------------------------------
1023.14/289.22	
1023.14/289.22	(108) QDPOrderProof (EQUIVALENT)
1023.14/289.22	We use the reduction pair processor [LPAR04,JAR06].
1023.14/289.22	
1023.14/289.22	
1023.14/289.22	The following pairs can be oriented strictly and are deleted.
1023.14/289.22	
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	The remaining pairs can at least be oriented weakly.
1023.14/289.22	Used ordering:  Polynomial interpretation [POLO]:
1023.14/289.22	
1023.14/289.22	   POL(0(x_1)) = 1
1023.14/289.22	   POL(0^1(x_1)) = x_1
1023.14/289.22	   POL(1(x_1)) = 0
1023.14/289.22	   POL(2(x_1)) = x_1
1023.14/289.22	   POL(3(x_1)) = 0
1023.14/289.22	   POL(4(x_1)) = x_1
1023.14/289.22	   POL(5(x_1)) = 0
1023.14/289.22	
1023.14/289.22	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
1023.14/289.22	
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))))))
1023.14/289.22	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.22	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.22	   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))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))
1023.14/289.22	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.14/289.22	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))
1023.14/289.22	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	
1023.14/289.22	----------------------------------------
1023.14/289.22	
1023.14/289.22	(109)
1023.14/289.22	Obligation:
1023.14/289.22	Q DP problem:
1023.14/289.22	The TRS P consists of the following rules:
1023.14/289.22	
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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)))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	The TRS R consists of the following rules:
1023.14/289.22	
1023.14/289.22	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.22	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.22	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.22	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.22	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.14/289.22	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.22	   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))))))))))))
1023.14/289.22	   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))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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))))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	Q is empty.
1023.14/289.22	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.22	----------------------------------------
1023.14/289.22	
1023.14/289.22	(110) QDPOrderProof (EQUIVALENT)
1023.14/289.22	We use the reduction pair processor [LPAR04,JAR06].
1023.14/289.22	
1023.14/289.22	
1023.14/289.22	The following pairs can be oriented strictly and are deleted.
1023.14/289.22	
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	The remaining pairs can at least be oriented weakly.
1023.14/289.22	Used ordering:  Polynomial interpretation [POLO]:
1023.14/289.22	
1023.14/289.22	   POL(0(x_1)) = 0
1023.14/289.22	   POL(0^1(x_1)) = x_1
1023.14/289.22	   POL(1(x_1)) = x_1
1023.14/289.22	   POL(2(x_1)) = 0
1023.14/289.22	   POL(3(x_1)) = x_1
1023.14/289.22	   POL(4(x_1)) = 1
1023.14/289.22	   POL(5(x_1)) = 0
1023.14/289.22	
1023.14/289.22	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
1023.14/289.22	
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))))))
1023.14/289.22	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.22	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.22	   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))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))
1023.14/289.22	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.14/289.22	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))
1023.14/289.22	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	
1023.14/289.22	----------------------------------------
1023.14/289.22	
1023.14/289.22	(111)
1023.14/289.22	Obligation:
1023.14/289.22	Q DP problem:
1023.14/289.22	The TRS P consists of the following rules:
1023.14/289.22	
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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)))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	The TRS R consists of the following rules:
1023.14/289.22	
1023.14/289.22	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.22	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.22	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.22	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.22	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.14/289.22	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.22	   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))))))))))))
1023.14/289.22	   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))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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))))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	Q is empty.
1023.14/289.22	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.22	----------------------------------------
1023.14/289.22	
1023.14/289.22	(112) MRRProof (EQUIVALENT)
1023.14/289.22	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.
1023.14/289.22	
1023.14/289.22	
1023.14/289.22	Strictly oriented rules of the TRS R:
1023.14/289.22	
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	Used ordering: Polynomial interpretation [POLO]:
1023.14/289.22	
1023.14/289.22	   POL(0(x_1)) = x_1
1023.14/289.22	   POL(0^1(x_1)) = 2*x_1
1023.14/289.22	   POL(1(x_1)) = x_1
1023.14/289.22	   POL(2(x_1)) = 1 + x_1
1023.14/289.22	   POL(3(x_1)) = x_1
1023.14/289.22	   POL(4(x_1)) = 2*x_1
1023.14/289.22	   POL(5(x_1)) = x_1
1023.14/289.22	
1023.14/289.22	
1023.14/289.22	----------------------------------------
1023.14/289.22	
1023.14/289.22	(113)
1023.14/289.22	Obligation:
1023.14/289.22	Q DP problem:
1023.14/289.22	The TRS P consists of the following rules:
1023.14/289.22	
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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)))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	The TRS R consists of the following rules:
1023.14/289.22	
1023.14/289.22	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.22	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.22	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.22	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.22	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.14/289.22	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.22	   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))))))))))))
1023.14/289.22	   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))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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))))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	Q is empty.
1023.14/289.22	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.22	----------------------------------------
1023.14/289.22	
1023.14/289.22	(114) MRRProof (EQUIVALENT)
1023.14/289.22	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.
1023.14/289.22	
1023.14/289.22	
1023.14/289.22	Strictly oriented rules of the TRS R:
1023.14/289.22	
1023.14/289.22	   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))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	Used ordering: Polynomial interpretation [POLO]:
1023.14/289.22	
1023.14/289.22	   POL(0(x_1)) = x_1
1023.14/289.22	   POL(0^1(x_1)) = x_1
1023.14/289.22	   POL(1(x_1)) = x_1
1023.14/289.22	   POL(2(x_1)) = x_1
1023.14/289.22	   POL(3(x_1)) = 2*x_1
1023.14/289.22	   POL(4(x_1)) = 1 + 2*x_1
1023.14/289.22	   POL(5(x_1)) = 2*x_1
1023.14/289.22	
1023.14/289.22	
1023.14/289.22	----------------------------------------
1023.14/289.22	
1023.14/289.22	(115)
1023.14/289.22	Obligation:
1023.14/289.22	Q DP problem:
1023.14/289.22	The TRS P consists of the following rules:
1023.14/289.22	
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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)))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	The TRS R consists of the following rules:
1023.14/289.22	
1023.14/289.22	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.22	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.22	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.22	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.22	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.14/289.22	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.22	   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))))))))))))
1023.14/289.22	   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))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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))))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	Q is empty.
1023.14/289.22	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.22	----------------------------------------
1023.14/289.22	
1023.14/289.22	(116) MRRProof (EQUIVALENT)
1023.14/289.22	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.
1023.14/289.22	
1023.14/289.22	Strictly oriented dependency pairs:
1023.14/289.22	
1023.14/289.22	   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))))))))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	Strictly oriented rules of the TRS R:
1023.14/289.22	
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	Used ordering: Polynomial interpretation [POLO]:
1023.14/289.22	
1023.14/289.22	   POL(0(x_1)) = 2 + 2*x_1
1023.14/289.22	   POL(0^1(x_1)) = 3*x_1
1023.14/289.22	   POL(1(x_1)) = x_1
1023.14/289.22	   POL(2(x_1)) = 2 + 2*x_1
1023.14/289.22	   POL(3(x_1)) = 2 + 2*x_1
1023.14/289.22	   POL(4(x_1)) = 3*x_1
1023.14/289.22	   POL(5(x_1)) = 2 + 2*x_1
1023.14/289.22	
1023.14/289.22	
1023.14/289.22	----------------------------------------
1023.14/289.22	
1023.14/289.22	(117)
1023.14/289.22	Obligation:
1023.14/289.22	Q DP problem:
1023.14/289.22	The TRS P consists of the following rules:
1023.14/289.22	
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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)))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	The TRS R consists of the following rules:
1023.14/289.22	
1023.14/289.22	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.22	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.22	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.22	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.22	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.14/289.22	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.22	   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))))))))))))
1023.14/289.22	   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))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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))))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	Q is empty.
1023.14/289.22	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.22	----------------------------------------
1023.14/289.22	
1023.14/289.22	(118) MRRProof (EQUIVALENT)
1023.14/289.22	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.
1023.14/289.22	
1023.14/289.22	
1023.14/289.22	Strictly oriented rules of the TRS R:
1023.14/289.22	
1023.14/289.22	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.14/289.22	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.14/289.22	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	Used ordering: Polynomial interpretation [POLO]:
1023.14/289.22	
1023.14/289.22	   POL(0(x_1)) = 2*x_1
1023.14/289.22	   POL(0^1(x_1)) = 2*x_1
1023.14/289.22	   POL(1(x_1)) = x_1
1023.14/289.22	   POL(2(x_1)) = 2*x_1
1023.14/289.22	   POL(3(x_1)) = 1 + 2*x_1
1023.14/289.22	   POL(4(x_1)) = 2*x_1
1023.14/289.22	   POL(5(x_1)) = x_1
1023.14/289.22	
1023.14/289.22	
1023.14/289.22	----------------------------------------
1023.14/289.22	
1023.14/289.22	(119)
1023.14/289.22	Obligation:
1023.14/289.22	Q DP problem:
1023.14/289.22	The TRS P consists of the following rules:
1023.14/289.22	
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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)))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	The TRS R consists of the following rules:
1023.14/289.22	
1023.14/289.22	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.22	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.22	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.22	   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))))))))))))
1023.14/289.22	   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))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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))))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	Q is empty.
1023.14/289.22	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.22	----------------------------------------
1023.14/289.22	
1023.14/289.22	(120) MRRProof (EQUIVALENT)
1023.14/289.22	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.
1023.14/289.22	
1023.14/289.22	Strictly oriented dependency pairs:
1023.14/289.22	
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	Strictly oriented rules of the TRS R:
1023.14/289.22	
1023.14/289.22	   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))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	Used ordering: Polynomial interpretation [POLO]:
1023.14/289.22	
1023.14/289.22	   POL(0(x_1)) = 1 + x_1
1023.14/289.22	   POL(0^1(x_1)) = x_1
1023.14/289.22	   POL(1(x_1)) = 1 + 2*x_1
1023.14/289.22	   POL(2(x_1)) = x_1
1023.14/289.22	   POL(3(x_1)) = x_1
1023.14/289.22	   POL(4(x_1)) = x_1
1023.14/289.22	   POL(5(x_1)) = x_1
1023.14/289.22	
1023.14/289.22	
1023.14/289.22	----------------------------------------
1023.14/289.22	
1023.14/289.22	(121)
1023.14/289.22	Obligation:
1023.14/289.22	Q DP problem:
1023.14/289.22	The TRS P consists of the following rules:
1023.14/289.22	
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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)))))))))))
1023.14/289.22	
1023.14/289.22	The TRS R consists of the following rules:
1023.14/289.22	
1023.14/289.22	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.14/289.22	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.14/289.22	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.14/289.22	   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))))))))))))
1023.14/289.22	   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))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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)))))))))))))
1023.14/289.22	   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))))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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)))))))))))))))
1023.14/289.22	   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))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))
1023.14/289.22	   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))))))))))))))))))))))))))
1023.14/289.22	   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)))))))))))))))))))))))))))))
1023.14/289.22	
1023.14/289.22	Q is empty.
1023.14/289.22	We have to consider all minimal (P,Q,R)-chains.
1023.14/289.22	----------------------------------------
1023.14/289.22	
1023.14/289.22	(122) MRRProof (EQUIVALENT)
1023.14/289.22	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.
1023.14/289.22	
1023.14/289.22	Strictly oriented dependency pairs:
1023.31/289.23	
1023.31/289.23	   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)))))))))))
1023.31/289.23	
1023.31/289.23	Strictly oriented rules of the TRS R:
1023.31/289.23	
1023.31/289.23	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.31/289.23	   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))))))))))))))
1023.31/289.23	   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))))))))))))))))))
1023.31/289.23	
1023.31/289.23	Used ordering: Polynomial interpretation [POLO]:
1023.31/289.23	
1023.31/289.23	   POL(0(x_1)) = 1 + 2*x_1
1023.31/289.23	   POL(0^1(x_1)) = x_1
1023.31/289.23	   POL(1(x_1)) = x_1
1023.31/289.23	   POL(2(x_1)) = 3 + x_1
1023.31/289.23	   POL(3(x_1)) = x_1
1023.31/289.23	   POL(4(x_1)) = x_1
1023.31/289.23	   POL(5(x_1)) = x_1
1023.31/289.23	
1023.31/289.23	
1023.31/289.23	----------------------------------------
1023.31/289.23	
1023.31/289.23	(123)
1023.31/289.23	Obligation:
1023.31/289.23	Q DP problem:
1023.31/289.23	The TRS P consists of the following rules:
1023.31/289.23	
1023.31/289.23	   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)))))))))))))))
1023.31/289.23	
1023.31/289.23	The TRS R consists of the following rules:
1023.31/289.23	
1023.31/289.23	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.31/289.23	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.31/289.23	   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))))))))))))
1023.31/289.23	   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))))))))))))
1023.31/289.23	   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)))))))))))))
1023.31/289.23	   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)))))))))))))
1023.31/289.23	   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)))))))))))))
1023.31/289.23	   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)))))))))))))))
1023.31/289.23	   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)))))))))))))))
1023.31/289.23	   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))))))))))))))))
1023.31/289.23	   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))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))
1023.31/289.23	   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))))))))))))))))))))))))
1023.31/289.23	   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))))))))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))))))))
1023.31/289.23	   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))))))))))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))))))))))))
1023.31/289.23	
1023.31/289.23	Q is empty.
1023.31/289.23	We have to consider all minimal (P,Q,R)-chains.
1023.31/289.23	----------------------------------------
1023.31/289.23	
1023.31/289.23	(124) MRRProof (EQUIVALENT)
1023.31/289.23	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.
1023.31/289.23	
1023.31/289.23	
1023.31/289.23	Strictly oriented rules of the TRS R:
1023.31/289.23	
1023.31/289.23	   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)))))))))))))
1023.31/289.23	   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)))))))))))))))
1023.31/289.23	   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)))))))))))))))))))
1023.31/289.23	   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))))))))))))))))))))))))
1023.31/289.23	
1023.31/289.23	Used ordering: Polynomial interpretation [POLO]:
1023.31/289.23	
1023.31/289.23	   POL(0(x_1)) = 1 + 2*x_1
1023.31/289.23	   POL(0^1(x_1)) = x_1
1023.31/289.23	   POL(1(x_1)) = 2*x_1
1023.31/289.23	   POL(2(x_1)) = 2*x_1
1023.31/289.23	   POL(3(x_1)) = 2*x_1
1023.31/289.23	   POL(4(x_1)) = 2*x_1
1023.31/289.23	   POL(5(x_1)) = 2*x_1
1023.31/289.23	
1023.31/289.23	
1023.31/289.23	----------------------------------------
1023.31/289.23	
1023.31/289.23	(125)
1023.31/289.23	Obligation:
1023.31/289.23	Q DP problem:
1023.31/289.23	The TRS P consists of the following rules:
1023.31/289.23	
1023.31/289.23	   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)))))))))))))))
1023.31/289.23	
1023.31/289.23	The TRS R consists of the following rules:
1023.31/289.23	
1023.31/289.23	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.31/289.23	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.31/289.23	   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))))))))))))
1023.31/289.23	   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))))))))))))
1023.31/289.23	   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)))))))))))))
1023.31/289.23	   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)))))))))))))
1023.31/289.23	   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)))))))))))))))
1023.31/289.23	   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))))))))))))))))
1023.31/289.23	   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))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))
1023.31/289.23	   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))))))))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))))))))
1023.31/289.23	   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))))))))))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))))))))))))
1023.31/289.23	
1023.31/289.23	Q is empty.
1023.31/289.23	We have to consider all minimal (P,Q,R)-chains.
1023.31/289.23	----------------------------------------
1023.31/289.23	
1023.31/289.23	(126) MRRProof (EQUIVALENT)
1023.31/289.23	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.
1023.31/289.23	
1023.31/289.23	
1023.31/289.23	Strictly oriented rules of the TRS R:
1023.31/289.23	
1023.31/289.23	   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))))))))))))
1023.31/289.23	
1023.31/289.23	Used ordering: Polynomial interpretation [POLO]:
1023.31/289.23	
1023.31/289.23	   POL(0(x_1)) = x_1
1023.31/289.23	   POL(0^1(x_1)) = 2*x_1
1023.31/289.23	   POL(1(x_1)) = x_1
1023.31/289.23	   POL(2(x_1)) = 2*x_1
1023.31/289.23	   POL(3(x_1)) = x_1
1023.31/289.23	   POL(4(x_1)) = 2*x_1
1023.31/289.23	   POL(5(x_1)) = 1 + 2*x_1
1023.31/289.23	
1023.31/289.23	
1023.31/289.23	----------------------------------------
1023.31/289.23	
1023.31/289.23	(127)
1023.31/289.23	Obligation:
1023.31/289.23	Q DP problem:
1023.31/289.23	The TRS P consists of the following rules:
1023.31/289.23	
1023.31/289.23	   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)))))))))))))))
1023.31/289.23	
1023.31/289.23	The TRS R consists of the following rules:
1023.31/289.23	
1023.31/289.23	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.31/289.23	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.31/289.23	   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))))))))))))
1023.31/289.23	   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)))))))))))))
1023.31/289.23	   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)))))))))))))
1023.31/289.23	   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)))))))))))))))
1023.31/289.23	   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))))))))))))))))
1023.31/289.23	   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))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))
1023.31/289.23	   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))))))))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))))))))
1023.31/289.23	   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))))))))))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))))))))))))
1023.31/289.23	
1023.31/289.23	Q is empty.
1023.31/289.23	We have to consider all minimal (P,Q,R)-chains.
1023.31/289.23	----------------------------------------
1023.31/289.23	
1023.31/289.23	(128) MRRProof (EQUIVALENT)
1023.31/289.23	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.
1023.31/289.23	
1023.31/289.23	Strictly oriented dependency pairs:
1023.31/289.23	
1023.31/289.23	   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)))))))))))))))
1023.31/289.23	
1023.31/289.23	Strictly oriented rules of the TRS R:
1023.31/289.23	
1023.31/289.23	   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))))))))))))
1023.31/289.23	   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)))))))))))))))
1023.31/289.23	   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)))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))))))))))))
1023.31/289.23	
1023.31/289.23	Used ordering: Polynomial interpretation [POLO]:
1023.31/289.23	
1023.31/289.23	   POL(0(x_1)) = 2*x_1
1023.31/289.23	   POL(0^1(x_1)) = x_1
1023.31/289.23	   POL(1(x_1)) = 1 + 2*x_1
1023.31/289.23	   POL(2(x_1)) = 1 + 2*x_1
1023.31/289.23	   POL(3(x_1)) = 2*x_1
1023.31/289.23	   POL(4(x_1)) = 1 + 2*x_1
1023.31/289.23	   POL(5(x_1)) = 2*x_1
1023.31/289.23	
1023.31/289.23	
1023.31/289.23	----------------------------------------
1023.31/289.23	
1023.31/289.23	(129)
1023.31/289.23	Obligation:
1023.31/289.23	Q DP problem:
1023.31/289.23	P is empty.
1023.31/289.23	The TRS R consists of the following rules:
1023.31/289.23	
1023.31/289.23	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.31/289.23	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.31/289.23	   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)))))))))))))
1023.31/289.23	   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)))))))))))))
1023.31/289.23	   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))))))))))))))))
1023.31/289.23	   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))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))
1023.31/289.23	   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))))))))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))))))))
1023.31/289.23	   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))))))))))))))))))))))))))
1023.31/289.23	
1023.31/289.23	Q is empty.
1023.31/289.23	We have to consider all minimal (P,Q,R)-chains.
1023.31/289.23	----------------------------------------
1023.31/289.23	
1023.31/289.23	(130) PisEmptyProof (EQUIVALENT)
1023.31/289.23	The TRS P is empty. Hence, there is no (P,Q,R) chain.
1023.31/289.23	----------------------------------------
1023.31/289.23	
1023.31/289.23	(131)
1023.31/289.23	YES
1023.31/289.23	
1023.31/289.23	----------------------------------------
1023.31/289.23	
1023.31/289.23	(132)
1023.31/289.23	Obligation:
1023.31/289.23	Q DP problem:
1023.31/289.23	The TRS P consists of the following rules:
1023.31/289.23	
1023.31/289.23	   5^1(4(3(1(2(1(1(0(x1)))))))) -> 5^1(4(3(2(1(1(1(0(x1))))))))
1023.31/289.23	   5^1(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5^1(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.31/289.23	   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)))))))))))))))
1023.31/289.23	   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)))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))))))))
1023.31/289.23	   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))))))))))))))))))))))))))
1023.31/289.23	
1023.31/289.23	The TRS R consists of the following rules:
1023.31/289.23	
1023.31/289.23	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.31/289.23	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.31/289.23	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.31/289.23	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.31/289.23	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.31/289.23	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.31/289.23	   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))))))))))))
1023.31/289.23	   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))))))))))))
1023.31/289.23	   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)))))))))))))
1023.31/289.23	   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)))))))))))))
1023.31/289.23	   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)))))))))))))
1023.31/289.23	   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))))))))))))))
1023.31/289.23	   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)))))))))))))))
1023.31/289.23	   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)))))))))))))))
1023.31/289.23	   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)))))))))))))))
1023.31/289.23	   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))))))))))))))))
1023.31/289.23	   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))))))))))))))))))
1023.31/289.23	   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))))))))))))))))))
1023.31/289.23	   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))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))
1023.31/289.23	   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))))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))))
1023.31/289.23	   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))))))))))))))))))))))
1023.31/289.23	   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))))))))))))))))))))))
1023.31/289.23	   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))))))))))))))))))))))))
1023.31/289.23	   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))))))))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))))))))
1023.31/289.23	   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))))))))))))))))))))))))))
1023.31/289.23	   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))))))))))))))))))))))))))
1023.31/289.23	   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))))))))))))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))))))))))))
1023.31/289.23	   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))))))))))))))))))))))))))))))
1023.31/289.23	
1023.31/289.23	Q is empty.
1023.31/289.23	We have to consider all minimal (P,Q,R)-chains.
1023.31/289.23	----------------------------------------
1023.31/289.23	
1023.31/289.23	(133) QDPOrderProof (EQUIVALENT)
1023.31/289.23	We use the reduction pair processor [LPAR04,JAR06].
1023.31/289.23	
1023.31/289.23	
1023.31/289.23	The following pairs can be oriented strictly and are deleted.
1023.31/289.23	
1023.31/289.23	   5^1(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5^1(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.31/289.23	   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)))))))))))))))
1023.31/289.23	The remaining pairs can at least be oriented weakly.
1023.31/289.23	Used ordering:  Polynomial interpretation [POLO]:
1023.31/289.23	
1023.31/289.23	   POL(0(x_1)) = x_1
1023.31/289.23	   POL(1(x_1)) = x_1
1023.31/289.23	   POL(2(x_1)) = 1
1023.31/289.23	   POL(3(x_1)) = 0
1023.31/289.23	   POL(4(x_1)) = 1 + x_1
1023.31/289.23	   POL(5(x_1)) = x_1
1023.31/289.23	   POL(5^1(x_1)) = x_1
1023.31/289.23	
1023.31/289.23	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
1023.31/289.23	
1023.31/289.23	   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)))))))))))))))
1023.31/289.23	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.31/289.23	   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))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))))))))
1023.31/289.23	   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))))))))))))))))))))))))))))
1023.31/289.23	   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))))))))))))
1023.31/289.23	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.31/289.23	   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)))))))))))))
1023.31/289.23	   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)))))))))))))
1023.31/289.23	   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)))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))))
1023.31/289.23	   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))))))))))))))))))))))))))))))
1023.31/289.23	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.31/289.23	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.31/289.23	   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))))))))))))
1023.31/289.23	   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)))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))))
1023.31/289.23	   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))))))))))))))))))))))))))
1023.31/289.23	   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))))))))))))))))))
1023.31/289.23	   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)))))))))))))))
1023.31/289.23	   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))))))))))))))))))))
1023.31/289.23	   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))))))))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))))))))))))
1023.31/289.23	   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))))))))))))))
1023.31/289.23	   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)))))))))))))
1023.31/289.23	   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))))))))))))))))
1023.31/289.23	   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))))))))))))))))))
1023.31/289.23	   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))))))))))))))))))))))
1023.31/289.23	   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))))))))))))))))))))))
1023.31/289.23	   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))))))))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))))))))))))
1023.31/289.23	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.31/289.23	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.31/289.23	   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)))))))))))))))
1023.31/289.23	   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)))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))))))))
1023.31/289.23	   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))))))))))))))))))))))))))
1023.31/289.23	
1023.31/289.23	
1023.31/289.23	----------------------------------------
1023.31/289.23	
1023.31/289.23	(134)
1023.31/289.23	Obligation:
1023.31/289.23	Q DP problem:
1023.31/289.23	The TRS P consists of the following rules:
1023.31/289.23	
1023.31/289.23	   5^1(4(3(1(2(1(1(0(x1)))))))) -> 5^1(4(3(2(1(1(1(0(x1))))))))
1023.31/289.23	   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)))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))
1023.31/289.23	   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)))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))
1023.31/289.24	
1023.31/289.24	The TRS R consists of the following rules:
1023.31/289.24	
1023.31/289.24	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.31/289.24	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.31/289.24	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.31/289.24	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.31/289.24	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.31/289.24	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.31/289.24	   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))))))))))))
1023.31/289.24	   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))))))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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))))))))))))))
1023.31/289.24	   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)))))))))))))))
1023.31/289.24	   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)))))))))))))))
1023.31/289.24	   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)))))))))))))))
1023.31/289.24	   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))))))))))))))))
1023.31/289.24	   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))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))))))
1023.31/289.24	
1023.31/289.24	Q is empty.
1023.31/289.24	We have to consider all minimal (P,Q,R)-chains.
1023.31/289.24	----------------------------------------
1023.31/289.24	
1023.31/289.24	(135) QDPOrderProof (EQUIVALENT)
1023.31/289.24	We use the reduction pair processor [LPAR04,JAR06].
1023.31/289.24	
1023.31/289.24	
1023.31/289.24	The following pairs can be oriented strictly and are deleted.
1023.31/289.24	
1023.31/289.24	   5^1(4(3(1(2(1(1(0(x1)))))))) -> 5^1(4(3(2(1(1(1(0(x1))))))))
1023.31/289.24	The remaining pairs can at least be oriented weakly.
1023.31/289.24	Used ordering:  Polynomial interpretation [POLO]:
1023.31/289.24	
1023.31/289.24	   POL(0(x_1)) = 0
1023.31/289.24	   POL(1(x_1)) = 1
1023.31/289.24	   POL(2(x_1)) = 0
1023.31/289.24	   POL(3(x_1)) = x_1
1023.31/289.24	   POL(4(x_1)) = x_1
1023.31/289.24	   POL(5(x_1)) = 0
1023.31/289.24	   POL(5^1(x_1)) = x_1
1023.31/289.24	
1023.31/289.24	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
1023.31/289.24	
1023.31/289.24	   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)))))))))))))))
1023.31/289.24	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.31/289.24	   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))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))
1023.31/289.24	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))))))
1023.31/289.24	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.31/289.24	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.31/289.24	   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))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))
1023.31/289.24	   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)))))))))))))))
1023.31/289.24	   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))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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))))))))))))))))
1023.31/289.24	   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))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))))))
1023.31/289.24	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.31/289.24	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.31/289.24	   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)))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))
1023.31/289.24	
1023.31/289.24	
1023.31/289.24	----------------------------------------
1023.31/289.24	
1023.31/289.24	(136)
1023.31/289.24	Obligation:
1023.31/289.24	Q DP problem:
1023.31/289.24	The TRS P consists of the following rules:
1023.31/289.24	
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))
1023.31/289.24	
1023.31/289.24	The TRS R consists of the following rules:
1023.31/289.24	
1023.31/289.24	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.31/289.24	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.31/289.24	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.31/289.24	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.31/289.24	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.31/289.24	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.31/289.24	   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))))))))))))
1023.31/289.24	   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))))))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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))))))))))))))
1023.31/289.24	   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)))))))))))))))
1023.31/289.24	   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)))))))))))))))
1023.31/289.24	   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)))))))))))))))
1023.31/289.24	   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))))))))))))))))
1023.31/289.24	   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))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))))))
1023.31/289.24	
1023.31/289.24	Q is empty.
1023.31/289.24	We have to consider all minimal (P,Q,R)-chains.
1023.31/289.24	----------------------------------------
1023.31/289.24	
1023.31/289.24	(137) MRRProof (EQUIVALENT)
1023.31/289.24	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.
1023.31/289.24	
1023.31/289.24	
1023.31/289.24	Strictly oriented rules of the TRS R:
1023.31/289.24	
1023.31/289.24	   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))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))
1023.31/289.24	
1023.31/289.24	Used ordering: Polynomial interpretation [POLO]:
1023.31/289.24	
1023.31/289.24	   POL(0(x_1)) = x_1
1023.31/289.24	   POL(1(x_1)) = x_1
1023.31/289.24	   POL(2(x_1)) = x_1
1023.31/289.24	   POL(3(x_1)) = 2*x_1
1023.31/289.24	   POL(4(x_1)) = 2 + 2*x_1
1023.31/289.24	   POL(5(x_1)) = x_1
1023.31/289.24	   POL(5^1(x_1)) = x_1
1023.31/289.24	
1023.31/289.24	
1023.31/289.24	----------------------------------------
1023.31/289.24	
1023.31/289.24	(138)
1023.31/289.24	Obligation:
1023.31/289.24	Q DP problem:
1023.31/289.24	The TRS P consists of the following rules:
1023.31/289.24	
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))
1023.31/289.24	
1023.31/289.24	The TRS R consists of the following rules:
1023.31/289.24	
1023.31/289.24	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.31/289.24	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.31/289.24	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.31/289.24	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.31/289.24	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.31/289.24	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.31/289.24	   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))))))))))))
1023.31/289.24	   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))))))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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))))))))))))))
1023.31/289.24	   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)))))))))))))))
1023.31/289.24	   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)))))))))))))))
1023.31/289.24	   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)))))))))))))))
1023.31/289.24	   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))))))))))))))))
1023.31/289.24	   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))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))))))
1023.31/289.24	
1023.31/289.24	Q is empty.
1023.31/289.24	We have to consider all minimal (P,Q,R)-chains.
1023.31/289.24	----------------------------------------
1023.31/289.24	
1023.31/289.24	(139) MRRProof (EQUIVALENT)
1023.31/289.24	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.
1023.31/289.24	
1023.31/289.24	
1023.31/289.24	Strictly oriented rules of the TRS R:
1023.31/289.24	
1023.31/289.24	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.31/289.24	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.31/289.24	   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))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))
1023.31/289.24	
1023.31/289.24	Used ordering: Polynomial interpretation [POLO]:
1023.31/289.24	
1023.31/289.24	   POL(0(x_1)) = x_1
1023.31/289.24	   POL(1(x_1)) = x_1
1023.31/289.24	   POL(2(x_1)) = 2*x_1
1023.31/289.24	   POL(3(x_1)) = 1 + 2*x_1
1023.31/289.24	   POL(4(x_1)) = 2*x_1
1023.31/289.24	   POL(5(x_1)) = x_1
1023.31/289.24	   POL(5^1(x_1)) = 2*x_1
1023.31/289.24	
1023.31/289.24	
1023.31/289.24	----------------------------------------
1023.31/289.24	
1023.31/289.24	(140)
1023.31/289.24	Obligation:
1023.31/289.24	Q DP problem:
1023.31/289.24	The TRS P consists of the following rules:
1023.31/289.24	
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))
1023.31/289.24	
1023.31/289.24	The TRS R consists of the following rules:
1023.31/289.24	
1023.31/289.24	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.31/289.24	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.31/289.24	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.31/289.24	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.31/289.24	   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))))))))))))
1023.31/289.24	   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))))))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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))))))))))))))
1023.31/289.24	   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)))))))))))))))
1023.31/289.24	   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)))))))))))))))
1023.31/289.24	   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)))))))))))))))
1023.31/289.24	   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))))))))))))))))
1023.31/289.24	   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))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))))))
1023.31/289.24	
1023.31/289.24	Q is empty.
1023.31/289.24	We have to consider all minimal (P,Q,R)-chains.
1023.31/289.24	----------------------------------------
1023.31/289.24	
1023.31/289.24	(141) MRRProof (EQUIVALENT)
1023.31/289.24	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.
1023.31/289.24	
1023.31/289.24	Strictly oriented dependency pairs:
1023.31/289.24	
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	
1023.31/289.24	Strictly oriented rules of the TRS R:
1023.31/289.24	
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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)))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))))))
1023.31/289.24	
1023.31/289.24	Used ordering: Polynomial interpretation [POLO]:
1023.31/289.24	
1023.31/289.24	   POL(0(x_1)) = 1 + x_1
1023.31/289.24	   POL(1(x_1)) = 2*x_1
1023.31/289.24	   POL(2(x_1)) = x_1
1023.31/289.24	   POL(3(x_1)) = x_1
1023.31/289.24	   POL(4(x_1)) = 2*x_1
1023.31/289.24	   POL(5(x_1)) = 2*x_1
1023.31/289.24	   POL(5^1(x_1)) = x_1
1023.31/289.24	
1023.31/289.24	
1023.31/289.24	----------------------------------------
1023.31/289.24	
1023.31/289.24	(142)
1023.31/289.24	Obligation:
1023.31/289.24	Q DP problem:
1023.31/289.24	The TRS P consists of the following rules:
1023.31/289.24	
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))
1023.31/289.24	
1023.31/289.24	The TRS R consists of the following rules:
1023.31/289.24	
1023.31/289.24	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.31/289.24	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.31/289.24	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.31/289.24	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.31/289.24	   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))))))))))))
1023.31/289.24	   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))))))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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))))))))))))))
1023.31/289.24	   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)))))))))))))))
1023.31/289.24	   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)))))))))))))))
1023.31/289.24	   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))))))))))))))))
1023.31/289.24	   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))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))))))
1023.31/289.24	
1023.31/289.24	Q is empty.
1023.31/289.24	We have to consider all minimal (P,Q,R)-chains.
1023.31/289.24	----------------------------------------
1023.31/289.24	
1023.31/289.24	(143) MRRProof (EQUIVALENT)
1023.31/289.24	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.
1023.31/289.24	
1023.31/289.24	
1023.31/289.24	Strictly oriented rules of the TRS R:
1023.31/289.24	
1023.31/289.24	   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))))))))))))
1023.31/289.24	
1023.31/289.24	Used ordering: Polynomial interpretation [POLO]:
1023.31/289.24	
1023.31/289.24	   POL(0(x_1)) = x_1
1023.31/289.24	   POL(1(x_1)) = 2*x_1
1023.31/289.24	   POL(2(x_1)) = 2*x_1
1023.31/289.24	   POL(3(x_1)) = x_1
1023.31/289.24	   POL(4(x_1)) = 2*x_1
1023.31/289.24	   POL(5(x_1)) = 2 + 2*x_1
1023.31/289.24	   POL(5^1(x_1)) = 2*x_1
1023.31/289.24	
1023.31/289.24	
1023.31/289.24	----------------------------------------
1023.31/289.24	
1023.31/289.24	(144)
1023.31/289.24	Obligation:
1023.31/289.24	Q DP problem:
1023.31/289.24	The TRS P consists of the following rules:
1023.31/289.24	
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))
1023.31/289.24	
1023.31/289.24	The TRS R consists of the following rules:
1023.31/289.24	
1023.31/289.24	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.31/289.24	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.31/289.24	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.31/289.24	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.31/289.24	   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))))))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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))))))))))))))
1023.31/289.24	   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)))))))))))))))
1023.31/289.24	   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)))))))))))))))
1023.31/289.24	   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))))))))))))))))
1023.31/289.24	   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))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))))))
1023.31/289.24	
1023.31/289.24	Q is empty.
1023.31/289.24	We have to consider all minimal (P,Q,R)-chains.
1023.31/289.24	----------------------------------------
1023.31/289.24	
1023.31/289.24	(145) MRRProof (EQUIVALENT)
1023.31/289.24	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.
1023.31/289.24	
1023.31/289.24	
1023.31/289.24	Strictly oriented rules of the TRS R:
1023.31/289.24	
1023.31/289.24	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.31/289.24	   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))))))))))))))
1023.31/289.24	   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))))))))))))))))))
1023.31/289.24	
1023.31/289.24	Used ordering: Polynomial interpretation [POLO]:
1023.31/289.24	
1023.31/289.24	   POL(0(x_1)) = 2*x_1
1023.31/289.24	   POL(1(x_1)) = 2 + 2*x_1
1023.31/289.24	   POL(2(x_1)) = 2 + 2*x_1
1023.31/289.24	   POL(3(x_1)) = x_1
1023.31/289.24	   POL(4(x_1)) = x_1
1023.31/289.24	   POL(5(x_1)) = 2*x_1
1023.31/289.24	   POL(5^1(x_1)) = x_1
1023.31/289.24	
1023.31/289.24	
1023.31/289.24	----------------------------------------
1023.31/289.24	
1023.31/289.24	(146)
1023.31/289.24	Obligation:
1023.31/289.24	Q DP problem:
1023.31/289.24	The TRS P consists of the following rules:
1023.31/289.24	
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))
1023.31/289.24	
1023.31/289.24	The TRS R consists of the following rules:
1023.31/289.24	
1023.31/289.24	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.31/289.24	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.31/289.24	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.31/289.24	   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))))))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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)))))))))))))))
1023.31/289.24	   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)))))))))))))))
1023.31/289.24	   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))))))))))))))))
1023.31/289.24	   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))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))))))
1023.31/289.24	
1023.31/289.24	Q is empty.
1023.31/289.24	We have to consider all minimal (P,Q,R)-chains.
1023.31/289.24	----------------------------------------
1023.31/289.24	
1023.31/289.24	(147) MRRProof (EQUIVALENT)
1023.31/289.24	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.
1023.31/289.24	
1023.31/289.24	
1023.31/289.24	Strictly oriented rules of the TRS R:
1023.31/289.24	
1023.31/289.24	   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)))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))))))
1023.31/289.24	
1023.31/289.24	Used ordering: Polynomial interpretation [POLO]:
1023.31/289.24	
1023.31/289.24	   POL(0(x_1)) = x_1
1023.31/289.24	   POL(1(x_1)) = x_1
1023.31/289.24	   POL(2(x_1)) = 1 + x_1
1023.31/289.24	   POL(3(x_1)) = x_1
1023.31/289.24	   POL(4(x_1)) = 2*x_1
1023.31/289.24	   POL(5(x_1)) = 2*x_1
1023.31/289.24	   POL(5^1(x_1)) = x_1
1023.31/289.24	
1023.31/289.24	
1023.31/289.24	----------------------------------------
1023.31/289.24	
1023.31/289.24	(148)
1023.31/289.24	Obligation:
1023.31/289.24	Q DP problem:
1023.31/289.24	The TRS P consists of the following rules:
1023.31/289.24	
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))
1023.31/289.24	
1023.31/289.24	The TRS R consists of the following rules:
1023.31/289.24	
1023.31/289.24	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.31/289.24	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.31/289.24	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.31/289.24	   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))))))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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)))))))))))))))
1023.31/289.24	   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))))))))))))))))
1023.31/289.24	   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))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))))))
1023.31/289.24	
1023.31/289.24	Q is empty.
1023.31/289.24	We have to consider all minimal (P,Q,R)-chains.
1023.31/289.24	----------------------------------------
1023.31/289.24	
1023.31/289.24	(149) MRRProof (EQUIVALENT)
1023.31/289.24	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.
1023.31/289.24	
1023.31/289.24	Strictly oriented dependency pairs:
1023.31/289.24	
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	
1023.31/289.24	Strictly oriented rules of the TRS R:
1023.31/289.24	
1023.31/289.24	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	
1023.31/289.24	Used ordering: Polynomial interpretation [POLO]:
1023.31/289.24	
1023.31/289.24	   POL(0(x_1)) = 2*x_1
1023.31/289.24	   POL(1(x_1)) = x_1
1023.31/289.24	   POL(2(x_1)) = x_1
1023.31/289.24	   POL(3(x_1)) = 1 + 2*x_1
1023.31/289.24	   POL(4(x_1)) = 2*x_1
1023.31/289.24	   POL(5(x_1)) = x_1
1023.31/289.24	   POL(5^1(x_1)) = 2*x_1
1023.31/289.24	
1023.31/289.24	
1023.31/289.24	----------------------------------------
1023.31/289.24	
1023.31/289.24	(150)
1023.31/289.24	Obligation:
1023.31/289.24	Q DP problem:
1023.31/289.24	The TRS P consists of the following rules:
1023.31/289.24	
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))
1023.31/289.24	
1023.31/289.24	The TRS R consists of the following rules:
1023.31/289.24	
1023.31/289.24	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.31/289.24	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.31/289.24	   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))))))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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)))))))))))))))
1023.31/289.24	   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))))))))))))))))
1023.31/289.24	   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))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))))))
1023.31/289.24	
1023.31/289.24	Q is empty.
1023.31/289.24	We have to consider all minimal (P,Q,R)-chains.
1023.31/289.24	----------------------------------------
1023.31/289.24	
1023.31/289.24	(151) MRRProof (EQUIVALENT)
1023.31/289.24	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.
1023.31/289.24	
1023.31/289.24	Strictly oriented dependency pairs:
1023.31/289.24	
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	
1023.31/289.24	Strictly oriented rules of the TRS R:
1023.31/289.24	
1023.31/289.24	   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))))))))))))
1023.31/289.24	   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)))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))))))
1023.31/289.24	
1023.31/289.24	Used ordering: Polynomial interpretation [POLO]:
1023.31/289.24	
1023.31/289.24	   POL(0(x_1)) = 2*x_1
1023.31/289.24	   POL(1(x_1)) = 2 + 2*x_1
1023.31/289.24	   POL(2(x_1)) = x_1
1023.31/289.24	   POL(3(x_1)) = 2*x_1
1023.31/289.24	   POL(4(x_1)) = x_1
1023.31/289.24	   POL(5(x_1)) = x_1
1023.31/289.24	   POL(5^1(x_1)) = x_1
1023.31/289.24	
1023.31/289.24	
1023.31/289.24	----------------------------------------
1023.31/289.24	
1023.31/289.24	(152)
1023.31/289.24	Obligation:
1023.31/289.24	Q DP problem:
1023.31/289.24	The TRS P consists of the following rules:
1023.31/289.24	
1023.31/289.24	   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)))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))
1023.31/289.24	
1023.31/289.24	The TRS R consists of the following rules:
1023.31/289.24	
1023.31/289.24	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.31/289.24	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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))))))))))))))))
1023.31/289.24	   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))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))
1023.31/289.24	
1023.31/289.24	Q is empty.
1023.31/289.24	We have to consider all minimal (P,Q,R)-chains.
1023.31/289.24	----------------------------------------
1023.31/289.24	
1023.31/289.24	(153) DependencyGraphProof (EQUIVALENT)
1023.31/289.24	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 2 less nodes.
1023.31/289.24	----------------------------------------
1023.31/289.24	
1023.31/289.24	(154)
1023.31/289.24	TRUE
1023.31/289.24	
1023.31/289.24	----------------------------------------
1023.31/289.24	
1023.31/289.24	(155)
1023.31/289.24	Obligation:
1023.31/289.24	Q DP problem:
1023.31/289.24	The TRS P consists of the following rules:
1023.31/289.24	
1023.31/289.24	   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))))))))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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))))))))))))))))
1023.31/289.24	   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))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))))))
1023.31/289.24	
1023.31/289.24	The TRS R consists of the following rules:
1023.31/289.24	
1023.31/289.24	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.31/289.24	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.31/289.24	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.31/289.24	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.31/289.24	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.31/289.24	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.31/289.24	   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))))))))))))
1023.31/289.24	   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))))))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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))))))))))))))
1023.31/289.24	   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)))))))))))))))
1023.31/289.24	   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)))))))))))))))
1023.31/289.24	   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)))))))))))))))
1023.31/289.24	   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))))))))))))))))
1023.31/289.24	   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))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))))))
1023.31/289.24	
1023.31/289.24	Q is empty.
1023.31/289.24	We have to consider all minimal (P,Q,R)-chains.
1023.31/289.24	----------------------------------------
1023.31/289.24	
1023.31/289.24	(156) QDPOrderProof (EQUIVALENT)
1023.31/289.24	We use the reduction pair processor [LPAR04,JAR06].
1023.31/289.24	
1023.31/289.24	
1023.31/289.24	The following pairs can be oriented strictly and are deleted.
1023.31/289.24	
1023.31/289.24	   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))))))))))))))))))))))
1023.31/289.24	The remaining pairs can at least be oriented weakly.
1023.31/289.24	Used ordering:  Polynomial interpretation [POLO]:
1023.31/289.24	
1023.31/289.24	   POL(0(x_1)) = 0
1023.31/289.24	   POL(1(x_1)) = 1
1023.31/289.24	   POL(2(x_1)) = 0
1023.31/289.24	   POL(3(x_1)) = 0
1023.31/289.24	   POL(4(x_1)) = 0
1023.31/289.24	   POL(4^1(x_1)) = x_1
1023.31/289.24	   POL(5(x_1)) = 0
1023.31/289.24	
1023.31/289.24	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
1023.31/289.24	
1023.31/289.24	   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))))))))))))
1023.31/289.24	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))))))
1023.31/289.24	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.31/289.24	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.31/289.24	   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)))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))
1023.31/289.24	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.31/289.24	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.31/289.24	   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))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))
1023.31/289.24	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.31/289.24	   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))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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))))))))))))))))
1023.31/289.24	   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))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))))))
1023.31/289.24	
1023.31/289.24	
1023.31/289.24	----------------------------------------
1023.31/289.24	
1023.31/289.24	(157)
1023.31/289.24	Obligation:
1023.31/289.24	Q DP problem:
1023.31/289.24	The TRS P consists of the following rules:
1023.31/289.24	
1023.31/289.24	   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))))))))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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))))))))))))))))
1023.31/289.24	   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))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))))))
1023.31/289.24	
1023.31/289.24	The TRS R consists of the following rules:
1023.31/289.24	
1023.31/289.24	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.31/289.24	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.31/289.24	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.31/289.24	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.31/289.24	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.31/289.24	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.31/289.24	   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))))))))))))
1023.31/289.24	   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))))))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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))))))))))))))
1023.31/289.24	   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)))))))))))))))
1023.31/289.24	   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)))))))))))))))
1023.31/289.24	   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)))))))))))))))
1023.31/289.24	   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))))))))))))))))
1023.31/289.24	   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))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))))))
1023.31/289.24	
1023.31/289.24	Q is empty.
1023.31/289.24	We have to consider all minimal (P,Q,R)-chains.
1023.31/289.24	----------------------------------------
1023.31/289.24	
1023.31/289.24	(158) QDPOrderProof (EQUIVALENT)
1023.31/289.24	We use the reduction pair processor [LPAR04,JAR06].
1023.31/289.24	
1023.31/289.24	
1023.31/289.24	The following pairs can be oriented strictly and are deleted.
1023.31/289.24	
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))
1023.31/289.24	The remaining pairs can at least be oriented weakly.
1023.31/289.24	Used ordering:  Polynomial interpretation [POLO]:
1023.31/289.24	
1023.31/289.24	   POL(0(x_1)) = 1
1023.31/289.24	   POL(1(x_1)) = x_1
1023.31/289.24	   POL(2(x_1)) = x_1
1023.31/289.24	   POL(3(x_1)) = 0
1023.31/289.24	   POL(4(x_1)) = x_1
1023.31/289.24	   POL(4^1(x_1)) = x_1
1023.31/289.24	   POL(5(x_1)) = 1 + x_1
1023.31/289.24	
1023.31/289.24	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
1023.31/289.24	
1023.31/289.24	   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))))))))))))
1023.31/289.24	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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)))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))
1023.31/289.24	   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))))))))))))))))))))))))))))))
1023.31/289.24	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.31/289.24	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.31/289.24	   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)))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))
1023.31/289.24	   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)))))))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))))))
1023.39/289.25	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.39/289.25	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.39/289.25	   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))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))
1023.39/289.25	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	   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)))))))))))))))
1023.39/289.25	   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))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))))))
1023.39/289.25	   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))))))))))))))
1023.39/289.25	   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)))))))))))))
1023.39/289.25	   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))))))))))))))))
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))))))
1023.39/289.25	
1023.39/289.25	
1023.39/289.25	----------------------------------------
1023.39/289.25	
1023.39/289.25	(159)
1023.39/289.25	Obligation:
1023.39/289.25	Q DP problem:
1023.39/289.25	The TRS P consists of the following rules:
1023.39/289.25	
1023.39/289.25	   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))))))))))))))
1023.39/289.25	   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))))))))))))))))
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))))))
1023.39/289.25	
1023.39/289.25	The TRS R consists of the following rules:
1023.39/289.25	
1023.39/289.25	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.39/289.25	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.39/289.25	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.39/289.25	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.39/289.25	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.39/289.25	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.39/289.25	   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))))))))))))
1023.39/289.25	   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))))))))))))
1023.39/289.25	   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)))))))))))))
1023.39/289.25	   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)))))))))))))
1023.39/289.25	   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)))))))))))))
1023.39/289.25	   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))))))))))))))
1023.39/289.25	   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)))))))))))))))
1023.39/289.25	   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)))))))))))))))
1023.39/289.25	   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)))))))))))))))
1023.39/289.25	   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))))))))))))))))
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))))))))))
1023.39/289.25	
1023.39/289.25	Q is empty.
1023.39/289.25	We have to consider all minimal (P,Q,R)-chains.
1023.39/289.25	----------------------------------------
1023.39/289.25	
1023.39/289.25	(160) MRRProof (EQUIVALENT)
1023.39/289.25	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.
1023.39/289.25	
1023.39/289.25	Strictly oriented dependency pairs:
1023.39/289.25	
1023.39/289.25	   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))))))))))))))))))))))
1023.39/289.25	
1023.39/289.25	Strictly oriented rules of the TRS R:
1023.39/289.25	
1023.39/289.25	   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))))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))))))))))
1023.39/289.25	
1023.39/289.25	Used ordering: Polynomial interpretation [POLO]:
1023.39/289.25	
1023.39/289.25	   POL(0(x_1)) = x_1
1023.39/289.25	   POL(1(x_1)) = x_1
1023.39/289.25	   POL(2(x_1)) = x_1
1023.39/289.25	   POL(3(x_1)) = 2*x_1
1023.39/289.25	   POL(4(x_1)) = 2 + 2*x_1
1023.39/289.25	   POL(4^1(x_1)) = 2*x_1
1023.39/289.25	   POL(5(x_1)) = 2*x_1
1023.39/289.25	
1023.39/289.25	
1023.39/289.25	----------------------------------------
1023.39/289.25	
1023.39/289.25	(161)
1023.39/289.25	Obligation:
1023.39/289.25	Q DP problem:
1023.39/289.25	The TRS P consists of the following rules:
1023.39/289.25	
1023.39/289.25	   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))))))))))))))
1023.39/289.25	   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))))))))))))))))
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))))))
1023.39/289.25	
1023.39/289.25	The TRS R consists of the following rules:
1023.39/289.25	
1023.39/289.25	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.39/289.25	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.39/289.25	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.39/289.25	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.39/289.25	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.39/289.25	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.39/289.25	   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))))))))))))
1023.39/289.25	   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))))))))))))
1023.39/289.25	   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)))))))))))))
1023.39/289.25	   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)))))))))))))
1023.39/289.25	   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)))))))))))))
1023.39/289.25	   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))))))))))))))
1023.39/289.25	   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)))))))))))))))
1023.39/289.25	   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)))))))))))))))
1023.39/289.25	   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)))))))))))))))
1023.39/289.25	   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))))))))))))))))
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))))))
1023.39/289.25	
1023.39/289.25	Q is empty.
1023.39/289.25	We have to consider all minimal (P,Q,R)-chains.
1023.39/289.25	----------------------------------------
1023.39/289.25	
1023.39/289.25	(162) MRRProof (EQUIVALENT)
1023.39/289.25	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.
1023.39/289.25	
1023.39/289.25	
1023.39/289.25	Strictly oriented rules of the TRS R:
1023.39/289.25	
1023.39/289.25	   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)))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))))))
1023.39/289.25	
1023.39/289.25	Used ordering: Polynomial interpretation [POLO]:
1023.39/289.25	
1023.39/289.25	   POL(0(x_1)) = 1 + 2*x_1
1023.39/289.25	   POL(1(x_1)) = x_1
1023.39/289.25	   POL(2(x_1)) = 1 + 2*x_1
1023.39/289.25	   POL(3(x_1)) = x_1
1023.39/289.25	   POL(4(x_1)) = 2*x_1
1023.39/289.25	   POL(4^1(x_1)) = 2*x_1
1023.39/289.25	   POL(5(x_1)) = 1 + 2*x_1
1023.39/289.25	
1023.39/289.25	
1023.39/289.25	----------------------------------------
1023.39/289.25	
1023.39/289.25	(163)
1023.39/289.25	Obligation:
1023.39/289.25	Q DP problem:
1023.39/289.25	The TRS P consists of the following rules:
1023.39/289.25	
1023.39/289.25	   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))))))))))))))
1023.39/289.25	   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))))))))))))))))
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))))))
1023.39/289.25	
1023.39/289.25	The TRS R consists of the following rules:
1023.39/289.25	
1023.39/289.25	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.39/289.25	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.39/289.25	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.39/289.25	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.39/289.25	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.39/289.25	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.39/289.25	   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))))))))))))
1023.39/289.25	   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))))))))))))
1023.39/289.25	   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)))))))))))))
1023.39/289.25	   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)))))))))))))
1023.39/289.25	   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)))))))))))))
1023.39/289.25	   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))))))))))))))
1023.39/289.25	   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)))))))))))))))
1023.39/289.25	   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)))))))))))))))
1023.39/289.25	   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))))))))))))))))
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))))))
1023.39/289.25	
1023.39/289.25	Q is empty.
1023.39/289.25	We have to consider all minimal (P,Q,R)-chains.
1023.39/289.25	----------------------------------------
1023.39/289.25	
1023.39/289.25	(164) MRRProof (EQUIVALENT)
1023.39/289.25	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.
1023.39/289.25	
1023.39/289.25	
1023.39/289.25	Strictly oriented rules of the TRS R:
1023.39/289.25	
1023.39/289.25	   2(0(1(2(5(0(1(2(3(1(x1)))))))))) -> 2(1(3(2(2(0(0(5(1(1(x1))))))))))
1023.39/289.25	   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)))))))))))))
1023.39/289.25	   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)))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))))
1023.39/289.25	
1023.39/289.25	Used ordering: Polynomial interpretation [POLO]:
1023.39/289.25	
1023.39/289.25	   POL(0(x_1)) = 1 + x_1
1023.39/289.25	   POL(1(x_1)) = x_1
1023.39/289.25	   POL(2(x_1)) = x_1
1023.39/289.25	   POL(3(x_1)) = x_1
1023.39/289.25	   POL(4(x_1)) = x_1
1023.39/289.25	   POL(4^1(x_1)) = x_1
1023.39/289.25	   POL(5(x_1)) = 2*x_1
1023.39/289.25	
1023.39/289.25	
1023.39/289.25	----------------------------------------
1023.39/289.25	
1023.39/289.25	(165)
1023.39/289.25	Obligation:
1023.39/289.25	Q DP problem:
1023.39/289.25	The TRS P consists of the following rules:
1023.39/289.25	
1023.39/289.25	   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))))))))))))))
1023.39/289.25	   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))))))))))))))))
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))))))
1023.39/289.25	
1023.39/289.25	The TRS R consists of the following rules:
1023.39/289.25	
1023.39/289.25	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.39/289.25	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.39/289.25	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.39/289.25	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.39/289.25	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.39/289.25	   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))))))))))))
1023.39/289.25	   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))))))))))))
1023.39/289.25	   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)))))))))))))
1023.39/289.25	   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)))))))))))))
1023.39/289.25	   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))))))))))))))
1023.39/289.25	   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)))))))))))))))
1023.39/289.25	   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))))))))))))))))
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))))))
1023.39/289.25	
1023.39/289.25	Q is empty.
1023.39/289.25	We have to consider all minimal (P,Q,R)-chains.
1023.39/289.25	----------------------------------------
1023.39/289.25	
1023.39/289.25	(166) QDPOrderProof (EQUIVALENT)
1023.39/289.25	We use the reduction pair processor [LPAR04,JAR06].
1023.39/289.25	
1023.39/289.25	
1023.39/289.25	The following pairs can be oriented strictly and are deleted.
1023.39/289.25	
1023.39/289.25	   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))))))))))))))))
1023.39/289.25	The remaining pairs can at least be oriented weakly.
1023.39/289.25	Used ordering:  Polynomial interpretation [POLO]:
1023.39/289.25	
1023.39/289.25	   POL(0(x_1)) = x_1
1023.39/289.25	   POL(1(x_1)) = 1 + x_1
1023.39/289.25	   POL(2(x_1)) = 0
1023.39/289.25	   POL(3(x_1)) = x_1
1023.39/289.25	   POL(4(x_1)) = 1 + x_1
1023.39/289.25	   POL(4^1(x_1)) = x_1
1023.39/289.25	   POL(5(x_1)) = 1
1023.39/289.25	
1023.39/289.25	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
1023.39/289.25	
1023.39/289.25	   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))))))))))))
1023.39/289.25	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.39/289.25	   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)))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))
1023.39/289.25	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.39/289.25	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))))))
1023.39/289.25	   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))))))))))))
1023.39/289.25	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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)))))))))))))))
1023.39/289.25	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))))
1023.39/289.25	   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))))))))))))))
1023.39/289.25	   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)))))))))))))
1023.39/289.25	   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))))))))))))))))
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))))))
1023.39/289.25	
1023.39/289.25	
1023.39/289.25	----------------------------------------
1023.39/289.25	
1023.39/289.25	(167)
1023.39/289.25	Obligation:
1023.39/289.25	Q DP problem:
1023.39/289.25	The TRS P consists of the following rules:
1023.39/289.25	
1023.39/289.25	   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))))))))))))))
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))))))
1023.39/289.25	
1023.39/289.25	The TRS R consists of the following rules:
1023.39/289.25	
1023.39/289.25	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.39/289.25	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.39/289.25	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.39/289.25	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.39/289.25	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.39/289.25	   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))))))))))))
1023.39/289.25	   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))))))))))))
1023.39/289.25	   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)))))))))))))
1023.39/289.25	   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)))))))))))))
1023.39/289.25	   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))))))))))))))
1023.39/289.25	   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)))))))))))))))
1023.39/289.25	   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))))))))))))))))
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))))))
1023.39/289.25	
1023.39/289.25	Q is empty.
1023.39/289.25	We have to consider all minimal (P,Q,R)-chains.
1023.39/289.25	----------------------------------------
1023.39/289.25	
1023.39/289.25	(168) MRRProof (EQUIVALENT)
1023.39/289.25	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.
1023.39/289.25	
1023.39/289.25	
1023.39/289.25	Strictly oriented rules of the TRS R:
1023.39/289.25	
1023.39/289.25	   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))))))))))))
1023.39/289.25	   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)))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))
1023.39/289.25	
1023.39/289.25	Used ordering: Polynomial interpretation [POLO]:
1023.39/289.25	
1023.39/289.25	   POL(0(x_1)) = 2*x_1
1023.39/289.25	   POL(1(x_1)) = 2*x_1
1023.39/289.25	   POL(2(x_1)) = 2*x_1
1023.39/289.25	   POL(3(x_1)) = x_1
1023.39/289.25	   POL(4(x_1)) = 2*x_1
1023.39/289.25	   POL(4^1(x_1)) = 2*x_1
1023.39/289.25	   POL(5(x_1)) = 2 + x_1
1023.39/289.25	
1023.39/289.25	
1023.39/289.25	----------------------------------------
1023.39/289.25	
1023.39/289.25	(169)
1023.39/289.25	Obligation:
1023.39/289.25	Q DP problem:
1023.39/289.25	The TRS P consists of the following rules:
1023.39/289.25	
1023.39/289.25	   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))))))))))))))
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))))))
1023.39/289.25	
1023.39/289.25	The TRS R consists of the following rules:
1023.39/289.25	
1023.39/289.25	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.39/289.25	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.39/289.25	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.39/289.25	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.39/289.25	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.39/289.25	   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))))))))))))
1023.39/289.25	   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)))))))))))))
1023.39/289.25	   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)))))))))))))
1023.39/289.25	   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))))))))))))))
1023.39/289.25	   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)))))))))))))))
1023.39/289.25	   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))))))))))))))))
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))))))
1023.39/289.25	
1023.39/289.25	Q is empty.
1023.39/289.25	We have to consider all minimal (P,Q,R)-chains.
1023.39/289.25	----------------------------------------
1023.39/289.25	
1023.39/289.25	(170) MRRProof (EQUIVALENT)
1023.39/289.25	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.
1023.39/289.25	
1023.39/289.25	Strictly oriented dependency pairs:
1023.39/289.25	
1023.39/289.25	   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)))))))))))))))))))))))))))))
1023.39/289.25	
1023.39/289.25	Strictly oriented rules of the TRS R:
1023.39/289.25	
1023.39/289.25	   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))))))))))))
1023.39/289.25	   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)))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))))))
1023.39/289.25	
1023.39/289.25	Used ordering: Polynomial interpretation [POLO]:
1023.39/289.25	
1023.39/289.25	   POL(0(x_1)) = x_1
1023.39/289.25	   POL(1(x_1)) = 2 + 2*x_1
1023.39/289.25	   POL(2(x_1)) = x_1
1023.39/289.25	   POL(3(x_1)) = 2*x_1
1023.39/289.25	   POL(4(x_1)) = 2 + 2*x_1
1023.39/289.25	   POL(4^1(x_1)) = x_1
1023.39/289.25	   POL(5(x_1)) = 2*x_1
1023.39/289.25	
1023.39/289.25	
1023.39/289.25	----------------------------------------
1023.39/289.25	
1023.39/289.25	(171)
1023.39/289.25	Obligation:
1023.39/289.25	Q DP problem:
1023.39/289.25	The TRS P consists of the following rules:
1023.39/289.25	
1023.39/289.25	   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))))))))))))))
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	
1023.39/289.25	The TRS R consists of the following rules:
1023.39/289.25	
1023.39/289.25	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.39/289.25	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.39/289.25	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.39/289.25	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.39/289.25	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.39/289.25	   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)))))))))))))
1023.39/289.25	   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)))))))))))))
1023.39/289.25	   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))))))))))))))
1023.39/289.25	   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))))))))))))))))
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))))))
1023.39/289.25	
1023.39/289.25	Q is empty.
1023.39/289.25	We have to consider all minimal (P,Q,R)-chains.
1023.39/289.25	----------------------------------------
1023.39/289.25	
1023.39/289.25	(172) MRRProof (EQUIVALENT)
1023.39/289.25	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.
1023.39/289.25	
1023.39/289.25	
1023.39/289.25	Strictly oriented rules of the TRS R:
1023.39/289.25	
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))
1023.39/289.25	
1023.39/289.25	Used ordering: Polynomial interpretation [POLO]:
1023.39/289.25	
1023.39/289.25	   POL(0(x_1)) = 3 + x_1
1023.39/289.25	   POL(1(x_1)) = 2*x_1
1023.39/289.25	   POL(2(x_1)) = x_1
1023.39/289.25	   POL(3(x_1)) = x_1
1023.39/289.25	   POL(4(x_1)) = 2*x_1
1023.39/289.25	   POL(4^1(x_1)) = 2*x_1
1023.39/289.25	   POL(5(x_1)) = x_1
1023.39/289.25	
1023.39/289.25	
1023.39/289.25	----------------------------------------
1023.39/289.25	
1023.39/289.25	(173)
1023.39/289.25	Obligation:
1023.39/289.25	Q DP problem:
1023.39/289.25	The TRS P consists of the following rules:
1023.39/289.25	
1023.39/289.25	   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))))))))))))))
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	
1023.39/289.25	The TRS R consists of the following rules:
1023.39/289.25	
1023.39/289.25	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.39/289.25	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.39/289.25	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.39/289.25	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.39/289.25	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.39/289.25	   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)))))))))))))
1023.39/289.25	   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)))))))))))))
1023.39/289.25	   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))))))))))))))
1023.39/289.25	   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))))))))))))))))
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))))
1023.39/289.25	   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)))))))))))))))))))))))))
1023.39/289.25	   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))))))))))))))))))))))))))
1023.39/289.25	
1023.39/289.25	Q is empty.
1023.39/289.25	We have to consider all minimal (P,Q,R)-chains.
1023.39/289.25	----------------------------------------
1023.39/289.25	
1023.39/289.25	(174) MRRProof (EQUIVALENT)
1023.39/289.25	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.
1023.39/289.25	
1023.39/289.25	
1023.39/289.25	Strictly oriented rules of the TRS R:
1023.39/289.25	
1023.39/289.25	   2(0(2(3(1(1(0(3(5(2(x1)))))))))) -> 2(0(2(3(1(1(3(0(5(2(x1))))))))))
1023.39/289.25	   5(1(2(3(1(3(2(0(0(3(x1)))))))))) -> 5(1(3(2(1(3(2(0(0(3(x1))))))))))
1023.39/289.25	   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)))))))))))))))))))
1023.39/289.25	
1023.39/289.25	Used ordering: Polynomial interpretation [POLO]:
1023.39/289.25	
1023.39/289.25	   POL(0(x_1)) = 2*x_1
1023.39/289.25	   POL(1(x_1)) = 2*x_1
1023.39/289.25	   POL(2(x_1)) = 2*x_1
1023.39/289.25	   POL(3(x_1)) = 2 + 2*x_1
1023.39/289.25	   POL(4(x_1)) = 2*x_1
1023.39/289.25	   POL(4^1(x_1)) = x_1
1023.39/289.26	   POL(5(x_1)) = 2 + 2*x_1
1023.39/289.26	
1023.39/289.26	
1023.39/289.26	----------------------------------------
1023.39/289.26	
1023.39/289.26	(175)
1023.39/289.26	Obligation:
1023.39/289.26	Q DP problem:
1023.39/289.26	The TRS P consists of the following rules:
1023.39/289.26	
1023.39/289.26	   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))))))))))))))
1023.39/289.26	   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))))))))))))))))))
1023.39/289.26	
1023.39/289.26	The TRS R consists of the following rules:
1023.39/289.26	
1023.39/289.26	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.39/289.26	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.39/289.26	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.39/289.26	   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)))))))))))))
1023.39/289.26	   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)))))))))))))
1023.39/289.26	   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))))))))))))))
1023.39/289.26	   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))))))))))))))))
1023.39/289.26	   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))))))))))))))))))
1023.39/289.26	   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))))))))))))))))))
1023.39/289.26	   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)))))))))))))))))))
1023.39/289.26	   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)))))))))))))))))))
1023.39/289.26	   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))))))))))))))))))))))))
1023.39/289.26	   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)))))))))))))))))))))))))
1023.39/289.26	   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))))))))))))))))))))))))))
1023.39/289.26	
1023.39/289.26	Q is empty.
1023.39/289.26	We have to consider all minimal (P,Q,R)-chains.
1023.39/289.26	----------------------------------------
1023.39/289.26	
1023.39/289.26	(176) MRRProof (EQUIVALENT)
1023.39/289.26	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.
1023.39/289.26	
1023.39/289.26	Strictly oriented dependency pairs:
1023.39/289.26	
1023.39/289.26	   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))))))))))))))
1023.39/289.26	   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))))))))))))))))))
1023.39/289.26	
1023.39/289.26	Strictly oriented rules of the TRS R:
1023.39/289.26	
1023.39/289.26	   0(1(3(3(2(3(0(2(0(0(4(x1))))))))))) -> 0(1(3(3(2(3(2(0(0(0(4(x1)))))))))))
1023.39/289.26	   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))))))))))))))
1023.39/289.26	   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))))))))))))))))))
1023.39/289.26	
1023.39/289.26	Used ordering: Polynomial interpretation [POLO]:
1023.39/289.26	
1023.39/289.26	   POL(0(x_1)) = 2*x_1
1023.39/289.26	   POL(1(x_1)) = 2 + 2*x_1
1023.39/289.26	   POL(2(x_1)) = 2 + 2*x_1
1023.39/289.26	   POL(3(x_1)) = 2*x_1
1023.39/289.26	   POL(4(x_1)) = 2 + 2*x_1
1023.39/289.26	   POL(4^1(x_1)) = 2*x_1
1023.39/289.26	   POL(5(x_1)) = 2*x_1
1023.39/289.26	
1023.39/289.26	
1023.39/289.26	----------------------------------------
1023.39/289.26	
1023.39/289.26	(177)
1023.39/289.26	Obligation:
1023.39/289.26	Q DP problem:
1023.39/289.26	P is empty.
1023.39/289.26	The TRS R consists of the following rules:
1023.39/289.26	
1023.39/289.26	   5(4(3(1(2(1(1(0(x1)))))))) -> 5(4(3(2(1(1(1(0(x1))))))))
1023.39/289.26	   1(3(3(5(2(2(5(1(x1)))))))) -> 1(3(5(3(2(2(5(1(x1))))))))
1023.39/289.26	   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)))))))))))))
1023.39/289.26	   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)))))))))))))
1023.39/289.26	   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))))))))))))))))
1023.39/289.26	   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))))))))))))))))))
1023.39/289.26	   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)))))))))))))))))))
1023.39/289.26	   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)))))))))))))))))))
1023.39/289.26	   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))))))))))))))))))))))))
1023.39/289.26	   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)))))))))))))))))))))))))
1023.39/289.26	   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))))))))))))))))))))))))))
1023.39/289.26	
1023.39/289.26	Q is empty.
1023.39/289.26	We have to consider all minimal (P,Q,R)-chains.
1023.39/289.26	----------------------------------------
1023.39/289.26	
1023.39/289.26	(178) PisEmptyProof (EQUIVALENT)
1023.39/289.26	The TRS P is empty. Hence, there is no (P,Q,R) chain.
1023.39/289.26	----------------------------------------
1023.39/289.26	
1023.39/289.26	(179)
1023.39/289.26	YES
1023.55/289.36	EOF